1 indiana standards for mathematics (2014) instructional shifts in college and career readiness 1

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Indiana Standards for Mathematics (2014)Instructional Shifts in College and Career Readiness

2Agenda

Where to find the resources Productive .vs. Unproductive Beliefs Process Standards – Guide and Facilitate Lesson Planning for Differentiation –

Questions Grades 9 – 12 Productive Questioning and Higher

Order Thinking Questions. How to Prepare for the Changes in Assessment

Current Standards can be found at: http://www.doe.in.gov/standards Mathematics Standards and Resources can be found at: http://www.doe.in.gov/standards/mathematics Content Framework Development Tools can be found at: http://www.doe.in.gov/content-framework-development-tool.pdf

Online Communities of Practice can be found at: http://www.doe.in.gov/elearning/online-communities-practiceCurriculum Resources can be found at: http://www.doe.in.gov/achievement/curriculum

Where to find the Resources

3

http://www.doe.in.gov/standards

http://www.doe.in.gov/standards

http://www.doe.in.gov/standards/mathematics



http://www.doe.in.gov/sites/default/files/standards/content-framework-development-tool.pdf

http://www.doe.in.gov/sites/default/files/standards/content-framework-development-tool.pdf

http://www.doe.in.gov/elearning/online-communities-practice



http://www.doe.in.gov/achievement/curriculum

Assessment Resources can be found at: http://www.doe.in.gov/assessment ISTEP+ Resources can be found at: http://www.doe.in.gov/assessment/istep-grades-3-8 ECA Resources can be found at: http://www.doe.in.gov/assessment/end-course-assessments-ecas

WIDA Standards Resources can be found at: http://www.doe.in.gov/elme/wida

Where to find the Resources

4

http://www.doe.in.gov/assessment

http://www.doe.in.gov/assessment/istep-grades-3-8

http://www.doe.in.gov/assessment/end-course-assessments-ecas



http://www.doe.in.gov/elme/wida-english-language-development-eld-standards-framework

http://www.doe.in.gov/elme/wida-english-language-development-eld-standards-framework

Productive .vs. Unproductive Beliefs for Teaching and Learning Mathematics

Unproductive Beliefs Productive Beliefs

Mathematics learning should focus onpracticing procedures and memorizing basic number combinations.

Mathematics learning should focus on developing understanding of concepts and procedures through problem solving, reasoning, and discourse.

Students need only to learn and use the same standard computational algorithms and the same prescribed methods to solve algebraic problems.

All students need to have a range of strategies and approaches from which tochoose in solving problems, including, but not limited to, general methods, standard algorithms, and procedures.

The role of the teacher is to tell studentsexactly what definitions, formulas, andrules they should know and demonstratehow to use this information to solvemathematics problems.

The role of the teacher is to engagestudents in tasks that promote reasoningand problem solving and facilitate discourse that moves students toward shared understanding of mathematics.

Effective Teaching and Learning. (2014). In Principles to Actions : Ensuring mathematical success for all (p. 11). Reston, VA: NCTM.

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Productive .vs. Unproductive Beliefs for Teaching and Learning Mathematics

Unproductive Beliefs Productive Beliefs

Students can learn to apply mathematicsonly after they have mastered the basicskills.

Students can learn mathematics throughexploring and solving contextual andmathematical problems.

The role of the student is to memorizeinformation that is presented and then use it to solve routine problems on homework, quizzes, and tests.

The role of the student is to be activelyinvolved in making sense of mathematicstasks by using varied strategies andrepresentations, justifying solutions, making connections to prior knowledge or familiar contexts and experiences, and considering the reasoning of others.

An effective teacher makes the mathematics easy for students by guiding them step by step through problem solving to ensure that they are not frustrated or confused.

An effective teacher provides studentswith appropriate challenge, encouragesperseverance in solving problems, andsupports productive struggle in learningmathematics.


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7 Process Standards for Mathematics

The Process Standards demonstrate the ways in which students should develop conceptual understanding of mathematical content, and the ways in which students should synthesize and apply mathematical skills. PS.1: Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway, rather than simply jumping into a solution attempt. They consider analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” and "Is my answer reasonable?" They understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students understand how mathematical ideas interconnect and build on one another to produce a coherent whole.


