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for Study Island Standards Mastery and

Benchmark Assessment Components

Copyright © 2014 by Edmentum. All Rights Reserved.

Technical Manual

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Contents Tables ........................................................................................................................................................... iv

Figures .......................................................................................................................................................... v

Edmentum Research Team ......................................................................................................................... vi

I. Overview ............................................................................................................................................... 1

Purpose of Study Island ............................................................................................................................ 1

Purpose of This Report ............................................................................................................................. 1

II. Study Island Programs .......................................................................................................................... 2

The History of Study Island and Educational Accountability Standards ................................................... 2

Study Island Standards Mastery Component ........................................................................................... 3

Study Island Benchmark Assessment Component ................................................................................... 3

III. Study Island Items ............................................................................................................................. 4

Item Types................................................................................................................................................. 4

Technology-Enhanced Item Types ....................................................................................................... 4

Item Development ..................................................................................................................................... 5

Criteria for Selecting Reading Passages .............................................................................................. 6

Determining Readability Levels for Reading Passages ........................................................................ 7

IV. Benchmark Assessment Test Development ..................................................................................... 8

Study Island Common Core Mathematics Benchmark Test Specifications .............................................. 8

Standards .............................................................................................................................................. 8

Test Design ........................................................................................................................................... 9

Test Blueprints ...................................................................................................................................... 9

Study Island Common Core ELA Benchmark Test Specifications ......................................................... 10

Standards ............................................................................................................................................ 10

Test Design ......................................................................................................................................... 11

Test Blueprints .................................................................................................................................... 11

Comparability of Study Island Benchmark Assessments ....................................................................... 12

Comparability Guidelines .................................................................................................................... 12

Next-Generation Benchmark Assessments ............................................................................................ 13

New Item Types .................................................................................................................................. 14

Comparable forms ............................................................................................................................... 14

Pretested Items ................................................................................................................................... 14

V. Scores and Reporting ......................................................................................................................... 14

Scores and Score Interpretation ............................................................................................................. 14

Standards Mastery Component Scores .............................................................................................. 15

Benchmark Assessment Component Scores ..................................................................................... 15

Reporting ................................................................................................................................................. 15

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Standards Mastery Component Reports ............................................................................................. 15

Benchmark Assessment Component Reports .................................................................................... 18

VI. Security ........................................................................................................................................... 20

Data, Server, and Internet Security ......................................................................................................... 20

FERPA Compliance and Study Island .................................................................................................... 20

Use of Dynamic Items ............................................................................................................................. 20

Randomization of Items, Item Order, and Answer Options .................................................................... 20

User Access Security .............................................................................................................................. 21

Test Administration Window Security ..................................................................................................... 21

Multiple Benchmark Assessment Forms Available ................................................................................. 21

VII. Reliability and Validity ..................................................................................................................... 21

Reliability ................................................................................................................................................. 21

Validity ..................................................................................................................................................... 22

Content Validity ................................................................................................................................... 22

Construct Validity ................................................................................................................................ 23

Alignment to Standards–Study Island Common Core ........................................................................ 26

VIII. Analysis of Study Island Common Core Standards Mastery Item Pools ........................................ 27

Item Difficulty (p-value) Statistics by Grade-Level Form ..................................................................... 28

IX. Analysis of Study Island Common Core Benchmark Assessments ................................................ 31

Demographic Summary of Benchmark Assessment Data ...................................................................... 31

Sample Refinement and Data Cleanup .............................................................................................. 31

Time of Benchmark Administration ..................................................................................................... 32

Demographics of Benchmark Assessment Data Sample ................................................................... 37

Item Analysis of Common Core Benchmark Assessment Data .............................................................. 48

Classical Item Difficulty Indices ........................................................................................................... 48

Item Difficulty (p-value) Statistics by Grade-Level Benchmark Test Form ......................................... 49

Item-Total Correlation ......................................................................................................................... 52

Item-Total (Point-Biserial) Correlation Statistic by Grade Level Benchmark Test Form..................... 52

Test Analysis of Common Core Benchmark Assessment Data .............................................................. 55

Form Reliability Estimates and SEM Values by Grade-Level Benchmark Test Form ........................ 55

Benchmark Test Reporting Category Subscores.................................................................................... 60

Benchmark Test Administration Time ................................................................................................. 62

Administration of Multiple Benchmarks Across a School Year ........................................................... 63

X. Summary ............................................................................................................................................. 67

References .................................................................................................................................................. 68

Appendix A. ................................................................................................................................................. 69

Study Island Standards Mastery Mathematics Common Core Standards Item Difficulty Statistics ....... 69

Histograms of Item Difficulty statistics by grade level (Note that items with less than 100 student

responses are excluded) ......................................................................................................................... 69

Appendix B. ................................................................................................................................................. 75

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Study Island Standards Mastery Reading Common Core Standards Item Difficulty Statistics .............. 75

Histograms of Item Difficulty statistics by grade level (Note that items with less than 100 student

responses are excluded) ......................................................................................................................... 75

Appendix C. ................................................................................................................................................. 81

Study Island Common Core State Standards Benchmark Assessment Forms ...................................... 81

Histograms of Percent-Correct Score Distributions for Mathematics by grade level and form .............. 81

Appendix D. ............................................................................................................................................... 118

Study Island Common Core State Standards Benchmark Assessment Forms .................................... 118

Histograms of Percent-Correct Score Distributions for English Language Arts by grade level and form

.............................................................................................................................................................. 118

Appendix E. ............................................................................................................................................... 155

Study Island Common Core State Standards Benchmark Assessment Forms .................................... 155

Reporting Category Subscore Intercorrelation Tables for Mathematics and English Language Arts .. 155

Appendix F. ............................................................................................................................................... 174

Study Island Benchmark Assessment Alignment to the Common Core State Standards .................... 174

Grades 3–8 Mathematics, Algebra 1, Geometry, and Algebra 2 Standards Maps ............................... 174

Appendix G. .............................................................................................................................................. 290

Study Island Benchmark Assessment Alignment to the Common Core State Standards .................... 290

Grades 3–11 English Language Arts Standards Maps ......................................................................... 290

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Tables

Table 1. Study Island item types ................................................................................................................... 5 Table 2. Types of passages .......................................................................................................................... 7 Table 3. Number of items per benchmark assessment form (mathematics) ................................................ 9 Table 4. Grades 3–5 mathematics benchmark test blueprint ....................................................................... 9 Table 5. Grades 6–8 mathematics benchmark test blueprint ....................................................................... 9 Table 6. Algebra 1 benchmark test blueprint .............................................................................................. 10 Table 7. Geometry benchmark test blueprint .............................................................................................. 10 Table 8. Algebra 2 benchmark test blueprint .............................................................................................. 10 Table 9. Number of items per benchmark assessment form (ELA) ............................................................ 11 Table 10. Grades 3–6 ELA benchmark test blueprint ................................................................................. 11 Table 11. Grades 7–9 ELA benchmark test blueprint ................................................................................. 12 Table 12. Grades 10 and 11 ELA benchmark test blueprint ....................................................................... 12 Table 13. Test item comparability characteristics ....................................................................................... 13 Table 14. Number of Study Island standards mastery component items (Common Core standards)

excluded from analysis for having fewer than 100 student responses ....................................................... 28 Table 15. Summary of Study Island standards mastery component (mathematics) .................................. 29 Table 16. Summary of Study Island standards mastery component (ELA) ................................................ 29 Table 17. Summary of difficulty statistics for Study Island standards mastery component technology-

enhanced items (mathematics) ................................................................................................................... 30 Table 18. Summary of difficulty statistics for Study Island standards mastery component technology-

enhanced items (ELA) ................................................................................................................................. 30 Table 19. Percentage of examinees by grade level (high school mathematics courses) ........................... 31 Table 20. Percentage of examinees by grade level (high school ELA courses) ........................................ 32 Table 21. Racial and ethnic background—Demographics summary by grade level (mathematics) .......... 42 Table 22. Racial and ethnic background—Demographics summary by grade level (ELA) ........................ 45 Table 23. Summary of Common Core benchmark assessment item difficulty statistics (mathematics) .... 50 Table 24. Summary of Common Core benchmark assessment item difficulty statistics (ELA) .................. 51 Table 25. Summary of Common Core benchmark assessment item-total correlation (mathematics) ....... 53 Table 26. Summary of Common Core benchmark assessment item-total correlation (ELA) ..................... 54 Table 27. Summary of Common Core benchmark test scores and reliability estimates (mathematics) .... 56 Table 28. Common Core benchmark test reliability estimates by grade-level form (mathematics) ........... 58 Table 29. Summary of Common Core benchmark test scores and reliability estimates (ELA) .................. 59 Table 30. Common Core benchmark test reliability estimates by grade-level form (ELA) ......................... 60 Table 31. Summary of Common Core benchmark test administration time (mathematics) ....................... 62 Table 32. Summary of Common Core benchmark test administration time (ELA) ..................................... 63 Table 33. Mean Common Core benchmark test score by number of benchmark administrations

(mathematics) ............................................................................................................................................. 65 Table 34. Mean Common Core benchmark test score by number of benchmark administrations (ELA) .. 66

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Figures

Figure 1. Percentage of seventh-grade students who were proficient before and after Study Island

implementation. Based on results reported in the Bernard 2013 study. ..................................................... 24 Figure 2. Percentage of questions answered correctly, by grade, from 2008–09 to 2010–11. Based on

results reported in the Bernard 2013 study. ................................................................................................ 25 Figure 3. Summary of mathematics benchmark time of testing by grade level and form ........................... 33 Figure 4. Summary of high school mathematics benchmark time of testing by form ................................. 34 Figure 5. Summary of ELA benchmark time of testing by grade level and form ........................................ 35 Figure 6. Summary of high school ELA benchmark time of testing by grade level and form ..................... 36 Figure 7. States of examinees in analysis—Demographics summary by grade level (mathematics) ........ 38 Figure 8. States of examinees in analysis—Demographics summary by grade level (ELA) ...................... 39 Figure 9. States of examinees in analysis—Demographics summary by grade level (high school

mathematics) ............................................................................................................................................... 40 Figure 10. States of examinees in analysis—Demographics summary by grade level (high school ELA) 41 Figure 11. Sample benchmark reporting category intercorrelation matrix .................................................. 61 Figure 12. Students taking multiple administrations of Common Core benchmark tests (mathematics) ... 64 Figure 13. Students taking multiple administrations of Common Core benchmark tests (ELA) ................. 64

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Edmentum Research Team

Irene McAfee, Ph.D. Director of Research

Michael Yoes, Ph.D. Psychometrician

Michelle Frost, Ph.D. Research Analyst

Anne Schwalbe, MA Education Research Analyst

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Technical Manual for Study Island Standards Mastery and Benchmark Assessment Components

I. Overview

Purpose of Study Island

Study Island’s K–12 standards mastery and benchmark assessment products help students master the specific content

outlined in state content standards to improve performance in skill areas tested on state assessments. Study Island

pinpoints areas of mastery and targets areas where help is needed.

Study Island comprises two primary components, an online standards mastery program and benchmark assessments for

use in assessing student knowledge and skills. Both the standards mastery component and the benchmark assessments

are available to match state standards and the Common Core State Standards. Study Island is used by over 10 million

students in over 19,000 schools. The standards mastery component is dynamic and self-paced, allowing teachers to

customize instruction to students’ needs and allowing students to study in standard test format, interactive game mode, or

interactive classroom response systems. The benchmark assessments are fixed tests that can be used for class or

district-wide benchmarking throughout the year.

Purpose of This Report

Standards for Educational and Psychological Testing (AERA, APA, & NCME, 1999) requires that test developers and

publishers produce a technical manual that provides information documenting the technical quality of an assessment and

its items. This report contains technical information for the Study Island Common Core benchmark assessments in math

and English language arts for grades 3 through 8 and high school. The information included in this report is intended for

use by those who evaluate tests, interpret scores, or use test results in making educational decisions. It is assumed that

the reader has some technical knowledge of test construction and measurement procedures.

Because Study Island also includes a standards mastery component that is widely used as a formative classroom

assessment tool, this report also addresses the quality of the items used for this standards mastery pool.

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II. Study Island Programs

The History of Study Island and Educational Accountability Standards

Study Island was founded in 2000, the same year that the federal Elementary and Secondary Education Act (ESEA) was

redefined and became known as the No Child Left Behind (NCLB) Act of 2001. The Study Island program was designed

to meet the needs of schools and students in this new era of education reform and accountability. By 2002, Study Island

was available in Texas and Oklahoma and soon after expanded into Ohio, North Carolina, New York, and Michigan,

servicing 180 schools. In 2003, Study Island continued its rapid growth plan and added six more states, expanding its

coverage to 750 schools. When Study Island was initially implemented, test items were written to align specifically to each

state’s reading and math standards. The program itself consisted only of the standards mastery component.

In 2007, the program expanded to include Study Island benchmark assessments that could be used as a formative assessment tool for teachers to guide instruction. Four comparable benchmark forms were developed for each grade level. There were 30 items per form, and all were multiple-choice.

In 2009, a project called the Common Core State Standards Initiative (CCSSI) was organized by the Council of Chief State School Officers (CCSSO) and the National Governors Association Center for Best Practices (NAG Center). CCSSI coordinated a state-led effort to develop academic standards and create national unity regarding what students should know and be able to do. In 2010, the first set of Common Core State Standards (CCSS) was released. Within a few months of the release, the standards were endorsed by 45 states and the District of Columbia. Publishers began to align their materials to them; technology companies created software and curriculum aligned to them. In 2011, forward-thinking Study Island began to align its test items to the CCSS. During this time, Study Island use expanded to approximately 11 million students in nearly 23,700 schools in 50 states.

In 2012, PLATO Learning, now known as Edmentum, acquired Archipelago Learning and its suite of learning products, including Study Island. In conjunction with the acquisition, PLATO Learning decided to write a full set of totally new benchmark test items to align to the Common Core. As with the original test item bank, only multiple-choice items were developed. However, a new process to refine and improve the alignment of the items to the standards was implemented.

Along with the development and release of the CCSS, two consortia were created to develop assessments related to those standards. The Partnership for Assessment of Readiness for College and Careers (PARCC) is one of two groups that are working with states to develop assessments that measure whether students are on track for success in college and their careers. The PARCC computer-based assessments in mathematics and English language arts (ELA) are expected to give more complete information about students’ readiness for learning after high school as well as provide tools to help teachers customize learning to meet student needs.

The Smarter Balanced Assessment Consortium (SBAC) is also developing a CCSS-aligned system of assessments for ELA and mathematics. The Smarter Balanced assessments are computer-adaptive and designed for grades 3–8 and 11. The assessments are summative and will be administered during the last 12 weeks of the school year. The assessments will be used to describe student achievement and growth of student learning as part of program evaluation and school, district, and state accountability systems. Study Island benchmark assessments were built to reflect the two federally funded consortia’s assessment blueprints.

The development of this latest set of items marked the beginning of item-type expansion to reflect the items on the PARCC and SBAC assessments. These 21st century items were written to reflect higher order thinking and inquiry with technology-enhanced items designed to incorporate the depth of knowledge (DOK) guidelines. The new item types include constructed response, multiple response, hot text, hot spot, graphical gap match, matched pairs, cloze, sequencing, and fill in the blank.

Study Island continues to monitor the CCSSI and the two related testing consortia, PARCC and SBAC. Edmentum’s flexibility and keen awareness of the standards movement enable it to adjust and customize standards mastery and benchmark assessments quickly and regularly. Edmentum continues to look for ways to make Study Island more user-friendly for all of its users.

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Study Island Standards Mastery Component

The standards mastery component of Study Island is designed to provide targeted practice to help students master the skills specified in content standards. The items presented to students closely model items on high-stakes standardized assessments, giving students the opportunity to become familiar with item formats while practicing skills. The standards mastery component of Study Island can also be used as a formative classroom assessment tool. Teachers have the option to select items aligned to the standards they are teaching and can track student mastery of those standards. Study Island standards mastery provides rapid feedback to students and teachers.

Study Island standards mastery is divided into sections based on subject (math, reading, etc.). Each subject comprises approximately 15 to 30 topics, and each topic corresponds to a standard, or multiple related standards, from a specific state or CCSS–based curriculum. Topics consist of a lesson and a bank of practice questions with explanations. The student’s goal in the standards mastery component of Study Island is to earn a blue ribbon in, or pass, every topic. A student who passes every topic has demonstrated proficiency in all areas tested.

There are several different study-session modes in the standards mastery component. In game mode, students get to play a short game every time they answer a question correctly. Teachers can also use Study Island in a classroom response system or turn items into printable worksheets.

There are also several tools that teachers can take advantage of to meet the individual needs of students with special needs. In the multiple-choice format, you can change the number of answer choices from four to three. You can also lower the score it takes for an individual student to earn a blue ribbon. Finally, there is a text-to-speech option where students with special needs can highlight text and the have the question and answer choices read to them.

Study Island is not meant to be used as a primary curriculum; rather, it is a supplemental tool that reinforces what is being taught. However, there are mini lessons for review before or during each individual standard’s specific set of questions. This allows students to have a quick refresher on material that was covered in depth during class instructional time.

Study Island Benchmark Assessment Component

In addition to its standards mastery component, Study Island offers a benchmarking component. The benchmarking component provides a set of four benchmark tests designed to be taken periodically throughout the school year. The benchmark tests are typically about 30 items long and mirror the structure and item types found in state assessments (including the new Common Core assessments). Therefore, the results of each benchmark test will closely reflect how students would perform on high-stakes assessments.

In The Role of Interim Assessments in a Comprehensive Assessment System (Aspen Institute, 2007), a paper sponsored by the National Center for the Improvement of Educational Assessment, interim assessment is defined as a benchmark assessment used to (1) evaluate student mastery of specific goals within a specific time frame and (2) provide information to inform decisions both in the classroom and at the school or district level. The timing and administration of interim assessments are typically controlled at the school or district level, and results may be used to evaluate programs, diagnose gaps in student learning, or predict students’ ability to succeed on higher-stakes summative assessments.

The Common Core benchmark assessments are designed to provide information concerning the strengths and needs areas for individual students, classrooms, schools, and districts. Tests based on the current CCSS are available in ELA for grades 3 through 11 and mathematics for grades 3 through 8, plus algebra 1, geometry, and algebra 2.

The Common Core benchmark assessments provide reporting data that can be used to inform instruction in the classroom and share progress and needs areas with parents and students. Educators can use data from the Common Core benchmark assessments to assist in planning instruction to increase student achievement, better focus classroom instructional time, and allow more efficient use of staff development time and sources.

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III. Study Island Items

The Study Island standards mastery and benchmark components both use items developed to align to content standards

and to closely model items found on high-stakes assessments. This section describes the item types and the

development process used to ensure that all items meet quality standards.

Item Types

The new PARCC and SBAC item types measure a deeper, more critical understanding of the CCSS. On technology-

based exams, students must demonstrate what they have learned in the classroom by conceptualizing, applying, and

executing on the content in ways that they cannot with traditional pen-and-paper exams. For example, hot-spot questions

ensure interaction with questions through media-rich graphics and illustrations, and constructed-response questions

require critical thinking and evidence-based support.

In response to the CCSS, Edmentum has undertaken major development efforts to not only ensure that existing

instructional and assessment resources align to the standards but to create new solutions for students and educators that

are written specifically to produce Common Core outcomes.

The two assessment consortia have indicated that the operational Common Core assessments currently in development

will employ additional item types such as performance tasks, extended constructed response, writing prompts, and

additional technology-enhanced items. While the consortia have provided examples of these item types, specifications

regarding how many of these item types the new tests should contain have not been released. Edmentum is currently

developing and field-testing next-generation assessment items and is following the work of the two consortia closely. New

item formats will be incorporated into the Study Island Common Core benchmark assessments as the consortia reveal

their plans for including such items.

Technology-Enhanced Item Types

Edmentum’s web-based solutions are designed to help schools and districts prepare for more rigorous and interactive

web-based exams. Study Island now includes new technology-enhanced item types, available in third through eighth

grades and high school, designed to promote higher order thinking and inquiry. Built using the DOK guidelines, these new

item types ensure that each item is written to the appropriate DOK level and that students are exposed to the appropriate

content.

The new Study Island item types are mobile compatible and align with the CCSS assessments under development by

both SBAC and PARCC.

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Table 1. Study Island item types

Multiple Choice Students choose the single best answer.

Constructed Response

Students construct a response using evidence from the question or reading passage to support their view.

Multiple Response

Students can select more than one correct answer in a multiple-choice format.

Cloze

Students select a response from a drop-down menu in an equation or sentence.

Sequence

Students click an image and move it to the correct location on the screen to arrange a sequence and create the correct overall

answer.

Matched Pairs

Students move answers from one area on the screen to another and create matching pairs.

Hot Text

Text choices are identified for the student within an item, and the student selects the correct text answer or answers with the

cursor.

Hot Spot

Using the cursor, the student identifies a location in an image that represents the correct answer.

Fill in the Blank

The student enters an alphanumeric response in an open box in an item. An item may have more than one open box.

Graphical Gap Match

Using the cursor, students drag one image to another to answer the question.

Item Development

The test-development process is an iterative, recursive process that includes multiple reviews and quality checks. Input

for the design was taken from the Common Core State Standards and Appendices as well as the current information from

SBAC and PARCC. Additionally, new items were written to focus on higher order thinking skills.

Study Island Common Core benchmark tests were initially released in 2012 and were developed using best-practice

criteria emphasized by leading assessment expert Thomas M. Haladyna. The central goal in test writing is to develop a

series of high-quality items. High-quality items closely measure the intended learning objective and lack ambiguity. There

are several barriers to meeting this objective, including ambiguous statements, excessive words, difficult vocabulary,

unclear instructions, and bias (Haladyna, 2004). All Study Island items, whether written for the standards mastery

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component or for the benchmark assessment component, are developed using the same best-practice guidelines and

development process.

Edmentum has defined quality by following principles set forth by leaders in assessment. These item development

guidelines are documented in a series of style guides. These guides include subject-specific style guides for each Study

Island content area: math, ELA, science, and social studies.

The following process is used to develop new Study Island items.

Follow quality guidelines. Following guidelines and principles helps reduce ambiguity and ensure that the item matches the intended learning outcome. Edmentum uses these principles as guidelines for writing all item types: o Use novel material to test higher-level learning. o Avoid trivial content.

o Avoid irrelevant information (window dressing). o Avoid trick items.

o Meet the readability needs of the audience.

Provide targeted trainings. Trainings are developed around each subject area (math, ELA, science, and social studies) to guide writers in creating new items. Sets of sample items are written and peer-reviewed by Edmentum subject matter experts (SME). Using the quality results of the review as a needs assessment, subject area leads then hold team meetings to identify which training sessions to develop. These targeted trainings include topics such as writing grade-level-appropriate items, best practices in assessment writing, Edmentum’s acceptance criteria for quality assurance, and avoiding bias in item writing.

Evaluate quality. Each item goes through two rounds of review by curriculum experts. Each round is completed by a different expert. If the author and the reviewer disagree during any review round, the subject area manager is consulted for further guidance. After each review round, the author makes corrections based on comments from the expert, and the expert checks the author’s corrections to ensure that all comments were adequately addressed.

Criteria for Selecting Reading Passages

Reading passages submitted for inclusion in Study Island must meet specific criteria. After developing frameworks and

reporting categories, the ELA curriculum specialists select passages based on these criteria:

genre

source

quality

content

lack of bias

gender appropriateness

diversity

length

suitability for reporting categories

reading level

graphics

Review Process for Passages Each passage is reviewed for developmental appropriateness, readability level, gender correctness, racial diversity, and

bias-free content by content specialists.

Types of Passages Table 2 provides examples of literary and informational selections found in the Common Core benchmarks.

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Table 2. Types of passages

Literary Selections Informational Selections

excerpts short stories fairy tales

myths drama

poetry historical fiction

• articles • essays • graphics, tables, charts • editorials

informational web pages

Determining Readability Levels for Reading Passages

Passages that accompany reading and language arts test items receive readability levels. Determining readability is not a

precise metric or science. Reading experts continue to debate and evolve the formulas of various readability scales.

Edmentum uses several methods when determining readability levels.

Computerized Leveling: Flesch-Kincaid Readability Tool This grade-level formula relies on numbers of syllables, words, and sentences. Edmentum uses the Microsoft Word

Flesch-Kincaid readability tool to provide readability statistics for passages. Passages must fall within 1.5 grade levels

above or below the grade level of the benchmark test. For example, passages on the fifth-grade benchmark assessment

must score 3.5 to 6.5 on the Flesch-Kincaid readability scale.

EDL Core Vocabularies Edmentum uses EDL Core Vocabularies in Reading, Mathematics, Science, and Social Studies as a resource for

determining appropriate word choice for specific grade levels (Taylor, 1989).

Expert Judgment Edmentum relies not only on established readability formulas and core word lists but also on the judgment of its content

specialists for determining appropriate readability of passages and items. Edmentum uses the experience of its

educational specialists, who are former teachers and have an understanding of students’ critical- and creative-thinking

skills at specific grade levels. Edmentum’s educational specialists also consider a passage’s unity, structure, degree of

interest and appeal, as well as the sophistication of concepts and themes presented, to determine its appropriateness.

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IV. Benchmark Assessment Test Development

While Edmentum uses the same item development process for Study Island’s standards mastery and benchmark

components, the benchmark assessments are designed as fixed tests that can be used as grade- or district-level

benchmark or interim assessments. Because of this, additional development processes are used to design Study Island

benchmarks.

SMEs create test structures (or test specifications) for each subject area of the Common Core benchmark test structure

by synthesizing information from national standards. SMEs take the following steps to define each test structure, which

includes reporting category titles, the objectives within each reporting category, and the approximate number of test items

within each objective.

Recognize common topics. Using documentation produced by state and national education agencies, SMEs recognize the units and objectives taught.

Analyze topics. SMEs do an analysis that compares common topics and objectives across state and Common Core standards, looking for overlap and agreement.

Draft test designs. SMEs create a blueprint for the Study Island benchmarks, making sure to include the most important topics and objectives found in the CCSS. Objectives are organized into reporting categories using the breakdown of strands, domains, and clusters in the standards.

Develop test items. Test items are developed to meet the stated objectives.

Study Island Common Core Mathematics Benchmark Test

Specifications

In 2012, Study Island’s Common Core mathematics tests became available to customers. The frameworks and reporting

categories of the Common Core benchmark tests for 2012 (grades 3–8 plus algebra 1, geometry, and algebra 2) are

based on the current CCSS.

Determining the test construct, or framework, is the first stage of design. The CCSS and test specifications are analyzed

and recorded in the test framework. The framework represents the target objectives for testing.

Reporting categories are determined based on frameworks and test specifications. These reporting categories represent

organized, summative headings of the objectives recorded in the frameworks.

Reporting categories serve as the basis of the student reports that indicate progress and needs as determined by the

Common Core benchmark.

Standards

The test framework for mathematics for grades 3–8 and high school (algebra 1, geometry, and algebra 2) is based on the

CCSS for math: all items on the grades 3–8 and high school benchmark tests were designed to measure specific CCSS

objectives. Items appearing on the grade-level forms are organized into the content categories defined by the CCSS.

Additionally, the Standards for Mathematical Practice are embedded throughout the Study Island benchmarks grade-level

assessment forms.

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Test Design

Table 3 summarizes the number of items contained within each grade-level mathematics form of Study Island’s Common

Core benchmark assessment in math. At each grade level, four forms are available for administration.

Table 3. Number of items per benchmark assessment form (mathematics)

Grade/Content Area

Number of Items per Form

Number of Grade-Level Forms

3 30 4

4 30 4

5 30 4

6 30 4

7 30 4

8 30 4

Algebra 1 30 4

Geometry 30 4

Algebra 2 30 4

Test Blueprints

The distribution of emphasis for Common Core content strands for mathematics is shown in tables 4 through 8.

Table 4. Grades 3–5 mathematics benchmark test blueprint

CCSS Reporting Category

Grade 3 Grade 4 Grade 5

Items % Items % Items %

Operations and Algebraic Thinking

8 27 7 23 6 20

Measurement and Data 8 27 7 23 6 20

Number and Operations–Fractions

4 13 7 23 6 20

Number and Operations in Base Ten

6 20 5 17 6 20

Geometry 4 13 4 13 6 20

Total 30 100 30 100 30 100

Table 5. Grades 6–8 mathematics benchmark test blueprint

CCSS Reporting Category

Grade 6 Grade 7 Grade 8

Items % Items % Items %

Expressions and Equations

8 27 6 20 8 27

The Number System 9 30 4 13 4 13

Ratios and Proportional Relationships

4 13 7 23 N/A N/A

Statistics and Probability

4 13 5 17 5 17

Geometry 5 17 8 27 6 20

Functions N/A N/A N/A N/A 7 23

Total 30 100 30 100 30 100

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Table 6. Algebra 1 benchmark test blueprint

CCSS Reporting Category Items %

Number and Quantity 4 13

Algebra 11 37

Functions 10 33

Statistics and Probability 5 17

Total 30 100

Table 7. Geometry benchmark test blueprint

CCSS Reporting Category Items %

Congruence 5 17

Expressing Geometric Properties with Equations 4 13

Similarity, Right Triangles, and Trigonometry 5 17

Modeling with Geometry 4 13

Circles 4 13

Geometric Measurement and Dimension 4 13

Statistics and Probability 4 13

Total 30 100

Table 8. Algebra 2 benchmark test blueprint

CCSS Reporting Category Items %

Number and Quantity 4 13

Algebra 10 33

Functions 10 33

Statistics and Probability 6 20

Total 30 100

Study Island Common Core ELA Benchmark Test Specifications

Study Island Common Core ELA benchmarks contain four versions of tests designed for a particular grade. The forms are

designed to be as comparable to the first test form as possible to provide data that can be used to track student progress.

The frameworks and reporting categories of the Common Core ELA benchmark tests for 2012 are based on the approved

standards posted on the CCSS website (www.corestandards.org).

Determining the test construct, or framework, is the first stage of design. The CCSS and test specifications are analyzed

and recorded in the test framework. The framework represents the target objectives for testing.

Reporting categories are determined on the basis of frameworks and test specifications. These reporting categories

represent organized, summative headings of the objectives recorded in the frameworks. Reporting categories serve as

the basis of the student reports that indicate progress and needs as determined by the Common Core benchmark.

Standards

The ELA test framework for grades 3–11 is based on the CCSS for ELA: all items on the grades 3–11 benchmark tests

were designed to measure specific CCSS objectives. Items appearing on the grade-level forms are organized into the

content categories defined by the CCSS.

(11)

Test Design

Table 9 summarizes the number of items contained within each grade-level form of Study Island’s Common Core ELA

benchmark assessment. At each grade level, four forms are available for administration. Each form was developed to the

same content specifications.

Table 9. Number of items per benchmark assessment form (ELA)

Grade/Content Area

Number of Items per Form

Number of Grade-Level Forms

3 30 4

4 30 4

5 30 4

6 30 4

7 30 4

8 30 4

9 30 4

10 30 4

11 30 4

Test Blueprints

The distribution of emphasis for Common Core ELA benchmark content strands is shown in tables 10–12.

