florida dept. of educationbureau of curriculum & instruction1 math coaches/contact meeting...
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Bureau of Curriculum & Instruction 1Florida Dept. of Education
Math Coaches/Contact MeetingDecember 14, 2012Course Descriptions/Learning Goals
Bureau of Curriculum & Instruction 2
Florida’s CCSS Implementation Plan
Florida Dept. of Education
Full Implementation Grade K
Begin Implementation of Literacy Standards in ALL Content Areas for Grades 6-12
Begin Implementation of Rich and Complex Text and Informational Text for Grades K-12
Phase 1 (2011-2012)
Full Implementation Grades K-1 (BCPS K-2)
Full Implementation of Literacy Standards in ALL Content Areas for Grades 6-12
Continue Implementation of Rich and Complex Text and Informational Text for Grades K-12
Phase 2 (2012-2013)
Full Implementation Grades K-2
Implementation of a Blended Curriculum (CCSS and Supplemental NGSSS Aligned to FCAT 2.0 and EOCs) for Grades 3-12
Continue Implementation of Rich and Complex Text and Informational Text for Grades K-12
Phase 3 (2013-2014)
Full Implementation Grades K-12
PARCC Assessments Aligned to CCSS
Phase 4 (2014-2015)
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Course Requirements and Standards
Curriculum Mapping in Layers
“Chunks” or Big Ideas
Florida Dept. of Education
Major Learning Goals
Identify major learning goals for a specific course by integrating across content areas and “chunking” the standards into a few big ideas
Develop a projected timeline for instruction by mapping the major learning goals across the semester or year as appropriate for the course
Progression Scales for Major Learning Goals
Describe the learning progressions and develop a scale or rubric for at least one of the major learning goals for the course
(Day 2)
Progress Monitoring AssessmentsDescribe at least one assessment item that is appropriate for each of the levels beginning with Level 2 on the learning progression scale
Draft a blueprint for future progress monitoring assessments based upon the curriculum map (or pacing guide) and anticipated learning progressions
(Day 2)
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Current Way of Work
• Given the full implementation of Florida’s NGSSS what three words might we use to describe instruction in Florida?– Standards-Based Instruction
• What often guides the development of our curriculum maps or pacing guides?– Test Item Specifications
• What tools might we use to monitor the progress of our students?– Focus Mini-Assessments (Benchmark Assessments)
Florida Dept. of Education
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Florida Transitions toCommon Core State Standards
Next Generation Standards• Standards-based instruction• Test item specifications guide
development of curriculum maps
• Focus mini-assessments aligned to individual benchmarks and used to monitor student progress
• Teaching benchmarks in isolation results in long lists of tasks to master
Common Core Standards• Standards-based instruction
facilitated by learning goals• Big ideas and learning goals guide the
development of curriculum maps• Learning progressions or scales
describe expectations for student progress in attaining the learning goals
• Assessments used to monitor student progress are aligned directly to the learning progressions or scales
• Teaching big ideas narrows the focus and allows students to delve deeper for a greater depth of understanding
Florida Dept. of Education
Common Core State Standards for Mathematics
• Domains are larger groups of related standards. Standards from different domains may sometimes be closely related
• Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject.
• Standards define what students should understand and be able to do.
Domains for K-12K 1 2 3 4 5 6 7 8 HS
Counting
and Cardinality
(CC)
Number and
Quantity
Number and Operations in Base Ten (NBT) The Number System
Number and Operations-Fractions
(NF)
Ratios and Proportional Relationships
(RP)
Operations and Algebraic Thinking (OA)Functions (F)
Expressions and Equations (EE)
Algebra (A)
Geometry (G)
Measurement and Data (MD)
Statistics and Probability (SP)
High School Conceptual Categories
• Number and Quantity (N)
• Algebra (A)
• Functions (F)
• Modeling (*)
• Geometry (G)
• Statistics and Probability (S)
Florida’s Numbering ofthe Common Core State Standards
MACC.4.OA.2.4
Subject Grade Domain Cluster Standard
MACC.912.N-RN.2.3
Subject Grade Category Domain Cluster Standard
• MACC.4.OA Operations and Algebraic Thinking
• MACC.4.OA.2 Gain familiarity with factors and multiples
• MACC.4.OA.2.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
Domain
Cluster
Standard
• MACC.912.N Number and Quantity
• MACC.912.N-RN The Real Number System
• MACC.912.N-RN.2 Use properties of rational and irrational numbers
• MACC.912.N-RN.2.3 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.