The Process Standards demonstrate the ways in which students should develop conceptual understanding of mathematical content, and the ways in which students should synthesize and apply mathematical skills.

PS.2: Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.


The Process Standards demonstrate the ways in which students should develop conceptual understanding of mathematical content, and the ways in which students should synthesize and apply mathematical skills. PS.3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They analyze situations by breaking them into cases and recognize and use counterexamples. They organize their mathematical thinking, justify their conclusions and communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. They justify whether a given statement is true always, sometimes, or never. Mathematically proficient students participate and collaborate in a mathematics community. They listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.



PS.4: Model with mathematics.

Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace using a variety of appropriate strategies. They create and use a variety of representations to solve problems and to organize and communicate mathematical ideas. Mathematically proficient students apply what they know and are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.



PS.1: Make sense of problems and persevere in solving them.




PS.5: Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Mathematically proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. Mathematically proficient students identify relevant external mathematical resources, such as digital content, and use them to pose or solve problems. They use technological tools to explore and deepen their understanding of concepts and to support the development of learning mathematics. They use technology to contribute to concept development, simulation, representation, reasoning, communication and problem solving.



PS.6: Attend to precision.

Mathematically proficient students communicate precisely to others. They use clear definitions, including correct mathematical language, in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They express solutions clearly and logically by using the appropriate mathematical terms and notation. They specify units of measure and label axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently and check the validity of their results in the context of the problem. They express numerical answers with a degree of precision appropriate for the problem context.



PS.1: Make sense of problems and persevere in solving them.




PS.7: Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. They step back for an overview and shift perspective. They recognize and use properties of operations and equality. They organize and classify geometric shapes based on their attributes. They see expressions, equations, and geometric figures as single objects or as being composed of several objects.

PS.8: Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated and look for general methods and shortcuts. They notice regularity in mathematical problems and their work to create a rule or formula. Mathematically proficient students maintain oversight of the process, while attending to the details as they solve a problem. They continually evaluate the reasonableness of their intermediate results.

16 Process Standards “Look Fors”

PS.1: Make sense of problems and persevere in solving them.Students: Are actively engaged in solving problems Teacher: Provides time for and facilitates the discussion of problem solutions PS.2: Reason abstractly and quantitatively.Students: Use varied representations and approaches when solving problems Teacher: Provides a range of representations of mathematical ideas and problem situations and encourages varied solution paths PS.3: Construct viable arguments and critique the reasoning of others.Students: Understand and use prior learning in constructing arguments Teacher: Provides opportunities for students to listen to or read the conclusions and arguments of others PS.4: Model with mathematics.Students: Apply mathematics learned to problems they solve and reflect on results Teacher: Provides a variety of contexts for students to apply the mathematics learned Adapted from Dr. Skip Fennell (PDF Document) – ACTM Presentation in Little Rock AK – 11/8/2012

17 Process Standards “Look Fors”

PS.5: Use appropriate tools strategically.Students: Use technological tools to deepen understanding Teacher: Uses appropriate tools (e.g. manipulatives) instructionally to strengthen the development of mathematical understanding PS.6: Attend to precision.Students: Based on a problemTeacher: Emphasizes the importance of mathematical vocabulary and models precise communication. PS.7: Look for and make use of structure.Students: Look for, develop, and generalize arithmetic expressions Teacher: Provides time for applying and discussing properties PS. 8: Look for and express regularity in repeated reasoning.Students: Use repeated applications to generalize properties Teacher: Models and encourages students to look for and discuss regularity in reasoningAdapted from Dr. Skip Fennell (PDF Document) – ACTM Presentation in Little Rock AK – 11/8/2012

18 Lesson Plan Template

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Relating the Mathematics being taught to the StudentsPlanning Questions - To think about as a teacher while

planningPre-Assessing Questions - For teacher to ask for pre-

assessing students. Include higher order thinking questions while pre-assessing

Differentiation Questions - How can I adjust this lessons for student’s needs

Examples, Activities and TasksResources and MaterialsAccess and Engagement for ALL Students


LESSON ELEMENTPROVIDE STUDENT-FRIENDLY TRANSLATION WHERE APPLICABLE

1. Grade level Indiana Academic Standard(s) 2014 the lesson targets include: 2. Learning Target(s):

3. Relating the Learning to Students: 4. Assessment Criteria for Success: 5. - Content Area Literacy standards for History /Social Studies, Science, & Technical Subjects:

- Math Process Standard(s):

Indiana Academic Standards2014 Lesson Plan Alignment TemplateSubject(s): ______________________ Period(s): ___________ Grade(s): ______________Teacher(s): ________________________________________ School: __________________The lesson plan alignment tool provides examples of the instructional elements that should be included in daily planning and practice for the Indiana Academic Standards. The template is designed as a developmental tool for teachers and those who support teachers. It can also be used to observe a lesson and provide feedback or to guide lesson planning and reflection.