Table 10. Grades 3–6 ELA benchmark test blueprint

CCSS Reporting Category

Grade 3 Grade 4 Grade 5 Grade 6

Items % Items % Items % Items %

Reading Standards for Literature

7 23 7 23 7 23 7 23

Reading Standards for Informational Texts

7 23 7 23 7 23 7 23

Writing Standards 4 13 4 13 4 13 4 13

Language Standards 12 40 12 40 12 40 12 40

Total 30 100 30 100 30 100 30 100

(12)

Table 11. Grades 7–9 ELA benchmark test blueprint

CCSS Reporting Category

Grade 7 Grade 8 Grade 9

Items % Items % Items %

Reading Standards for Literature 7 23 7 23 10 33

Reading Standards for Informational Texts 7 23 7 23 10 33

Writing Standards 4 13 4 13 4 13

Language Standards 12 40 12 40 6 20

Total 30 100 30 100 30 100

Table 12. Grades 10 and 11 ELA benchmark test blueprint

CCSS Reporting Category

Grade 10 Grade 11

Items % Items %

Reading Standards for Literature 10 33 10 33

Reading Standards for Informational Texts 10 33 10 33

Writing Standards 4 13 4 13

Language Standards 6 20 6 20

Total 30 100 30 100

Comparability of Study Island Benchmark Assessments

Study Island benchmark assessments are created by SMEs to detailed test specifications. The test specification is like a

blueprint: it shows the standards and objectives that the test is written to, including the numbers and types of questions

that should appear on a test form.

For the Common Core benchmark assessments described in this manual, four comparable benchmark assessment forms

may be administered. Each of these four benchmark forms (within a specific grade, subject area, and prescribed

standards that the assessment is aligned to) is carefully constructed to be as similar as possible with the other three forms

at that grade level and subject area.

Comparability Guidelines

Comparability guidelines were created to accomplish these goals:

Prevent information gaps about the issue of comparability.

Document rules for comparable test and item creation for Edmentum’s assessment products.

Comparable passages are written according to the same readability and reading-ease scales. Comparable

passages represent identical genres, lengths, and textual attributes. Primary genres are expository, narrative, and

poetic texts.

Comparable tests are written as alternate and comparable forms of assessments that align with blueprint

specifications. Alternate forms have comparable items with an equivalent format, the same item count, and a

distribution that follows designated objectives and reporting categories.

(13)

Each student is allowed to take each benchmark test form only once, even if the school schedules two different testing

periods for the same benchmark test.

Criteria considered during the process of developing the Study Island Common Core benchmark assessments include the

following (note that these criteria are in addition to the item-development process described elsewhere in this manual):

• Content coverage and match to test design. Test developers complete an initial sorting of items into sets based on a balance of CCSS reporting categories across forms as well as a match to the test specifications.

• Visual balance. Item sets are reviewed to ensure similar length and density of selected items (e.g., length and complexity of reading selections, number of graphics).

• Item difficulty and complexity. Difficulty of items is determined through a combination of expert judgment and the use of pretest (or prior) item statistics, where those are available. The resulting benchmark assessment forms are designed to be judged similar in level of difficulty and complexity across the forms.

• Response option balance. Each item set is checked to verify that it contains a roughly equivalent number of key options (A, B, C, and D).

When continually developing new tests that mix new items written specifically for the new tests with high-quality items

from the existing database, a tension sometimes arises between comparability and quality criteria. Edmentum develops

new tests with an eye on improving item quality while remaining aware that comparability between existing items and new

items may not be optimal for writing the highest quality new items possible. The following characteristics apply to a test as

a whole, rather than to individual test items.

Table 13. Test item comparability characteristics

Test Characteristic Edmentum Rule or Procedure

number of items Each test should have same number of items on all versions.

reporting categories Each test should have same reporting categories and same number of items within each category as previous versions.

length Test length should be comparable to previous versions.

It should be noted that comparable forms are not necessarily equivalent to equated forms. Test equating, or linking, is a

statistical process through which test score outcomes are all placed on a common scale. Typically with equated test

forms, the test outcome is reported as a scaled score rather than a raw score or a percentage. When test forms are

equated, the score outcome from any of the test forms can be directly compared. The test equating process takes into

account minor variations in the overall difficulty level of the different test forms.

Next-Generation Benchmark Assessments

Beginning with the 2014–15 school year, Study Island will incorporate new design elements that represent even better

alignment with assessment best practices.

The adoption of Common Core standards by 46 states has brought many changes to K–12 education. One of these

changes is new and different state summative assessments. Because Study Island benchmark assessments need to

emulate and align with state summative assessments, they must change as the state assessments do. The next-

generation benchmarks include multiple-choice questions as well as technology-enhanced items (drag and drop, hot spot,

hot text, multiple response, cloze, fill in the blank), and constructed-response items. Each next-generation benchmark

assessment is aligned with state, PARCC, and SBAC summative assessment blueprints. The assessment of critical-

thinking skills is an integral part of new summative assessments; therefore, next-generation Study Island benchmark

assessments are being designed to help educators understand where students stand in relation to college and career

readiness standards such as the CCSS.

(14)

New Item Types

In addition to multiple-choice questions, next-generation benchmarks will include new, interactive item types such as drag

and drop, hot spot, hot text, multiple response, cloze, and fill in the blank. In addition, benchmarks will include

constructed-response questions with rubrics for teacher grading. Edmentum is adding new item types to the Study Island

benchmarks in response to the changes that many state tests will adopt as they move to computer tests instead of paper-

and-pencil tests. To preserve the simulated test experience, benchmarks will include only the new item types that are

specified in the state’s test blueprints.

Most of the next-generation benchmark assessments contain one or more constructed-response items. Constructed-

response items are teacher graded (or graded by a school-assigned grader) using a supplied scoring rubric. The

maximum number of points available for a constructed-response item is determined by the complexity of the item and

ranges from 1 to 4 points. The number of points awarded by the grader for each constructed-response item is entered into

the form’s grading key. Those points are then added (automatically) to the machine-graded points for a final raw score of

the benchmark assessment.

Comparable forms

Benchmark test forms are being designed to achieve a more advanced degree of comparability. Though items currently

assess the same reporting category across all forms, future benchmark items will assess the same standard and DOK

level as well. In cases where a single standard is broad and encompasses several concepts, the same concept will be

assessed on each form. The new benchmark test forms are being designed based on a combination of content similarity

and test specifications as well as pretested item-difficulty data to improve the statistical match of the overall difficulty level

of the benchmark assessment forms. While the benchmark assessment forms are not currently psychometrically equated,

every effort is made to use all available information to create comparable benchmark test forms.

Pretested Items

The majority of the items on each benchmark test come from existing banks of pretested items. This includes the new

interactive (technology-enhanced) item types. Using response data from thousands of students, Edmentum developers

track the item difficulty value, or the percentage of students who got each item correct. Items with difficulty values above

85% or below 20% are scrutinized before they are included in any new test forms. This process allows exclusion of items

that have proven to be too easy or too hard for users. Before any item is excluded, it is carefully examined to see how it

measures the standard it is intended to measure and whether the difficulty level (either too easy or too difficult) is simply a

function of the difficulty of the new Common Core standards. (In such cases the item may be retained because it is the

standard that is easy or difficult.) Where necessary, a few items without pretest data may be used to ensure the quality of

the content representation of the benchmark assessment form or to provide closer alignment with the CCSS.

V. Scores and Reporting

Study Island allows teachers and administrators to make use of student achievement data to improve instruction by

providing relevant scores and reports. The reports generated by Study Island include data aggregated in multiple ways.

Users can choose the score reports they would like to view from an easy-to-use menu, or they can set up reports to be

automatically emailed.

Scores and Score Interpretation

It is important to remember that the scores from Study Island (either the standards mastery component or the benchmark

assessment component) are only individual pieces of information about a student’s academic performance. Study Island

scores should be considered alongside other sources of information about the student’s proficiency, such as classroom

assignments, tests, and grades.

(15)

Standards Mastery Component Scores

Raw Scores (Number-Correct Scores) Raw scores indicate the actual number of items to which the student responded correctly out of the total number of items

in a given Study Island topic.

Percentage Scores (Percentage-Correct Scores) A percentage score is the percent of test items answered correctly within a Study Island topic. These scores are one of

the primary indicators of a student’s performance.

The percentages in the blue ribbon report are not percentages of questions correct. They show the progress of the

student through the program and are based upon the number of topics the student has passed.

Benchmark Assessment Component Scores

Raw Scores (Number-Correct Scores) Raw scores indicate the actual number of items or tasks to which the student responded correctly out of the total number

of items responded to. Raw scores are the primary indicator of a student’s performance in the different subject content

areas, providing some information about a student’s proficiency in individual standards.

Percentage Scores (Percentage-Correct Scores) A percentage score is the percentage of test items answered correctly (or percentage of total points attained by the

student). These scores can be useful when describing a student’s performance on a teacher-made test or on a criterion-

referenced test.

In the next-generation benchmarks, the addition of constructed-response items that may have a score worth more than a

single point requires altering the score representations on reports. Previous representations of percentage scores have

been in terms of questions answered correctly. Going forward, raw scores will be presented in terms of points earned. For

example, a 30-item benchmark with five constructed-response items, each worth four points, will have a total of 45 points

possible. Percentage scores will be calculated against the total points possible.

Both raw scores and percentage-correct scores have a disadvantage: There is no way of directly comparing the number

correct (or percentage correct) on one benchmark test form with the number correct on another benchmark test form. The

interpretation of these scores is related to the difficulty level of the test items on each particular test or form. Because

each test has a unique level of difficulty, there is no common way to interpret these scores; there is no frame of reference.

Reporting

Study Island provides administrators and teachers with a variety of reports that can be customized to their specific needs.

These detailed reports provide data on school activity and progress, overall student performance, and disaggregated

benchmark data. Many reports can be pulled across multiple dimensions and are easily exported to Excel.

Standards Mastery Component Reports

Streamlined progress monitoring is an element essential to effective district- and building-level management.

District Level Reports District-level reports provide a tool from which administrators can oversee progress across buildings, grade levels, or

individual student demographics.

Gradebook Report

o View a breakdown of student progress within a subject.

o Monitor usage and performance at each school site.

o Identify performance trends across the district.

(16)

School Comparison Report

o Compare performance and Study Island usage among selected schools.

Student Login Report

o View student login information for the past three months. Click a student’s name to see specific login dates and

times.

o Monitor usage to ensure students are fully engaged in the program.

o View detailed individual student login information.

o View teacher usage information by school.

Suggested Topics Report

o Identify the strengths and weaknesses of schools (for students in the same grade level and subject).

o Highlight areas in which the district is excelling and areas where additional intervention support is needed.

Blue Ribbon Report

o Review the number of blue ribbons students have earned, summarized at the school level within the district.

o Identify and recognize high achievers.

o View blue ribbons (percentage of topics completed) earned by grade level.

District Summary Report

o View a summary of school performance by date.

o Review data for all schools taking benchmark tests in a district.

o Gain a high-level overview of program performance and usage.

o View performance at a specific point of time.

o Monitor growth and track performance over time across benchmark tests.

Program Participation Report

o Quickly view Study Island program coverage across the district

o List all the programs and the schools that subscribe to them.

Weekly District Report

o Review the activity for all grade-level programs during a specific week within the school district.

o View graphic representations of overall school usage district-wide by date.

o Access a quick summary overview, displayed graphically, to gather talking points for administrators to discuss

school progress.

School-Level (Building) Reports Building-level reports provide data to monitor student, class, and school-wide progress, allowing school leaders to identify

areas needing additional practice and individualize instruction based on student needs.

Class Gradebook Report

o View a breakdown of student progress within a subject.

o View a list of students by class and their Study Island statistics.

Assignment Report

o View results for an assignment created in Class Manager.

o View progress in a specific set of topics assigned to students.

o Filter the report by date, time, and day.

Weekly Report

o Review activity for all grade-level programs during a specific week.

o View overall weekly and yearly usage statistics for each program.

o View the overall number of questions taken, percentage correct per grade level for each program and subject,

number of students passing, and percentage of program completed for the year.

(17)

Blue Ribbon Report

o See the number of blue ribbons students have earned, summarized at the school level within the district. Note:

The percentages in this report are not percentages of questions correct. They show the progress of the student

through the program and are based upon the number of topics the student has passed.

RTI Report

o Use Study Island’s RTI Report to monitor student progress.

o Track individual student RTI progress by topic. Performance progression over time is illustrated graphically and

statistically.

o Review a student’s work in a topic over time, including building block topics. Assign the same topic at least once a

week over a period of four weeks, implementing intervention strategies after each testing session based on the

student’s results.

Weekly Campus Report

o View graphic representations of detailed educator and student usage on a school-wide basis.

o View at-a-glance interactive graphs of student statistics, usage, logins, and enrollment.

o Automatically email a report on overall usage for a school to recipients.

Individual Student Report

o View individual student progress and Study Island usage.

o See a list of recommended topics for additional focus based on individual student results.

o Review a student’s missed questions.

o Filter the report by date, time, and day.

High Score Report

o Review student performance on games.

o See how many high-score tables each student is on. (There is a unique high-score table for each Study Island

game.)

o View the number of instances a first, second, or third place ranking has been achieved by the student on the

school and state high score table.

Class Summary Report

o Quickly view strengths and weaknesses of a class.

o See what topics students have completed, and map class progress to the curriculum guide.

o View a summary of class performance across all subjects or by individual subjects.

o Filter the report by date, time, and day.

o Identify how students are performing relative to state standards and reporting categories.

Trend Report

Choose among three different graphs:

o Usage Graph: Shows the weekly usage for each subject. It is useful to view how much time students are

spending on Study Island over time.

o Cumulative Performance Graph: Shows the total percentage correct since the start of Study Island for each

subject. It is useful to see how the percentage-correct scores change over time.

o Performance Graph: Shows the weekly percentage correct for each subject. The report includes statistics for all

students in a school who used the program during the specified period.

Login Report

o View detailed individual student login information.

o View student login information for the past three months. Click a student’s name to see specific dates and times.

Class Comparison Report

o Compare usage and performance between classes and grade levels.

o Compare performance and Study Island usage among selected classes and grade levels.

o Identify and recognize high-performing classes.

o Filter the report by date, time, and date.

(18)

Suggested Topics Report

o View a list of topics that need improvement, sorted by priority.

o Identify the strengths and weaknesses of the class.

Statewide Comparison Report

o View a snapshot of class and student progress measured against state- and school-wide performance.

o View graphs comparing school and state performance.

Benchmarking Report (see Benchmark Assessment Component Reports)

o View data for all students taking a benchmark test at a school. Data includes a summary of each class and grade

level.

o View performance at a specific point in time.

o Monitor growth and track performance over time across benchmark tests.

o Use the item analysis feature.

Classroom Response Session Report

o View detailed reports of a completed classroom response session.

o Track individual student and whole-group progress during classroom response sessions.

Teacher Information and Reports The Teacher Page is a dashboard featuring quick-access links to commonly used teacher features. The Teacher Page

consists of My Class and My Assignment sections, which include direct links to features available in the Class Manager.

Teachers can also find a list of the reports they have automatically emailed (in My Emailed Reports) and a snapshot of the

top-five blue-ribbon earners (in Blue Ribbon Snapshot). Finally, located under Teachers’ Lounge and Announcements,

teachers will find direct links to Implementation Ideas, Power User Information, Study Island Social Networking, and

exciting new Study Island Announcements.

Study Island enables teachers to group students into specific classes. Classes are simply groupings. A student can be in

more than one class at a time, and there is no limit to the number of classes you can create. Classes can also include

students from more than one grade level. The Class Page and creation of classes is an optional feature and is not

required to use the Study Island program.

From the Teacher Page, you can:

Create assignments for an individual student.

Easily view student progress.

See class averages.

Send messages to all students in your class.

Make a Class Page and class assignments.

Send automatic emails to parents.

View student activity in real-time.

Benchmark Assessment Component Reports

There are five different benchmark assessment reports from which to choose:

Gradebook Format

Class Summary

Class Comparison

Individual Student Format

School-wide Executive Summary

(19)

Gradebook Format This report provides an overall view of the benchmark performance of a class. Teachers can also see what objectives to

focus more class time on or to re-teach. Report features include:

View and analyze student percentages broken down by reporting category (objectives).

Select Item Analysis to see all students who selected incorrect or correct answers.

Sort on any column heading.

Class Summary Use this report to view and analyze class statistics for the benchmark. The report highlights areas where your class has

scored well and where help is needed. This can help you know which topics to focus on when planning lessons. This

report:

provides an overview of the assessments, how many students tested, and the percentage of students in each

proficiency category (Advanced, Proficient, Basic, Below Basic)

can be sorted by column

can disaggregate by subgroups

Class Comparison This report allows teachers to view and analyze student performance on specific questions and objectives. It allows

comparison of classes across grade levels.

Individual Student Format Use this report to analyze individual student statistics for each benchmark in a particular subject. This report:

allows the user to choose a benchmark report for a specific student

reveals the strength and weakness areas of individual students

can be used for creating tutoring groups and re-teaching

is useful for writing IEPs

School-wide Executive Summary This report is similar to the Class Summary report but includes school-wide data. Use it to view and analyze data for all

students taking a benchmark test. In this report, you can also generate graphs to show school-wide progress for each

benchmark test.

(20)

VI. Security

Edmentum implements a variety of security measures to protect the integrity of Study Island benchmark assessment and

standards mastery programs.

Data, Server, and Internet Security

Edmentum does not share student records or student data with anyone. The Study Island database servers are

electronically secured using best-of-breed firewall solutions from Cisco. The Study Island database servers are located in

a physically secured data center with 24-7-365 closed-circuit video monitoring and logging at all entry points. Photo ID

access cards are required at the point of entry. Perimeter doors alarms are monitored 24-7-365.

Edmentum maintains a designated engineer as manager of data security and protection. All Edmentum employees who

have access to student records receive training in security and how to best assure proper protection of student data. All

employees with access to student data are required to sign a confidentiality agreement. Breach of company policies

regarding data security results in immediate discipline, up to and including termination. Breach of student privacy may

also make a violator subject to penalties under the Family Educational Rights and Privacy Act (FERPA).

Edmentum employs a third-party vendor to test its systems and ensure data integrity several times per year. Edmentum,

with customer permission, may use school or district-wide statistics as part of its efficacy research and promotional

pieces; in all cases, individual student identity and data are never revealed. For customers that require still higher security

precautions, Edmentum offers the option of encrypting the transmission of data to and from Study Island and its

customers using SSL encryption technology using the URL https://secure.studyisland.com.

FERPA Compliance and Study Island

FERPA is a federal law designed to protect the privacy of students’ education records. The law applies to all schools that

receive funds under an applicable program of the US Department of Education. Because of the wording of the act, which

originated in 1974 and did not envision the Internet, all computer records in Study Island are considered to be education

records protected by the act. What this means, in practice, is that students have the right to expect that any student

records within Study Island, including their names and other identifying information, will not be viewable by guests and

others who are not school officials.

Use of Dynamic Items

Study Island makes use of intelligent technology to create dynamic and generative content within the mathematics

standards mastery component, providing a unique (and more secure) experience for every student. Although the format of

a question will remain constant, the program automatically generates the content of the questions, creating a unique and

varied set of questions within each learning objective. Therefore, even if students are concurrently practicing the same

standard at the same level, each student will see unique question content within the question format. Taken together, the

dynamic features of the program can afford teachers the confidence that students are applying their own knowledge in

each Study Island session.

Randomization of Items, Item Order, and Answer Options

Randomization is implemented three unique ways inside of Study Island.

Randomized selection of items within a topic is done only within the standards mastery component. Within a specified

topic, items are randomly selected from a pool of aligned standards mastery items that correspond to that topic. This is

done as an aid to maintaining the integrity of the standards mastery component.

Randomization of item presentation order is primarily used in the benchmark assessment component. Although students

will ultimately see the same questions within a benchmark form, the order of the questions will vary for each student.

Question order may also be randomized in the standards mastery component for the pre- and posttest assessments

within a module. Basically, any time there is a fixed set of items that constitute some type of Study Island assessment, the

order of presentation of the items is randomized.

(21)

Randomization of the answer options is done both in the standards mastery component and in the benchmark

assessments component (only for multiple-choice style items). The randomization of answer options is done to help

reduce item exposure and memorability of items.

User Access Security

Authorized use of Study Island is controlled with user name and password control. Each student and teacher should have

a unique password. If you choose to give each student the same initial password, you should check the “force reset of

password upon login” option to preserve data security. The administrator and teachers will have access to the updated

information via the Password List link.

User names must be unique within the Study Island national database so that statistics can be created for each student. If

you try to register a student and the system will not accept that particular user name, it means that another student

(possibly from a different school) is already using that user name and you should enter a different user name.

Test Administration Window Security

For Study Island benchmark assessments, the student must be assigned to a test administration window of time. Only test

administrators may create a benchmark assessment test administration window. This effectively precludes students from

seeing any benchmark assessment content until the test administrator makes the test available to the students for some

defined time period.

When a student logs into Study Island during a scheduled benchmark time period, the student will be able to see and take

the benchmark test. The student will not be able to access other Study Island topics in the standards mastery component

for that subject until the scheduled benchmark test is complete.

Students do not have to complete the benchmark in one session. They can click the Save for Later button and return later

to finish as long as they resume the test within the scheduled testing window.

Multiple Benchmark Assessment Forms Available

For the Common Core benchmark assessments described in this manual, there are four comparable benchmark

assessment forms that may be administered. Availability of these alternative forms provides an additional layer of test

security for test administrators who are concerned with benchmark test security.

Each student will be allowed to take each benchmark test only once, even if the school schedules two different testing

periods for the same benchmark test.

VII. Reliability and Validity

Educators need detailed information about individual student achievement. They use this information to place students in

appropriate classes and to form instructional groups within a class. They also use it to help parents and other

stakeholders understand the strengths of a particular student’s educational development as well as the areas that need

further instruction. When constructed and used properly, educational assessments are efficient tools that yield consistent,

valid, and precise information concerning student achievement and growth.

Reliability and validity are critical aspects of the educational measurement process.

Reliability

Reliability is a primary requirement of measurement. Reliability is defined as the consistency of measures obtained from a

measurement tool. For example, when an object is weighed on a scale, one expects that additional measurements of the

same object with the same scale will have similar results. With repeated observations, it can be determined that the scale

measurements are consistent and reliable. Educational assessments that yield consistent results with repeated testing or

within different portions of the same test are considered reliable. Those that provide inconsistent results are unreliable and

(22)

of less use to educators. Therefore, one of the primary goals in creating an educational assessment is to create an

assessment that has reliable scores.

Precision is the level of detail that the assessment can render. Precision is directly related to reliability. Tests with high

reliability yield scores with greater precision, whereas tests with lower reliability have scores with less precision. A scale

capable of measuring weight to the nearest ounce is more precise than a scale that measures to the nearest pound. With

a more precise scale, the amount of error in any single measurement is less than one ounce if the person taking the

measurements is consistent.

In educational assessment, precision (commonly referred to as error) can be thought of in the same manner. The amount

of error to be expected in a test score is commonly referred to as the standard error of measurement (SEM). A more

precise assessment instrument allows educators to see the difference between two similar students better than a less

precise instrument. It is for this reason that measurement precision is valuable to educators and is therefore one of the

primary goals in designing an educational assessment. Precision is affected by the amount of information obtained from

each test question and the number of questions on a test. Test developers can optimize the precision available for a test

of a given length by developing a test that yields a high amount of information from each item.

Reliability of the benchmark assessments was determined using an internal consistency approach involving coefficient

alpha (α). These estimates of reliability, along with the SEM for each of the benchmark assessment forms, are discussed

in the test analysis section of this manual.

Validity

Validity is another quality that is important in designing and evaluating assessments. Validity can be defined as the degree

to which an educational assessment measures what it purports to measure. This attribute of a test and its scores is

fundamental to the quality of the measurement.

There are three critical aspects of validity:

content validity–the degree to which an assessment measures the entire range of what students are expected to learn in a classroom

construct validity–the degree to which scores from an assessment in a content area correspond to other indicators of student achievement in the same content area

criterion validity–the degree to which the scores from an assessment (in a content area) are able to predict some specified outcome (criterion)

Standards for Educational and Psychological Testing (AERA, APA & NCME, 1999) provides a framework for describing

the sources of evidence that should be considered when constructing a validity argument. The three types of validity listed

above address different aspects of validity. Each source of validity contributes to a body of evidence about the

comprehensive validity of score interpretations.

Content Validity

Content validity is the extent to which an assessment is an accurate measure of the full range of Common Core or state-

specific standards. In educational assessment, this is highly dependent upon the curriculum. For example, a generic

mathematics assessment may contain content that differs greatly from the content that is expected to be taught in the

classroom. On the other hand, a mathematics assessment designed to gauge the spectrum of content in the curriculum

fits the content needs of the classroom, school, district, or state more completely. The latter, more valid assessment is

clearly more valuable to educators in understanding student achievement. Edmentum’s Study Island Common Core

benchmark assessments have been developed to specifically measure the CCSS.

Content validity is the primary indicator of validity for standards-based assessments. Evidence on content validity provides

key information on how well the assessment tasks represent the curriculum and standards for each grade-level form of a

specific content area. Content validation is informed by the item development process, including how the test blueprints

and test items align to the curriculum and standards that the assessment is intended to measure, in this case the CCSS.

Evidence of content validity based on test content was extensively described in the test development and test

specifications sections of this manual. Components of validity evidence based on test content include item alignment with

the CCSS; item- and test-development processes; item bias and content appropriateness review processes; adherence to

(23)

the test specifications; use of standardized administration procedures, with accommodated options for participation; and

appropriate test administration training. As discussed previously, all Study Island items are aligned by extensively trained

curriculum and assessment experts and undergo several rounds of review for content fidelity and appropriateness. Finally,

tests are administered in a standardized manner, given their computer-based format, with allowable accommodations,

and all test coordinators and administrators are required to familiarize themselves with and adhere to all of the procedures

outlined in the Study Island Administrator Manual.

The alignment of test content with the CCSS maps is presented in appendix F (for mathematics) and appendix G (for

ELA). These alignment maps are presented there both as a summary of the general Study Island development and as

further detailed content validity evidence supporting the Study Island benchmark assessments.

Construct Validity

Edmentum is committed to providing the latest research on the construct validity of Study Island to current and

prospective users. Construct validity pertains to the degree to which the scores from an assessment in a content area

correspond to (or converge with) other indicators of student achievement in that same content area (convergent validity).

In practice, it is often the purpose of the research that distinguishes whether the results are in support of construct validity

or criterion validity. Both types of validity can involve an attempt to validate the relationship between an assessment score

outcome and some external measure. In the case of Study Island, because the external measures (state-specific

assessments) differ, it seems like most of the evidence of a relationship thus far might be best described as construct

validity. Regardless of classification, the information is offered as evidence of the validity of the Study Island benchmark

assessments.

A recent example of such research investigated the relationship of the Study Island standards mastery component with a

state standards–based achievement test (the Minnesota Comprehensive Assessment, or MCA). This independent

research can be found in an August 2013 doctoral dissertation submitted to the faculty at the University of Minnesota

(Bernard, 2013).

The study examined existing fifth-grade through eighth-grade student data from a small rural school in Minnesota. Data

for this study were collected over a seven-year time frame, from the 2005–06 school year to the 2011–12 school year.

During these school years, 463 total students moved in cohorts through grades 5 through 8.

Bernard (2013) describes the unique opportunity to evaluate the Study Island program as follows:

This particular school implemented CAI through an ILS in the 7th and 8th grades’ curriculum at the beginning of the 2008–2009 school year. In the previous years, no CAI was integrated or used in classroom instruction. Within the data, two natural breaks were found. These breaks can be seen as before and after the implementation of the CAI program for the students. When the students were in 5th and 6th grade, or “elementary school,” they did not receive CAI. When those students moved into 7th and 8th grades, or “middle school,” they did receive CAI after the 2008–09 school year. The changes in the students’ MCA scores can be examined because of this. The second natural break in the data was within the grades that implemented CAI. The 7th and 8th grade MCA scores can be examined for differences before and after the implementation year of 2008–09. The specific ILS program that was used to try to increase achievement in the area of mathematics is Study Island (Edmentum, 2013b). This program was the focus of study in this research.

The content that the students received through Study Island was aligned to the Minnesota state mathematics standards in

place at that time. Those standards serve as guidelines by which Minnesota schools align their curriculum.

One of the central questions of this research was examining the data to see whether there was a significant difference

between the MCA scores of students who used Study Island and those who did not use Study Island. The data were

analyzed to see if there were differences in the students’ MCA scores before and after their use of Study Island. The

findings from the Bernard 2013 study are summarized in figure 1.

(24)

Figure 1. Percentage of seventh-grade students who were proficient before and after

Study Island implementation. Based on results reported in the Bernard 2013 study.

Correlations were also sought between the different usage and proficiency levels of the students as measured by Study

Island and their proficiency levels as measured by the MCA. These different usage measures were further broken down

by the two different types of question modes in Study Island: game mode and test (practice) mode.

Although a number of Study Island indicators were analyzed for relationship with the MCA scores (i.e., number of

sessions, number of questions, number of questions answered correctly, total time, and percentage of questions

answered correctly), only the percentage of questions answered correctly resulted in consistently strong correlations. The

reported correlation between the Study Island percentage correct score and the MCA scaled score was 0.73 for seventh

grade and 0.55 for eighth grade.

Bernard discusses the results of the study that examined the impact of the game mode on student performance as

follows:

First, the percentage of questions that the students answered correctly in game mode and practice mode were

calculated. These values were then charted on a bar chart for a visual representation . . . For the groups

examined, on average, students answered more of the game mode questions correctly than they did the practice

mode. The eighth grade individually and seventh and eighth grades (middle school) combined group’s differences

were seen to be significant.

68%

81%

56%

76%

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100%

Before SI After SI

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8th Grade

(25)

Figure 2. Percentage of questions answered correctly, by grade, from 2008–09 to

2010–11. Based on results reported in the Bernard 2013 study.

In his conclusion, Bernard (2013) states:

Significant differences were found when individual grade levels were compared before and after the

implementation of Study Island. When looking at the grades grouped together as elementary and middle school,

the middle school showed significant growth on the MCA after the implementation of Study Island, but the

elementary did not. If the elementary had shown significant differences in growth during these years, then the

significant difference in the middle school could be much more easily attributed to other factors besides the Study

Island program. This adds to the assertion by Study Island that its program will increase the proficiency of the

students who use it. . . .

One of the possible causes for the high overall correlation (0.63) between the percent correct on Study Island and

proficiency on the MCA could be that the questions on Study Island have a high level of alignment with the

Minnesota State Standards that are tested by the MCA. The Study Island website makes this claim and the data

that was found in this study add to the credibility of this claim.

Finally, Bernard discusses the potentially positive motivational effect of the Study Island game mode:

Teachers should not concentrate on when the students are answering the game based questions or the practice

based questions. They should focus more on whether the students are answering the questions correctly. The

students in this study answered significantly more questions correctly when they played in game mode. This could

have been because they were motivated to concentrate harder, and answer the question correctly so that they

could play the game afterwards. As stated before, if the student answered the question incorrectly, they had to try

again until they answered it correctly for both types of questions. The difference was that if they did not answer

correctly on the first try in game mode, then they did not get to play the game afterward.

In summary, the results of the Bernard (2013) dissertation study appear to provide strong evidence of the construct

validity of Study Island. Additional research on how well data from Study Island, as an assessment in a given content

area, correspond to other indicators of student achievement in that same content area will be added to the Study Island

research base over time.

77% 73%

76%

88% 93% 91%

79% 82% 80%

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(26)

Other studies in Michigan, Kansas, and Pennsylvania find similar results (Dube, 2011; Ostroski, 2012; Viviano, 2011).

Study Island content is aligned to state standards in each of these states. Dube finds evidence that seventh-grade math

performance on the Study Island standards mastery component is strongly correlated with performance on the math

section of the Michigan Educational Assessment Program (2011). Furthermore, findings from a group of at-risk high

school students in Kansas also show moderate to high levels of correlation between Study Island performance and both

math and reading state assessment performance (Ostroski, 2012). Finally, research conducted in a Philadelphia vo-tech

school that contained a large percentage of students in special education also found that proficiency on Study Island is

associated with performance on both the Pennsylvania System of School Assessment and the NOCTI, a standardized

test for student studying career and technical programs in high schools (Viviano, 2011).