Domain
Cluster
Standard
Category
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SAMPLE LESSONM/J MATHEMATICS 2 – RATIONAL NUMBERS
The New “Look and Feel” of Instruction with Common Core
Florida Dept. of Education
Please refer
to sample
lesson!
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Course: Lesson Plan Sample
Goal:
Objective(s):
Essential Question:
Engaging Activity and Discussion Questions:
Formative Assessment Task:
Differentiated Instruction Strategies:
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Learning Goal
Students demonstrate proficiency with addition, subtraction, multiplication, and division of rational numbers expressed using decimals and fractions, and they are able to explain their thinking at a conceptual level.
Florida Dept. of Education
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Objective
Students demonstrate fluency* when performing operations (addition, subtraction, multiplication, and division) with benchmark fractions and their decimal equivalents. Benchmark fractions include tenths, eighths, sixths, fifths, fourths, thirds, and halves.
Florida Dept. of Education
*Fluency is the ability to compute flexibly, accurately, efficiently, and appropriately.
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Essential Question
Why is it important to build a sound foundation in your conceptual understanding of operations with fractions, and why is it just as important to recognize benchmark fractions and their decimal equivalents?
Florida Dept. of Education
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Performance Task
Jeri and Tawny were both presented with the same problem; yet, they arrived at two different answers. Their complete responses are shown below.
Jeri simply wrote ) = 1Tawny showed considerably more details and wrote
3 (0.) = (0.) + (0.) + (0.) = 0.
Who has the correct answer and why?Florida Dept. of Education
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Course: M/J Math 2 (1205040) Lesson Plan Sample
Goal: Students demonstrate proficiency with addition, subtraction, multiplication, and division of rational numbers expressed using decimals and fractions, and they are able to explain their thinking at a conceptual level.
Objective(s): Students demonstrate fluency when performing operations (addition, subtraction, multiplication, and division) with benchmark fractions and their decimal equivalents. Benchmark fractions include tenths, eighths, sixths, fifths, fourths, thirds, and halves.
Essential Question:
Why is it important to build a sound foundation in your conceptual understanding of operations with fractions, and why is it just as important to recognize benchmark fractions and their decimal equivalents?
Engaging Activity and Discussion Questions:
Students should be presented with the formative assessment task shown below and the teacher should read the question aloud. Initially, students should explore their thinking independently while making notes of interesting observations and/or any questions they may have. Students should then share their thinking with others in their small group; they should take turns asking questions of others, and adjust their own notes. Once everyone has had an opportunity to share their thinking and ask all their questions, students should once again work independently to finalize their response.
Formative Assessment Task:
Differentiated Instruction Strategies:
Some students may need to explore the problem visually using grid paper or manipulatives such as Unifix cubes, fraction tiles, or a ruler.ELL students may need to use a bilingual dictionary to construct their response; they may also need to reference their glossary for this unit.Some students may need a hardcopy of the problem versus just projecting it on an overhead screen.
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Discuss It!
• Based upon this lesson, how might you describe the new “look and feel” of instruction with Common Core?
Florida Dept. of Education
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Course Requirements and Standards
Curriculum Mapping in Layers
Florida Dept. of Education
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Step 1 - Course Descriptions• General Information
– Course Code– Title– Credit– Graduation Requirement– Course Length
• Critical Areas of Focus or General Description• NGSSS Requirements for 2013-14 Assessments• Related Benchmarks
– Common Core Literacy Standards– Common Core Mathematical Practices– Common Core Mathematics Standards
Florida Dept. of Education
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Critical Areas of Focus
Florida Dept. of Education
• Look at the 2013-2014 Course Description for your selected grade level/course
• Read each critical area/unit• As a group, summarize the main idea of each
critical area in 1 – 2 sentences.
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Grade 3 Math - Critical Areas of Focus
1. Developing understanding of multiplication and division and strategies for multiplication and division within 100
2. Developing understanding of fractions, especially unit fractions (fractions with numerator 1)
3. Developing understanding of the structure of rectangular arrays and of area
4. Describing and analyzing two-dimensional shapes
Florida Dept. of Education
Grade 3Course
Grade 3Course
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Course Requirements and Standards
Curriculum Mapping in Layers
“Chunks” or Big Ideas
Florida Dept. of Education
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Step 2 - “Chunking”
• Begin with the course descriptions and standards and benchmarks.