6. Academic Vocabulary:

7. Examples/Activities/Tasks:

8. Resources/Materials:

9. Access and Engagement for All:

10. Differentiation/Accommodations:

Indiana Academic Standards Aligned Lesson: ReflectionIn addition, please choose ONE question below to respond to after you have taught the lesson OR create your own question and respond to it after you have taught the lesson.

1. How did this lesson support 21st Century Skills?2. How did this lesson reflect academic rigor?3. How did this lesson cognitively engage students? 4. How did this lesson engage students in collaborative learning and enhance their

collaborative learning skills?

21 Posing Purposeful Questions

Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.


Four Types of Questions1.Gathering Information2.Probing Thinking3.Making the mathematics visible4.Encouraging reflection and justification

22 Posing Purposeful Questions

Question type Description Examples

Gathering information

Students recall facts, definitions, or procedures.

• When you write an equation, what does the equal sign tell you?

• What is the formula for finding the area of a rectangle?

Probing thinking Students explain, elaborate, or clarify their thinking, including articulating thesteps in solution methods or the completion of a task.

• As you drew that number line, what decisions did you make so that you could represent 7 fourths on it?

• Can you show and explain more about how you used a table to find the answer to the Smartphone Plans task?


23

Question type Description Examples

Making the mathematicsvisible

Students discuss mathematical structures and make connections among mathematical ideas and relationships.

What does your equation have to do with the band concert situation?

How does that array relate to multiplication and division?

Encouraging reflectionand justification

Students reveal deeperunderstanding of theirreasoning and actions,including making an argument for the validity of their work.

• How might you prove that 51 is the solution?

• How do you know that the sum of two odd numbers will always be even?


Posing Purposeful Questions

24Depth of Knowledge

(DOK) Levels

25Depth of Knowledge

(DOK) Activities

26Constructed Response

Extended ResponseQuestions

I would suggest every 2 – 3 weeks having students practice working Extended Response and Constructed Response styles of questions. You can also Google “Constructed Response Math Questions” and find some great resources like: https://www4.uwm.edu/Org/mmp/_resources/CR_Items.htm http://mdk12.org/assessments/k_8/items/cr_grade5_math.html http://mcsed.net/Page/268

Likewise if you Google “Extended Response Math Questions” and find some great resources like:https://www.k12.wa.us/Mathematics/ReleasedItems.aspx http://www.riroe.com/site/nims/problem-solving-and-extended-response/

You can refine or narrow your search criteria using a specific grade level or mathematical concept and/or standard. These are great practice on this type of question. They may not be the exact same as the questions your students will be seeing on the ISTEP+ but the practice with this type of questions will help them considerably with the questions they will see and be asked to work on the Indiana ISTEP+.

https://www4.uwm.edu/Org/mmp/_resources/CR_Items.htm

http://mdk12.org/assessments/k_8/items/cr_grade5_math.html

http://mcsed.net/Page/268

https://www.k12.wa.us/Mathematics/ReleasedItems.aspx

http://www.riroe.com/site/nims/problem-solving-and-extended-response/

27Assessment Update for

Educators

ISTEP+: ECAs

Assessment Items – General Notes…

Mathematics Icons will not appear on the Spring 2015 Math items, as

Mathematical Process Standard 5 requires the use of appropriate tools strategically.

The Spring 2015 Math assessment will include items that measure fluency as demonstrated “efficiently” and “accurately” by students.

When creating an expression or equation, students must define the variable.

Gridded-Response items will appear as part of the pencil-and-paper version for Part 2 in grades 4 – 8.