Alignment to Standards–Study Island Common Core

Detailed information about Study Island mathematics alignment with the CCSS is provided in appendix F. See appendix G

for detailed information on Study Island ELA alignment with the CCSS.

(27)

VIII. Analysis of Study Island Common Core Standards Mastery Item Pools

All items on Edmentum’s Study Island Common Core standards mastery component for which sufficient student response

data have been obtained (defined as at least 100 student responses to an item) were evaluated in terms of item difficulty

according to standard classical test theory practices. Difficulty is defined as the proportion of students answering a given

item correctly. The difficulty index ranges from 0.0 to 1.0. Although this index is traditionally described as a measure of

difficulty, it is more appropriately thought of as an “easiness index” because larger values indicate easier items. An index

of 0.0 indicates that no students answered the item correctly, and an index of 1.0 indicates that all students answered the

item correctly.

Tables 15 and 16 summarize the item difficulty statistics for the standards mastery component items. Note that only items

that have had at least 100 student responses are included in these summaries: table 14 provides the numbers of

Common Core standards mastery items that did not meet the threshold of having at least 100 student responses and

were therefore excluded from the summary analysis. Student response data for the standards mastery component

analyses were based on all student responses to the Common Core standards mastery items. There was no information

with those responses to identify users or what state they were from. The only filter on extracting this standards mastery

data was the “at least 100 student responses” constraint mentioned above.

New items are constantly being created for the Study Island standards mastery component: the items examined in this

analysis were only Common Core (not state-specific) standards and were measured at a fixed point in time.

Note that there are “dynamic” items in mathematics (table 15). These are items that are essentially computer generated

according to prescribed rules such that the question and the answer options vary across students and occasions. The use

of dynamic items reduces the overall size requirements of the mathematics Common Core standards mastery item pool

because each question can be administered in slightly varying form. For purposes of determining the item difficulty index,

all responses to a specific question were grouped together for purposes of determining item difficulty. While this may not

be an optimal approach to determining the difficulty level of a dynamic item, it is hoped that the variant forms of the

question may distribute normally and the combining of data will remain informative.

Tables 17 and 18 summarize the item difficulty statistics for the technology-enhanced items in the Study Island Common

Core standards mastery component item pools. Again, only items that have had at least 100 student responses are

included. Keep in mind that new items are always being created for the Study Island standards mastery component. This

analysis reflects the items in use at a fixed point in time.

The distributions (histograms) of the standards mastery item difficulty values for the Study Island Common Core item

pools are presented in appendix A (for mathematics) and appendix B (for ELA).

(28)

Table 14. Number of Study Island standards mastery component items (Common Core

standards) excluded from analysis for having fewer than 100 student responses

Grade Subject Area

Number of Items Excluded from Analysis

*

3 Mathematics 181

4 Mathematics 116

5 Mathematics 283

6 Mathematics 79

7 Mathematics 106

8 Mathematics 982

9 Mathematics 811

10 Mathematics 2,975

11 Mathematics 1,125

TOTAL: 6,658

3 ELA 111

4 ELA 103

5 ELA 64

6 ELA 65

7 ELA 80

8 ELA 77

9 ELA 33

10 ELA 111

11 ELA 585

TOTAL: 1,229 *May include some technology-enhanced items.

Item Difficulty (p-value) Statistics by Grade-Level Form

Total Number of Items–the number of items in the Common Core standards mastery item pool for that grade level

Mean P–the average (mean) of the item difficulty statistics

Median P–the median (50th percentile) of the item difficulty statistics

Min.–the minimum item difficulty statistic

Max.–the maximum item difficulty statistic

(29)

Table 15. Summary of Study Island standards mastery component (mathematics)

Grade

Total Number

of Items*†

Number of Dynamic Items

*† Mean P Median P SD Min. Max.

3 1,223 689 0.69 0.72 0.20 0.03 0.99

4 1,390 708 0.66 0.68 0.21 0.09 0.99

5 1,013 585 0.62 0.63 0.19 0.11 0.99

6 1,270 757 0.62 0.64 0.20 0.06 0.99

7 1,369 892 0.56 0.56 0.19 0.06 0.99

8 1,290 684 0.58 0.58 0.19 0.07 0.99

9 1,362 972 0.57 0.59 0.18 0.01 0.95

10 2,871 1,934 0.54 0.54 0.16 0.08 0.96

11 432 322 0.57 0.58 0.16 0.11 0.98

Total 10,997 7,543 *Includes only Common Core, not state-specific, standards mastery items.

†Does not include items with fewer than 100 student responses.

Table 16. Summary of Study Island standards mastery component (ELA)

Grade Number

of Items*†

Mean P Median P SD Min. Max.

3 2,448 0.71 0.73 0.15 0.09 0.99

4 2,539 0.71 0.73 0.16 0.09 0.99

5 2,576 0.72 0.74 0.16 0.10 0.99

6 2,513 0.70 0.72 0.16 0.06 1.00

7 2,281 0.70 0.73 0.16 0.09 0.98

8 2,609 0.70 0.72 0.16 0.06 0.99

9 1,691 0.69 0.71 0.16 0.11 0.99

10 2,100 0.69 0.71 0.16 0.04 0.99

11 1,534 0.70 0.74 0.18 0.06 0.99

Total 20,291 *Includes only Common Core, not state-specific, standards mastery items.

†Does not include items with fewer than 100 student responses.

(30)

Table 17. Summary of difficulty statistics for Study Island standards mastery component

technology-enhanced items (mathematics)

Grade Number of

Items*+†

Mean P Median P SD Min. Max.

3 143 0.48 0.48 0.22 0.03 0.99

4 166 0.40 0.36 0.20 0.09 0.93

5 114 0.45 0.40 0.21 0.11 0.99

6 156 0.37 0.34 0.18 0.06 0.89

7 121 0.24 0.21 0.13 0.06 0.68

8 122 0.38 0.34 0.20 0.07 0.96

9 88 0.26 0.22 0.17 0.01 0.72

10 23 0.35 0.32 0.19 0.09 0.74

11 19 0.34 0.31 0.16 0.10 0.64

Total 952

*Includes only Common Core, not state-specific, standards mastery items.

+Includes technology-enhanced items only.

†Does not include items with fewer than 100 student responses.

Table 18. Summary of difficulty statistics for Study Island standards mastery component

technology-enhanced items (ELA)

Grade Number of

Items*+†

Mean P Median P SD Min. Max.

3 80 0.54 0.58 0.21 0.11 0.93

4 116 0.51 0.51 0.21 0.09 0.96

5 109 0.52 0.49 0.21 0.10 0.96

6 91 0.59 0.60 0.23 0.06 0.97

7 73 0.56 0.59 0.20 0.09 0.96

8 76 0.53 0.52 0.21 0.06 0.95

9 73 0.46 0.48 0.18 0.11 0.81

10 85 0.46 0.45 0.20 0.04 0.89

11 96 0.41 0.38 0.20 0.06 0.89

Total 799

*Includes only Common Core, not state-specific, standards mastery items.

+Includes technology-enhanced items only.

†Does not include items with fewer than 100 student responses.

(31)

IX. Analysis of Study Island Common Core Benchmark Assessments

Demographic Summary of Benchmark Assessment Data

The examinees in the sample benchmark assessment data reported here represent a large number of schools. In total,

the Study Island Common Core benchmark assessment is available in 46 states plus the District of Columbia. These

schools and districts have been among the first to implement Common Core benchmarks into their assessment plans for

student achievement. The student response data in these analyses represents students over a period from January 2012

through March 2014.

Sample Refinement and Data Cleanup

Item and test analyses were conducted using the response data of on-grade-level students only for grades 3–8

mathematics and ELA benchmarks (e.g., the sixth-grade item statistics are based solely on sixth-grade students). For

high school courses, however, students may be in a different grade than the typical grade level at which a course might

generally be given. The grade levels of the sample of examinees included in the analyses of mathematics courses are

given in table 19. The grade levels of the sample of examinees for high school ELA courses are in table 20.

Students with missing responses were deleted from all benchmark assessment–related analyses.

Table 19. Percentage of examinees by grade level (high school mathematics courses)

Course Grade Level Percentage of

Examinees

Algebra 1 7 0.7

Common Core 8 2.2

9 39.5

10 30.8

11 19.6

12 7.1

Geometry 8 0.9

Common Core 9 18.3

10 50.8

11 25.7

12 4.3

Algebra 2 9 7.2

Common Core 10 25.7

11 42.6

12 24.5

(32)

Table 20. Percentage of examinees by grade level (high school ELA courses)

Course Grade Level Percentage of

Examinees

Grade 9 ELA 8 2.3

Common Core 9 64.3

10 32.0

11 1.2

12 0.2

Grade 10 ELA 9 7.5

Common Core 10 75.5

11 12.7

12 4.3

Grade 11 ELA 9 3.0

Common Core 10 9.0

11 66.5

12 21.5

Time of Benchmark Administration

Dividing the test administration dates into two categories—fall (August through December) and spring (January through

July)—provides an indication of what percentage of testing is done earlier in the academic year as opposed to later in the

year. This dichotomized time of benchmark administration is presented graphically in figures 3 through 6. For grades 3

through 8, there is a consistent pattern of form 1 primarily being administered in the fall. Form 2 appears to be split, being

administered about half the time in the fall and half the time in the spring. Forms 3 and 4 appear to be consistently

administered in the spring of the academic year. Note that the time of year that the benchmark form is administered is

important because these are standards-based tests. When a standards-based test is administered early in the academic

year, the students will not have received instruction on much of the content taught at that grade level (at that point in

time). This makes the test appear to be more challenging than it would seem if it were administered in the spring.

The differences in the time of year for administrating the benchmark forms make it difficult to compare across the four

benchmark assessment forms because the classical test theory item statistics would be affected by students having

received different amounts of instruction at the time of testing.

(33)

Figure 3. Summary of mathematics benchmark time of testing by grade level and form

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Grade Level and Benchmark Form Number

Percentage of Mathematics Benchmark Tests Administered

by Time of Academic Year (Grades 3–8)

Spring

Fall

(34)

(Key: A1 = Algebra 1, G = Geometry, and A2 = Algebra 2)

Figure 4. Summary of high school mathematics benchmark time of testing by form

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Percentage of Mathematics Benchmark Tests Administered

by Time of Academic Year (High School Courses)

Spring

Fall

(35)

Figure 5. Summary of ELA benchmark time of testing by grade level and form

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3-1 3-2 3-3 3-4 4-1 4-2 4-3 4-4 5-1 5-2 5-3 5-4 6-1 6-2 6-3 6-4 7-1 7-2 7-3 7-4 8-1 8-2 8-3 8-4

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Grade Level and Benchmark Form Number

Percentage of ELA Benchmark Tests Administered

by Time of Academic Year (Grades 3–8)

Spring

Fall

(36)

Figure 6. Summary of high school ELA benchmark time of testing by grade level and form

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9-1 9-2 9-3 9-4 10-1 10-2 10-3 10-4 11-1 11-2 11-3 11-4

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Grade Level and Benchmark Form Number

Percentage of ELA Benchmark Tests Administered

by Time of Academic Year (High School Courses)

Spring

Fall

(37)

Demographics of Benchmark Assessment Data Sample

Figures 7 through 10 show which states the students in these benchmark data analyses are from. Note that the

geographic and regional representation of students is dependent upon which states (and ultimately, which local education

agencies, districts, and schools) used the Common Core benchmark assessments for Study Island from January 2012

through March 2014. Many Study Island users implement only the standards mastery component and therefore would not

be represented in the Common Core benchmark assessment sample. Also, many Study Island benchmark assessment

users are currently using Study Island benchmark assessments matched to state-specific standards instead of Common

Core benchmark assessments. As the CCSS and the initial PARCC and Smarter Balanced assessments become more

widely implemented, it is anticipated that the representation of students will improve, although some states have already

indicated their intention to develop their own state standards and state-specific assessments.

For the majority of students, the demographic data that had been voluntarily loaded and entered into the Study Island

system was quite sparse. The data that could be entered consists of (1) gender, (2) race and ethnic background, (3)

economic status, (4) English proficiency, (5) gifted, (6) migrant, and (7) special education. For grade 3, between 66

percent and 88 percent of the student benchmark response data (depending on the variable) had no demographic

information entered into the Study Island system. Given the sparseness of the subset of students with demographic

information, there is no evidence that the demographic information that does exist in the system is at all representative of

the larger set of students who did not have any demographic information entered. The demographic results summarized

here are offered with a caution about the lack of information about their representativeness. Only the results for race and

ethnic background (tables 21 and 22) are provided in this report. Although the results for race and ethnic background do

not appear to be nationally representative, it is important to keep in mind that these are standards-based assessments,

and required Common Core knowledge and student mastery will be required of all students.

The origins, and representativeness, of these samples should be kept in mind when examining the item and test analysis

information (resulting from these students) that is presented in this technical manual.

(38)

Figure 7. States of examinees in analysis—Demographics summary by grade level (mathematics)

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States of Examinees in Analyses Grades 3–8 Study Island Mathematics

Common Core Benchmark Assessments

Gr 3

Gr 4

Gr 5

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Gr 8

(39)

Figure 8. States of examinees in analysis—Demographics summary by grade level (ELA)

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States of Examinees in Analyses Grades 3–8 Study Island ELA

Common Core Benchmark Assessments

Gr 3

Gr 4

Gr 5

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Gr 8

(40)

Figure 9. States of examinees in analysis—Demographics summary by grade level (high school mathematics)

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States of Examinees in Analyses High School Study Island Mathematics

Common Core Benchmark Assessments

Algebra 1

Geometry

Algebra 2

(41)

Figure 10. States of examinees in analysis—Demographics summary by grade level (high school ELA)

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(42)

Table 21. Racial and ethnic background—Demographics summary by grade level (mathematics)

Grade Subject Variable Percentage of Students

3 Math Asian 6.2

African American 9.4

Hispanic 14.0

American Indian/Alaska Native 3.9

Multiracial 1.5

Pacific Islander/Native Hawaiian 0.1

White 64.9

4 Math Asian

5.1

African American 9.2

Hispanic 13.8

American Indian/Alaska Native 3.7

Multiracial 1.4

Pacific Islander/Native Hawaiian 0.1

White 66.7

5 Math Asian 4.9

African American 9.5

Hispanic 13.0

American Indian/Alaska Native 2.1

Multiracial 1.2

Pacific Islander/Native Hawaiian 0.1

White 69.2

6 Math Asian 2.6

African American 13.8

(43)

Hispanic 10.5

American Indian/Alaska Native 2.2

Multiracial 2.3

Pacific Islander/Native Hawaiian 0.1

White 68.6

7 Math Asian 3.2

African American 13.5

Hispanic 10.1

American Indian/Alaska Native 2.7

Multiracial 1.3

Pacific Islander/Native Hawaiian 0.1

White 69.1

8 Math Asian 2.3

African American 12.5

Hispanic 9.8

American Indian/Alaska Native 2.6

Multiracial 2.1

Pacific Islander/Native Hawaiian 0.1

White 70.7

7–12 Algebra 1 Asian --

African American 26.1

Hispanic 2.2

American Indian/Alaska Native 25.4

Multiracial 3.7

Pacific Islander/Native Hawaiian 0.3

(44)

White 42.3

8–12 Geometry Asian 1.3

African American 13.9

Hispanic 2.3

American Indian/Alaska Native 16.1

Multiracial 3.2

Pacific Islander/Native Hawaiian --

White 63.3

9–12 Algebra 2 Asian 0.7

African American 10.9

Hispanic 0.3

American Indian/Alaska Native 16.6

Multiracial 1.4

Pacific Islander/Native Hawaiian --

White 70.1

(45)

Table 22. Racial and ethnic background—Demographics summary by grade level (ELA)

Grade Subject Variable Percentage of Students

3 ELA Asian 4.9

African American 9.9

Hispanic 13.4

American Indian/Alaska Native 3.8

Multiracial 1.7

Pacific Islander/Native Hawaiian 0.1

White 66.2

4 ELA Asian 3.9

African American 9.9

Hispanic 12.3

American Indian/Alaska Native 3.9

Multiracial 1.8

Pacific Islander/Native Hawaiian 0.1

White 69.2

5 ELA Asian 4.1

African American 10.3

Hispanic 12.2

American Indian/Alaska Native 4.2

Multiracial 1.5

Pacific Islander/Native Hawaiian 0.1

White 67.6

6 ELA Asian 2.5

African American 14.4

(46)

Hispanic 13.8

American Indian/Alaska Native 6.2

Multiracial 2.8

Pacific Islander/Native Hawaiian 0.1

White 60.2

7 ELA Asian 3.2

African American 14.9

Hispanic 15.7

American Indian/Alaska Native 5.8

Multiracial 1.5

Pacific Islander/Native Hawaiian 0.1

White 58.8

8 ELA Asian 2.7

African American 12.7

Hispanic 15.7

American Indian/Alaska Native 3.8

Multiracial 2.3

Pacific Islander/Native Hawaiian 0.1

White 62.7

9 ELA Asian 0.9

African American 17.9

Hispanic 2.0

American Indian/Alaska Native 20.3

Multiracial 2.6

Pacific Islander/Native Hawaiian 0.4

(47)

White 55.9

10 ELA Asian 0.6

African American 20.9

Hispanic 1.7

American Indian/Alaska Native 23.6

Multiracial 3.4

Pacific Islander/Native Hawaiian 0.0

White 49.7

11 ELA Asian 1.5

African American 12.1

Hispanic 2.5

American Indian/Alaska Native 13.6

Multiracial 4.0

Pacific Islander/Native Hawaiian 0.2

White 66.1

(48)

Item Analysis of Common Core Benchmark Assessment Data

As noted in Brown (1983), “A test is only as good as the items it contains.” A complete evaluation of a test’s quality must

include an evaluation of each item. Both Standards for Educational and Psychological Testing (AERA, APA & NCME,

1999) and the Code of Fair Testing Practices in Education (Joint Committee on Testing Practices, 2004) include

standards for identifying quality items. Items should assess only knowledge or skills that are identified as part of the

domain being tested and should avoid assessing irrelevant factors. Items should also be unambiguous and free of

grammatical errors, potentially insensitive content or language, and other confounding characteristics. In addition, items

must not unfairly disadvantage students in particular racial, ethnic, or gender groups.

Both qualitative and quantitative analyses are conducted to ensure that Edmentum’s Study Island Common Core

benchmark assessment items meet these standards. Qualitative analyses are described in earlier sections of this report;

this section focuses on quantitative evaluations. Statistical (and psychometric) evaluations in this section are presented in

terms of difficulty indices and item-total correlation indices. The item analyses presented here are based on

administrations of items contained in Edmentum’s Study Island Common Core benchmark assessments through March

2014.

Classical Item Difficulty Indices

All items on Edmentum’s Study Island Common Core benchmark assessments for which sufficient student response data

have been obtained were evaluated in terms of item difficulty according to standard, classical test-theory practices.

Difficulty is defined as the average proportion of points achieved on an item and is measured by obtaining the average

score on an item and dividing it by the maximum possible score for the item. Multiple-choice items are scored

dichotomously (correct versus incorrect); so, for these items, the difficulty index is simply the proportion of students who

correctly answered the item. The difficulty index is computed as the average proportion of points achieved, so the difficulty

indices for all items use a scale that ranges from 0.0 to 1.0. Although this index is traditionally described as a measure of

difficulty, it is more appropriately thought of as an “easiness index” because larger values indicate easier items. An index

of 0.0 indicates that no students answered the item correctly, and an index of 1.0 indicates that all students answered the

item correctly.

Items that are answered correctly by almost all students provide little information about differences in student abilities, but

they do indicate knowledge or skills that have been mastered by most students. Similarly, items that are correctly

answered by very few students provide little information about differences in student abilities but may indicate knowledge

or skills that have not yet been mastered by most students. In general, to provide the best measurement, difficulty indices

should range from near-chance performance (0.25 for four-option multiple-choice items) to 0.90, with the majority of items

generally falling between around 0.4 and 0.7. However, on a standards-referenced assessment such as Edmentum’s

Study Island Common Core benchmark assessment, it may be appropriate to include some items with very low or very

high item difficulty values to ensure sufficient content coverage.

Tables 23 and 24 summarize classical item difficulty statistics for each grade level form by content area (mathematics and

ELA).

Overall, a look at the statistical summaries of the item difficulties (within a grade level and form) in tables 23 and 24

appears to indicate that the test forms are rigorous. Rigor is not necessarily a bad thing, provided that it accurately reflects

the challenges of achieving mastery of specific standards. Excluding the high school mathematics courses, which may

represent a unique subpopulation, the mean percentage score column reflects that an average student is only able to

answer about 50 percent to 70 percent of the questions correctly.

There are at least four factors that may potentially be contributing to the apparent difficulty level of the Study Island

Common Core benchmark assessment forms (across all grade levels and both major content areas):

Time-of-testing influence: The students taking form 1—and to a somewhat lesser extent, the students taking form 2—of the Study Island Common Core benchmark assessments are generally being assessed in the fall of the school year (as shown in figures 6 and 8) and may not have been thoroughly exposed to the on-grade content that is covered by these benchmark assessments.

Rigor of Common Core standards: The standards being assessed by the Study Island Common Core benchmark assessments are themselves rigorous; it is not surprising that in these early stages of CCSS curriculum implementation, students and schools may not appear to show high student achievement levels.

(49)

Representativeness of on-grade samples of students: The population of on-grade students who take the Study Island benchmark exams may not be representative of all on-grade students. In classical test theory, the item difficulty statistic is confounded by the characteristics of the group of students who responded to each item.

Motivation level of students: If students are not sufficiently motivated to provide their best effort on a benchmark assessment, it is likely that the lowered motivation level will adversely impact their performance. If the motivation level is not optimal for a significant number of students, then the assessment will appear to be more difficult (statistically) than it would otherwise appear to be (if the motivation level were higher.) Motivation is likely to be more of a factor as grade level increases.

It is likely that all of these factors may be contributing to varying degrees in making the Study Island Common Core

benchmark assessment forms (across grades 3 through 8) appear rigorous.

Item Difficulty (p-value) Statistics by Grade-Level Benchmark Test Form

Number of Items on Form: The number of items on the grade-level benchmark assessment form

Mean P: The average (mean) of the item difficulty statistics for the benchmark test form; also the average proportion-correct score

Median P: The median (50th Percentile) of the item difficulty statistics for the benchmark test form;

Min: The minimum item difficulty statistic for the benchmark test form

Max: The maximum item difficulty statistic for the benchmark test form

(50)

Table 23. Summary of Common Core benchmark assessment item difficulty statistics

(mathematics)

Grade Form Number of Students

Number of Items on Form Mean P Median P Min. Max.

3

1 34,501

30

0.62 0.69 0.19 0.88

2 24,702 0.62 0.69 0.14 0.95

3 17,930 0.71 0.75 0.21 0.96

4 7,997 0.69 0.73 0.13 0.95

4

1 38,477

30

0.54 0.54 0.18 0.91

2 27,722 0.61 0.63 0.20 0.96

3 17,992 0.61 0.60 0.36 0.94

4 8,449 0.65 0.66 0.26 0.93

5

1 39,297

30

0.43 0.43 0.12 0.92

2 34,627 0.51 0.50 0.21 0.87

3 18,179 0.61 0.65 0.10 0.87

4 7,885 0.64 0.69 0.28 0.98

6

1 30,838

30

0.49 0.50 0.16 0.92

2 20,687 0.51 0.51 0.10 0.87

3 14,026 0.59 0.61 0.14 0.93

4 6,551 0.53 0.47 0.24 0.94

7

1 27,201

30

0.40 0.36 0.07 0.82

2 18,207 0.40 0.39 0.14 0.66

3 11,496 0.53 0.50 0.24 0.91

4 4,950 0.47 0.49 0.14 0.85

8

1 25,146

30

0.42 0.42 0.18 0.76

2 16,218 0.49 0.45 0.17 0.82

3 10,052 0.56 0.57 0.25 0.80

4 4,221 0.51 0.49 0.15 0.81

Algebra 1

1 1,968

30

0.40 0.37 0.24 0.68

2 1,138 0.38 0.34 0.16 0.79

3 1,167 0.37 0.34 0.19 0.71

4 639 0.43 0.37 0.13 0.76

Geometry

1 1,282

30

0.34 0.30 0.18 0.87

2 946 0.36 0.32 0.15 0.88

3 834 0.41 0.41 0.08 0.91

4 167 0.37 0.35 0.10 0.81

Algebra 2

1 866

30

0.33 0.29 0.13 0.70

2 889 0.37 0.37 0.14 0.66

3 919 0.37 0.34 0.19 0.72

4 153 0.43 0.43 0.09 0.85

(51)

Table 24. Summary of Common Core benchmark assessment item difficulty statistics

(ELA)

Grade Form Number of Students

Number of Items on Form Mean P Median P Min. Max.

3

1 33,954

30

0.51 0.50 0.33 0.80

2 25,509 0.61 0.61 0.35 0.83

3 18,437 0.65 0.66 0.38 0.81

4 8,383 0.58 0.55 0.41 0.77

4

1 37,330

30

0.57 0.57 0.29 0.77

2 29,648 0.64 0.65 0.27 0.91

3 20,316 0.70 0.71 0.32 0.89

4 8,976 0.64 0.63 0.40 0.87

5

1 38,046

30

0.66 0.68 0.37 0.86

2 29,487 0.68 0.69 0.42 0.91

3 19,839 0.71 0.73 0.46 0.87

4 8,507 0.72 0.73 0.47 0.90

6

1 32,773

30

0.62 0.66 0.16 0.86

2 21,804 0.69 0.68 0.37 0.91

3 13,221 0.68 0.69 0.39 0.87

4 7,132 0.75 0.77 0.47 0.88

7

1 30,340

30

0.70 0.75 0.28 0.89

2 19,662 0.71 0.74 0.29 0.88

3 12,544 0.68 0.69 0.40 0.92

4 5,751 0.72 0.72 0.53 0.90

8

1 28,748

30

0.67 0.68 0.27 0.92

2 18,543 0.68 0.75 0.33 0.88

3 11,654 0.70 0.71 0.41 0.91

4 4,858 0.68 0.71 0.33 0.81

9

1 3,268

30

0.52 0.50 0.21 0.90

2 943 0.55 0.57 0.17 0.84

3 963 0.59 0.64 0.15 0.89

4 614 0.65 0.66 0.37 0.88

10

1 1,734

30

0.56 0.57 0.21 0.82

2 858 0.63 0.67 0.27 0.88

3 864 0.65 0.69 0.26 0.89

4 266 0.60 0.61 0.27 0.80

11

1 1,691

30

0.70 0.74 0.34 0.89

2 963 0.62 0.65 0.21 0.86

3 1,120 0.64 0.60 0.38 0.86

4 484 0.56 0.56 0.13 0.81

(52)

Item-Total Correlation

Higher-ability students performing better on an item than lower-ability students is a desirable item characteristic. The

correlation between student performance on a single item and total test score (item-total correlation) is a commonly used

measure of this item characteristic. Within classical test theory, item-total correlation is sometimes referred to as the

item’s discrimination because it indicates the extent to which successful performance on an item discriminates between

high- and low-scoring examinees on the test. For multiple-choice items, the corresponding statistic is commonly referred

to as a point-biserial correlation. The theoretical range of these statistics is from -1.0 to 1.0, with a typical observed range

from 0.15 to 0.60. When point-biserial correlations approach zero, or become negative, it is a signal that the item does not

appear to be functioning appropriately.

Examining the minimums in tables 25 and 26, which summarize the item-total (point-biserial) correlations, shows that

there are clearly some items with near-zero or negative correlations. These items need further review by curriculum

content experts to verify the appropriateness of the items’ content as referenced against the item matches the CCSS for

that grade level and content area. With the exception of grade 9 ELA, the possibility of at least one low item-total

correlation seems to be limited to mathematics. Keep in mind that the same three factors mentioned in the item difficulty

section (factors contributing toward making items appear more difficult) can also have an effect on item-total correlation

statistics. Item-total correlation statistics can be constrained if students are not doing as well on the benchmark

assessment because it is early in the academic year, if the Common Core curriculum is truly just a lot more difficult, or if

the group of students does not have as much variability in overall benchmark scores.

Tables 25 and 26 summarize item-total (point-biserial) correlations for each grade-level form by content area

(mathematics and ELA).

Item-Total (Point-Biserial) Correlation Statistic by Grade Level

Benchmark Test Form

Number of Items on Form–the number of items on the grade-level benchmark assessment form

Mean R–the average (mean) of the item-total correlation statistics for the benchmark test form

Median R–the median (50th percentile) of the item-total correlation statistics for the benchmark test form

Min.–the minimum item-total correlation statistic for the benchmark test form

Max.–the maximum item-total correlation statistic for the benchmark test form

(53)

Table 25. Summary of Common Core benchmark assessment item-total correlation

(mathematics)

Grade Form Number of Students

Number of Items on Form

Mean R Point-

Biserial

Median R Point-

Biserial Min. Max.

3

1 34,501

30

0.42 0.44 0.05 0.58

2 24,702 0.37 0.39 0.10 0.56

3 17,930 0.39 0.41 0.15 0.54

4 7,997 0.42 0.42 0.15 0.58

4

1 38,477

30

0.36 0.39 0.08 0.53

2 27,722 0.37 0.39 0.17 0.50

3 17,992 0.39 0.39 0.22 0.59

4 8,449 0.42 0.43 0.26 0.59

5

1 39,297

30

0.36 0.37 0.15 0.52

2 34,627 0.37 0.37 0.23 0.49

3 18,179 0.43 0.44 0.09 0.55

4 7,885 0.41 0.44 -0.01 0.54

6

1 30,838

30

0.35 0.36 0.11 0.50

2 20,687 0.35 0.37 -0.03 0.48

3 14,026 0.36 0.37 0.19 0.47

4 6,551 0.36 0.38 0.16 0.47

7

1 27,201

30

0.31 0.32 0.00 0.46

2 18,207 0.34 0.35 0.07 0.51

3 11,496 0.35 0.36 0.06 0.50

4 4,950 0.36 0.39 0.03 0.56

8

1 25,146

30

0.35 0.35 0.16 0.52

2 16,218 0.37 0.38 0.17 0.47

3 10,052 0.38 0.41 0.16 0.54

4 4,221 0.37 0.39 0.10 0.52

Algebra 1

1 1,968

30

0.33 0.34 0.09 0.49

2 1,138 0.29 0.31 0.10 0.44

3 1,167 0.28 0.29 0.01 0.44

4 639 0.31 0.33 0.00 0.50

Geometry

1 1,282

30

0.25 0.25 0.10 0.45

2 946 0.26 0.27 0.09 0.41

3 834 0.27 0.26 0.12 0.45

4 167 0.31 0.33 0.07 0.54

Algebra 2

1 866

30

0.25 0.27 0.11 0.41

2 889 0.32 0.35 0.14 0.52

3 919 0.25 0.25 0.05 0.42

4 153 0.30 0.31 0.10 0.49

(54)

Table 26. Summary of Common Core benchmark assessment item-total correlation (ELA)

Grade Form Number of Students

Number of Items on Form

Mean R Point-

Biserial

Median R Point-

Biserial Min. Max.

