Session 2K-5 Mathematics

Common Core State Standards

Bell Work Activity

• Handout #1– The Common Core State

Standards for Mathematics from A to Z

• List words that begin with each letter of the alphabet that identify aspects of the Common Core State Standards for Mathematics.

Handout #1

Common Core From A to Z

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“We live in a time of vast changes that include accelerating globalization, mounting quantities of information, the dominating influence of science and technology, and the clash of civilizations. Those changes call for new ways of learning and thinking in school, business, and the professions.” -Howard Gardner

Five Minds for the Future (2007)

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Expected Outcomes

• Become familiar with the structure of the Common Core State Standards for Mathematics.2

Enhance knowledge of the Common Core Standards for Mathematical Practice. 3

4Understand how the critical areas bring focus to key mathematical concepts for students to learn at each grade level.

5 Consider how the learning progressions can be used to inform curriculum and guide instruction.

• Enhance knowledge base of the Common Core Standards for Mathematics.1

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Understanding Teachers

Aligned

McCallum

Guided by Principles

Standards

National Focus NGA

Habits of

Mind

Organized

International Benchmarked

Building Foundation

CCSSO Daro

Progressions

Joint effort

Vision

Quality

Knowledge

Zimba

Robust, Relevant,

Real-world

Whole Child Approach

Learner-focused Life-long

skills

Ensuring Education Focus

BalancedClarity

Critical AreasClusters Domains

Evidenced-based

Illustrative Mathematics

Sense-making

Rigor

Research-based

Procedural fluency

ProficiencyPARCC

OpportunitiesMathematical Practice

XYOU

FluencyApplication

Coherence

Timeline

Developmental Level

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High School Conceptual Categories

http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

• Number and Quantity (N)

• Algebra (A)

• Functions (F)

• Modeling (*)

• Geometry (G)

• Statistics and Probability (S)A-Z

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

Geometry (G)

Measurement and Data (MD)

Statistics and Probability (SP)A-Z

Domain

Domain

Domain

Domain

Cluster Headings

Cluster Headings

Cluster Headings

Cluster Headings

9A-Z

Domain

Cluster Headings

Standards

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Florida’s Numbering ofthe Common Core State Standards

MACC.K.CC.2.5

Subject Grade Domain Cluster StandardSubject Mathematics Common Core

Grade K

Domain Counting and Cardinality

Cluster Count to tell the number of objects

Standard Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

11A-Z

Standards for Mathematical Practice“The Standards for Mathematical Practice are unique in that they describe how teachers need to teach to ensure their students become mathematically proficient. We were purposeful in calling them standards because then they won’t be ignored.” - Bill McCallum

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Use appropriate tools strategically5

Attend to precision6

Look for and make sense of structure7

Look for and express regularity in repeated reasoning

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Standards for Mathematical Practice

Make sense of problems and persevere in solving them

1

Reason abstractly and quantitatively2

Construct viable arguments and critique the reasoning of others

3

Model with mathematics4

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Handout

A-Z

Florida’s Common Core State Standards Implementation Timeline

Year/Grade Level K 1 2 3-8 9-12

2011-2012 FL L L L L

2012-2013 F L F L L L L

2013-2014CCSS fully implemented

F L F L F L B L B L

2014-2015CCSS fully implemented and

assessed

F L F L F L F L F L

F - full implementation of CCSS for all content areasL – begin full implementation of content area literacy standards including: (1) use of

informational text, text complexity, quality and range in all grades (K-12), and (2) CCSS Literacy Standards in History/Social Studies, Science, and Technical Subjects (6-12)

B - blended instruction of CCSS with Next Generation Sunshine State Standards (NGSSS); last year of NGSSS assessed on FCAT 2.0

http://www.fldoe.org/bii/pdf/CCSS-ImplementationTimeline.pdf 14A-Z

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Standards for Mathematical Practice

Reasoning and

Explaining

Seeing Structure and Generalizing

Overarching Habits of Mind of a Productive Mathematical Thinker

2. Reason abstractly and quantitatively

3. Construct viable arguments and

critique the reasoning of others

Modeling and

Using Tools

4. Model with mathematics

5. Use appropriate tools strategically

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

1. Make sense of problems and persevere in solving them6. Attend to precision

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The Standards for Mathematical Practice

• Please locate the Common Core State Standards for Mathematics.

• Take a moment to examine the first three words of the narrative description for each of the 8 mathematical practices.

• What do you notice?

Mathematically Proficient Students…

Page 6

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Digital TaskYour Digital Task is to:

• Read your assigned Mathematical Practice.

• Identify the words (verbs) that illustrate the student actions for this practice.

• Text the words on one continuous line with spaces between each word.

Example: #..... create analysis model describe demonstrate….

Handout

Expectations

Students understanding and using definitions. Students justifying and explaining their thinking and listening to arguments of others and deciding if they make sense..

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Students planning solution pathways, monitoring and evaluating their progress and asking “Does this make sense?”

1

Students knowing and using different properties of operations and objects and creating a coherent representation of the problem at hand.

2

Students applying and using mathematics to solve problems connected to real-life situations. Students using models to represent, analyze and interpret results.