29Designing the Spring 2015 ISTEP+

(Grades 3-8)

ISTEP+ Part 1 March Administration – Applied Skills Items (Online

voluntary)• Paper/Pencil Testing Window: March 2 - 11, 2015• Online Testing Window: March 2 - 13, 2015

ISTEP+ Part 2 April/May Administration (Online required)

• Paper/Pencil Testing Window (Requires Pre-Approval): April 27 – May 8, 2015

Multiple-Choice and Gridded-Response Items• Online Testing Window: April 27 – May 15, 2015

Multiple-Choice and Technology-Enhanced Items

30Acuity Assessments: Grades 3-8

English/Language Arts and Mathematics

• Replace Predictive and Diagnostic paths

• Aligned to the CCR 2014 Indiana Academic Standards

• 3 administrations – serve as pretest/diagnostic assessment

31Assessment-focused Professional

Development: Grades 3-8

September/October – recorded WebEx Sessions Focused on:

• Use of Instructional and Assessment Guidance• Sample open-ended items based on new CCR

standards• Technology-enhanced item types

32 “Experience College- and Career-Ready Assessment”

Tool: Grades 3-8

Release October 1; open through spring• Technology-enhanced item types• Training for students and educators• Engaging and interactive

Teachers are encouraged to use Experience CCRA as an instructional tool in the

classroom!

33Designing the Spring 2015 ISTEP+ End of Course Assessments (ECAs)

Spring 2015 ECAs will include two components: • Graduation examination

* Aligned to IAS (2000 Algebra I, 2006 English 10)

• Accountability assessment* Aligned to CCR IAS (2014 Algebra I and

English 10)

Watch for additional ECA updates coming later this fall!

.

Graduation Examination & Accountability Assessment

Implementation Year Grade

ECA (IAS 2000

Algebra I, 2006 English 10)

ECA (CCR IAS 2014

Algebra I, English 10)

Grade 10 Summative Assessment

Graduation Examination

Accountability Assessment

2014-15

Grade 10Graduation

ExaminationAccountability Assessment

Grade 11 Retest

Grade 12 Retest

Adults Retest

2015-16

Grade 10Graduation

Examination X

Grade 11 Retest

Grade 12 Retest

Adults Retest

2016-17

Grade 10 X X

Grade 11 Retest

Grade 12 Retest

Adults Retest

2017-18

Grade 10 X X

Grade 11 Retest

Grade 12 Retest

Adults Retest

2018-19

Grade 10 X X

Grade 11 Retest

Grade 12 Retest

Adults Retest

2019-20

Grade 10 X X

Grade 11 Retest

Grade 12 Retest

Adults Retest

35Acuity Assessments: ECAs

Acuity for Algebra I and English 10

• Continue Predictive forms for the ECAs* Assesses Graduation Examination content

• NEW CCR-aligned items for use by teachers* Assesses accountability assessment content

36Assessment-focused Professional

Development: ECAs

Late Fall – recorded WebEx Sessions Focused on:

• Use of Instructional and Assessment Guidance• Sample open-ended items based on new CCR

standards• Technology-enhanced item types

37 “Experience College- and Career-Ready Assessment”

Tool: ECAs

Teachers are encouraged to use Experience CCRA as an instructional tool

in the classroom!

Release in January• Technology-enhanced item types• Training for students and educators• Engaging and interactive

.

Future Assessments: Beginning in 2015-16

Assessment Resolution includes:• Summative Assessment (Grades 3-10)

* Grade 10 ISTEP+ becomes new Graduation Examination

* Phase-out ECAs (Algebra I, English 10)* High School Science Assessment based on

Biology I• IREAD-3 • Alternate assessments (Grades 3-10)• Formative assessments (Grades K-10)• College- and Career-Readiness Exam (Grade 11)• Grade 11, 12 assessments (focused on college

and career)

Item Specificatio

ns; Test Blueprints

Content and Bias/Sensitivi

ty Reviews

Item Development; Internal IDOE Item

Review

Revise/Select Items

Pilot Items/ Administer Operational

Test

Standards Setting (Cut-

Score Setting)

Blue font = Educator Involvement

Assessment Development Journey

39

40

.