3

1 33,954

30

0.42 0.42 0.25 0.60

2 25,509 0.42 0.43 0.26 0.56

3 18,437 0.43 0.46 0.25 0.56

4 8,383 0.43 0.44 0.34 0.52

4

1 37,330

30

0.42 0.43 0.19 0.55

2 29,648 0.43 0.46 0.10 0.56

3 20,316 0.44 0.46 0.19 0.55

4 8,976 0.42 0.43 0.29 0.56

5

1 38,046

30

0.44 0.45 0.16 0.56

2 29,487 0.44 0.42 0.27 0.54

3 19,839 0.44 0.45 0.31 0.54

4 8,507 0.44 0.47 0.25 0.54

6

1 32,773

30

0.41 0.42 0.09 0.55

2 21,804 0.44 0.46 0.21 0.56

3 13,221 0.43 0.43 0.11 0.53

4 7,132 0.45 0.45 0.28 0.57

7

1 30,340

30

0.43 0.46 0.08 0.55

2 19,662 0.41 0.43 0.07 0.54

3 12,544 0.43 0.43 0.19 0.53

4 5,751 0.44 0.46 0.25 0.57

8

1 28,748

30

0.41 0.43 0.13 0.55

2 18,543 0.42 0.45 0.12 0.60

3 11,654 0.42 0.46 0.17 0.56

4 4,858 0.44 0.46 0.23 0.56

9

1 3,268

30

0.40 0.43 0.12 0.54

2 943 0.37 0.38 -0.03 0.53

3 963 0.43 0.47 0.07 0.62

4 614 0.45 0.46 0.19 0.61

10

1 1,734

30

0.40 0.42 0.13 0.56

2 858 0.41 0.43 0.11 0.56

3 864 0.47 0.51 0.18 0.60

4 266 0.45 0.46 0.18 0.66

11

1 1,691

30

0.47 0.48 0.28 0.61

2 963 0.39 0.38 0.19 0.57

3 1,120 0.44 0.43 0.20 0.61

4 484 0.40 0.40 0.08 0.60

(55)

It should be noted that any comparison of statistical indices across grade levels is complicated because classical item

statistics are population dependent. Direct comparisons across grade levels (or even across test forms) would require that

either the items or the students be common across groups. Because that is not the case, it cannot be determined whether

differences in performance across grade levels are because of differences in student abilities, differences in item

difficulties (reflecting differences in the difficulty level of content), or both.

Test Analysis of Common Core Benchmark Assessment Data

Tables 27 and 29 summarize the psychometric characteristics of the benchmark assessment forms as a whole.

Histograms of the benchmark assessment number-correct score distributions, along with a reference normal curve for the

data reported in the tables, appear in appendix C (mathematics) and appendix D (ELA).

Form Reliability Estimates and SEM Values by Grade-Level Benchmark

Test Form

Mean Score–the average number-correct (raw) score obtained on the benchmark exam form.

Mean Percentage Score–the average score expressed as a percent-correct value on a scale from 0 to 100 percent.

SD Score-the standard deviation of the number-correct scores for students taking the benchmark exam form.

Reliability (α)–the internal consistency (coefficient alpha) estimate of reliability for the benchmark exam form. This value is expressed on a scale ranging from 0.0 to 1.0: the higher the reliability estimate, the more precision there is associated with the student score values. In general, values above 0.8 are acceptable. Reliability estimates are influenced by the underlying dimensionality of the test, however, so you see the drop in values for mathematics from grade 8 and the high school mathematics courses. Mathematics assessments (i.e., algebra and geometry) become much more multidimensional at this level.

SEM–the standard error of measurement for scores from the benchmark exam form. SEM provides an estimate of the precision that may be associated with any number-correct score from the benchmark exam form. In general, an individual’s true score is contained within +/- 1 SEM of the obtained score about 68% of the time. A true score represents the individual’s hypothetical score that would be obtained under a situation where the exam had perfect reliability.

(56)

Table 27. Summary of Common Core benchmark test scores and reliability estimates

(mathematics)

Grade Form Number of Students

Number of Items on

Form Mean Score

Mean Score

(%) SD

Score Reliability

(α)

SEM

3

1 34,501

30

18.53 61.78 5.53 0.83 2.25

2 24,702 18.53 61.78 4.76 0.78 2.24

3 17,930 21.20 70.67 4.64 0.81 2.05

4 7,997 20.84 69.48 5.04 0.83 2.09

4

1 38,477

30

16.21 54.05 5.08 0.77 2.42

2 27,722 18.20 60.65 4.91 0.78 2.30

3 17,992 18.44 61.47 5.32 0.81 2.32

4 8,449 19.45 64.82 5.45 0.83 2.22

5

1 39,297

30

12.79 42.63 4.95 0.77 2.37

2 34,627 15.22 50.74 5.14 0.78 2.40

3 18,179 18.21 60.71 5.81 0.85 2.26

4 7,885 19.31 64.36 5.24 0.82 2.21

6

1 30,838

30

14.80 49.35 4.71 0.75 2.34

2 20,687 15.21 50.70 4.77 0.76 2.36

3 14,026 17.55 58.50 4.74 0.75 2.35

4 6,551 15.89 52.97 4.80 0.76 2.35

7

1 27,201

30

11.98 39.92 4.19 0.68 2.36

2 18,207 11.89 39.64 4.85 0.75 2.44

3 11,496 15.80 52.68 4.79 0.74 2.42

4 4,950 14.09 46.98 5.08 0.78 2.40

8

1 25,146

30

12.46 41.52 4.94 0.76 2.43

2 16,218 14.60 48.67 5.28 0.78 2.49

3 10,052 16.69 55.65 5.32 0.79 2.42

4 4,221 15.17 50.56 5.20 0.79 2.40

Algebra 1

1 1,968

30

11.91 39.69 4.68 0.72 2.50

2 1,138 11.32 37.74 4.07 0.64 2.44

3 1,167 11.09 36.98 4.00 0.62 2.46

4 639 12.76 42.55 4.43 0.70 2.44

Geometry

1 1,282

30

10.07 33.58 3.38 0.48 2.43

2 946 10.69 35.63 3.60 0.53 2.48

3 834 12.27 40.91 3.73 0.57 2.44

4 167 11.23 37.43 4.32 0.69 2.42

Algebra 2

1 866

30

9.89 32.98 3.42 0.50 2.41

2 889 11.04 36.81 4.49 0.71 2.43

3 919 11.13 37.08 3.59 0.51 2.51

4 153 12.90 43.01 4.08 0.67 2.35

(57)

Note that all of the current Study Island benchmark assessment forms are only 30 items in length, whereas higher-stakes

summative assessments (e.g., state assessments) typically are longer than this. Reliability is directly related to the length

of an assessment. The Study Island Common Core benchmark assessment forms are designed so they can be easily

administered during a classroom period as an aid for educators and administrators to assess student learning. Given the

reduced length of the current Study Island Common Core benchmark assessment forms, the reliability estimates in table

27 (while lower than the ELA estimates) appear to be reasonable given that the transition to the Common Core standards

is still in the early stages of being thoroughly integrated into curricula. The reliability estimates for the high school

mathematics courses, however, are much more variable because of the much smaller samples for those benchmark

assessments.

A follow-up analysis was conducted on the grade 7, form 1, mathematics student response data, which had the lowest

estimated reliability coefficient (0.68) among the grades 3 through 8 mathematics forms. It did appear that a higher

percentage of the benchmark administrations for that particular form tended to occur much earlier in the academic year

than in other grade levels. When the examinee data was restricted to just those students being administered form 1 in the

spring of the school year (N = 614; defined as testing in April, May, or June), the estimate of reliability increased to 0.779,

which is similar to the other estimates of reliability for the mathematics Common Core benchmark assessments.

Overall, the Common Core mathematics benchmark test scores appear to reflect the rigor of the new Common Core

mathematics standards. This seemed particularly to be the case when comparing the mathematics scores with the ELA

scores, beginning in the middle school grades (6–8).

The reliability of these benchmark forms if the tests were longer (i.e., more similar to the length of higher-stakes tests) can

be estimated using the Spearman-Brown prophesy formula. This provides an estimate of the reliability for a longer test,

assuming that the lengthier test was composed of additional items with characteristics similar to characteristics of items in

the 30-item tests. The results of the reliability estimates for hypothetical 45-item and 60-item benchmark tests are shown

in table 28 for grades 3–8 mathematics. (The high school benchmark assessments are based on much lower sample

sizes, so this type of analysis is therefore not advisable.)

(58)

Table 28. Common Core benchmark test reliability estimates by grade-level form

(mathematics)

Spearman-Brown Estimates

Grade Form

Number of Items on

Form SD

Score Reliability

(α)

Number of

Items

S-B Estimate Reliability

(α45)

Number of

Items

S-B Estimate Reliability

(α60)

3

1

30

5.53 0.83

45

0.88

60

0.91

2 4.76 0.78 0.84 0.88

3 4.64 0.81 0.86 0.90

4 5.04 0.83 0.88 0.91

4

1

30

5.08 0.77

45

0.83

60

0.87

2 4.91 0.78 0.84 0.88

3 5.32 0.81 0.86 0.90

4 5.45 0.83 0.88 0.91

5

1

30

4.95 0.77

45

0.83

60

0.87

2 5.14 0.78 0.84 0.88

3 5.81 0.85 0.89 0.92

4 5.24 0.82 0.87 0.90

6

1

30

4.71 0.75

45

0.82

60

0.86

2 4.77 0.76 0.83 0.86

3 4.74 0.75 0.82 0.86

4 4.80 0.76 0.83 0.86

7

1

30

4.19 0.68

45

0.76

60

0.81

2 4.85 0.75 0.82 0.86

3 4.79 0.74 0.81 0.85

4 5.08 0.78 0.84 0.88

8

1

30

4.94 0.76

45

0.83

60

0.86

2 5.28 0.78 0.84 0.88

3 5.32 0.79 0.85 0.88

4 5.20 0.79 0.85 0.88

As can be seen in table 28, if these benchmark assessments had been as long as comparable state assessment tests,

the reliability of these benchmark assessments would be much higher. Edmentum designed the current Study Island

Common Core standards benchmark forms to be easily administered in a single classroom period, realizing that the trade-

off for supporting educators might be a reduction in the potential reliability of these benchmark assessments. The fact that

a 60-item test would have much higher reliability estimates, however, attests to the quality of these benchmark forms as

they compare with state assessments.

(59)

Table 29. Summary of Common Core benchmark test scores and reliability estimates

(ELA)

Grade Form Number of Students

Number of Items on

Form Mean Score

Mean Score

(%) SD

Score Reliability

(α)

SEM

3

1 33,954

30

15.38 51.28 6.08 0.84 2.45

2 25,509 18.33 61.09 5.98 0.84 2.38

3 18,437 19.58 65.28 5.94 0.85 2.33

4 8,383 17.50 58.35 6.25 0.85 2.42

4

1 37,330

30

16.96 56.53 6.00 0.84 2.42

2 29,648 19.07 63.56 5.87 0.85 2.30

3 20,316 20.91 69.69 5.83 0.85 2.23

4 8,976 19.20 63.99 5.84 0.84 2.36

5

1 38,046

30

19.90 66.34 6.00 0.86 2.28

2 29,487 20.37 67.89 5.77 0.85 2.24

3 19,839 21.43 71.45 5.69 0.85 2.21

4 8,507 21.49 71.65 5.62 0.85 2.21

6

1 32,773

30

18.51 61.69 5.51 0.82 2.32

2 21,804 20.66 68.87 5.78 0.85 2.23

3 13,221 20.34 67.80 5.68 0.84 2.27

4 7,132 22.59 75.29 5.61 0.86 2.11

7

1 30,340

30

21.12 70.39 5.44 0.84 2.20

2 19,662 21.18 70.61 5.16 0.82 2.20

3 12,544 20.36 67.87 5.64 0.84 2.27

4 5,751 21.51 71.71 5.64 0.85 2.20

8

1 28,748

30

20.08 66.95 5.44 0.83 2.26

2 18,543 20.52 68.40 5.26 0.82 2.21

3 11,654 20.91 69.70 5.38 0.83 2.22

4 4,858 20.42 68.08 5.89 0.85 2.28

9

1 3,268

30

15.61 52.04 5.68 0.82 2.39

2 943 16.38 54.60 5.14 0.78 2.43

3 963 17.71 59.04 5.84 0.85 2.30

4 614 19.38 64.61 6.15 0.86 2.31

10

1 1,734

30

16.81 56.02 5.72 0.82 2.43

2 858 18.92 63.08 5.49 0.82 2.33

3 864 19.37 64.56 6.37 0.88 2.23

4 266 17.91 59.70 6.44 0.87 2.36

11

1 1,691

30

21.07 70.25 6.12 0.87 2.18

2 963 18.49 61.63 5.30 0.80 2.36

3 1,120 19.17 63.89 5.92 0.85 2.32

4 484 16.75 55.82 5.69 0.82 2.41

Comparing the mean percent-correct values in table 29 with those in table 27, it appears that schools may be further

along in integrating the ELA Common Core standards into their curricula than in integrating the Common Core

mathematics standards. The mean percent-correct values (with the exception of form 1 for grades 3 and 4) are in the 60

to 70 percent range, which is reasonable for an appropriately targeted standards-referenced assessment.

(60)

The reliability estimates for the ELA benchmark assessment forms are also a bit higher than those for mathematics. Note,

however, that the ELA benchmark assessment forms are similarly limited in the level of reliability they might attain

because the assessments are not as long as higher-stakes statewide assessments. Still, the level of reliability estimates

for the Study Island Common Core benchmark forms is reasonable given the length of the assessments. The consistency

of the reliability estimates for the ELA Common Core benchmark assessment forms is encouraging.

As was done for the mathematics benchmarks, the Spearman-Brown method was used to estimate the reliability for

hypothetical benchmark forms of 45 and 60 items. The results for grades 3 through 8 are shown in table 30.

Table 30. Common Core benchmark test reliability estimates by grade-level form (ELA)

Spearman-Brown Estimates

Grade Form

Number of Items on

Form SD

Score Reliability

(α)

Number of

Items

S-B Estimate Reliability

(α45)

Number of

Items

S-B Estimate Reliability

(α60)

3

1

30

6.08 0.84

45

0.89

60

0.91

2 5.98 0.84 0.89 0.91

3 5.94 0.85 0.89 0.92

4 6.25 0.85 0.89 0.92

4

1

30

6.00 0.84

45

0.89

60

0.91

2 5.87 0.85 0.89 0.92

3 5.83 0.85 0.89 0.92

4 5.84 0.84 0.89 0.91

5

1

30

6.00 0.86

45

0.90

60

0.92

2 5.77 0.85 0.89 0.92

3 5.69 0.85 0.89 0.92

4 5.62 0.85 0.89 0.92

6

1

30

5.51 0.82

45

0.87

60

0.90

2 5.78 0.85 0.89 0.92

3 5.68 0.84 0.89 0.91

4 5.61 0.86 0.90 0.92

7

1

30

5.44 0.84

45

0.89

60

0.91

2 5.16 0.82 0.87 0.90

3 5.64 0.84 0.89 0.91

4 5.64 0.85 0.89 0.92

8

1

30

5.44 0.83

45

0.88

60

0.91

2 5.26 0.82 0.87 0.90

3 5.38 0.83 0.88 0.91

4 5.89 0.85 0.89 0.92

Benchmark Test Reporting Category Subscores

Each Study Island Common Core benchmark assessment provides subscores for each CCSS reporting category. The

CCSS reporting categories for these benchmark assessments were detailed earlier in the sections on the Study Island

Common Core benchmark test specifications for mathematics and ELA (see section IV).

The CCSS reporting category subscores were correlated with the overall benchmark assessment total (number-correct)

score and with each of the other CCSS reporting category subscores. This analysis yields an intercorrelation matrix for

each subject area, grade level, and benchmark form. Appendix E contains the intercorrelation matrix tables.

(61)

An example of such a reporting category subscore intercorrelation matrix is shown in figure 11 (for grade 3 mathematics,

form 1).

Grade 3 Mathematics Common Core

Benchmark Reporting Categories

1 Operations and Algebraic Thinking (8)

2 Number and Operations in Base Ten (6)

3 Number and Operations–Fractions (4)

4 Measurement and Data (8)

5 Geometry (4)

Number of items in parentheses

Grade 3 Mathematics, Form 1

Reporting Category Intercorrelations

1 2 3 4 5

1 --

2 0.63 --

3 0.34 0.28 --

4 0.57 0.54 0.27 --

5 0.40 0.38 0.25 0.40 --

Total 0.87 0.80 0.51 0.80 0.60

Figure 11. Sample benchmark reporting category intercorrelation matrix

The first CCSS reporting category for grade 3 mathematics is Operations and Algebraic Thinking: there are eight

benchmark assessment items that map to that CCSS reporting category. The Operations and Algebraic Thinking reporting

category (designated as reporting category 1) is highly correlated with the total (number-correct) score for the benchmark

as a whole (r = 0.87). That reporting category is moderately correlated with reporting category 2 (r = 0.63) and category 4

(r = 0.57). The correlation of reporting category 1 with reporting categories 3 (fractions) and 5 (geometry) is somewhat

lower. The lower correlations tend to indicate that, in this example, the individual reporting category subscores may be

measuring unique aspects of mathematics). Certainly, fractions and geometry are less familiar mathematical concepts to

many third-grade students. It is also useful to keep in mind that the time of year when a student is being assessed is

important. If students are being assessed near the beginning of third grade (much more likely with form 1), they are less

likely to be familiar with material that may be introduced during the course of their mathematics instruction for that school

year.

Looking at the reporting category intercorrelation tables in appendix E, it is generally the case that in ELA, the reporting

category intercorrelations are higher than the corresponding mathematics reporting category intercorrelations, indicating

that reading skills seem to be more strongly related to, or dependent upon, one another than the various skills contributing

to mathematics proficiency.

Keep in mind that the subscores are based on only a small number of items (in some cases as few as four). As a result of

the reduced number of items contributing to reporting category subscores, interpretations of these subscores should be

cautious as these scores are much less reliable than the overall (total) benchmark test score. The reporting category

subscores are best used as general formative assessment indicators that can provide additional information to educators

about skill areas where a student might be struggling and need additional help or, conversely, skill areas where the

student seems to have stronger performance, or mastery of those concepts.

(62)

Benchmark Test Administration Time

Although the Study Island benchmark assessments are not explicitly time limited, the assessment forms are constructed

so they can generally be administered during a one-hour period. Edmentum undertook an analysis of the time spent

completing the Common Core benchmark test administration. The benchmark test administration times, within a specific

grade level and subject area, were combined across forms since all current benchmark forms, within a grade level and

subject area, are the same length.

Ideally, 90 percent of the students (or more) should be completing the assessment within the one-hour period (i.e., the

90th percentile should ideally be less than or equal to 60 minutes). Tables 31 and 32 show the Common Core benchmark

test administration time summaries for mathematics and ELA by grade level. The mean and median (i.e., 50th percentile)

times are indicated in these tables. The tables also include the benchmark test administration time corresponding to the

90th percentile (i.e., the time when 90 percent of the examinees have finished the benchmark test in that amount of time

or less). The fact that the 90th percentile times are (with the exception of grade 7 math) all less than 60 minutes provides

empirical support that these Common Core benchmark tests are indeed appropriately designed for administration in a

one-hour period for the vast majority of students.

Table 31. Summary of Common Core benchmark test administration time (mathematics)

Grade Form Number of Students

Number of Items on Form

Mean Time

(minutes)

Median Time

(minutes)

90th Percentile (minutes)

3 1–4 85,004 30 24.21 21.57 39.53

4 1–4 92,370 30 30.22 27.35 48.60

5 1–4 99,455 30 35.02 32.18 55.35

6 1–4 71,786 30 36.43 33.83 57.53

7 1–4 61,387 30 39.50 36.98 62.43

8 1–4 55,417 30 33.59 31.70 53.55

Algebra 1 1–4 4,859 30 33.40 32.37 55.68

Geometry 1–4 3,169 30 33.35 30.73 58.50

Algebra 2 1–4 2,812 30 34.44 33.10 54.35

(63)

Table 32. Summary of Common Core benchmark test administration time (ELA)

Grade Form Number of Students

Number of Items on Form

Mean Time

(minutes)

Median Time

(minutes)

90th Percentile (minutes)

3 1–4 85,987 30 33.19 30.60 53.80

4 1–4 95,946 30 33.84 31.30 53.47

5 1–4 95,502 30 35.81 33.25 56.15

6 1–4 74,719 30 32.24 29.75 49.93

7 1–4 68,178 30 30.38 27.95 46.45

8 1–4 63,643 30 30.29 27.97 45.65

9 1–4 5,745 30 33.15 31.92 48.37

10 1–4 3,682 30 31.90 30.16 47.75

11 1–4 4,238 30 32.41 30.52 49.23

Administration of Multiple Benchmarks Across a School Year

Most Study Island implementations conduct periodic administration of benchmark assessments to track student progress

toward Common Core standards mastery. Repeated administration of a benchmark within a school year is accomplished

by administering a benchmark form that has not been previously administered. The benchmark forms are carefully

constructed to be comparable in terms of content representativeness based on prescribed test specifications aligned to

the Common Core standards.

Across grade levels, about 50 percent of the students taking Study Island Common Core benchmark assessments take at

least one repeated benchmark test administration. Overall, across the academic year, about 30 percent of students in

grades 3 through 8 participate in a second benchmark test administration, 15 percent of all students go on to participate in

a third benchmark test administration, and about 5 percent of all students go on to participate in a fourth benchmark test

administration. This pattern of student participation in multiple benchmark administrations throughout the school year was

consistent across grades 3 through 8 and across both major subject areas (mathematics and ELA). Note that high school

level benchmark assessment results are not included because the percentages of repeat benchmark test takers were low.

Figures 12 and 13 summarize the numbers of students who take multiple benchmark assessment administrations. Note

that the figures distinguish between students who took only one benchmark test (1st Admin) and students who took the

first administration and at least one additional benchmark administration (1st Admin +).

(64)

Figure 12. Students taking multiple administrations of Common Core benchmark tests

(mathematics)

Figure 13. Students taking multiple administrations of Common Core benchmark tests

(ELA)

Although it is not possible to say specifically that the four benchmark assessment forms are equated, each of the forms

was carefully constructed to match a detailed Common Core benchmark test blueprint. It can be expected that the

differences in terms of overall difficulty across the four benchmark forms are likely to be relatively small given the attention

to quality benchmark test construction practices and guidelines.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Gr 3 Gr 4 Gr 5 Gr 6 Gr 7 Gr 8

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ee

Sam

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4th Admin

3rd Admin

2nd Admin

1st Admin +

1st Admin

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Gr 3 Gr 4 Gr 5 Gr 6 Gr 7 Gr 8

Pe

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Sam

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3rd Admin

2nd Admin

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1st Admin

(65)

The data in tables 33 and 34 was calculated as if the four benchmark assessment forms were equated, which cannot be

evaluated at this point. The tables show the combined mean benchmark assessment scores across forms for the first,

second, third, and fourth benchmark administered. These results are only shown for grades 3 through 8 because the

number of examinees drops so much for the high school Common Core benchmarks. The far-right column shows the

change in the mean test score from the first benchmark administration mean test score. Keep in mind that these results

are based on an untestable assumption of equated tests (i.e., unity equating).

Table 33. Mean Common Core benchmark test score by number of benchmark

administrations (mathematics)

Grade Subject Benchmark

Administration Number of Students

Mean Benchmark Test Score (out of 30)

Change in Mean from

First Admin.

3 Math 1 24,183 18.33 --

2 24,183 19.04 +0.71

3 13,644 21.28 +2.95

4 4,388 21.98 +3.65

4 Math 1 26,602 16.32 --

2 26,602 18.34 +2.02

3 14,507 18.71 +2.39

4 4,432 20.51 +4.19

5 Math 1 28,088 12.96 --

2 28,088 15.65 +2.69

3 17,293 17.40 +4.44

4 6,514 19.92 +6.96

6 Math 1 20,612 14.77 --

2 20,612 15.51 +0.74

3 11,267 17.47 +2.70

4 3,781 17.00 +2.23

7 Math 1 17,774 12.03 --

2 17,774 12.42 +0.39

3 9,409 15.68 +3.65

4 2,937 14.52 +2.49

8 Math 1 15,647 12.58 --

2 15,647 14.87 +2.29

3 8,087 16.50 +3.92

4 2,477 16.10 +3.52

(66)

Table 34. Mean Common Core benchmark test score by number of benchmark

administrations (ELA)

Grade Subject Benchmark

Administration Number of Students

Mean Benchmark Test Score (out of 30)

Change in Mean from

First Admin.

3 ELA 1 25,407 15.65 --

2 25,407 18.50 +2.85

3 13,314 19.65 +4.00

4 3,971 18.55 +2.90

4 ELA 1 29,185 17.25 --

2 29,185 19.39 +2.14

3 15,060 21.13 +3.88

4 4,613 20.26 +3.01

5 ELA 1 28,270 20.05 --

2 28,270 20.58 +0.53

3 14,592 21.83 +1.78

4 4,978 22.17 +2.12

6 ELA 1 21,130 18.84 --

2 21,130 20.77 +1.93

3 10,763 20.89 +2.05

4 4,113 22.80 +3.96

7 ELA 1 19,033 21.20 --

2 19,033 21.14 -0.06

3 10,695 20.84 -0.36

4 3,510 22.12 +0.92

8 ELA 1 17,307 20.39 --

2 17,307 20.67 +0.28

3 9,074 21.18 +0.78

4 2,903 20.90 +0.51

As can be seen in tables 33 and 34, when the benchmark forms are assumed interchangeable in terms of test scores, there is a general tendency for the mean test score to increase across benchmark test administrations over time. With the exception of grade 7 ELA, the change in the mean test score (as measured against the mean score from the first benchmark administration) is always positive. The pattern of increasing mean scores across benchmark test administrations is most consistent for the first through third benchmark administrations. With the fourth benchmark administration, the increases in mean scores are not as consistent, but recall that only about 5 percent of the examinees took four benchmark administrations, so the inconsistency may simply reflect the smaller number of examinees who had four benchmark administrations. Still, the general tendency of increasing test scores over benchmark administrations, as the students progress through the school year, is encouraging. The change in the mean test score compared with the first benchmark administration (far-right column) also presents evidence of sensitivity of the benchmark forms to show changes in student proficiency on the Common Core standards over time. Given the assumptions involved, no further analysis was done with these mean score results (e.g., testing whether the changes in means are statistically significant).

(67)

X. Summary

The Common Core State Standards are widely considered to be more rigorous than existing state-specific standards. Through careful item and test development, Edmentum has developed the Study Island Common Core standards mastery and benchmark assessment components specifically to measure proficiency in meeting these new, more challenging standards.

The item- and test-level analyses and evidence presented support the validity and reliability of the current Study Island Common Core benchmark assessments. These results seem to reflect the increased cognitive challenge of the Common Core standards. Students are going to be challenged by the new standards and corresponding assessments.

The next generation of Study Island Common Core benchmark assessments is already under development. Three types of Common Core assessments will be available. The new Study Island benchmark forms will prove to be another step forward in benchmark assessment. The introduction of more interactive technology-enhanced items and constructed-response questions will increase alignment to the Common Core assessments (either PARCC or SBAC) and state-specific standards. A technical manual for the next generation of the Study Island Common Core benchmark assessments will be produced once data from its initial year of administration is available.

As evidenced by the item- and test-development procedures and empirical data presented in this manual, the Study Island Common Core benchmark assessment solution from Edmentum provides accurate information for educators wanting to track student progress relative to the new standards and assessments.

(68)

References

Achieve, Inc., The Education Trust, & Thomas B. Fordham Foundation. (2004). Ready or not: Creating a high school

diploma that counts. Washington, DC: American Diploma Project. Retrieved from http://www.achieve.org/files/ReadyorNot.pdf

American Educational Research Association, American Psychological Association, & National Council on Measurement in

Education. (1999). Standards for educational and psychological testing. Washington, DC: American Educational Research Association.

The Aspen Institute. (2007). The role of interim assessments in a comprehensive assessment system: A policy brief.

Washington, DC: Perie, M., Marion, S., Gong, B., & Wurtzel, J. Retrieved from http://www.aspeninstitute.org/sites/default/files/content/docs/education/ed_PolicyBriefFINAL.pdf

Bernard, B. T. (2013). Student achievement and the use of the program Study Island (Unpublished doctoral dissertation). University of Minnesota, Minneapolis. Retrieved from http://hdl.handle.net/11299/157665

The Brookings Institution. (2006). The 2006 Brown Center report on American education: How well are American students

learning? Washington, DC: Loveless, T. Retrieved from http://www.brookings.edu/~/media/research/files/reports/2006/10/education%20loveless/10education_loveless.pdf

Brown, F. G. (1983). Principles of educational and psychological testing (3rd ed.). Fort Worth: Holt, Rinehart and Winston. Dube, P. J. (2011). Attempting to improve standardized test results using Study Island’s web-based mastery program

(Unpublished master’s thesis). Michigan Technological University, Houghton. Haladyna, T. M. (2004). Developing and validating multiple-choice test items. Hillsdale, NJ: Lawrence Erlbaum

Associates. Joint Committee on Testing Practices. (2004). Code of fair testing practices in education. Washington, DC. Kolen, M. J., & Brennan, R. L. (1995). Test equating, scaling, and linking: Methods and practices. New York, NY:

Springer-Verlag. Linn, R. L., & Miller, M. D. (2005). Measurement and assessment in teaching (9th ed.). Upper Saddle River, NJ: Merrill. Ostroski, T. C. (2012). The impact of Study Island as a formative assessment tool (Unpublished doctoral dissertation).

Baker University, Baldwin City, KS.

Porter, A., McMaken, J., Hwang, J., & Yang, R. (2011). Common core standards: The new US intended curriculum. Educational Researcher, 40(3), 103–116. doi: 10.3102/0013189X11405038

Taylor, S. E. (1989). EDL core vocabularies: Reading, mathematics, science, social studies. Austin, TX: Steck-Vaughn Publishing.

Viviano, T. A. (2011). What impact does the software Study Island have on 4Sight, PSSA, and NOCTI assessments of part-time CTE students? (Unpublished doctoral dissertation). Pennsylvania State University, State College.

(69)

Appendix A.

Study Island Standards Mastery Mathematics Common Core Standards Item Difficulty Statistics

Histograms of Item Difficulty statistics by grade level (Note that items with less than 100 student responses are excluded)

(70)

(71)

(72)

(73)

(74)

(75)

Appendix B.

Study Island Standards Mastery Reading Common Core Standards Item Difficulty Statistics

Histograms of Item Difficulty statistics by grade level (Note that items with less than 100 student responses are excluded)

(76)

(77)

(78)

(79)

(80)

(81)

Appendix C.