• “Chunk” the critical area into smaller major areas of focus.
• Sort the standards and/or benchmarks contained in the course description based upon these major areas of focus (there will likely be some overlapping of standards).
Florida Dept. of Education
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Grade 4– Critical Area #1(1) Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context. .Florida Dept. of Education
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Grade 4“Chunking” SampleCritical Area 1: Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. In this unit:1. Students apply their understanding of models for multiplication (equal-sized
groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products.
2. Students develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems.
3. Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context. .
Florida Dept. of Education
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“Chunking” Standards1. Students apply their understanding of models for multiplication
(equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products.
– MACC.4.OA.1.1 -MA.4.G.3.2– MACC.4.OA.1.2 -MACC.K12.MP.1.1– MACC.4.OA.1.3 -MACC.K12.MP.4.1– MACC.4.OA.2.4 -MACC.K12.MP.6.1– MACC.4.NBT.2.5 -MACC.K12.MP.7.1– MACC.4.MD.1.1 -MACC.K12.MP.8.1– MACC.4.MD.1.3
Florida Dept. of Education
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Course Requirements and Standards
Curriculum Mapping in Layers
“Chunks” or Big Ideas
Florida Dept. of Education
Major Learning Goals
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Step 3 - Learning Goals
The Learning Goal (Defines what students should know and be able to do.)1. Students demonstrate their understanding of multiplication by using
various methods to compute products of multi-digit whole numbers. Students can accurately estimate or mentally calculate products.
Florida Dept. of Education
The “Chunk” (Describes the integrated/related content standards students are expected to learn.)1. Students apply their understanding of models for multiplication (equal-sized groups,
arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products.
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• Learning Goals, Scales, and Learning Activities• For more information:
– https://www.floridaschoolleaders.org– https://www.floridaschoolleaders.org/resources/in
dex.aspx
Florida Dept. of Education
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State and Map Learning Goals
• Select one learning goal to share with group and using chart paper record the learning goal and “chunked” standards.
Florida Dept. of Education
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• Learning Objectives
• •
• Learning Objectives
• •
• Learning Objectives
• Learning Objectives
Florida Dept. of Education
Mapping Learning Goals
Learning Goal 1
Learning Goal 2
Learning Goal 3
Learning Goal 4
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State and Map Learning Goals
• Begin the mapping process to identify when these learning goals will be taught using 2013-2014 Curriculum Map.
Florida Dept. of Education
2013-2014 Mathematics Curriculum Map
Week/Quarter 1 2 3 4 5 6 7 8 9
1 LG6LG7
LG5
LG1LG2
2
LG1LG2LG5LG6LG7
3 LG5LG6
4 LG5LG6
Resources • Florida Common Core
– http://www.fldoe.org/schools/ccc.asp– http://www.fldoe.org/schools/BlastOff.asp
• Common Core State Standards for Mathematics– http://www.corestandards.org
• Solution Tree– http
://files.solution-tree.com/pdfs/Reproducibles_CCMLG/repros/table%202.2mathematicalpractices--look-forsasclassroomindicators.pdf
• CPALMS– http://www.floridastandards.org
• The Teaching Channel– https://www.teachingchannel.org
• Illustrative Mathematics– http://illustrativemathematics.org/
• Inside Mathematics– http://www.insidemathematics.org/index.php/common-core-standards
• Progressions Documents – http://ime.math.arizona.edu/progressions
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Resources
• Figure This– http://figurethis.org/index.html
• New York Times– http://learning.blogs.nytimes.com/2012/09/26/n-ways-to
-apply-algebra-with-the-new-york-times/• NCTM Illuminations
• http://illuminations.nctm.org/• NCTM Navigation Series
– http://www.nctm.org/catalog/productsview.aspx?id=110
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Objectives for Day 1 – Status Check
• Participants will:
Identify major learning goals for a specific course by integrating across content areas and “chunking” the standards into a few big ideas, and
Develop a projected timeline for instruction by mapping the major learning goals across the semester or year as appropriate for the course.
Florida Dept. of Education