Activity ECA Timeline

Specification Review Meetings and Test Blueprint Development

September 2014

Passage Review Meetings September 2014

Item Development September/October 2014

Content and Bias/Sensitivity Review Meetings November 2014

Pilot New ECA Items During Late Winter Testing Window

February/March 2015

Form Selection and Build March 2015

Administer Assessment April/May 2015

Standards Setting (Cut-Score Setting) Summer 2015

ECA Development & Implementation Blue font = Educator Involvement

41Support for Educators:

ECAs – Projected TimelineSupport Timeline

Test Blueprints Posted Late Fall

Instructional and Assessment Guidance Posted Late Fall

Acuity CCR-aligned Items Available in October

Professional Development (Recorded Sessions): Open-ended items and Technology-Enhanced Items

December/January

Experience College- and Career-Ready Assessment (Sample technology-enhanced items for use with students, teachers, parents, and others)

Early JanuaryStay tuned for more information!

42Instructional and Assessment

Guidance

• Provides “granular” view of standards

• Informs curricular and instructional priorities

• Provides transparency regarding assessments ECA graduation examination ECA accountability assessment

+, , –

43Instructional and Assessment Guidance 2014-15

Mathematics – Grade 5

• Represents standards that may be assessed on ISTEP+ Part 1 and ISTEP+ Part 2. All standards may be assessed on ISTEP+ Part 2.

Symbol Content Priority Approximate Instructional Time

P+ Critical 50 – 75%

P Important 25 – 50%

P– Additional 5 – 10%

Strand 1Number Sense

Strand 2Computation

Strand 3Algebraic Thinking

Strand 4Geometry

Strand 5Measurement

Strand 6Data Analysis

Strand 7Mathematical

Process

5.NS.1 P *5.C.1 P+ *5.AT.1 P+ 5.G.1 P *5.M.1 P+5.DS.1

*P *PS.1 P+

5.NS.2 P 5.C.2 P+ *5.AT.2 P+ *5.G.2 P 5.M.2 P 5.DS.2 P *PS.2 P+

5.NS.3 P– 5.C.3 P– *5.AT.3 P *5.M.3 P+ *PS.3 P+

5.NS.4 P– 5.C.4 P+ *5.AT.4 P 5.M.4 P *PS.4 P+

5.NS.5 P– 5.C.5 P+ *5.AT.5 P+ *5.M.5 P+ *PS.5 P+

5.NS.6 P 5.C.6 P– 5.AT.6 P *5.M.6 P *PS.6 P+

5.C.7 P+ 5.AT.7 P *PS.7 P+

*5.C.8 P+ *5.AT.8 P *PS.8 P+

*5.C.9 P+

Sample

44Resources for

Assessment Guidance

• School Test Coordinator (STC)

• Corporation Test Coordinator (CTC)

• Office of Student Assessment Telephone: (317) 232-9050 Email: [email protected] Website: http://www.doe.in.gov/assessment

mailto:[email protected]

http://www.doe.in.gov/assessment

45

45

ISTEP+ Mathematics Update

Grades 6-8 , 2014-15

4646 Mathematics Standards (2014)


Dive into the standards Correlation Documents Resource Guides Vertical Articulation Documents



4747Fluency Standards

Fluency standards in Grades 2 through Algebra I

Fluency means efficient and accurate Attain fluency by the end of the year Fluency items on ISTEP+ will not allow a

calculator

4848 Mathematical Process Standards

Help students develop the Process Standards on a daily basis while connecting them to math content.

4949MP 2 & 3

Reasoning and Explaining

Students must make sense of quantities and their relationships in problem situations.

Provide time for students to think, share, and write about quantities in tasks & how they relate

Encourage varied representations to solve tasks Evaluate arguments and work of others

5050 MP 4 & 5Modeling and Using Tools

Provide multiple opportunities for students to apply math in real world tasks

Help students build their “toolbox” and encourage them to think about using their tools to solve math problems eventually without prompting them to use the tools Pencil and paper, concrete models, ruler,

protractor, calculator, spreadsheet, computer algebra system, statistical packs, dynamic geometry software

5151MP 7 & 8

Seeing Structure and Generalizing

Encourage not always “attacking” a problem immediately

Encourage students to look for patterns and ways to make the task easier or to assist in solving the task

Encourage students to look for and build patterns that might lead to further understanding