Study Island Common Core State Standards Benchmark Assessment Forms

Histograms of Percent-Correct Score Distributions for Mathematics by grade level and form

(82)

Study Island Grade 3 Common Core Mathematics – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(83)

Study Island Grade 3 Common Core Mathematics – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(84)

Study Island Grade 3 Common Core Mathematics – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(85)

Study Island Grade 3 Common Core Mathematics – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(86)

Study Island Grade 4 Common Core Mathematics – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(87)

Study Island Grade 4 Common Core Mathematics – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(88)

Study Island Grade 4 Common Core Mathematics – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(89)

Study Island Grade 4 Common Core Mathematics – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(90)

Study Island Grade 5 Common Core Mathematics – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(91)

Study Island Grade 5 Common Core Mathematics – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(92)

Study Island Grade 5 Common Core Mathematics – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(93)

Study Island Grade 5 Common Core Mathematics – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(94)

Study Island Grade 6 Common Core Mathematics – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(95)

Study Island Grade 6 Common Core Mathematics – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(96)

Study Island Grade 6 Common Core Mathematics – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(97)

Study Island Grade 6 Common Core Mathematics – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(98)

Study Island Grade 7 Common Core Mathematics – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(99)

Study Island Grade 7 Common Core Mathematics – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(100)

Study Island Grade 7 Common Core Mathematics – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(101)

Study Island Grade 7 Common Core Mathematics – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(102)

Study Island Grade 8 Common Core Mathematics – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(103)

Study Island Grade 8 Common Core Mathematics – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(104)

Study Island Grade 8 Common Core Mathematics – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(105)

Study Island Grade 8 Common Core Mathematics – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(106)

Study Island Algebra 1 Common Core Mathematics – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(107)

Study Island Algebra 1 Common Core Mathematics – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(108)

Study Island Algebra 1 Common Core Mathematics – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(109)

Study Island Algebra 1 Common Core Mathematics – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(110)

Study Island Geometry Common Core Mathematics – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(111)

Study Island Geometry Common Core Mathematics – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(112)

Study Island Geometry Common Core Mathematics – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(113)

Study Island Geometry Common Core Mathematics – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(114)

Study Island Algebra 2 Common Core Mathematics – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(115)

Study Island Algebra 2 Common Core Mathematics – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(116)

Study Island Algebra 2 Common Core Mathematics – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(117)

Study Island Algebra 2 Common Core Mathematics – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(118)

Appendix D.

Study Island Common Core State Standards Benchmark Assessment Forms

Histograms of Percent-Correct Score Distributions for English Language Arts by grade level and form

(119)

Study Island Grade 3 Common Core Language-Arts – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(120)

Study Island Grade 3 Common Core Language-Arts – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(121)

Study Island Grade 3 Common Core Language-Arts – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(122)

Study Island Grade 3 Common Core Language-Arts – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(123)

Study Island Grade 4 Common Core Language-Arts – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(124)

Study Island Grade 4 Common Core Language-Arts – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(125)

Study Island Grade 4 Common Core Language-Arts – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(126)

Study Island Grade 4 Common Core Language-Arts – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(127)

Study Island Grade 5 Common Core Language-Arts – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(128)

Study Island Grade 5 Common Core Language-Arts – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(129)

Study Island Grade 5 Common Core Language-Arts – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(130)

Study Island Grade 5 Common Core Language-Arts – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(131)

Study Island Grade 6 Common Core Language-Arts – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(132)

Study Island Grade 6 Common Core Language-Arts – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(133)

Study Island Grade 6 Common Core Language-Arts – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(134)

Study Island Grade 6 Common Core Language-Arts – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(135)

Study Island Grade 7 Common Core Language-Arts – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(136)

Study Island Grade 7 Common Core Language-Arts – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(137)

Study Island Grade 7 Common Core Language-Arts – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(138)

Study Island Grade 7 Common Core Language-Arts – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(139)

Study Island Grade 8 Common Core Language-Arts – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(140)

Study Island Grade 8 Common Core Language-Arts – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(141)

Study Island Grade 8 Common Core Language-Arts – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(142)

Study Island Grade 8 Common Core Language-Arts – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(143)

Study Island Grade 9 Common Core Language-Arts – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(144)

Study Island Grade 9 Common Core Language-Arts – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(145)

Study Island Grade 9 Common Core Language-Arts – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(146)

Study Island Grade 9 Common Core Language-Arts – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(147)

Study Island Grade 10 Common Core Language-Arts – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(148)

Study Island Grade 10 Common Core Language-Arts – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(149)

Study Island Grade 10 Common Core Language-Arts – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(150)

Study Island Grade 10 Common Core Language-Arts – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(151)

Study Island Grade 11 Common Core Language-Arts – Benchmark Form 1 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(152)

Study Island Grade 11 Common Core Language-Arts – Benchmark Form 2 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(153)

Study Island Grade 11 Common Core Language-Arts – Benchmark Form 3 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(154)

Study Island Grade 11 Common Core Language-Arts – Benchmark Form 4 Distribution of Student Scores

Solid line shows a theoretical normal distribution for comparison

(155)

Appendix E.

Study Island Common Core State Standards Benchmark Assessment Forms

Reporting Category Subscore Intercorrelation Tables for Mathematics and English Language Arts

(156)

Grade 3 Mathematics Common Core Benchmark Reporting Categories 1 Operations and Algebraic Thinking (8)

2 Number and Operations in Base Ten (6) 3 Number and Operations - Fractions (4) 4 Measurement and Data (8)

5 Geometry (4)

Number of items in parentheses

Grade 3 Mathematics - Form 1

Grade 3 Mathematics - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.63 --

2 0.61 --

3 0.34 0.28 --

3 0.40 0.34 --

4 0.57 0.54 0.27 --

4 0.52 0.49 0.36 --

5 0.40 0.38 0.25 0.40 --

5 0.29 0.25 0.24 0.30 --

Total 0.87 0.80 0.51 0.80 0.60

Total 0.84 0.76 0.62 0.77 0.55

Grade 3 Mathematics - Form 2

Grade 3 Mathematics - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.53 --

2 0.56 --

3 0.33 0.30 --

3 0.38 0.39 --

4 0.42 0.43 0.30 --

4 0.54 0.55 0.44 --

5 0.27 0.25 0.23 0.27 --

5 0.40 0.42 0.36 0.45

Total 0.81 0.75 0.57 0.71 0.53

Total 0.79 0.78 0.63 0.83 0.69

(157)

Grade 4 Mathematics Common Core Benchmark Reporting Categories 1 Operations and Algebraic Thinking (7)

2 Number and Operations in Base Ten (5) 3 Number and Operations - Fractions (7) 4 Measurement and Data (7)

5 Geometry (4)

Number of items in parentheses

Grade 4 Mathematics - Form 1

Grade 4 Mathematics - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.50 --

2 0.51 --

3 0.46 0.36 --

3 0.49 0.47 --

4 0.45 0.40 0.35 --

4 0.49 0.48 0.49 --

5 0.29 0.22 0.24 0.23 --

5 0.32 0.29 0.33 0.38 --

Total 0.82 0.72 0.71 0.71 0.49

Total 0.77 0.75 0.77 0.80 0.56

Grade 4 Mathematics - Form 2

Grade 4 Mathematics - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.45 --

2 0.44 --

3 0.41 0.38 --

3 0.52 0.48 --

4 0.46 0.45 0.45 --

4 0.54 0.49 0.61 --

5 0.31 0.28 0.33 0.39 --

5 0.34 0.30 0.39 0.42 --

Total 0.75 0.70 0.73 0.79 0.61

Total 0.75 0.71 0.82 0.85 0.61

(158)

Grade 5 Mathematics Common Core Benchmark Reporting Categories 1 Operations and Algebraic Thinking (6)

2 Number and Operations in Base Ten (6) 3 Number and Operations - Fractions (6) 4 Measurement and Data (6)

5 Geometry (6)

Number of items in parentheses

Grade 5 Mathematics - Form 1

Grade 5 Mathematics - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.44 --

2 0.49 --

3 0.35 0.40 --

3 0.49 0.55 --

4 0.35 0.35 0.44 --

4 0.48 0.46 0.53 --

5 0.33 0.31 0.26 0.28 --

5 0.45 0.42 0.46 0.41 --

Total 0.73 0.73 0.70 0.68 0.62

Total 0.75 0.77 0.82 0.75 0.71

Grade 5 Mathematics - Form 2

Grade 5 Mathematics - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.44 --

2 0.51 --

3 0.34 0.37 --

3 0.43 0.49 --

4 0.44 0.40 0.42 --

4 0.48 0.47 0.50 --

5 0.34 0.32 0.28 0.33 --

5 0.35 0.34 0.31 0.35 --

Total 0.72 0.72 0.71 0.73 0.63

Total 0.75 0.77 0.77 0.78 0.59

(159)

Grade 6 Mathematics Common Core Benchmark Reporting Categories 1 Ratios and Proportional Relationships (4) 2 The Number System (9)

3 Expressions and Equations (8) 4 Geometry (5)

5 Statistics and Probability (4)

Number of items in parentheses

Grade 6 Mathematics - Form 1

Grade 6 Mathematics - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.46 --

2 0.37 --

3 0.44 0.49 --

3 0.37 0.50 --

4 0.26 0.33 0.31 --

4 0.21 0.31 0.29 --

5 0.20 0.24 0.21 0.18 --

5 0.25 0.32 0.31 0.17 --

Total 0.69 0.82 0.77 0.57 0.46

Total 0.59 0.81 0.80 0.56 0.56

Grade 6 Mathematics - Form 2

Grade 6 Mathematics - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.48 --

2 0.43 --

3 0.40 0.46 --

3 0.42 0.44 --

4 0.30 0.34 0.36 --

4 0.40 0.43 0.45 --

5 0.29 0.32 0.31 0.24 --

5 0.22 0.27 0.26 0.29 --

Total 0.68 0.81 0.77 0.61 0.56

Total 0.67 0.79 0.76 0.73 0.53

(160)

Grade 7 Mathematics Common Core Benchmark Reporting Categories 1 Ratios and Proportional Relationships (7) 2 The Number System (4)

3 Expressions and Equations (6) 4 Geometry (8)

5 Statistics and Probability (5)

Number of items in parentheses

Grade 7 Mathematics - Form 1

Grade 7 Mathematics - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.36 --

2 0.47 --

3 0.33 0.30 --

3 0.45 0.34 --

4 0.35 0.31 0.34 --

4 0.34 0.33 0.27 --

5 0.22 0.23 0.20 0.22 --

5 0.39 0.34 0.29 0.29 --

Total 0.73 0.63 0.67 0.73 0.49

Total 0.80 0.68 0.69 0.65 0.64

Grade 7 Mathematics - Form 2

Grade 7 Mathematics - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.44 --

2 0.47 --

3 0.35 0.39 --

3 0.49 0.49 --

4 0.37 0.38 0.34 --

4 0.37 0.42 0.41 --

5 0.40 0.39 0.32 0.33 --

5 0.37 0.37 0.39 0.31 --

Total 0.76 0.70 0.67 0.71 0.68

Total 0.76 0.74 0.78 0.71 0.63

(161)

Grade 8 Mathematics Common Core

Benchmark Reporting Categories 1 The Number System (4)

2 Expressions and Equations (8) 3 Functions (7)

4 Geometry (6) 5 Statistics and Probability (5)

Number of items in parentheses

Grade 8 Mathematics - Form 1

Grade 8 Mathematics - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.51 --

2 0.43 --

3 0.33 0.39 --

3 0.35 0.54 --

4 0.29 0.35 0.29 --

4 0.26 0.38 0.37 --

5 0.33 0.39 0.34 0.30 --

5 0.31 0.47 0.46 0.34 --

Total 0.71 0.80 0.69 0.62 0.65

Total 0.61 0.83 0.79 0.64 0.70

Grade 8 Mathematics - Form 2

Grade 8 Mathematics - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5

1 --

1 --

2 0.53 --

2 0.51 --

3 0.32 0.45 --

3 0.33 0.45 --

4 0.26 0.37 0.35 --

4 0.31 0.40 0.35 --

5 0.25 0.38 0.44 0.32 --

5 0.30 0.46 0.39 0.33 --

Total 0.64 0.82 0.75 0.64 0.65

Total 0.66 0.84 0.71 0.65 0.68

(162)

Algebra 1 Common Core Benchmark Reporting Categories

1 Number and Quantity (4) 2 Algebra (11)

3 Functions (10) 4 Statistics and Probability (5)

Number of items in parentheses

Algebra 1 - Form 1

Algebra 1 - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.28 --

2 0.28 --

3 0.24 0.39 --

3 0.17 0.27 --

4 0.25 0.46 0.28 --

4 0.42 0.29 0.20 --

Total 0.52 0.85 0.71 0.67

Total 0.61 0.75 0.63 0.67

Algebra 1 - Form 2

Algebra 1 - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.25 --

2 0.34 --

3 0.18 0.36 --

3 0.31 0.44 --

4 0.20 0.36 0.24 --

4 0.29 0.43 0.34 --

Total 0.49 0.82 0.71 0.62

Total 0.56 0.82 0.76 0.70

(163)

Geometry Common Core

Benchmark Reporting Categories

1 CO - Congruence (5)

2 GPE - Expressing Geometric Properties with Equations (4)

3 SRT - Similarity, Right Triangles, and Trigonometry (5)

4 MG - Modeling with Geometry (4)

5 C - Circles (4) 6 GMD - Geometric Measurement and Dimension (4)

7 Statistics and Probability (5) Number of items in parentheses

Geometry - Form 1

Geometry - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 --

1 --

2 0.12 --

2 0.22 --

3 0.17 0.16 --

3 0.18 0.11 --

4 0.17 0.13 0.17 --

4 0.28 0.11 0.17 --

5 0.13 0.09 0.14 0.16 --

5 0.25 0.12 0.08 0.14 --

6 0.09 0.10 0.11 0.11 0.13 --

6 0.12 0.12 0.19 0.18 0.06 --

7 0.09 0.04 0.11 0.14 0.09 0.07 --

7 0.14 0.07 0.12 0.13 0.08 0.07 --

Total 0.54 0.47 0.55 0.52 0.49 0.44 0.45

Total 0.67 0.48 0.53 0.54 0.49 0.44 0.43

Geometry - Form 2

Geometry - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4 5

1 2 3 4 5 6 7

1 --

1 --

2 0.12 --

2 0.12 --

3 0.23 0.18 --

3 0.42 0.22 --

4 0.20 0.13 0.21 --

4 0.28 0.09 0.26 --

5 0.19 0.06 0.27 0.17 --

5 0.24 0.12 0.31 0.24 --

6 0.11 0.02 0.09 0.06 0.16 --

6 0.48 0.15 0.35 0.28 0.26 --

7 0.05 0.07 0.14 0.05 0.08 0.08 --

7 0.16 0.08 0.21 0.27 0.08 0.15 --

Total 0.58 0.43 0.65 0.49 0.54 0.41 0.40

Total 0.71 0.41 0.72 0.58 0.52 0.67 0.44

(164)

Algebra 2 Common Core Benchmark Reporting Categories

1 Number and Quantity (4) 2 Algebra (10)

3 Functions (10) 4 Statistics and Probability (6)

Number of items in parentheses

Algebra 2 - Form 1

Algebra 2 - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.31 --

2 0.26 --

3 0.19 0.22 --

3 0.11 0.21 --

4 0.12 0.18 0.04 --

4 0.06 0.24 0.19 --

Total 0.57 0.75 0.61 0.52

Total 0.50 0.75 0.64 0.57

Algebra 2 - Form 2

Algebra 2 - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.45 --

2 0.28 --

3 0.24 0.39 --

3 0.32 0.31 --

4 0.21 0.33 0.30 --

4 0.26 0.31 0.36 --

Total 0.61 0.83 0.70 0.64

Total 0.57 0.77 0.74 0.66

(165)

Grade 3 Language-Arts Common Core Benchmark Reporting Categories

1 Reading Standards for Literature (7) 2 Reading Standards for Informational Texts (7)

3 Writing Standards (4) 4 Language Standards (12)

Number of items in parentheses

Grade 3 Language-Arts - Form 2

Grade 3 Language-Arts - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.51 --

2 0.54 --

3 0.53 0.46 --

3 0.49 0.54 --

4 0.58 0.51 0.55 --

4 0.58 0.59 0.55 --

Total 0.82 0.77 0.74 0.87

Total 0.80 0.81 0.73 0.89

Grade 3 Language-Arts - Form 2

Grade 3 Language-Arts - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.56 --

2 0.57 --

3 0.52 0.51 --

3 0.49 0.43 --

4 0.58 0.58 0.57 --

4 0.62 0.59 0.52 --

Total 0.81 0.81 0.74 0.88

Total 0.82 0.80 0.69 0.89

(166)

Grade 4 Language-Arts Common Core Benchmark Reporting Categories

1 Reading Standards for Literature (7) 2 Reading Standards for Informational Texts (7)

3 Writing Standards (4) 4 Language Standards (12)

Number of items in parentheses

Grade 4 Language-Arts - Form 2

Grade 4 Language-Arts - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.51 --

2 0.58 --

3 0.44 0.43 --

3 0.49 0.54 --

4 0.59 0.54 0.54 --

4 0.56 0.56 0.50 --

Total 0.81 0.77 0.69 0.89

Total 0.83 0.81 0.72 0.85

Grade 4 Language-Arts - Form 2

Grade 4 Language-Arts - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.57 --

2 0.58 --

3 0.52 0.48 --

3 0.46 0.45 --

4 0.61 0.57 0.52 --

4 0.54 0.56 0.52 --

Total 0.84 0.81 0.72 0.87

Total 0.81 0.81 0.70 0.86

(167)

Grade 5 Language-Arts Common Core Benchmark Reporting Categories

1 Reading Standards for Literature (7) 2 Reading Standards for Informational Texts (7)

3 Writing Standards (4) 4 Language Standards (12)

Number of items in parentheses

Grade 5 Language-Arts - Form 2

Grade 5 Language-Arts - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.58 --

2 0.53 --

3 0.50 0.47 --

3 0.53 0.48 --

4 0.60 0.59 0.53 --

4 0.58 0.56 0.59 --

Total 0.82 0.81 0.71 0.88

Total 0.81 0.80 0.75 0.87

Grade 5 Language-Arts - Form 2

Grade 5 Language-Arts - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.55 --

2 0.58 --

3 0.52 0.47 --

3 0.53 0.41 --

4 0.59 0.51 0.57 --

4 0.63 0.54 0.58 --

Total 0.82 0.79 0.74 0.87

Total 0.84 0.78 0.72 0.88

(168)

Grade 6 Language-Arts Common Core Benchmark Reporting Categories

1 Reading Standards for Literature (7) 2 Reading Standards for Informational Texts (7)

3 Writing Standards (4) 4 Language Standards (12)

Number of items in parentheses

Grade 6 Language-Arts - Form 2

Grade 6 Language-Arts - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.53 --

2 0.56 --

3 0.52 0.48 --

3 0.47 0.40 --

4 0.55 0.52 0.53 --

4 0.58 0.55 0.53 --

Total 0.80 0.79 0.74 0.86

Total 0.82 0.79 0.70 0.87

Grade 6 Language-Arts - Form 2

Grade 6 Language-Arts - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.53 --

2 0.58 --

3 0.43 0.45 --

3 0.54 0.53 --

4 0.58 0.59 0.59 --

4 0.61 0.62 0.57 --

Total 0.78 0.81 0.71 0.89

Total 0.83 0.82 0.74 0.89

(169)

Grade 7 Language-Arts Common Core Benchmark Reporting Categories

1 Reading Standards for Literature (7) 2 Reading Standards for Informational Texts (7)

3 Writing Standards (4) 4 Language Standards (12)

Number of items in parentheses

Grade 7 Language-Arts - Form 2

Grade 7 Language-Arts - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.54 --

2 0.50 --

3 0.54 0.44 --

3 0.38 0.31 --

4 0.61 0.50 0.57 --

4 0.59 0.41 0.53 --

Total 0.84 0.76 0.74 0.88

Total 0.80 0.72 0.65 0.87

Grade 7 Language-Arts - Form 2

Grade 7 Language-Arts - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.56 --

2 0.53 --

3 0.51 0.48 --

3 0.53 0.58 --

4 0.53 0.53 0.45 --

4 0.55 0.60 0.58 --

Total 0.81 0.80 0.70 0.85

Total 0.80 0.82 0.77 0.87

(170)

Grade 8 Language-Arts Common Core Benchmark Reporting Categories

1 Reading Standards for Literature (7) 2 Reading Standards for Informational Texts (7)

3 Writing Standards (4) 4 Language Standards (12)

Number of items in parentheses

Grade 8 Language-Arts - Form 2

Grade 8 Language-Arts - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.54 --

2 0.55 --

3 0.49 0.48 --

3 0.53 0.54 --

4 0.56 0.53 0.51 --

4 0.54 0.48 0.47 --

Total 0.82 0.80 0.72 0.85

Total 0.81 0.80 0.73 0.83

Grade 8 Language-Arts - Form 2

Grade 8 Language-Arts - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.60 --

2 0.64 --

3 0.42 0.43 --

3 0.53 0.54 --

4 0.56 0.52 0.40 --

4 0.57 0.57 0.56 --

Total 0.84 0.81 0.63 0.84

Total 0.84 0.83 0.74 0.86

(171)

Grade 9 Language-Arts Common Core Benchmark Reporting Categories

1 Reading Standards for Literature (10) 2 Reading Standards for Informational Texts (10)

3 Writing Standards (4) 4 Language Standards (6)

Number of items in parentheses

Grade 9 Language-Arts - Form 2

Grade 9 Language-Arts - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.63 --

2 0.59 --

3 0.51 0.46 --

3 0.59 0.49 --

4 0.40 0.37 0.33 --

4 0.51 0.47 0.44 --

Total 0.88 0.86 0.67 0.61

Total 0.89 0.82 0.74 0.71

Grade 9 Language-Arts - Form 2

Grade 9 Language-Arts - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.48 --

2 0.67 --

3 0.43 0.48 --

3 0.57 0.59 --

4 0.35 0.36 0.40 --

4 0.45 0.47 0.43 --

Total 0.81 0.81 0.70 0.65

Total 0.88 0.88 0.76 0.68

(172)

Grade 10 Language-Arts Common Core Benchmark Reporting Categories

1 Reading Standards for Literature (10) 2 Reading Standards for Informational Texts (10)

3 Writing Standards (4) 4 Language Standards (6)

Number of items in parentheses

Grade 10 Language-Arts - Form 2

Grade10 Language-Arts - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.60 --

2 0.72 --

3 0.49 0.50 --

3 0.56 0.58 --

4 0.40 0.42 0.36 --

4 0.55 0.54 0.50 --

Total 0.85 0.86 0.69 0.66

Total 0.90 0.90 0.74 0.73

Grade 10 Language-Arts - Form 2

Grade 10 Language-Arts - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.59 --

2 0.71 --

3 0.49 0.46 --

3 0.55 0.53 --

4 0.46 0.44 0.46 --

4 0.45 0.50 0.40 --

Total 0.85 0.84 0.69 0.71

Total 0.89 0.90 0.71 0.68

(173)

Grade 11 Language-Arts Common Core Benchmark Reporting Categories

1 Reading Standards for Literature (10) 2 Reading Standards for Informational Texts (10)

3 Writing Standards (4) 4 Language Standards (6)

Number of items in parentheses

Grade 11 Language-Arts - Form 2

Grade11 Language-Arts - Form 3

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.64 --

2 0.63 --

3 0.50 0.50 --

3 0.45 0.42 --

4 0.62 0.59 0.47 --

4 0.58 0.54 0.38 --

Total 0.88 0.88 0.68 0.79

Total 0.88 0.86 0.62 0.76

Grade 11 Language-Arts - Form 2

Grade 11 Language-Arts - Form 4

Reporting Category Intercorrelations

Reporting Category Intercorrelations

1 2 3 4

1 2 3 4

1 --

1 --

2 0.54 --

2 0.54 --

3 0.41 0.40 --

3 0.38 0.41 --

4 0.47 0.48 0.39 --

4 0.53 0.56 0.28 --

Total 0.83 0.83 0.63 0.74

Total 0.84 0.84 0.59 0.77

(174)

Appendix F.

Study Island Benchmark Assessment Alignment to the Common Core State Standards

Grades 3–8 Mathematics, Algebra 1, Geometry, and Algebra 2 Standards Maps

(175)

Grade 3 Mathematics – Alignment to Common Core

Standard Study Island Topic

Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.

3.OA.1 - Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

Model Multiplication and Division

3.OA.2 - Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

Model Multiplication and Division

3.OA.3 - Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Real World Problems

(176)

Grade 3 Mathematics – Alignment to Common Core

Standard Study Island Topic

3.OA.4 - Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 = ?.

Number Sentences

Understand properties of multiplication and the relationship between multiplication and division.

3.OA.5 - Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Multiplication and Division Properties

3.OA.6 - Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Multiplication and Division Properties

Multiply and divide within 100.

3.OA.7 - Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Multiplication and Division Facts

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Grade 3 Mathematics – Alignment to Common Core

Standard Study Island Topic

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

3.OA.8 - Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Estimate Solutions

Real World Problems

Two-Step Real World Problems

3.OA.9 - Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Number Patterns

Number and Operations in Base Ten

Use place value understanding and properties of operations to perform multi-digit arithmetic.

3.NBT.1 - Use place value understanding to round whole numbers to the nearest 10 or 100.

Rounding Numbers

3.NBT.2 - Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Addition and Subtraction

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Grade 3 Mathematics – Alignment to Common Core

Standard Study Island Topic

3.NBT.3 - Multiply one-digit whole numbers by multiples of 10 in the range 1090 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Multiply by Multiples of 10

Number and OperationsFractions

Develop understanding of fractions as numbers.

3.NF.1 - Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Fractions

3.NF.2 - Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Fractions

a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

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Grade 3 Mathematics – Alignment to Common Core

Standard Study Island Topic

3.NF.3 - Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Comparing Fractions

Equivalent Fractions

a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or

Measurement and Data

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

3.MD.1 - Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Time / Time Elapsed

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Grade 3 Mathematics – Alignment to Common Core

Standard Study Island Topic

3.MD.2 - Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Capacity and Mass

Represent and interpret data.

3.MD.3 - Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

Graphs

3.MD.4 - Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters.

Graphs

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Grade 3 Mathematics – Alignment to Common Core

Standard Study Island Topic

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

3.MD.5 - Recognize area as an attribute of plane figures and understand concepts of area measurement.

Area

a. A square with side length 1 unit, called a unit square, is said to have one square unitof area, and can be used to measure area.

b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

3.MD.6 - Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Area

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Grade 3 Mathematics – Alignment to Common Core

Standard Study Island Topic

3.MD.7 - Relate area to the operations of multiplication and addition.

Area

a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning.

d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

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Grade 3 Mathematics – Alignment to Common Core

Standard Study Island Topic

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

3.MD.8 - Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Perimeter

Geometry

Reason with shapes and their attributes.

3.G.1 - Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

2-Dimensional Shapes

3.G.2 - Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Shape Partitions

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Grade 4 Mathematics – Alignment to Common Core

Standard Study Island Topic

Operations and Algebraic Thinking

Use the four operations with whole numbers to solve problems.

4.OA.1 - Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Multiplicative Comparisons

4.OA.2 - Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Multiplicative Comparisons

Real World Problems

4.OA.3 - Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Estimate Solutions

Multiplicative Comparisons

Real World Problems

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Grade 4 Mathematics – Alignment to Common Core

Standard Study Island Topic

Gain familiarity with factors and multiples.

4.OA.4 - Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1100 is prime or composite.

Factors and Multiples

Generate and analyze patterns.

4.OA.5 - Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Patterns

Number and Operations in Base Ten

Generalize place value understanding for multi-digit whole numbers.

4.NBT.1 - Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Place Value

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Grade 4 Mathematics – Alignment to Common Core

Standard Study Island Topic

4.NBT.2 - Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Compare Numbers

Expanded Notation

Place Value

4.NBT.3 - Use place value understanding to round multi-digit whole numbers to any place.

Rounding Numbers

Use place value understanding and properties of operations to perform multi-digit arithmetic.

4.NBT.4 - Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Addition and Subtraction

4.NBT.5 - Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Multiplication

4.NBT.6 - Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Multiplication

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Grade 4 Mathematics – Alignment to Common Core

Standard Study Island Topic

Number and OperationsFractions

Extend understanding of fraction equivalence and ordering.

4.NF.1 - Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Equivalent Fractions

4.NF.2 - Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or

Compare Fractions

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Grade 4 Mathematics – Alignment to Common Core

Standard Study Island Topic

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NF.3 - Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Adding and Subtracting Fractions

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

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Grade 4 Mathematics – Alignment to Common Core

Standard Study Island Topic

4.NF.4 - Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Multiplying Fractions

a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Understand decimal notation for fractions, and compare decimal fractions.

4.NF.5 - Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Equivalent Fractions

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Grade 4 Mathematics – Alignment to Common Core

Standard Study Island Topic

4.NF.6 - Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Convert Fractions to Decimals

4.NF.7 - Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or

Compare Decimals

Measurement and Data

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

4.MD.1 - Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Units of Measurement

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Grade 4 Mathematics – Alignment to Common Core

Standard Study Island Topic

4.MD.2 - Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Measurement

4.MD.3 - Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Perimeter and Area

Represent and interpret data.

4.MD.4 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Represent and Interpret Data

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Grade 4 Mathematics – Alignment to Common Core

Standard Study Island Topic

Geometric measurement: understand concepts of angle and measure angles.

4.MD.5 - Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

Angle Measurement

a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle,and can be used to measure angles.

b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.6 - Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Angle Measurement

4.MD.7 - Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Angle Measurement

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Grade 4 Mathematics – Alignment to Common Core

Standard Study Island Topic

Geometry

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

4.G.1 - Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Angle Measurement

Angles

Points, Lines, Rays, and Segments

4.G.2 - Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Angles

Points, Lines, Rays, and Segments

4.G.3 - Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Symmetry

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Grade 5 Mathematics – Alignment to Common Core

Standard Study Island Topic

Operations and Algebraic Thinking

Write and interpret numerical expressions.

5.OA.1 - Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Numerical Expressions

5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Numerical Expressions

Analyze patterns and relationships.

5.OA.3 - Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Number Patterns

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Grade 5 Mathematics – Alignment to Common Core

Standard Study Island Topic

Number and Operations in Base Ten

Understand the place value system.

5.NBT.1 - Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Powers of Ten

5.NBT.2 - Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Powers of Ten

5.NBT.3 - Read, write, and compare decimals to thousandths.

Comparing Decimals

Representations of Decimals

a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.NBT.4 - Use place value understanding to round decimals to any place.

Rounding Decimals

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Grade 5 Mathematics – Alignment to Common Core

Standard Study Island Topic

Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.5 - Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply Whole Numbers

Real World Problems

5.NBT.6 - Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Model Division of Whole Numbers

Real World Problems

5.NBT.7 - Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add and Subtract Decimals

Multiply and Divide Decimals

Real World Problems

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Grade 5 Mathematics – Alignment to Common Core

Standard Study Island Topic

Number and OperationsFractions

Use equivalent fractions as a strategy to add and subtract fractions.

5.NF.1 - Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Add and Subtract Fractions

5.NF.2 - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Add and Subtract Fractions

Problem Solving with Fractions

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Grade 5 Mathematics – Alignment to Common Core

Standard Study Island Topic

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.3 - Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Division with Fractions

Problem Solving with Fractions

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Grade 5 Mathematics – Alignment to Common Core

Standard Study Island Topic

5.NF.4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Multiplication with Fractions

Problem Solving with Fractions

a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

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Grade 5 Mathematics – Alignment to Common Core

Standard Study Island Topic

5.NF.5 - Interpret multiplication as scaling (resizing), by:

Multiplication with Fractions

a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

5.NF.6 - Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Problem Solving with Fractions

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Grade 5 Mathematics – Alignment to Common Core

Standard Study Island Topic

5.NF.7 - Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Division with Fractions

Problem Solving with Fractions

a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

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Grade 5 Mathematics – Alignment to Common Core

Standard Study Island Topic

Measurement and Data

Convert like measurement units within a given measurement system.

5.MD.1 - Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Units of Measure

Represent and interpret data.

5.MD.2 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Representing and Interpreting Data

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

5.MD.3 - Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

Volume

a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unitof volume, and can be used to measure volume.

b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

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Grade 5 Mathematics – Alignment to Common Core

Standard Study Island Topic

5.MD.4 - Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Volume

5.MD.5 - Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Volume

a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

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Grade 5 Mathematics – Alignment to Common Core

Standard Study Island Topic

Geometry

Graph points on the coordinate plane to solve real-world and mathematical problems.

5.G.1 - Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

Coordinate System

5.G.2 - Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Coordinate System

Classify two-dimensional figures into categories based on their properties.

5.G.3 - Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

2-Dimensional Figures

5.G.4 - Classify two-dimensional figures in a hierarchy based on properties.

2-Dimensional Figures

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Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

Ratios and Proportional Relationships

Understand ratio concepts and use ratio reasoning to solve problems.

6.RP.1 - Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes.

Ratios and Ratio Language

6.RP.2 - Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is

3/4 cup of flour for each cup of sugar.

We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.

Unit Rates

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Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

6.RP.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Percents

Unit Rates

a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Units of Measurement

b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

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Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

The Number System

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.1 - Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (

2/3) ÷ (

3/4) and use a visual

fraction model to show the quotient; use the relationship between multiplication and division to explain that (

2/3) ÷ (

3/4) =

8/9 because

3/4 of

8/9 is

2/3. (In general,

(a/b) ÷ (

c/d) =

ad/bc.) How much chocolate

will each person get if 3 people share 1/2

lb of chocolate equally? How many 3/4-

cup servings are in 2/3 of a cup of

yogurt? How wide is a rectangular strip of land with length

3/4 mi and area

1/2

square mi?

Division of Fractions

Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.2 - Fluently divide multi-digit numbers using the standard algorithm.

Division of Whole Numbers

6.NS.3 - Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Arithmetic with Decimals

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Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

6.NS.4 - Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

Number Theory

Apply and extend previous understandings of numbers to the system of rational numbers.

6.NS.5 - Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Negative and Positive Numbers

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Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

6.NS.6 - Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

Coordinate Planes

Number Lines

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., (3) = 3, and that 0 is its own opposite.

b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

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Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

6.NS.7 - Understand ordering and absolute value of rational numbers.

Absolute Value

Negative and Positive Numbers

a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right.

Number Lines

b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write 3 °C > 7 °C to express the fact that 3 °C is warmer than 7 °C.

c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of 30 dollars, write |30| = 30 to describe the size of the debt in dollars.

d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars.

6.NS.8 - Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Coordinate Geometry

Coordinate Planes

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Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

Expressions and Equations

Apply and extend previous understandings of arithmetic to algebraic expressions.

6.EE.1 - Write and evaluate numerical expressions involving whole-number exponents.

Evaluate Expressions

Write Expressions

6.EE.2 - Write, read, and evaluate expressions in which letters stand for numbers.

Evaluate Expressions

Write Expressions

a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y.

b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s

3 and A

= 6 s2 to find the volume and surface

area of a cube with sides of length s = 1/2.

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Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

6.EE.3 - Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

Equivalent Expressions

6.EE.4 - Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

Equivalent Expressions

Reason about and solve one-variable equations and inequalities.

6.EE.5 - Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Solve Equations and Inequalities

6.EE.6 - Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Symbolize Problem Situations

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Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

6.EE.7 - Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Number Sentences

6.EE.8 - Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Number Sentences

Represent and analyze quantitative relationships between dependent and independent variables.

6.EE.9 - Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Quantitative Relationships

(214)

Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

Geometry

Solve real-world and mathematical problems involving area, surface area, and volume.

6.G.1 - Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Area

6.G.2 - Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Surface Area and Volume

6.G.3 - Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Coordinate Geometry

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Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

6.G.4 - Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Surface Area and Volume

Statistics and Probability

Develop understanding of statistical variability.

6.SP.1 - Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.

Statistical Analysis

6.SP.2 - Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Statistical Analysis

6.SP.3 - Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Statistical Analysis

(216)

Grade 6 Mathematics – Alignment to Common Core

Standard Study Island Topic

Summarize and describe distributions.

6.SP.4 - Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Graphing and Interpreting Data

6.SP.5 - Summarize numerical data sets in relation to their context, such as by:

Graphing and Interpreting Data

Statistical Analysis

a. Reporting the number of observations.

b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

(217)

Grade 7 Mathematics – Alignment to Common Core

Standard Study Island Topic

Ratios and Proportional Relationships

Analyze proportional relationships and use them to solve real-world and mathematical problems.

7.RP.1 - Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction

1/2/1/4 miles per

hour, equivalently 2 miles per hour.

Unit Rates

(218)

Grade 7 Mathematics – Alignment to Common Core

Standard Study Island Topic

7.RP.2 - Recognize and represent proportional relationships between quantities.

Proportional Relationships

Unit Rates

a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

7.RP.3 - Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Percents

Ratios and Proportions

(219)

Grade 7 Mathematics – Alignment to Common Core

Standard Study Island Topic

The Number System

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

7.NS.1 - Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Properties of Addition and Subtraction

Single-Step Real World Problems

a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

c. Understand subtraction of rational numbers as adding the additive inverse, p q = p + (q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

d. Apply properties of operations as strategies to add and subtract rational numbers.

(220)

Grade 7 Mathematics – Alignment to Common Core

Standard Study Island Topic

7.NS.2 - Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Properties of Multiplication and Division

Single-Step Real World Problems

a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (1)(1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then (p/q) = (p)/q = p/(q). Interpret quotients of rational numbers by describing real-world contexts.

c. Apply properties of operations as strategies to multiply and divide rational numbers.

d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

7.NS.3 - Solve real-world and mathematical problems involving the four operations with rational numbers.

Compute with Rational Numbers

Single-Step Real World Problems

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Grade 7 Mathematics – Alignment to Common Core

Standard Study Island Topic

Expressions and Equations

Use properties of operations to generate equivalent expressions.

7.EE.1 - Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Linear Expressions

7.EE.2 - Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that increase by 5% is the same as multiply by 1.05.

Linear Expressions

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

7.EE.3 - Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Multi-Step Real World Problems

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Grade 7 Mathematics – Alignment to Common Core

Standard Study Island Topic

7.EE.4 - Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Symbolize and Solve Equations

Symbolize and Solve Inequalities

a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

(223)

Grade 7 Mathematics – Alignment to Common Core

Standard Study Island Topic

Geometry

Draw construct, and describe geometrical figures and describe the relationships between them.

7.G.1 - Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Scale Drawings

7.G.2 - Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Three-Dimensional Figures

7.G.3 - Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Three-Dimensional Figures

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

7.G.4 - Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Circles

7.G.5 - Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Angles

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Grade 7 Mathematics – Alignment to Common Core

Standard Study Island Topic

7.G.6 - Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Area, Surface Area, and Volume

Statistics and Probability

Use random sampling to draw inferences about a population.

7.SP.1 - Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Sampling Analysis

7.SP.2 - Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Sampling Analysis

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Grade 7 Mathematics – Alignment to Common Core

Standard Study Island Topic

Draw informal comparative inferences about two populations.

7.SP.3 - Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

Central Tendency and Variability

7.SP.4 - Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Central Tendency and Variability

Investigate chance processes and develop, use, and evaluate probability models.

7.SP.5 - Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Probability

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Grade 7 Mathematics – Alignment to Common Core

Standard Study Island Topic

7.SP.6 - Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

Probability

7.SP.7 - Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Probability

a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

(227)

Grade 7 Mathematics – Alignment to Common Core

Standard Study Island Topic

7.SP.8 - Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Probability

a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

(228)

Grade 8 Mathematics – Alignment to Common Core

Standard Study Island Topic

The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.1 - Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Real Numbers

8.NS.2 - Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g.,

2). For example, by

truncating the decimal expansion of , show that is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Rational Approximations

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Grade 8 Mathematics – Alignment to Common Core

Standard Study Island Topic

Expressions and Equations

Work with radicals and integer exponents.

8.EE.1 - Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3

2 × 3

5 = 3

3 = 1/3

3 = 1/27.

Exponential Expressions

8.EE.2 - Use square root and cube root symbols to represent solutions to equations of the form x

2 = p and x

3 = p,

where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that is irrational.

Square and Cube Roots

8.EE.3 - Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 10

8 and the population of the world as 7

× 109, and determine that the world

population is more than 20 times larger.

Scientific Notation

8.EE.4 - Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Scientific Notation

(230)

Grade 8 Mathematics – Alignment to Common Core

Standard Study Island Topic

Understand the connections between proportional relationships, lines, and linear equations.

8.EE.5 - Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Proportional Relationships

8.EE.6 - Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Proportional Relationships

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Grade 8 Mathematics – Alignment to Common Core

Standard Study Island Topic

Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.7 - Solve linear equations in one variable.

Solving Linear Equations

a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

(232)

Grade 8 Mathematics – Alignment to Common Core

Standard Study Island Topic

8.EE.8 - Analyze and solve pairs of simultaneous linear equations.

Systems of Equations

a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

(233)

Grade 8 Mathematics – Alignment to Common Core

Standard Study Island Topic

Functions

Define, evaluate, and compare functions.

8.F.1 - Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Functions

8.F.2 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Functions

8.F.3 - Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s

2 giving the

area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Linear vs. Nonlinear

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Grade 8 Mathematics – Alignment to Common Core

Standard Study Island Topic

Use functions to model relationships between quantities.

8.F.4 - Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Linear Relationships

8.F.5 - Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Functions

Linear vs. Nonlinear

Geometry

Understand congruence and similarity using physical models, transparencies, or geometry software.

8.G.1 - Verify experimentally the properties of rotations, reflections, and translations:

NASL

a. Lines are taken to lines, and line segments to line segments of the same length.

Object Transformations

b. Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines.

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Grade 8 Mathematics – Alignment to Common Core

Standard Study Island Topic

8.G.2 - Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Similarity and Congruence

8.G.3 - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Object Transformations

8.G.4 - Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Similarity and Congruence

8.G.5 - Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Angles and Lines

Similarity and Congruence

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Grade 8 Mathematics – Alignment to Common Core

Standard Study Island Topic

Understand and apply the Pythagorean Theorem.

8.G.6 - Explain a proof of the Pythagorean Theorem and its converse.

Pythagorean Theorem

8.G.7 - Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Pythagorean Theorem

8.G.8 - Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Pythagorean Theorem

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G.9 - Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Volume

Statistics and Probability

Investigate patterns of association in bivariate data.

8.SP.1 - Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Scatter Plots

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Grade 8 Mathematics – Alignment to Common Core

Standard Study Island Topic

8.SP.2 - Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Best-Fit Linear Models

8.SP.3 - Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

Best-Fit Linear Models

8.SP.4 - Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

Two-Way Tables

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Unit 1: Relationships between Quantities and Reasoning with Equations

Reason quantitatively and use units to solve problems.

Working with quantities and the relationships between them provides grounding for work with expressions, equations, and functions.

N.Q.1 - Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Interpret Graphs

Quantities and Units

N.Q.2 - Define appropriate quantities for the purpose of descriptive modeling.

Quantities and Units

N.Q.3 - Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Quantities and Units

Interpret the structure of expressions.

Limit to linear expressions and to exponential expressions with integer exponents.

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

A.SSE.1 - Interpret expressions that represent a quantity in terms of its context.

Symbolize with Expressions

Symbolize with Linear and Exponential Expressions

a. Interpret parts of an expression, such as terms, factors, and coefficients.

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)

n as the product of P and a factor

not depending on P.

Create equations that describe numbers or relationships.

Limit A.CED.1 and A.CED.2 to linear and exponential equations, and, in the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs. Limit A.CED.3 to linear equations and inequalities. Limit A.CED.4 to formulas which are linear in the variable of interest.

A.CED.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Create Linear and Exponential Equations and Inequalities

Create Quadratic Equations and Inequalities

Solve Equations and Inequalities

A.CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Create Linear and Exponential Equations and Inequalities

Create Quadratic Equations and Inequalities

Solve Equations and Inequalities

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

A.CED.3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

Create Linear and Exponential Equations and Inequalities

Create Systems of Equations and Inequalities

Solve Equations and Inequalities

A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohms law V = IR to highlight resistance R.

Rewrite Equations

Rewrite Linear Variable Equations

Understand solving equations as a process of reasoning and explain the reasoning.

Students should focus on and master A.REI.1 for linear equations and be able to extend and apply their reasoning to other types of equations in future courses. Students will solve exponential equations with logarithms in Algebra II.

A.REI.1 - Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Properties of Arithmetic

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Solve equations and inequalities in one variable.

Extend earlier work with solving linear equations to solving linear inequalities in one variable and to solving literal equations that are linear in the variable being solved for. Include simple exponential equations that rely only on application of the laws of exponents, such as 5

x=125 or 2

x=1/16.

A.REI.3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Solve Linear Equations

Solve Linear Inequalities

Unit 2: Linear and Exponential Relationships

Extend the properties of exponents to rational exponents.

In implementing the standards in curriculum, these standards should occur before discussing exponential functions with continuous domains.

N.RN.1 - Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5

1/3 to be the cube

root of 5 because we want (51/3)

3 =

5(1/3

)3 to hold, so (5

1/3)3 must equal 5.

Rational Exponents

N.RN.2 - Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Rational Exponents

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Solve systems of equations.

Build on student experiences graphing and solving systems of linear equations from middle school to focus on justification of the methods used. Include cases where the two equations describe the same line (yielding infinitely many solutions) and cases where two equations describe parallel lines (yielding no solution); connect to GPE.5 when it is taught in Geometry, which requires students to prove the slope criteria for parallel lines.

A.REI.5 - Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Systems of Equations

A.REI.6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Systems of Equations

Represent and solve equations and inequalities graphically.

For A.REI.10, focus on linear and exponential equations and be able to adapt and apply that learning to other types of equations in future courses. For A.REI.11, focus on cases where f(x) and g(x) are linear or exponential.

A.REI.10 - Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Solve Equations by Graphing

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

A.REI.11 - Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Solve Equations by Graphing

A.REI.12 - Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Linear Inequalities in Two Variables

Understand the concept of a function and use function notation.

Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of functions at this stage is not advised. Students should apply these concepts throughout their future mathematics courses.

Draw examples from linear and exponential functions. In F.IF.3, draw connection to F.BF.2, which requires students to write arithmetic and geometric sequences. Emphasize arithmetic and geometric sequences as examples of linear and exponential functions.

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

F.IF.1 - Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Functions

F.IF.2 - Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Evaluate Functions

Functions

F.IF.3 - Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n > 1.

Sequences

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Interpret functions that arise in applications in terms of a context.

For F.IF.4 and 5, focus on linear and exponential functions. For F.IF.6, focus on linear functions and exponential functions whose domain is a subset of the integers. Unit 5 in this course and the Algebra II course address other types of functions.

F.IF.4 - For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Interpret Functions in Context

Interpret Quadratic Functions

F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

Domain of a Function

Interpret Quadratic Functions

F.IF.6 - Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Interpret Quadratic Functions

Rate of Change

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Analyze functions using different representations.

For F.IF.7a, 7e, and 9 focus on linear and exponentials functions. Include comparisons of two functions presented algebraically. For example, compare the growth of two linear functions, or two exponential functions such as y=3

n and

y=1002

F.IF.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Graphs of Functions

Graphs of Linear and Exponential Functions

a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F.IF.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Compare Properties of Linear and Exponential Functions

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Build a function that models a relationship between two quantities.

Limit to F.BF.1a, 1b, and 2 to linear and exponential functions. In F.BF.2, connect arithmetic sequences to linear functions and geometric sequences to exponential functions.

F.BF.1 - Write a function that describes a relationship between two quantities.

Writing Functions

Writing Quadratic Functions

a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

F.BF.2 - Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Sequences

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Build new functions from existing functions.

Focus on vertical translations of graphs of linear and exponential functions. Relate the vertical translation of a linear function to its y-intercept.

While applying other transformations to a linear graph is appropriate at this level, it may be difficult for students to identify or distinguish between the effects of the other transformations included in this standard.

F.BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Function Transformations

Linear and Exponential Function Transformations

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Construct and compare linear, quadratic, and exponential models and solve problems.

For F.LE.3, limit to comparisons between linear and exponential models. In constructing linear functions in F.LE.2, draw on and consolidate previous work in Grade 8 on finding equations for lines and linear functions (8.EE.6, 8.F.4).

F.LE.1 - Distinguish between situations that can be modeled with linear functions and with exponential functions.

Linear and Exponential Models

a. Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals.

b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

F.LE.2 - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Linear and Exponential Models

F.LE.3 - Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Compare Properties of Functions

Linear and Exponential Models

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Interpret expressions for functions in terms of the situation they model.

Limit exponential functions to those of the form f(x) = b

x + k.

F.LE.5 - Interpret the parameters in a linear or exponential function in terms of a context.

Linear and Exponential Models

Unit 3: Descriptive Statistics

Summarize, represent, and interpret data on a single count or measurement variable.

In grades 6 8, students describe center and spread in a data distribution. Here they choose a summary statistic appropriate to the characteristics of the data distribution, such as the shape of the distribution or the existence of extreme data points.

S.ID.1 - Represent data with plots on the real number line (dot plots, histograms, and box plots).

Comparing Data

S.ID.2 - Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Comparing Data

S.ID.3 - Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Comparing Data

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Summarize, represent, and interpret data on two categorical and quantitative variables.

Students take a more sophisticated look at using a linear function to model the relationship between two numerical variables. In addition to fitting a line to data, students assess how well the model fits by analyzing residuals.

S.ID.6b should be focused on linear models, but may be used to preview quadratic functions in Unit 5 of this course.

S.ID.5 - Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

Two-Way Frequency Tables

S.ID.6 - Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Scatter Plots

a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models.

b. Informally assess the fit of a function by plotting and analyzing residuals.

c. Fit a linear function for a scatter plot that suggests a linear association.

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Interpret linear models.

Build on studentswork with linear relationships in eighth grade and introduce the correlation coefficient. The focus here is on the computation and interpretation of the correlation coefficient as a measure of how well the data fit the relationship. The important distinction between a statistical relationship and a cause- and- effect relationship arises in S.ID.9.

S.ID.7 - Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Scatter Plots

S.ID.8 - Compute (using technology) and interpret the correlation coefficient of a linear fit.

Scatter Plots

S.ID.9 - Distinguish between correlation and causation. Scatter Plots

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Unit 4: Expressions and Equations

Interpret the structure of expressions.

Focus on quadratic and exponential expressions. For A.SSE.1b, exponents are extended from the integer exponents found in Unit 1 to rational exponents focusing on those that represent square or cube roots.

A.SSE.1 - Interpret expressions that represent a quantity in terms of its context.

Symbolize with Expressions

Symbolize with Linear and Exponential Expressions

a. Interpret parts of an expression, such as terms, factors, and coefficients.

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)

n as the product of P and a factor

not depending on P.

A.SSE.2 - Use the structure f an expression to identify ways to rewrite it. For example, see x

4 y

4 as (x

2)2 (y

2)2,

thus recognizing it as a difference of squares that can be factored as (x

2

y2)(x

2 + y

2).

Simplify Expressions

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Write expressions in equivalent forms to solve problems.

It is important to balance conceptual understanding and procedural fluency in work with equivalent expressions. For example, development of skill in factoring and completing the square goes hand-in-hand with understanding what different forms of a quadratic expression reveal.

A.SSE.3 - Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Quadratic Expressions

Symbolize with Expressions

a. Factor a quadratic expression to reveal the zeros of the function it defines.

b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15

t can be rewritten as (1.15

1/12)12t

≈ 1.012

12t to reveal the approximate

equivalent monthly interest rate if the annual rate is 15%.

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Perform arithmetic operations on polynomials.

Focus on polynomial expressions that simplify to forms that are linear or quadratic in a positive integer power of x.

A.APR.1 - Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Polynomial Expressions

Create equations that describe numbers or relationships.

Extend work on linear and exponential equations in Unit 1 to quadratic equations. Extend A.CED.4 to formulas involving squared variables.

A.CED.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Create Linear and Exponential Equations and Inequalities

Create Quadratic Equations and Inequalities

Solve Equations and Inequalities

A.CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Create Linear and Exponential Equations and Inequalities

Create Quadratic Equations and Inequalities

Solve Equations and Inequalities

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohms law V = IR to highlight resistance R.

Rewrite Equations

Rewrite Linear Variable Equations

Solve equations and inequalities in one variable.

Students should learn of the existence of the complex number system, but will not solve quadratics with complex solutions until Algebra II.

A.REI.4 - Solve quadratic equations in one variable.

Solve Quadratic Equations

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p)

2 = q that has the same

solutions. Derive the quadratic formula from this form.

b. Solve quadratic equations by inspection (e.g., for x

2 = 49), taking

square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Solve systems of equations.

Include systems consisting of one linear and one quadratic equation. Include systems that lead to work with fractions. For example, finding the intersections between x

2+y

2=1 and y = (x+1)/2 leads

to the point (3/5, 4/5) on the unit circle, corresponding to the Pythagorean triple 3

2+4

2=5

2.

A.REI.7 - Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x

2

+ y2 = 3.

Systems of Equations

Unit 5: Quadratic Functions and Modeling

Use properties of rational and irrational numbers.

Connect N.RN.3 to physical situations, e.g., finding the perimeter of a square of area 2.

N.RN.3 - Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Operations with Rational and Irrational Numbers

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Interpret functions that arise in applications in terms of a context.

Focus on quadratic functions; compare with linear and exponential functions studied in Unit 2.

F.IF.4 - For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Interpret Functions in Context

Interpret Quadratic Functions

F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

Domain of a Function

Interpret Quadratic Functions

F.IF.6 - Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Interpret Quadratic Functions

Rate of Change

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Analyze functions using different representations.

For F.IF.7b, compare and contrast absolute value, step and piecewise defined functions with linear, quadratic, and exponential functions. Highlight issues of domain, range, and usefulness when examining piecewise defined functions. Note that this unit, and in particular in F.IF.8b, extends the work begun in Unit 2 on exponential functions with integer exponents. For F.IF.9, focus on expanding the types of functions considered to include, linear, exponential, and quadratic.

Extend work with quadratics to include the relationship between coefficients and roots, and that once roots are known, a quadratic equation can be factored.

F.IF.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Graphs of Functions

Graphs of Linear and Exponential Functions

a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Graphs of Functions

a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)

t, y = (0.97)

t, y = (1.01)

12t, y =

(1.2)t/10

, and classify them as representing exponential growth or decay.

F.IF.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Compare Properties of Linear and Exponential Functions

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Build a function that models a relationship between two quantities.

Focus on situations that exhibit a quadratic relationship.

F.BF.1 - Write a function that describes a relationship between two quantities.

Writing Functions

Writing Quadratic Functions

a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Build new functions from existing functions.

For F.BF.3, focus on quadratic functions, and consider including absolute value functions. For F.BF.4a, focus on linear functions but consider simple situations where the domain of the function must be restricted in order for the inverse to exist, such as f(x) = x

2, x>0.

F.BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Function Transformations

Linear and Exponential Function Transformations

F.BF.4 - Find inverse functions.

Inverse Functions

a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2 x

3 or f(x) =

(x+1)/(x-1) for x =/ 1.

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Algebra 1 – Alignment to Common Core

Standard Study Island Topic

Construct and compare linear, quadratic, and exponential models and solve problems.

Compare linear and exponential growth to quadratic growth.

F.LE.3 - Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Compare Properties of Functions

Linear and Exponential Models

(264)

Geometry – Alignment to Common Core

Standard Study Island Topic

Unit 1: Congruence, Proof, and Constructions

Experiment with transformations in the plane. Build on student experience with rigid motions from earlier grades. Point out the basis of rigid motions in geometric concepts, e.g., translations move points a specified distance along a line parallel to a specified line; rotations move objects along a circular arc with a specified center through a specified angle.

G.CO.1 - Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Embedded

G.CO.2 - Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

Transformations in the Plane

G.CO.3 - Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Transformations in the Plane

G.CO.4 - Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Transformations in the Plane

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Geometry – Alignment to Common Core

Standard Study Island Topic

G.CO.5 - Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Transformations in the Plane

Understand congruence in terms of rigid motions. Rigid motions are at the foundation of the definition of congruence. Students reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems.

G.CO.6 - Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Congruence

G.CO.7 - Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Congruence

G.CO.8 - Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Congruence

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Geometry – Alignment to Common Core

Standard Study Island Topic

Prove geometric theorems. Encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two-column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning. Implementation of G.CO.10 may be extended to include concurrence of perpendicular bisectors and angle bisectors as preparation for G.C.3 in Unit 5.

G.CO.9 - Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segments endpoints.

Theorems and Proofs

G.CO.10 - Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Theorems and Proofs

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Geometry – Alignment to Common Core

Standard Study Island Topic

G.CO.11 - Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Theorems and Proofs

Make geometric constructions. Build on prior student experience with simple constructions. Emphasize the ability to formalize and explain how these constructions result in the desired objects.

Some of these constructions are closely related to previous standards and can be introduced in conjunction with them.

G.CO.12 - Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Geometric Constructions

G.CO.13 - Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Geometric Constructions

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Geometry – Alignment to Common Core

Standard Study Island Topic

Unit 2: Similarity, Proof, and Trigonometry

Understand similarity in terms of similarity transformations.

G.SRT.1 - Verify experimentally the properties of dilations given by a center and a scale factor.

Similarity and Similarity Transformations

a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G.SRT.2 - Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Similarity and Similarity Transformations

G.SRT.3 - Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Similarity and Similarity Transformations

Prove theorems involving similarity.

G.SRT.4 - Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

Similarity and Congruence of Triangles

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Geometry – Alignment to Common Core

Standard Study Island Topic

G.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Similarity and Congruence of Triangles

Define trigonometric ratios and solve problems involving right triangles.

G.SRT.6 - Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Right Triangle Trigonometry

G.SRT.7 - Explain and use the relationship between the sine and cosine of complementary angles.

Right Triangle Trigonometry

G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Right Triangle Trigonometry

Apply geometric concepts in modeling situations.

Focus on situations well modeled by trigonometric ratios for acute angles.

G.MG.1 - Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

Circles with Coordinates

Right Triangle Trigonometry

Two and Three-Dimensional Objects

G.MG.2 - Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*

Right Triangle Trigonometry

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Geometry – Alignment to Common Core

Standard Study Island Topic

G.MG.3 - Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*

Right Triangle Trigonometry

Apply trigonometry to general triangles.

With respect to the general case of the Laws of Sines and Cosines, the definitions of sine and cosine must be extended to obtuse angles.

G.SRT.10(+) - Prove the Laws of Sines and Cosines and use them to solve problems.

Law of Sines and Law of Cosines

G.SRT.11(+) - Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

Law of Sines and Law of Cosines

G.SRT.9(+) - Derive the formula A = 1/2 ab sin(C) for the area of a triangle

by drawing an auxiliary line from a vertex perpendicular to the opposite side.

Area of a Triangle

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Geometry – Alignment to Common Core

Standard Study Island Topic

Unit 3: Extending to Three Dimensions

Explain volume formulas and use them to solve problems.

Informal arguments for area and volume formulas can make use of the way in which area and volume scale under similarity transformations: when one figure in the plane results from another by applying a similarity transformation with scale factor k, its area is k

2 times the area of the first.

Similarly, volumes of solid figures scale by k

3 under a similarity

transformation with scale factor k.

G.GMD.1 - Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieris principle, and informal limit arguments.

N.A.

G.GMD.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Volume

Visualize the relation between two-dimensional and three-dimensional objects.

G.GMD.4 - Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Two and Three-Dimensional Objects

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Geometry – Alignment to Common Core

Standard Study Island Topic

Apply geometric concepts in modeling situations.

Focus on situations that require relating two- and three-dimensional objects, determining and using volume, and the trigonometry of general triangles.

G.MG.1 - Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

Circles with Coordinates

Right Triangle Trigonometry

Two and Three-Dimensional Objects

Unit 4: Connecting Algebra and Geometry Through Coordinates

Use coordinates to prove simple geometric theorems algebraically.

This unit has a close connection with the next unit. For example, a curriculum might merge G.GPE.1 and the Unit 5 treatment of G.GPE.4 with the standards in this unit. Reasoning with triangles in this unit is limited to right triangles; e.g., derive the equation for a line through two points using similar right triangles.

Relate work on parallel lines in G.GPE.5 to work on A.REI.5 in High School Algebra I involving systems of equations having no solution or infinitely many solutions.

G.GPE.7 provides practice with the distance formula and its connection with the Pythagorean theorem.

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Geometry – Alignment to Common Core

Standard Study Island Topic

G.GPE.4 - Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Circles with Coordinates

Coordinate Geometry

G.GPE.5 - Prove the slope criteria for parallel and perpendicular lines and uses them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Lines - Parallel, Perpendicular, and Ratios

G.GPE.6 - Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Lines - Parallel, Perpendicular, and Ratios

G.GPE.7 - Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Coordinate Geometry

Translate between the geometric description and the equation for a conic section.

The directrix should be parallel to a coordinate axis.

G.GPE.2 - Derive the equation of a parabola given a focus and directrix.

Parabola Equations

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Geometry – Alignment to Common Core

Standard Study Island Topic

Unit 5: Circles With and Without Coordinates

Understand and apply theorems about circles.

G.C.1 - Prove that all circles are similar. Circles without Coordinates

G.C.2 - Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Circles without Coordinates

G.C.3 - Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Circles without Coordinates

G.C.4(+) - Construct a tangent line from a point outside a given circle to the circle.

Circles without Coordinates

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Geometry – Alignment to Common Core

Standard Study Island Topic

Find arc lengths and areas of sectors of circles.

Emphasize the similarity of all circles. Note that by similarity of sectors with the same central angle, arc lengths are proportional to the radius. Use this as a basis for introducing radian as a unit of measure. It is not intended that it be applied to the development of circular trigonometry in this course.

G.C.5 - Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Circles without Coordinates

Translate between the geometric description and the equation for a conic section.

G.GPE.1 - Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Circles with Coordinates

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Geometry – Alignment to Common Core

Standard Study Island Topic

Use coordinates to prove simple geometric theorems algebraically.

Include simple proofs involving circles.

G.GPE.4 - Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Circles with Coordinates

Coordinate Geometry

Apply geometric concepts in modeling situations.

Focus on situations in which the analysis of circles is required.

G.MG.1 - Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

Circles with Coordinates

Right Triangle Trigonometry

Two and Three-Dimensional Objects

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Geometry – Alignment to Common Core

Standard Study Island Topic

Unit 6: Applications of Probability

Understand independence and conditional probability and use them to interpret data.

Build on work with two-way tables from Algebra I Unit 3 (S.ID.5) to develop understanding of conditional probability and independence.

S.CP.1 - Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (or, and, not).

Probability

S.CP.2 - Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Probability

S.CP.3 - Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

Probability

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Geometry – Alignment to Common Core

Standard Study Island Topic

S.CP.4 - Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

Probability

S.CP.5 - Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

Probability

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

S.CP.6 - Find the conditional probability of A given B as the fraction of Bs outcomes that also belong to A, and interpret the answer in terms of the model.

Probability

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Geometry – Alignment to Common Core

Standard Study Island Topic

S.CP.7 - Apply the Addition Rule, P(A or B) = P(A) + P(B) P(A and B), and interpret the answer in terms of the model.

Probability

S.CP.8(+) - Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

Probability

S.CP.9(+) - Use permutations and combinations to compute probabilities of compound events and solve problems.

Probability

Use probability to evaluate outcomes of decisions.

This unit sets the stage for work in Algebra II, where the ideas of statistical inference are introduced. Evaluating the risks associated with conclusions drawn from sample data (i.e. incomplete information) requires an understanding of probability concepts.

S.MD.6(+) - Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Probability

S.MD.7(+) - Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Probability

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Algebra 2 – Alignment to Common Core

Standard Study Island Topic

Unit 1: Polynomial, Rational, and Radical Relationships

A.APR.1 - Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Polynomial Expressions

A.APR.2 - Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x a is p(a), so p(a) = 0 if and only if (x a) is a factor of p(x).

Zeros of Polynomials

A.APR.3 - Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Zeros of Polynomials

A.APR.4 - Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x

2

+ y2)2 = (x

2 y

2)2 + (2xy)

2 can be used

to generate Pythagorean triples.

Polynomial Expressions

A.APR.5 (+) - Know and apply the Binomial Theorem for the expansion of (x + y)

n in powers of x and y for a

positive integer n, where x and y are any numbers, with coefficients determined for example by Pascals Triangle.