5252General Assessment Information

Mathematics ISTEP+ Gr.3-8

Reference Sheet Separate Ref. Sheet for Gr.4-8 Copy and print for students to use throughout the year No more Ref. icon on the test (MP5) Formulas and conversions are no longer embedded in

questions unless the information is needed and not contained in the Ref. Sheet

Gr.5: Volume of Right Rectangular Prism = l x w x h or B x h

5353 General Assessment InformationContinued – Calculator Information

Gr.6-8: calculator allowed on Applied Skills Test and 1 session of the May Test

Calculator allowed if in student’s IEP or 504 plan Maximum functionality: scientific calculator Scientific calculator recommended for Gr.6-8

Gr.7-8 gain familiarity with pi button and writing rounded and exact answers Ex: What is the circumference of a circle with a

diameter of 4.5 inches? Rounded to hundredths: 14.14 inches Exact answer: 4.5∏ inches

5454General Assessment Information

Continued

Applied Skills Items Sample items available in September Rubrics available in September

Technology Enhanced Items Practice session available in October

5555 Instructional and Assessment Guidance

Documents and Blueprints

Mathematics Grades 3-8 http://www.doe.in.gov/assessment/istep-gra

des-3-8



5656 Grades 6 – 8 Applied Skills

Show all steps needed to solve the problems without showing lengthy computation work.

For example: If a problem requires a step of 3.785 times 4.5, then show: 3.785 • 4.5 = 17.0325

Not necessary nor efficient!

5757Grade 6 – Applied Skills

SOME of the content that may be assessed on the Applied Skills Assessment Rate, ratio, and percent problems Evaluating numerical expressions including

evaluating the work of others (MP3) Writing expressions and equations (in 1 or 2

variables) including defining the variables

5858Grade 6 Clarifications

Division computations: quotients with remainders written as a fraction, mixed number, or decimal, but NOT with “R” to represent the remainder Ex: 15,266/68 could be written as either 224.5, 224 ½, 224

34⁄68, 449⁄2, or equivalent values; but not as 224 R34

Operations with integers is now in Gr.7 Although the difference of #’s on a # line (including

negative numbers) is in 6.NS.4 Teach “x” and “•” as multiplication symbols 6.NS.10: Some examples: unit pricing, constant

speed, percent problems, conversions within the same measurement system

5959 6.NS.10 Example Ed has 8 pieces of candy which

represents 40% of all the candy in his home. How many pieces of candy are in Ed’s home? Strategies may include using a double #

line diagram, tape diagram, tables of values, & equations

0% 100%

50%

40%

20%

84 16 20

80%

6060Tape Diagram

Draw a “strip of tape” Cut strip into known percent Build to 100% 8 = .40x

8 8 4

20%

40%

40%

6161 Grade 7 – Applied Skills SOME of the content that may be

assessed on the Applied Skills Assessment Rate, ratio, and percent problems Applying the properties of operations to create

equivalent linear expressions including evaluating the work of others (MP3)

Writing equations (in 1 or 2 variables) including defining the variables

Circumference and area of circle problems Volume of cylinder problems Surface Area (including nets) problems Use the Pi button on the calculator

Not “use 3.14 for pi” as previously referenced

6262 Grade 7 Clarifications 7.NS.1: Limit #’s to 200 or less 7.NS.2: Limit square roots to 144 or less 7.NS.3: Very basic introduction of irrational #’s

(only include the numbers identified in the standard)

7.C.(1-4): More conceptual in nature – see RG Teach using the pi button and writing rounded and

exact answers(7.GM.5-6) What is the circumference of a circle with a diameter of 4.5

inches? Rounded to hundredths: 14.14 inches Exact answer: 4.5∏ inches

6363Grade 8 – Applied Skills SOME of the content that may be assessed on

the Applied Skills Assessment Writing equations (in 1 or 2 variables)

including defining the variables and interpreting the slope and y-int.

Justifying linear equations in one variable as having one solution, infinitely many solutions, or no solutions (MP3)

Pythagorean Theorem problems Scatter plot problems

6464 Grade 8 Clarifications 8.AF.3: When studying functions, include the terms

independent and dependent variables, input and output values, x- and y-values

8.AF.4: Tasks should be qualitative in nature (See RG) 8.AF.5: Includes graphing a linear function, such as,

y = -2x - 4 Teach using the pi button and writing answers in

terms of pi (8.GM.2) 8.GM.4-5: Tasks do not include coordinate geometry 8.GM.6: Tasks include coordinate geometry 8.DSP.3: Equations should be written using an

informal approach – not using technology

6565 Defining Variables

Explicit in Standards: 5.AT.8 and 6.AF.3 Implied in Standards: 6.AF.5, 6.AF.10,

7.AF.2, 7.AF.9, 8.AF.1, and 8.AF.6 Example of previous ISTEP+ Item

A parking lot has 24 rows. Each row has the same number of parking spaces. The parking lot has a total of 768 parking spaces. Write an equation that can be used to determine the number of parking spaces (p) in each row.