Binomial Theorem

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Algebra 2 – Alignment to Common Core

Standard Study Island Topic

A.APR.6 - Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Simplify Rational Expressions

A.APR.7 (+) - Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Rational Expressions

A.REI.2 - Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Solve Rational and Radical Equations

A.REI.11 - Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Solve Equations by Graphing

Solve Equations Using Successive Approximations

Solve Equations Using Tables

(282)

Algebra 2 – Alignment to Common Core

Standard Study Island Topic

A.SSE.1 - Interpret expressions that represent a quantity in terms of its context.

Interpret Expressions

a. Interpret parts of an expression, such as terms, factors, and coefficients.

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)

n as the

product of P and a factor not depending on P.

A.SSE.2 - Use the structure of an expression to identify ways to rewrite it. For example, see x

4 y

4 as

(x2)2 (y

2)2, thus recognizing it as a

difference of squares that can be factored as (x

2 y

2)(x

2 + y

2).

Factor and Solve Polynomial Equations

A.SSE.4 - Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.

Geometric Series

F.IF.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Graphs of Polynomial Functions

Selecting Function Type from Context

c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

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Algebra 2 – Alignment to Common Core

Standard Study Island Topic

N.CN.1 - Know there is a complex number i such that i

2 = -1, and every

complex number has the form a + bi with a and b real.

Complex Numbers

N.CN.2 - Use the relation i2 = -1 and

the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Complex Numbers

N.CN.7 - Solve quadratic equations with real coefficients that have complex solutions.

Factor and Solve Polynomial Equations

N.CN.8 (+) - Extend polynomial identities to the complex numbers. For example, rewrite x

2 + 4 as (x +

2i)(x 2i).

Factor and Solve Polynomial Equations

N.CN.9 (+) - Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Factor and Solve Polynomial Equations

Unit 2: Trigonometric Functions

F.TF.1 - Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Unit Circle

F.TF.2 - Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Unit Circle

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Algebra 2 – Alignment to Common Core

Standard Study Island Topic

F.TF.5 - Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Interpret Functions in Context

F.TF.8 - Prove the Pythagorean identity sin

2(Θ) + cos

2(Θ) = 1 and

use it to find sin (Θ), cos (Θ), or tan (Θ), given sin (Θ), cos (Θ), or tan (Θ), and the quadrant of the angle.

Pythagorean Identity

Unit 3: Modeling with Functions

A.CED.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Create Equations and Inequalities

Solve Equations and Inequalities

A.CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Create Equations and Inequalities

Solve Equations and Inequalities

A.CED.3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

Create Equations and Inequalities

Create Systems of Equations and Inequalities

Solve Equations and Inequalities

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Algebra 2 – Alignment to Common Core

Standard Study Island Topic

A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohms law V = IR to highlight resistance R.

Rewrite Equations

F.BF.1 - Write a function that describes a relationship between two quantities.

Create Equations and Inequalities

b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

F.BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Function Transformations

F.BF.4 - Find inverse functions.

Inverse Functions

a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2 x

3 or f(x) = (x+1)/(x-1) for x ≠ 1.

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Algebra 2 – Alignment to Common Core

Standard Study Island Topic

F.IF.4 - For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Interpret Functions in Context

F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

Interpret Functions in Context

F.IF.6 - Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Interpret Functions in Context

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Algebra 2 – Alignment to Common Core

Standard Study Island Topic

F.IF.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Selecting Function Type from Context

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Properties of Functions

Selecting Function Type from Context

F.IF.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Properties of Functions

F.LE.4 - For exponential models, express as a logarithm the solution to a b

ct = d where a, c, and d are

numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Solve Exponential Models with Logarithms

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Algebra 2 – Alignment to Common Core

Standard Study Island Topic

Unit 4: Inferences and Conclusions from Data

S.IC.1 - Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Sampling and Experiments

S.IC.2 - Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

Sampling and Experiments

S.IC.3 - Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Sampling and Experiments

S.IC.4 - Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

Sampling and Experiments

S.IC.5 - Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Sampling and Experiments

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Algebra 2 – Alignment to Common Core

Standard Study Island Topic

S.IC.6 - Evaluate reports based on data. Sampling and Experiments

S.ID.4 - Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Normal Distribution

S.MD.6 (+) - Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Probability and Decision Making

S.MD.7 (+) - Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Probability and Decision Making

(290)

Appendix G.

Study Island Benchmark Assessment Alignment to the Common Core State Standards

Grades 3–11 English Language Arts Standards Maps

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Grade 3 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Literature

Key Ideas and Details

3.RL.1 - Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.

Asking and Answering Questions

3.RL.2 - Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed through key details in the text.

Lessons and Morals

Recounting Stories

3.RL.3 - Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events.

Characters

Sequence of Events

Setting

Craft and Structure

3.RL.4 - Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language.

Distinguishing Figurative Language

3.RL.5 - Refer to parts of stories, dramas, and poems when writing or speaking about a text, using terms such as chapter, scene, and stanza; describe how each successive part builds on earlier sections.

Parts of Text

3.RL.6 - Distinguish their own point of view from that of the narrator or those of the characters.

Point of View

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Grade 3 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Integration of Knowledge and Ideas

3.RL.7 - Explain how specific aspects of a texts illustrations contribute to what is conveyed by the words in a story (e.g., create mood, emphasize aspects of a character or setting).

Visual Elements

3.RL.9 - Compare and contrast the themes, settings, and plots of stories written by the same author about the same or similar characters (e.g., in books from a series).

Compare and Contrast

Range and Level of Text Complexity

3.RL.10 - By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 23 text complexity band independently and proficiently.

N.A.

Reading Standards for Informational Text

Key Ideas and Details

3.IT.1 - Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.

Asking and Answering Questions

3.IT.2 - Determine the main idea of a text; recount the key details and explain how they support the main idea.

Main Idea

Recounting Stories

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Grade 3 Language-Arts – Alignment to Common Core

Standard Study Island Topic

3.IT.3 - Describe the relationship between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text, using language that pertains to time, sequence, and cause/effect.

Cause and Effect

Compare and Contrast

Sequence of Events

Craft and Structure

3.IT.4 - Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area.

Academic Language

3.IT.5 - Use text features and search tools (e.g., key words, sidebars, hyperlinks) to locate information relevant to a given topic efficiently.

Text Features

3.IT.6 - Distinguish their own point of view from that of the author of a text.

Prior Knowledge and Beliefs

Integration of Knowledge and Ideas

3.IT.7 - Use information gained from illustrations (e.g., maps, photographs) and the words in a text to demonstrate understanding of the text (e.g., where, when, why, and how key events occur).

Visual Elements

3.IT.8 - Describe the logical connection between particular sentences and paragraphs in a text (e.g., comparison, cause/effect, first/second/third in a sequence).

Logical Connections

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Grade 3 Language-Arts – Alignment to Common Core

Standard Study Island Topic

3.IT.9 - Compare and contrast the most important points and key details presented in two texts on the same topic.

Compare and Contrast

Range and Level of Text Complexity

3.IT.10 - By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 23 text complexity band independently and proficiently.

N.A.

Reading Standards: Foundational Skills

Phonics and Word Recognition

3.F.3 - Know and apply grade-level phonics and word analysis skills in decoding words.

Roots and Affixes

Spelling

a. Identify and know the meaning of the most common prefixes and derivational suffixes.

Syllable Patterns

b. Decode words with common Latin suffixes.

c. Decode multisyllable words. d. Read grade-appropriate irregularly

spelled words.

Fluency

3.F.4 - Read with sufficient accuracy and fluency to support comprehension.

N.A.

a. Read on-level text with purpose and understanding.

b. Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.

c. Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

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Grade 3 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Writing Standards

Text Types and Purposes

3.W.1 - Write opinion pieces on topics or texts, supporting a point of view with reasons.

Appropriate Links

Introducing and Closing Topics

a. Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons.

Logical Connections

b. Provide reasons that support the opinion.

Providing Reasons and Details

c. Use linking words and phrases (e.g., because, therefore, since, for example) to connect opinion and reasons.

d. Provide a concluding statement or section.

3.W.2 - Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

Appropriate Links

Introducing and Closing Topics

a. Introduce a topic and group related information together; include illustrations when useful to aiding comprehension.

Logical Connections

b. Develop the topic with facts, definitions, and details.

Providing Reasons and Details

c. Use linking words and phrases (e.g., also, another, and, more, but) to connect ideas within categories of information.

d. Provide a concluding statement or section.

(296)

Grade 3 Language-Arts – Alignment to Common Core

Standard Study Island Topic

3.W.3 - Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.

Appropriate Links

Employing Dialogue

a. Establish a situation and introduce a narrator and/or characters; organize an event sequence that unfolds naturally.

Introducing and Closing Topics

b. Use dialogue and descriptions of actions, thoughts, and feelings to develop experiences and events or show the response of characters to situations.

Logical Connections

c. Use temporal words and phrases to signal event order.

d. Provide a sense of closure.

Production and Distribution of Writing

3.W.4 - With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose. (Grade-specific expectations for writing types are defined in standards 13 above.)

Task, Purpose, and Audience

3.W.5 - With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. (Editing for conventions should demonstrate command of Language standards 13 up to and including grade 3 on pages 28 and 29.)

Editing

Planning

Revising

3.W.6 - With guidance and support from adults, use technology to produce and publish writing (using keyboarding skills) as well as to interact and collaborate with others.

N.A.

(297)

Grade 3 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Research to Build Knowledge

3.W.7 - Conduct short research projects that build knowledge about a topic.

Gathering Information

3.W.8 - Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories.

Gathering Information

Taking Notes

Language Standards

Conventions in Writing and Speaking

3.L.1 - Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Adjectives and Adverbs

Nouns

a. Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences.

Pronouns

b. Form and use regular and irregular plural nouns.

Simple, Compound, and Complex Sentences

c. Use abstract nouns (e.g., childhood).

Subject-Verb Agreement

d. Form and use regular and irregular verbs.

Verbs

e. Form and use the simple (e.g., I walked; I walk; I will walk) verb tenses.

f. Ensure subject-verb and pronoun-antecedent agreement.*

g. Form and use comparative and superlative adjectives and adverbs, and choose between them depending on what is to be modified.

h. Use coordinating and subordinating conjunctions.

i. Produce simple, compound, and complex sentences.

(298)

Grade 3 Language-Arts – Alignment to Common Core

Standard Study Island Topic

3.L.2 - Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Capitalization

Possessives

a. Capitalize appropriate words in titles.

Punctuation

b. Use commas in addresses. Reference Materials

c. Use commas and quotation marks in dialogue.

Spelling

d. Form and use possessives. Syllable Patterns

e. Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness).

f. Use spelling patterns and generalizations (e.g., word families, position-based spellings, syllable patterns, ending rules, meaningful word parts) in writing words.

g. Consult reference materials, including beginning dictionaries, as needed to check and correct spellings.

Knowledge of Language

3.L.3 - Use knowledge of language and its conventions when writing, speaking, reading, or listening.

Using Words for Effect

a. Choose words and phrases for effect.*

b. Recognize and observe differences between the conventions of spoken and written standard English.

(299)

Grade 3 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Vocabulary Acquisition and Use

3.L.4 - Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies.

Context Clues

Multiple-Meaning Words

a. Use sentence-level context as a clue to the meaning of a word or phrase.

Reference Materials

b. Determine the meaning of the new word formed when a known affix is added to a known word (e.g., agreeable/disagreeable, comfortable/uncomfortable, care/careless, heat/preheat).

Roots and Affixes

c. Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., company, companion).

d. Use glossaries or beginning dictionaries, both print and digital, to determine or clarify the precise meaning of key words and phrases.

3.L.5 - Demonstrate understanding of word relationships and nuances in word meanings.

Connecting and Distinguishing Words

Distinguishing Figurative Language

a. Distinguish the literal and nonliteral meanings of words and phrases in context (e.g., take steps).

b. Identify real-life connections between words and their use (e.g., describe people who are friendly or helpful).

c. Distinguish shades of meaning among related words that describe states of mind or degrees of certainty (e.g., knew, believed, suspected, heard, wondered).

(300)

Grade 3 Language-Arts – Alignment to Common Core

Standard Study Island Topic

3.L.6 - Acquire and use accurately grade-appropriate conversational, general academic, and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them).

Embedded

(301)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Literature

Key Ideas and Details

4.RL.1 - Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.

Drawing Inferences

Events

Supporting Statements

4.RL.2 - Determine a theme of a story, drama, or poem from details in the text; summarize the text.

Summarizing Texts

Theme

4.RL.3 - Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g., a characters thoughts, words, or actions).

Characters

Events

Setting

Craft and Structure

4.RL.4 - Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters found in mythology (e.g., Herculean).

Characters

4.RL.5 - Explain major differences between poems, drama, and prose, and refer to the structural elements of poems (e.g., verse, rhythm, meter) and drama (e.g., casts of characters, settings, descriptions, dialogue, stage directions) when writing or speaking about a text.

Poetry and Drama

(302)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

4.RL.6 - Compare and contrast the point of view from which different stories are narrated, including the difference between first- and third-person narrations.

Comparing Point of View

Integration of Knowledge and Ideas

4.RL.7 - Make connections between the text of a story or drama and a visual or oral presentation of the text, identifying where each version reflects specific descriptions and directions in the text.

Visual Elements

4.RL.9 - Compare and contrast the treatment of similar themes and topics (e.g., opposition of good and evil) and patterns of events (e.g., the quest) in stories, myths, and traditional literature from different cultures.

Compare and Contrast

Range and Level of Text Complexity

4.RL.10 - By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 45 text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

(303)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Informational Text

Key Ideas and Details

4.IT.1 - Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.

Drawing Inferences

Supporting Statements

4.IT.2 - Determine the main idea of a text and explain how it is supported by key details; summarize the text.

Main Idea and Supporting Details

Summarizing Texts

4.IT.3 - Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text.

Explaining Events, Procedures, and Ideas

Craft and Structure

4.IT.4 - Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area.

Context Clues

4.IT.5 - Describe the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in a text or part of a text.

Text Structure

4.IT.6 - Compare and contrast a firsthand and secondhand account of the same event or topic; describe the differences in focus and the information provided.

Compare and Contrast

(304)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Integration of Knowledge and Ideas

4.IT.7 - Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears.

Visual Elements

4.IT.8 - Explain how an author uses reasons and evidence to support particular points in a text.

Supporting Statements

4.IT.9 - Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably.

Gathering Relevant Information

Range and Level of Text Complexity

4.IT.10 - By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 45 text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

Reading Standards: Foundational Skills

Phonics and Word Recognition

4.F.3 - Know and apply grade-level phonics and word analysis skills in decoding words.

Embedded

a. Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context.

(305)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Fluency

4.F.4 - Read with sufficient accuracy and fluency to support comprehension.

N.A.

a. Read on-level text with purpose and understanding.

b. Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.

c. Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

Writing Standards

Text Types and Purposes

4.W.1 - Write opinion pieces on topics or texts, supporting a point of view with reasons and information.

Introducing and Closing Topics

Sensory Words and Phrases

a. Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writers purpose.

Supporting Facts and Details

b. Provide reasons that are supported by facts and details.

Transitional Words and Phrases

c. Link opinion and reasons using words and phrases (e.g., for instance, in order to, in addition).

d. Provide a concluding statement or section related to the opinion presented.

(306)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

4.W.2 - Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

Headings

Introducing and Closing Topics

a. Introduce a topic clearly and group related information in paragraphs and sections; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.

Sensory Words and Phrases

b. Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.

Supporting Facts and Details

c. Link ideas within categories of information using words and phrases (e.g., another, for example, also, because).

Transitional Words and Phrases

d. Use precise language and domain-specific vocabulary to inform about or explain the topic.

e. Provide a concluding statement or section related to the information or explanation presented.

(307)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

4.W.3 - Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.

Introducing and Closing Topics

Sensory Words and Phrases

a. Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally.

Transitional Words and Phrases

b. Use dialogue and description to develop experiences and events or show the responses of characters to situations.

c. Use a variety of transitional words and phrases to manage the sequence of events.

d. Use concrete words and phrases and sensory details to convey experiences and events precisely.

e. Provide a conclusion that follows from the narrated experiences or events.

Production and Distribution of Writing

4.W.4 - Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 13 above.)

Task, Purpose, and Audience

(308)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

4.W.5 - With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. (Editing for conventions should demonstrate command of Language standards 13 up to and including grade 4 on pages 28 and 29.)

Editing

Planning

Revising

4.W.6 - With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting.

N.A.

Research to Build Knowledge

4.W.7 - Conduct short research projects that build knowledge through investigation of different aspects of a topic.

Gathering Relevant Information

4.W.8 - Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and categorize information, and provide a list of sources.

Gathering Relevant Information

Taking Notes

(309)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

4.W.9 - Draw evidence from literary or informational texts to support analysis, reflection, and research.

N.A.

a. Apply grade 4 Reading standards to literature (e.g., Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text [e.g., a characters thoughts, words, or actions].).

b. Apply grade 4 Reading standards to informational texts (e.g., Explain how an author uses reasons and evidence to support particular points in a text).

Range of Writing

4.W.10 - Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

N.A.

(310)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Language Standards

Conventions in Writing and Speaking

4.L.1 - Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Adjectives

Complete Sentences

a. Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why).

Frequently Confused Words

b. Form and use the progressive (e.g., I was walking; I am walking; I will be walking) verb tenses.

Prepositional Phrases

c. Use modal auxiliaries (e.g., can, may, must) to convey various conditions.

Relative Pronouns and Relative Adverbs

d. Order adjectives within sentences according to conventional patterns (e.g., a small red bag rather than a red small bag).

Spelling

e. Form and use prepositional phrases.

Subject-Verb Agreement

f. Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons.*

Verbs

g. Correctly use frequently confused words (e.g., to, too, two; there, their).*

(311)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

4.L.2 - Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Capitalization

Punctuation

a. Use correct capitalization. Spelling

b. Use commas and quotation marks to mark direct speech and quotations from a text.

c. Use a comma before a coordinating conjunction in a compound sentence.

d. Spell grade-appropriate words correctly, consulting references as needed.

Knowledge of Language

4.L.3 - Use knowledge of language and its conventions when writing, speaking, reading, or listening.

Punctuation

Sensory Words and Phrases

a. Choose words and phrases to convey ideas precisely.*

b. Choose punctuation for effect.*

c. Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion).

(312)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Vocabulary Acquisition and Use

4.L.4 - Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies.

Context Clues

Multiple-Meaning Words

a. Use context (e.g., definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase.

Roots and Affixes

b. Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph).

c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.

4.L.5 - Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

Idioms, Adages, and Proverbs

Similes and Metaphors

a. Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context.

Synonyms and Antonyms

b. Recognize and explain the meaning of common idioms, adages, and proverbs.

c. Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms).

(313)

Grade 4 Language-Arts – Alignment to Common Core

Standard Study Island Topic

4.L.6 - Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation).

Embedded

(314)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Literature

Key Ideas and Details

5.RL.1 - Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.

Drawing Inferences

Supporting Statements

5.RL.2 - Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text.

Characters

Summarizing Texts

Theme

5.RL.3 - Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details in the text (e.g., how characters interact).

Compare and Contrast

Events

Setting

Craft and Structure

5.RL.4 - Determine the meaning of words and phrases as they are used in a text, including figurative language such as metaphors and similes.

Metaphors and Similes

5.RL.5 - Explain how a series of chapters, scenes, or stanzas fits together to provide the overall structure of a particular story, drama, or poem.

Structures of Texts

(315)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

5.RL.6 - Describe how a narrators or speakers point of view influences how events are described.

Narrator's Point of View

Integration of Knowledge and Ideas

5.RL.7 - Analyze how visual and multimedia elements contribute to the meaning, tone, or beauty of a text (e.g., graphic novel, multimedia presentation of fiction, folktale, myth, poem).

Visual Elements

5.RL.9 - Compare and contrast stories in the same genre (e.g., mysteries and adventure stories) on their approaches to similar themes and topics.

Compare and Contrast

Range and Level of Text Complexity

5.RL.10 - By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 45 text complexity band independently and proficiently.

N.A.

Reading Standards for Informational Text

Key Ideas and Details

5.IT.1 - Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.

Drawing Inferences

Supporting Statements

5.IT.2 - Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text.

Main Idea and Supporting Details

Summarizing Texts

(316)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

5.IT.3 - Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text.

Compare and Contrast

Main Idea and Supporting Details

Craft and Structure

5.IT.4 - Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area.

Context Clues

5.IT.5 - Compare and contrast the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in two or more texts.

Text Structure

5.IT.6 - Analyze multiple accounts of the same event or topic, noting important similarities and differences in the point of view they represent.

Compare and Contrast

Integration of Knowledge and Ideas

5.IT.7 - Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently.

Locating Answers

5.IT.8 - Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s).

Using Evidence to Support Claims

(317)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

5.IT.9 - Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably.

Gathering Relevant Information

Range and Level of Text Complexity

5.IT.10 - By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 45 text complexity band independently and proficiently.

N.A.

Reading Standards: Foundational Skills

Phonics and Word Recognition

5.F.3 - Know and apply grade-level phonics and word analysis skills in decoding words.

Embedded

a. Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context.

Fluency

5.F.4 - Read with sufficient accuracy and fluency to support comprehension.

N.A.

a. Read on-level text with purpose and understanding.

b. Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.

c. Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

(318)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Writing Standards

Text Types and Purposes

5.W.1 - Write opinion pieces on topics or texts, supporting a point of view with reasons and information.

Supporting Facts and Details

Transitional Words and Phrases

a. Introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped to support the writers purpose.

b. Provide logically ordered reasons that are supported by facts and details.

c. Link opinion and reasons using words, phrases, and clauses (e.g., consequently, specifically).

d. Provide a concluding statement or section related to the opinion presented.

(319)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

5.W.2 - Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

Headings and Illustrations

Supporting Facts and Details

a. Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.

Transitional Words and Phrases

b. Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.

c. Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially).

d. Use precise language and domain-specific vocabulary to inform about or explain the topic.

e. Provide a concluding statement or section related to the information or explanation presented.

(320)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

5.W.3 - Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.

Choosing Words Precisely

Transitional Words and Phrases

a. Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally.

b. Use narrative techniques, such as dialogue, description, and pacing, to develop experiences and events or show the responses of characters to situations.

c. Use a variety of transitional words, phrases, and clauses to manage the sequence of events.

d. Use concrete words and phrases and sensory details to convey experiences and events precisely.

e. Provide a conclusion that follows from the narrated experiences or events.

Production and Distribution of Writing

5.W.4 - Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 13 above.)

Task, Purpose, and Audience

(321)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

5.W.5 - With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach. (Editing for conventions should demonstrate command of Language standards 13 up to and including grade 5 on pages 28 and 29.)

Editing

Planning

Revising

5.W.6 - With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of two pages in a single sitting.

N.A.

Research to Build Knowledge

5.W.7 - Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic.

Gathering Relevant Information

5.W.8 - Recall relevant information from experiences or gather relevant information from print and digital sources; summarize or paraphrase information in notes and finished work, and provide a list of sources.

Bibliographic Information

Gathering Relevant Information

Paraphrasing in Notes

(322)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

5.W.9 - Draw evidence from literary or informational texts to support analysis, reflection, and research.

N.A.

a. Apply grade 5 Reading standards to literature (e.g., Compare and contrast two or more characters, settings, or events in a story or a drama, drawing on specific details in the text [e.g., how characters interact]).

b. Apply grade 5 Reading standards to informational texts (e.g., Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point[s]).

Range of Writing

5.W.10 - Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

N.A.

(323)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Language Standards

Conventions in Writing and Speaking

5.L.1 - Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Adjectives and Adverbs

Conjunctions and Interjections

a. Explain the function of conjunctions, prepositions, and interjections in general and their function in particular sentences.

Prepositional Phrases

b. Form and use the perfect (e.g., I had walked; I have walked; I will have walked) verb tenses.

Pronoun-Antecedent Agreement

c. Use verb tense to convey various times, sequences, states, and conditions.

Subject-Verb Agreement

d. Recognize and correct inappropriate shifts in verb tense.*

Verbs

e. Use correlative conjunctions (e.g., either/or, neither/nor).

5.L.2 - Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Capitalization

Punctuation

a. Use punctuation to separate items in a series.*

Spelling

b. Use a comma to separate an introductory element from the rest of the sentence.

c. Use a comma to set off the words yes and no (e.g., Yes, thank you), to set off a tag question from the rest of the sentence (e.g., Its true, isnt it?), and to indicate direct address (e.g., Is that you, Steve?).

d. Use underlining, quotation marks, or italics to indicate titles of works.

e. Spell grade-appropriate words correctly, consulting references as needed.

(324)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Knowledge of Language

5.L.3 - Use knowledge of language and its conventions when writing, speaking, reading, or listening.

Compare and Contrast

Revising

a. Expand, combine, and reduce sentences for meaning, reader/listener interest, and style.

b. Compare and contrast the varieties of English (e.g., dialects, registers) used in stories, dramas, or poems.

Vocabulary Acquisition and Use

5.L.4 - Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 5 reading and content, choosing flexibly from a range of strategies.

Context Clues

Metaphors and Similes

a. Use context (e.g., cause/effect relationships and comparisons in text) as a clue to the meaning of a word or phrase.

Multiple Meaning Words

b. Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., photograph, photosynthesis).

Roots and Affixes

c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.

(325)

Grade 5 Language-Arts – Alignment to Common Core

Standard Study Island Topic

5.L.5 - Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

Idioms, Adages, and Proverbs

Synonyms and Antonyms

a. Interpret figurative language, including similes and metaphors, in context.

b. Recognize and explain the meaning of common idioms, adages, and proverbs.

c. Use the relationship between particular words (e.g., synonyms, antonyms, homographs) to better understand each of the words.

5.L.6 - Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although, nevertheless, similarly, moreover, in addition).

Embedded

(326)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Literature

Key Ideas and Details

6.RL.1 - Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Inferences

Textual Evidence

6.RL.2 - Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments.

Summary

Theme

6.RL.3 - Describe how a particular storys or dramas plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves toward a resolution.

Characters

Plot

Craft and Structure

6.RL.4 - Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of a specific word choice on meaning and tone.

Connotative Meanings

Figurative Meanings

Meaning and Tone

(327)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

6.RL.5 - Analyze how a particular sentence, chapter, scene, or stanza fits into the overall structure of a text and contributes to the development of the theme, setting, or plot.

Plot

Setting

Theme

6.RL.6 - Explain how an author develops the point of view of the narrator or speaker in a text.

Point of View

Integration of Knowledge and Ideas

6.RL.7 - Compare and contrast the experience of reading a story, drama, or poem to listening to or viewing an audio, video, or live version of the text, including contrasting what they see and hear when reading the text to what they perceive when they listen or watch.

N.A.

6.RL.9 - Compare and contrast texts in different forms or genres (e.g., stories and poems; historical novels and fantasy stories) in terms of their approaches to similar themes and topics.

Compare and Contrast

Range and Level of Text Complexity

6.RL.10 - By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

(328)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Informational Text

Key Ideas and Details

6.IT.1 - Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Inferences

Textual Evidence

6.IT.2 - Determine a central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments.

Central Ideas

Summary

6.IT.3 - Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text (e.g., through examples or anecdotes).

Central Ideas

Summary

Textual Evidence

Craft and Structure

6.IT.4 - Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.

Connotative Meanings

Figurative Meanings

6.IT.5 - Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of a text and contributes to the development of the ideas.

Central Ideas

Structure

6.IT.6 - Determine an authors point of view or purpose in a text and explain how it is conveyed in the text.

Point of View

Task, Purpose, and Audience

(329)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Integration of Knowledge and Ideas

6.IT.7 - Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue.

Gathering Relevant Information

6.IT.8 - Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not.

Evaluating Arguments

6.IT.9 - Compare and contrast one authors presentation of events with that of another (e.g., a memoir written by and a biography on the same person).

Compare and Contrast

Range and Level of Text Complexity

6.IT.10 - By the end of the year, read and comprehend literary nonfiction in the grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

(330)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Writing Standards

Text Types and Purposes

6.W.1 - Write arguments to support claims with clear reasons and relevant evidence.

Gathering Relevant Information

Introducing and Closing Topics

a. Introduce claim(s) and organize the reasons and evidence clearly.

Supporting and Developing Topics

b. Support claim(s) with clear reasons and relevant evidence, using credible sources and demonstrating an understanding of the topic or text.

Task, Purpose, and Audience

c. Use words, phrases, and clauses to clarify the relationships among claim(s) and reasons.

d. Establish and maintain a formal style.

e. Provide a concluding statement or section that follows from the argument presented.

(331)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

6.W.2 - Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.

Appropriate Transitions

Headings and Graphics

a. Introduce a topic; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.

Introducing and Closing Topics

b. Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples.

Structure

c. Use appropriate transitions to clarify the relationships among ideas and concepts.

Supporting and Developing Topics

d. Use precise language and domain-specific vocabulary to inform about or explain the topic.

Task, Purpose, and Audience

e. Establish and maintain a formal style.

Varied Sentence Structure

f. Provide a concluding statement or section that follows from the information or explanation presented.

(332)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

6.W.3 - Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.

Appropriate Transitions

Introducing and Closing Topics

a. Engage and orient the reader by establishing a context and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically.

Sensory Details

b. Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters.

Task, Purpose, and Audience

c. Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another.

d. Use precise words and phrases, relevant descriptive details, and sensory language to convey experiences and events.

e. Provide a conclusion that follows from the narrated experiences or events.

Production and Distribution of Writing

6.W.4 - Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 13 above.)

Task, Purpose, and Audience

(333)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

6.W.5 - With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach. (Editing for conventions should demonstrate command of Language standards 13 up to and including grade 6 on page 52.)

Editing

Planning

Revising

6.W.6 - Use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of three pages in a single sitting.

N.A.

Research to Build Knowledge

6.W.7 - Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate.

Gathering Relevant Information

6.W.8 - Gather relevant information from multiple print and digital sources; assess the credibility of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and providing basic bibliographic information for sources.

Citing Sources

Gathering Relevant Information

Quoting and Paraphrasing Data

(334)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

6.W.9 - Draw evidence from literary or informational texts to support analysis, reflection, and research.

N.A.

a. Apply grade 6 Reading standards to literature (e.g., Compare and contrast texts in different forms or genres [e.g., stories and poems; historical novels and fantasy stories] in terms of their approaches to similar themes and topics).

b. Apply grade 6 Reading standards to literary nonfiction (e.g., Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not).

Range of Writing

6.W.10 - Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

N.A.

(335)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Language Standards

Conventions in Writing and Speaking

6.L.1 - Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Adjectives and Adverbs

Pronouns

a. Ensure that pronouns are in the proper case (subjective, objective, possessive).

Subject-Verb Agreement

b. Use intensive pronouns (e.g., myself, ourselves).

c. Recognize and correct inappropriate shifts in pronoun number and person.*

d. Recognize and correct vague pronouns (i.e., ones with unclear or ambiguous antecedents).*

e. Recognize variations from standard English in their own and otherswriting and speaking, and identify and use strategies to improve expression in conventional language.*

6.L.2 - Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Capitalization

Punctuation

a. Use punctuation (commas, parentheses, dashes) to set off nonrestrictive/parenthetical elements.*

Spelling

b. Spell correctly.

(336)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Knowledge of Language

6.L.3 - Use knowledge of language and its conventions when writing, speaking, reading, or listening.

Task, Purpose, and Audience

Varied Sentence Structure

a. Vary sentence patterns for meaning, reader/listener interest, and style.*

b. Maintain consistency in style and tone.*

Vocabulary Acquisition and Use

6.L.4 - Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 6 reading and content, choosing flexibly from a range of strategies.

Context Clues

Dictionaries

a. Use context (e.g., the overall meaning of a sentence or paragraph; a words position or function in a sentence) as a clue to the meaning of a word or phrase.

Multiple Meaning Words

b. Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., audience, auditory, audible).

Roots and Affixes

c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech.

d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).

(337)

Grade 6 Language-Arts – Alignment to Common Core

Standard Study Island Topic

6.L.5 - Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

Connotative Meanings

Figurative Meanings

a. Interpret figures of speech (e.g., personification) in context.

Interrelationships of Words

b. Use the relationship between particular words (e.g., cause/effect, part/whole, item/category) to better understand each of the words.

c. Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., stingy, scrimping, economical, unwasteful, thrifty).

6.L.6 - Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Embedded

(338)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Literature

Key Ideas and Details

7.RL.1 - Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Inferences

Textual Evidence

7.RL.2 - Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text.

Summary

Theme

7.RL.3 - Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot).

Characterization

Development of Plot

Setting

Craft and Structure

7.RL.4 - Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of rhymes and other repetitions of sounds (e.g., alliteration) on a specific verse or stanza of a poem or section of a story or drama.

Connotative Meanings

Figurative Meanings

Rhymes and Repetition of Sounds

(339)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

7.RL.5 - Analyze how a dramas or poems form or structure (e.g., soliloquy, sonnet) contributes to its meaning.

Development of Plot

7.RL.6 - Analyze how an author develops and contrasts the points of view of different characters or narrators in a text.

Point of View

Integration of Knowledge and Ideas

7.RL.7 - Compare and contrast a written story, drama, or poem to its audio, filmed, staged, or multimedia version, analyzing the effects of techniques unique to each medium (e.g., lighting, sound, color, or camera focus and angles in a film).

N.A.

7.RL.9 - Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history.

Compare and Contrast

Range and Level of Text Complexity

7.RL.10 - By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

Reading Standards for Informational Text

Key Ideas and Details

7.IT.1 - Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Inferences

Textual Evidence

(340)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

7.IT.2 - Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text.

Central Ideas and Key Details

Summary

7.IT.3 - Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how individuals influence ideas or events).

Central Ideas and Key Details

Compare and Contrast

Textual Evidence

Craft and Structure

7.IT.4 - Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone.

Connotative Meanings

Figurative Meanings

Meaning and Tone

7.IT.5 - Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to the development of the ideas.

Central Ideas and Key Details

Text Structure

7.IT.6 - Determine an authors point of view or purpose in a text and analyze how the author distinguishes his or her position from that of others.

Author's Point of View

Task, Purpose, and Audience

(341)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Integration of Knowledge and Ideas

7.IT.7 - Compare and contrast a text to an audio, video, or multimedia version of the text, analyzing each mediums portrayal of the subject (e.g., how the delivery of a speech affects the impact of the words).

N.A.

7.IT.8 - Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims.

Evaluating Arguments

7.IT.9 - Analyze how two or more authors writing about the same topic shape their presentations of key information by emphasizing different evidence or advancing different interpretations of facts.

Compare and Contrast

Range and Level of Text Complexity

7.IT.10 - By the end of the year, read and comprehend literary nonfiction in the grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

(342)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Writing Standards

Text Types and Purposes

7.W.1 - Write arguments to support claims with clear reasons and relevant evidence.

Supporting and Developing Topics

a. Introduce claim(s), acknowledge alternate or opposing claims, and organize the reasons and evidence logically.

b. Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.

c. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), reasons, and evidence.

d. Establish and maintain a formal style.

e. Provide a concluding statement or section that follows from and supports the argument presented.

(343)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

7.W.2 - Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.

Appropriate Transitions

Headings and Graphics

a. Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.

Precise Language and Sensory Details

b. Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples.

Supporting and Developing Topics

c. Use appropriate transitions to create cohesion and clarify the relationships among ideas and concepts.

Text Structure

d. Use precise language and domain-specific vocabulary to inform about or explain the topic.

Varied Sentence Structure

e. Establish and maintain a formal style.

f. Provide a concluding statement or section that follows from and supports the information or explanation presented.

(344)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

7.W.3 - Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.

Appropriate Transitions

Precise Language and Sensory Details

a. Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically.

b. Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters.

c. Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another.

d. Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events.

e. Provide a conclusion that follows from and reflects on the narrated experiences or events.

(345)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Production and Distribution of Writing

7.W.4 - Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 13 above.)

Task, Purpose, and Audience

7.W.5 - With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed. (Editing for conventions should demonstrate command of Language standards 13 up to and including grade 7 on page 52.)

Editing

Planning

Revising

7.W.6 - Use technology, including the Internet, to produce and publish writing and link to and cite sources as well as to interact and collaborate with others, including linking to and citing sources.

Citing Information

(346)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Research to Build Knowledge

7.W.7 - Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation.

Gathering Information

7.W.8 - Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

Citing Information

Gathering Information

7.W.9 - Draw evidence from literary or informational texts to support analysis, reflection, and research.

N.A.

a. Apply grade 7 Reading standards to literature (e.g., Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history).

b. Apply grade 7 Reading standards to literary nonfiction (e.g. Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims).

(347)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Range of Writing

7.W.10 - Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

N.A.

Language Standards

Conventions in Writing and Speaking

7.L.1 - Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Adjectives and Adverbs

Misplaced and Dangling Modifiers

a. Explain the function of phrases and clauses in general and their function in specific sentences.

Phrases and Clauses

b. Choose among simple, compound, complex, and compound-complex sentences to signal differing relationships among ideas.

Pronouns

c. Place phrases and clauses within a sentence, recognizing and correcting misplaced and dangling modifiers.*

Subject-Verb Agreement

7.L.2 - Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Capitalization

Punctuation

a. Use a comma to separate coordinate adjectives (e.g., It was a fascinating, enjoyable movie but not He wore an old[,] green shirt).

Spelling

b. Spell correctly.

(348)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Knowledge of Language

7.L.3 - Use knowledge of language and its conventions when writing, speaking, reading, or listening.

Varied Sentence Structure

a. Choose language that expresses ideas precisely and concisely, recognizing and eliminating wordiness and redundancy.*

Vocabulary Acquisition and Use

7.L.4 - Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 7 reading and content, choosing flexibly from a range of strategies.

Context Clues

Multiple Meaning Words

a. Use context (e.g., the overall meaning of a sentence or paragraph; a words position or function in a sentence) as a clue to the meaning of a word or phrase.

Reference Materials

b. Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., belligerent, bellicose, rebel).

Roots and Affixes

c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech.

d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).

(349)

Grade 7 Language-Arts – Alignment to Common Core

Standard Study Island Topic

7.L.5 - Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

Connotative Meanings

Figurative Meanings

a. Interpret figures of speech (e.g., literary, biblical, and mythological allusions) in context.

Interrelationships of Words

b. Use the relationship between particular words (e.g., synonym/antonym, analogy) to better understand each of the words.

c. Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., refined, respectful, polite, diplomatic, condescending).

7.L.6 - Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Embedded

(350)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Literature

Key Ideas and Details

8.RL.1 - Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text.

Inferences

Textual Evidence

8.RL.2 - Determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text.

Objective Summary

Theme

8.RL.3 - Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision.

Characters

Plot

Setting

Craft and Structure

8.RL.4 - Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts.

Analyzing Comparisons

Denotations and Connotations

Interpreting Figures of Speech

Meaning and Tone

Relationships Between Words

(351)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

8.RL.5 - Compare and contrast the structure of two or more texts and analyze how the differing structure of each text contributes to its meaning and style.

Compare and Contrast

8.RL.6 - Analyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor.

Producing Suspense and Humor

Integration of Knowledge and Ideas

8.RL.7 - Analyze the extent to which a filmed or live production of a story or drama stays faithful to or departs from the text or script, evaluating the choices made by the director or actors.

N.A.

8.RL.9 - Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new.

Compare and Contrast

Range and Level of Text Complexity

8.RL.10 - By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of grades 68 text complexity band independently and proficiently.

N.A.

(352)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Informational Text

Key Ideas and Details

8.IT.1 - Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text.

Inferences

Textual Evidence

8.IT.2 - Determine a central idea of a text and analyze its development over the course of the text, including its relationship to supporting ideas; provide an objective summary of the text.

Central Ideas

Objective Summary

8.IT.3 - Analyze how a text makes connections among and distinctions between individuals, ideas, or events (e.g., through comparisons, analogies, or categories).

Analyzing Comparisons

Central Ideas

Compare and Contrast

Interpreting Figures of Speech

Relationships Between Words

Craft and Structure

8.IT.4 - Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts.

Analyzing Comparisons

Denotations and Connotations

Interpreting Figures of Speech

Meaning and Tone

Relationships Between Words

(353)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

8.IT.5 - Analyze in detail the structure of a specific paragraph in a text, including the role of particular sentences in developing and refining a key concept.

Analyzing Structures in Text

8.IT.6 - Determine an authors point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints.

Author's Point of View

Task, Purpose, and Audience

Integration of Knowledge and Ideas

8.IT.7 - Evaluate the advantages and disadvantages of using different mediums (e.g., print or digital text, video, multimedia) to present a particular topic or idea.

Compare and Contrast

8.IT.8 - Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced.

Evaluating Author's Claims

8.IT.9 - Analyze a case in which two or more texts provide conflicting information on the same topic and identify where the texts disagree on matters of fact or interpretation.

Compare and Contrast

Range and Level of Text Complexity

8.IT.10 - By the end of the year, read and comprehend literary nonfiction at the high end of the grades 68 text complexity band independently and proficiently.

N.A.

(354)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Writing Standards

Text Types and Purposes

8.W.1 - Write arguments to support claims with clear reasons and relevant evidence.

Appropriate Transitions

Introducing and Closing Topics

a. Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically.

Supporting and Developing Topics

b. Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.

c. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence.

d. Establish and maintain a formal style.

e. Provide a concluding statement or section that follows from and supports the argument presented.

(355)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

8.W.2 - Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.

Appropriate Transitions

Headings and Graphics

a. Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.

Introducing and Closing Topics

b. Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples.

Precise Language and Sensory Details

c. Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts.

Supporting and Developing Topics

d. Use precise language and domain-specific vocabulary to inform about or explain the topic.

Varied Sentence Structure

e. Establish and maintain a formal style.

f. Provide a concluding statement or section that follows from and supports the information or explanation presented.

(356)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

8.W.3 - Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.

Appropriate Transitions

Introducing and Closing Topics

a. Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically.

Precise Language and Sensory Details

b. Use narrative techniques, such as dialogue, pacing, description, and reflection, to develop experiences, events, and/or characters.

Supporting and Developing Topics

c. Use a variety of transition words, phrases, and clauses to convey sequence, signal shifts from one time frame or setting to another, and show the relationships among experiences and events.

d. Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events.

e. Provide a conclusion that follows from and reflects on the narrated experiences or events.

(357)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Production and Distribution of Writing

8.W.4 - Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 13 above.)

Task, Purpose, and Audience

8.W.5 - With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed. (Editing for conventions should demonstrate command of Language standards 13 up to and including grade 8 on page 52.)

Editing

Planning

Revising

8.W.6 - Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas efficiently as well as to interact and collaborate with others.

N.A.

Research to Build Knowledge

8.W.7 - Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

Gathering Relevant Information

(358)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

8.W.8 - Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

Citing Information

Gathering Relevant Information

Quoting and Paraphrasing Data

8.W.9 - Draw evidence from literary or informational texts to support analysis, reflection, and research.

N.A.

a. Apply grade 8 Reading standards to literature (e.g., Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new).

b. Apply grade 8 Reading standards to literary nonfiction (e.g., Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced).

Range of Writing

8.W.10 - Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

N.A.

(359)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Language Standards

Conventions in Writing and Speaking

8.L.1 - Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Active and Passive Voice

Adjectives and Adverbs

a. Explain the function of verbals (gerunds, participles, infinitives) in general and their function in particular sentences.

Phrases and Clauses

b. Form and use verbs in the active and passive voice.

Pronouns

c. Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood.

Subject-Verb Agreement

d. Recognize and correct inappropriate shifts in verb voice and mood.*

Using Verbs in Moods

Verbals

8.L.2 - Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Capitalization

Punctuation

a. Use punctuation (comma, ellipsis, dash) to indicate a pause or break.

Spelling

b. Use an ellipsis to indicate an omission.

c. Spell correctly.

(360)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Knowledge of Language

8.L.3 - Use knowledge of language and its conventions when writing, speaking, reading, or listening.

Active and Passive Voice

Using Verbs in Moods

a. Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact).

Vocabulary Acquisition and Use

8.L.4 - Determine or clarify the meaning of unknown and multiple-meaning words or phrases based on grade 8 reading and content, choosing flexibly from a range of strategies.

Context Clues

Multiple Meaning Words

a. Use context (e.g., the overall meaning of a sentence or paragraph; a words position or function in a sentence) as a clue to the meaning of a word or phrase.

Reference Materials

b. Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., precede, recede, secede).

Roots and Affixes

c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech.

d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).

(361)

Grade 8 Language-Arts – Alignment to Common Core

Standard Study Island Topic

8.L.5 - Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

Denotations and Connotations

Interpreting Figures of Speech

a. Interpret figures of speech (e.g. verbal irony, puns) in context.

Relationships Between Words

b. Use the relationship between particular words to better understand each of the words.

c. Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., bullheaded, willful, firm, persistent, resolute).

8.L.6 - Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Embedded

(362)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Literature

Key Ideas and Details

9-10.RL.1 - Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Inferences

Supporting Analysis

9-10.RL.2 - Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.

Objective Summary

Theme

9-10.RL.3 - Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme.

Characters

Plot

Setting

Theme

(363)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Craft and Structure

9-10.RL.4 - Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone).

Connotation and Denotation

Figures of Speech

Impact and Tone

9-10.RL.5 - Analyze how an authors choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise.

Plot

9-10.RL.6 - Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States, drawing on a wide reading of world literature.

Cultural Experience in Literature

Integration of Knowledge and Ideas

9-10.RL.7 - Analyze the representation of a subject or a key scene in two different artistic mediums, including what is emphasized or absent in each treatment (e.g., Audens Musee des Beaux Artsand Breughels Landscape with the Fall of Icarus).

Compare and Contrast

(364)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.RL.9 - Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare).

Plot

Range of Reading and Level of Text Complexity

9-10.RL.10 - By the end of grade 9, read and comprehend literature, including stories, dramas, and poems, in the grades 910 text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

By the end of grade 10, read and comprehend literature, including stories, dramas, and poems, at the high end of the grades 910 text complexity band independently and proficiently.

Reading Standards for Informational Text

Key Ideas and Details

9-10.IT.1 - Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Inferences

Supporting Analysis

9-10.IT.2 - Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.

Central Ideas

Objective Summary

(365)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.IT.3 - Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them.

Central Ideas

Compare and Contrast

Effectiveness of Structure

Craft and Structure

9-10.IT.4 - Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper).

Connotation and Denotation

Figures of Speech

Impact and Tone

Technical Meanings

9-10.IT.5 - Analyze in detail how an authors ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter).

Effectiveness of Structure

Evaluating Arguments

9-10.IT.6 - Determine an authors point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose.

Author's Point of View

(366)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Integration of Knowledge and Ideas

9-10.IT.7 - Analyze various accounts of a subject told in different mediums (e.g., a persons life story in both print and multimedia), determining which details are emphasized in each account.

Compare and Contrast

9-10.IT.8 - Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning.

Evaluating Arguments

9-10.IT.9 - Analyze seminal U.S. documents of historical and literary significance (e.g., Washingtons Farewell Address, the Gettysburg Address, Roosevelts Four Freedoms speech, Kings Letter from Birmingham Jail), including how they address related themes and concepts.

Analyzing Documents

Range of Reading and Level of Text Complexity

9-10.IT.10 - By the end of grade 9, read and comprehend literary nonfiction in the grades 910 text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

By the end of grade 10, read and comprehend literary nonfiction at the high end of the grades 910 text complexity band independently and proficiently.

(367)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Writing Standards

Text Types and Purposes

9-10.W.1 - Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

Effectiveness of Structure

Introducing and Closing Topics

a. Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence.

Precise Language

b. Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audiences knowledge level and concerns.

Supplying and Developing Evidence

c. Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.

Task, Purpose, and Audience

d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.

Transitions

e. Provide a concluding statement or section that follows from and supports the argument presented.

(368)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.W.2 - Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content.

Effectiveness of Structure

Formatting and Graphics

a. Introduce a topic; organize complex ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.

Introducing and Closing Topics

b. Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audiences knowledge of the topic.

Precise Language

c. Use appropriate and varied transitions to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.

Sentence Structure

d. Use precise language and domain-specific vocabulary to manage the complexity of the topic.

Supplying and Developing Evidence

e. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.

Transitions

f. Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic).

(369)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.W.3 - Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences.

Effectiveness of Structure

Introducing and Closing Topics

a. Engage and orient the reader by setting out a problem, situation, or observation, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events.

Precise Language

b. Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters.

Task, Purpose, and Audience

c. Use a variety of techniques to sequence events so that they build on one another to create a coherent whole.

d. Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters.

e. Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative.

(370)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Production and Distribution of Writing

9-10.W.4 - Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 13 above.)

Task, Purpose, and Audience

9-10.W.5 - Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. (Editing for conventions should demonstrate command of Language standards 13 up to and including grades 910 on page 54.)

Editing

Planning

Revising

9-10.W.6 - Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technologys capacity to link to other information and to display information flexibly and dynamically.

N.A.

(371)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Research to Build and Present Knowledge

9-10.W.7 - Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.

Credibility and Accuracy of Information

9-10.W.8 - Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation.

Credibility and Accuracy of Information

(372)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.W.9 - Draw evidence from literary or informational texts to support analysis, reflection, and research.

N.A.

a. Apply grades 910 Reading standards to literature (e.g., Analyze how an author draws on and transforms source material in a specific work [e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare]).

b. Apply grades 910 Reading standards to literary nonfiction (e.g., Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning).

Range of Writing

9-10.W.10 - Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.

N.A.

(373)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Language Standards

Conventions of Standard English

9-10.L.1 - Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Active and Passive Voice

Adjectives and Adverbs

a. Use parallel structure.* Parallel Structure

b. Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations.

Phrases and Clauses

Pronouns

Sentence Structure

Subject-Verb Agreement

Verb Tense

9-10.L.2 - Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Capitalization

Punctuation

a. Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent clauses.

Spelling

b. Use a colon to introduce a list or quotation.

c. Spell correctly.

(374)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Knowledge of Language

9-10.L.3 - Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.

Editing

a. Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Turabians Manual for Writers) appropriate for the discipline and writing type.

(375)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Vocabulary Acquisition and Use

9-10.L.4 - Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 910 reading and content, choosing flexibly from a range of strategies.

Context Clues

Multiple Meaning Words

a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a words position or function in a sentence) as a clue to the meaning of a word or phrase.

Reference Materials

b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., analyze, analysis, analytical; advocate, advocacy).

c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology.

d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).

(376)

Grade 9 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.L.5 - Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

Connotation and Denotation

Figures of Speech

a. Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text.

b. Analyze nuances in the meaning of words with similar denotations.

9-10.L.6 - Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Embedded

(377)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Literature

Key Ideas and Details

9-10.RL.1 - Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Inferences

Supporting Analysis

9-10.RL.2 - Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.

Objective Summary

Theme

9-10.RL.3 - Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme.

Characters

Plot

Setting

Theme

Craft and Structure

9-10.RL.4 - Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone).

Connotation and Denotation

Figures of Speech

Impact and Tone

(378)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.RL.5 - Analyze how an authors choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise.

Plot

9-10.RL.6 - Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States, drawing on a wide reading of world literature.

Cultural Experience in Literature

Integration of Knowledge and Ideas

9-10.RL.7 - Analyze the representation of a subject or a key scene in two different artistic mediums, including what is emphasized or absent in each treatment (e.g., Audens Musee des Beaux Artsand Breughels Landscape with the Fall of Icarus).

Compare and Contrast

9-10.RL.9 - Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare).

Plot

(379)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Range of Reading and Level of Text Complexity

9-10.RL.10 - By the end of grade 9, read and comprehend literature, including stories, dramas, and poems, in the grades 910 text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

By the end of grade 10, read and comprehend literature, including stories, dramas, and poems, at the high end of the grades 910 text complexity band independently and proficiently.

Reading Standards for Informational Text

Key Ideas and Details

9-10.IT.1 - Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Inferences

Supporting Analysis

9-10.IT.2 - Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.

Central Ideas

Objective Summary

9-10.IT.3 - Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them.

Central Ideas

Compare and Contrast

Effectiveness of Structure

(380)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Craft and Structure

9-10.IT.4 - Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper).

Connotation and Denotation

Figures of Speech

Impact and Tone

9-10.IT.5 - Analyze in detail how an authors ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter).

Effectiveness of Structure

9-10.IT.6 - Determine an authors point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose.

Author's Point of View

Integration of Knowledge and Ideas

9-10.IT.7 - Analyze various accounts of a subject told in different mediums (e.g., a persons life story in both print and multimedia), determining which details are emphasized in each account.

Compare and Contrast

9-10.IT.8 - Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning.

Evaluating Arguments

(381)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.IT.9 - Analyze seminal U.S. documents of historical and literary significance (e.g., Washingtons Farewell Address, the Gettysburg Address, Roosevelts Four Freedoms speech, Kings Letter from Birmingham Jail), including how they address related themes and concepts.

Analyzing Documents

Range of Reading and Level of Text Complexity

9-10.IT.10 - By the end of grade 9, read and comprehend literary nonfiction in the grades 910 text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

By the end of grade 10, read and comprehend literary nonfiction at the high end of the grades 910 text complexity band independently and proficiently.

(382)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Writing Standards

Text Types and Purposes

9-10.W.1 - Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

Effectiveness of Structure

Precise Language

a. Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence.

Supplying and Developing Evidence

b. Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audiences knowledge level and concerns.

Task, Purpose, and Audience

c. Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.

d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.

e. Provide a concluding statement or section that follows from and supports the argument presented.

(383)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.W.2 - Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content.

Effectiveness of Structure

Formatting and Graphics

a. Introduce a topic; organize complex ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.

Precise Language

b. Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audiences knowledge of the topic.

Sentence Structure

c. Use appropriate and varied transitions to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.

Supplying and Developing Evidence

d. Use precise language and domain-specific vocabulary to manage the complexity of the topic.

e. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.

f. Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic).

(384)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.W.3 - Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences.

Effectiveness of Structure

Precise Language

a. Engage and orient the reader by setting out a problem, situation, or observation, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events.

Task, Purpose, and Audience

b. Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters.

c. Use a variety of techniques to sequence events so that they build on one another to create a coherent whole.

d. Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters.

e. Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative.

(385)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Production and Distribution of Writing

9-10.W.4 - Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 13 above.)

Task, Purpose, and Audience

9-10.W.5 - Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. (Editing for conventions should demonstrate command of Language standards 13 up to and including grades 910 on page 54.)

Editing

Planning

Revising

9-10.W.6 - Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technologys capacity to link to other information and to display information flexibly and dynamically.

N.A.

(386)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Research to Build and Present Knowledge

9-10.W.7 - Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.

Credibility and Accuracy of Information

9-10.W.8 - Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation.

Citation Formats

Credibility and Accuracy of Information

(387)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.W.9 - Draw evidence from literary or informational texts to support analysis, reflection, and research.

N.A.

a. Apply grades 910 Reading standards to literature (e.g., Analyze how an author draws on and transforms source material in a specific work [e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare]).

b. Apply grades 910 Reading standards to literary nonfiction (e.g., Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning).

Range of Writing

9-10.W.10 - Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.

N.A.

(388)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Language Standards

Conventions of Standard English

9-10.L.1 - Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Active and Passive Voice

Adjectives and Adverbs

a. Use parallel structure.* Clauses and Phrases

b. Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations.

Parallel Structure

Pronouns

Sentence Structure

Subject-Verb Agreement

Verb Tense

9-10.L.2 - Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Capitalization

Punctuation

a. Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent clauses.

Spelling

b. Use a colon to introduce a list or quotation.

c. Spell correctly.

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Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Knowledge of Language

9-10.L.3 - Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.

Editing

a. Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Turabians Manual for Writers) appropriate for the discipline and writing type.

(390)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Vocabulary Acquisition and Use

9-10.L.4 - Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 910 reading and content, choosing flexibly from a range of strategies.

Context Clues

Multiple Meaning Words

a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a words position or function in a sentence) as a clue to the meaning of a word or phrase.

Reference Materials

b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., analyze, analysis, analytical; advocate, advocacy).

c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology.

d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).

9-10.L.5 - Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

Connotation and Denotation

Figures of Speech

a. Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text.

b. Analyze nuances in the meaning of words with similar denotations.

(391)

Grade 10 Language-Arts – Alignment to Common Core

Standard Study Island Topic

9-10.L.6 - Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Embedded

(392)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Reading Standards for Literature

Key Ideas and Details

11-12.RL.1 - Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain.

Inferences

Textual Evidence

11-12.RL.2 - Determine two or more themes or central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to produce a complex account; provide an objective summary of the text.

Objective Summary

Theme

11-12.RL.3 - Analyze the impact of the authors choices regarding how to develop and relate elements of a story or drama (e.g., where a story is set, how the action is ordered, how the characters are introduced and developed).

Characters

Plot

Setting

(393)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Craft and Structure

11-12.RL.4 - Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including words with multiple meanings or language that is particularly fresh, engaging, or beautiful. (Include Shakespeare as well as other authors.)

Impact and Tone

11-12.RL.5 - Analyze how an authors choices concerning how to structure specific parts of a text (e.g., the choice of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its overall structure and meaning as well as its aesthetic impact.

Plot

11-12.RL.6 - Analyze a case in which grasping point of view requires distinguishing what is directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement).

Understanding Layers of Meaning

Integration of Knowledge and Ideas

11-12.RL.7 - Analyze multiple interpretations of a story, drama, or poem (e.g., recorded or live production of a play or recorded novel or poetry), evaluating how each version interprets the source text. (Include at least one play by Shakespeare and one play by an American dramatist.)

N.A.

(394)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

11-12.RL.9 - Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics.

Analyzing U.S. Works and Documents

Range of Reading and Level of Text Complexity

11-12.RL.10 - By the end of grade 11, read and comprehend literature, including stories, dramas, and poems, in the grades 11CCR text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

By the end of grade 12, read and comprehend literature, including stories, dramas, and poems, at the high end of the grades 11CCR text complexity band independently and proficiently.

Reading Standards for Informational Text

Key Ideas and Details

11-12.IT.1 - Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain.

Inferences

Textual Evidence

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Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

11-12.IT.2 - Determine two or more central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to provide a complex analysis; provide an objective summary of the text.

Analyzing Multiple Ideas

Objective Summary

11-12.IT.3 - Analyze a complex set of ideas or sequence of events and explain how specific individuals, ideas, or events interact and develop over the course of the text.

Analyzing Multiple Ideas

Craft and Structure

11-12.IT.4 - Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze how an author uses and refines the meaning of a key term or terms over the course of a text (e.g., how Madison defines faction in Federalist No. 10).

Impact and Tone

Technical Meanings

11-12.IT.5 - Analyze and evaluate the effectiveness of the structure an author uses in his or her exposition or argument, including whether the structure makes points clear, convincing, and engaging.

Structuring Text

11-12.IT.6 - Determine an authors point of view or purpose in a text in which the rhetoric is particularly effective, analyzing how style and content contribute to the power, persuasiveness, or beauty of the text.

Author's Point of View

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Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Integration of Knowledge and Ideas

11-12.IT.7 - Integrate and evaluate multiple sources of information presented in different media or formats (e.g., visually, quantitatively) as well as in words in order to address a question or solve a problem.

Applying Sources of Information

11-12.IT.8 - Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning (e.g., in U.S. Supreme Court majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses).

Author's Argument

Author's Point of View

11-12.IT.9 - Analyze seventeenth-, eighteenth-, and nineteenth-century foundational U.S. documents of historical and literary significance (including The Declaration of Independence, the Preamble to the Constitution, the Bill of Rights, and Lincolns Second Inaugural Address) for their themes, purposes, and rhetorical features.

Analyzing U.S. Works and Documents

Range of Reading and Level of Text Complexity

11-12.IT.10 - By the end of grade 11, read and comprehend literary nonfiction in the grades 11CCR text complexity band proficiently, with scaffolding as needed at the high end of the range.

N.A.

By the end of grade 12, read and comprehend literary nonfiction at the high end of the grades 11CCR text complexity band independently and proficiently.

(397)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Writing Standards

Text Types and Purposes

11-12.W.1 - Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

Introducing and Closing Topics

Supplying and Developing Evidence

a. Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences claim(s), counterclaims, reasons, and evidence.

Task, Purpose, and Audience

b. Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audiences knowledge level, concerns, values, and possible biases.

Transitional Devices

c. Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.

d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.

e. Provide a concluding statement or section that follows from and supports the argument presented.

(398)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

11-12.W.2 - Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content.

Formatting and Graphics

Interpreting Figures of Speech

a. Introduce a topic; organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.

Introducing and Closing Topics

b. Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audiences knowledge of the topic.

Precise Language

c. Use appropriate and varied transitions and syntax to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.

Sentence Structures

d. Use precise language, domain-specific vocabulary, and techniques such as metaphor, simile, and analogy to manage the complexity of the topic.

Supplying and Developing Evidence

e. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.

Transitional Devices

f. Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic).

(399)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

11-12.W.3 - Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences.

Introducing and Closing Topics

Precise Language

a. Engage and orient the reader by setting out a problem, situation, or observation and its significance, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events.

Task, Purpose, and Audience

b. Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters.

c. Use a variety of techniques to sequence events so that they build on one another to create a coherent whole and build toward a particular tone and outcome (e.g., a sense of mystery, suspense, growth, or resolution).

d. Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters.

e. Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative.

(400)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Production and Distribution of Writing

11-12.W.4 - Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 13 above.)

Task, Purpose, and Audience

11-12.W.5 - Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. (Editing for conventions should demonstrate command of Language standards 13 up to and including grades 1112 on page 54.)

Editing

Planning

Revising

11-12.W.6 - Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information.

N.A.

(401)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Research to Build and Present Knowledge

11-12.W.7 - Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.

Applying Sources of Information

11-12.W.8 - Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation.

Applying Sources of Information

Citations

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Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

11-12.W.9 - Draw evidence form literary or informational texts to support analysis, reflection, and research.

N.A.

a. Apply grades 1112 Reading standards to literature (e.g., Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics).

b. Apply grades 1112 Reading standards to literary nonfiction (e.g., Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning [e.g., in U.S. Supreme Court Case majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses]).

Range of Writing

11-12.W.10 - Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.

N.A.

(403)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Language Standards

Conventions of Standard English

11-12.L.1 - Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Active and Passive Voice

Adjectives and Adverbs

a. Apply the understanding that usage is a matter of convention, can change over time, and is sometimes contested.

Editing

b. Resolve issues of complex or contested usage, consulting references (e.g., Merriam-Websters Dictionary of English Usage, Garners Modern American Usage) as needed.

Parallel Structure

Phrases and Clauses

Pronouns

Subject-Verb Agreement

Verbs and Mood

11-12.L.2 - Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Capitalization

Punctuation

a. Observe hyphenation conventions. Spelling

b. Spell correctly.

(404)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Knowledge of Language

11-12.L.3 - Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.

Editing

a. Vary syntax for effect, consulting references (e.g., Tuftes Artful Sentences) for guidance as needed; apply an understanding of syntax to the study of complex texts when reading.

(405)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

Vocabulary Acquisition and Use

11-12.L.4 - Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 1112 reading and content, choosing flexibly from a range of strategies.

Context Clues

Multiple Meaning Words

a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a words position or function in a sentence) as a clue to the meaning of a word or phrase.

Reference Materials

b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., conceive, conception, conceivable).

Understanding Layers of Meaning

c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, its etymology, or its standard usage.

d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).

(406)

Grade 11 Language-Arts – Alignment to Common Core

Standard Study Island Topic

11-12.L.5 - Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

Connotation and Denotation

Interpreting Figures of Speech

a. Interpret figures of speech (e.g., hyperbole, paradox) in context and analyze their role in the text.

b. Analyze nuances in the meaning of words with similar denotations.

11-12.L.6 - Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Embedded