6666Defining Variables

New ISTEP+ Item aligned to 6.AF.5 and MP.2, 4, and 6 A parking lot has 24 rows. Each row has the

same number of parking spaces. The parking lot has a total of 768 parking spaces.

Write an equation that can be used to determine the number of parking spaces in each row. Be sure to define the variable in your equation.

6767Attend to Precision

MP.6 Attend to Precision means precision in computations AND communication Precise communication: Let p

represent the number of parking spaces in each row

Not as precise: p is parking spaces If the answer is 1/3, then leave as

1/3…NOT 0.33

68

Assessment Items – General Notes…

Mathematics Icons will not appear on the Spring 2015 Math items, as

Mathematical Process Standard 5 requires the use of appropriate tools strategically.

The Spring 2015 Math assessment will include items that measure fluency as demonstrated “efficiently” and “accurately” by students.

When creating an expression or equation, students must define the variable.

69ISTEP+ Part 1 – Applied Skills Sample Items

The following items are samples, designed to use with teachers, as part of professional

development; and students, to familiarize them with items

aligned to the college- and career-ready 2014 Indiana Academic Standards.

These sample items are non-secure and

may be used by teachers and students.

70

A student claims that 8x – 2(4 + 3x) is equivalent to 3x. The student’s steps are shown. Expression: 8x – 2(4 + 3x)

Step 1: 8x – 8 + 3x Step 2: 8x + 3x – 8 Step 3: 11x – 8 Step 4: 3xPart ADescribe ALL errors in the student’s work.___________________________________________________________

___________________________________________________________

Math Grade 7 Constructed-Response

Math constructed-response items are

worth 2 points.

71

Part B

If the errors in the student’s work are corrected, what will be the final expression?

Show All Work

Expression ____________________

72Exemplary Response:In Step 1, the student did not apply the distributive property correctly. The student forgot to multiply -2 and 3x. In Step 4, the student should not have subtracted 8 from 11x because they are not like terms.OR Other valid descriptions of the errorsAND2x – 8 Sample Process:8x – 2(4 + 3x)8x – 8 – 6x2x – 8

73Lynn is baking 20 cakes. She needs blueberries, strawberries, and some other ingredients for her recipe.

-She needs 22 pounds of blueberries.-She needs twice as many pounds of blueberries as

she does strawberries.Part AWrite an equation that can be used to determine the number of pounds of strawberries Lynn needs. Be sure to define the variable in your equation.Define the variable

_________________________________________________________Equation

_________________________________________________________

Math Grade 6 Extended-Response

Math extended-response items are

worth 6 points.

74Part B

Lynn buys the blueberries for $3 per pound and the strawberries for $2 per pound.What is the total cost of the blueberries and strawberries?

Show All Work

Answer $ ________

75Part C

In addition to the cost of the berries, Lynn spends $52 on the other ingredients needed to make the 20 cakes. Lynn wants to make $5 for each cake she sells, taking into account the amount she spends on ALL ingredients. For how much should Lynn sell each cake in order to make $5 per cake? Use words, numbers, and/or symbols to justify your answer.

___________________________________________________________

___________________________________________________________

76Exemplary Response:

p represents the number of pounds of strawberries Lynn needs2p = 22 OR Other valid equation and definition of the variable

AND

$88

AND

Lynn should sell each cake for $12.

77Sample Process:2p = 22 P = 22/2 p = 11

22 x $3 = $6611 x $2 = $22$66 + $22 = $88

$88 + $52 = $140$140/20 = $7 per cake$7 + $5 = $12OROther valid process

7878Contact Information

Math Assessment Gr.6 – HS: ([email protected]) K – 5: Ben Kemp ([email protected])

Math College and Career Ready Office Bill Reed ([email protected])