4

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Expectations

Students being able to look closely to discern a pattern or structure. Students being able to shift perspectives. 7

Students communicating precisely to others. Students calculating accurately and efficiently, expressing numerical answers with a degree of precision appropriate for the problem context.

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Students evaluating the reasonableness of their results. Student Maintaining oversight of the process, while attending to the details.

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Students being familiar with tools appropriate for their grade or course and using technology tools to explore and deepen their understanding of concepts. Students being able to make sound decisions about when each of these tools might be helpful.

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http://www.wordle.net/show/wrdl/5360414/Mathematical_Practice_Actions20

Consider the Learners

• Over 240,000 ELLs in Florida

• Almost every district has ELLs

• 300 languages are spoken among ELLs

• 79% of ELLs are in Mainstream/Inclusion model classrooms

• ELLs are learning in the same classrooms as non-ELLs

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Making the Content Comprehensible

• Use the standards vocabulary as a teaching tool. “Generalize, develop, describe, analyze, apply, measure,” etc. are all words ELLs will hear in the classroom and need to understand.

• ELLs may know how to perform the skill using their language, they just may not yet have the English vocabulary.

• Use pictures, graphs, and charts whenever possible.

• Make use of root words and cognates. 22

Classroom Strategies

• Group ELLs with non-ELLs to work together.

• Allow more wait time for ELLs to respond.– Silence does not necessarily mean the student

does not know the answer, the ELL may be translating the answer and need more time.

• Remember that ELLs from different countries may display mathematical functions in different ways.

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K-5 Domains and Critical AreasKindergarten Domains Kindergarten Critical Areas

Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Measurement and Data Geometry

Representing and comparing whole numbers, initially with sets of objects. Describing shapes and space.

More learning time in Kindergarten should be devoted to number than to other topics

1st Grade Domains 1st Grade Critical Areas Operations and Algebraic Thinking Number and Operations in Base Ten Measurement and Data Geometry

Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20. Developing understanding of whole number relationships and place value, including grouping in tens and

ones. Developing understanding of linear measurement and measuring lengths as iterating length units. Reasoning about attributes of, and composing and decomposing geometric shapes.

2nd Grade Domains 2nd Grade Critical Areas Operations and Algebraic Thinking Number and Operations in Base Ten Measurement and Data Geometry

Extending understand of base-ten notation. Building fluency with addition and subtraction. Using standard units of measure. Describing and analyzing shapes.

3rd Grade Domains 3rd Grade Critical Areas Operations and Algebraic Thinking Number and Operation in Base Ten Number and Operation: Fractions Measurement and Data Geometry

Developing understanding of multiplication and division strategies for multiplication within 100. Developing understanding of fractions, especially unit fractions (fractions with numerator 1). Developing understanding of the structure of rectangular arrays and of area. Describing and analyzing two-dimensional shapes.

4th Grade Domains 4th Grade Critical Areas Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations: Fractions Measurement and Data Geometry

Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends.

Developing understanding of fractions equivalence, addition and subtraction of fractions with like denominators, multiplication of fractions by whole numbers.

Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

5th Grade Domains 5th Grade Critical Areas Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations: Fractions Measurement and Data Geometry

Developing fluency with addition and subtraction of fractions, developing understanding of the multiplication of fractions and of division of fractions in limited case (unit fractions divided by whole numbers and whole numbers divided by unit fractions).

Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations.

Developing understanding volume.

Handout #2

24A-Z

Two critical areas in KindergartenIn Kindergarten, instructional time should focus on two critical areas:

Page 9

http://www.corestandards.org/the-standards/mathematics/kindergarten/introduction/

More learning time in Kindergarten should be devoted to number than to other topics.

• Representing, relating, and operating on whole numbers, initially with sets of objects 1.

• Describing shapes and space2.

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Identify the Kindergarten Critical AreaCluster Heading Critical Area

Know number names and the count sequence.

Count to tell the number of objects.

Describe and compare measurable attributes.

Compare numbers.Identify and describe shapes.Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.Work with numbers 11-19 to gain foundations for place value.Classify objects and count the number of objects in each categoryAnalyze, compare, create, and compose shapes.

#1 Numbers

#1 Numbers

#1 Numbers

#1 Numbers#1 Numbers

#2 Shapes

#2 Shapes

#2 Shapes

#2 Shapes

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Four critical areas in 1st GradeIn Grade 1, instructional time should focus on four critical areas:

27Page 14

http://www.corestandards.org/the-standards/mathematics/grade-1/introduction

/

developing understanding of addition, subtraction, and strategies for addition and subtraction within 201.

developing understanding of whole number relationships and place value, including grouping in tens and ones2.

developing understanding of linear measurement and measuring lengths as iterating length units3.

reasoning about attributes of, and composing and decomposing geometric shapes4.

Identify the 1st Grade Critical AreasCluster Heading Critical Area

Represent and solve problems involving addition and subtraction.Use place value understanding and properties of operations to add and subtract.Represent and interpret data.Add and subtract within 20.Tell and write time.Work with addition and subtraction equations.Reason with shapes and their attributes.Understand place value.Measure lengths indirectly and by iterating length units.Extend the counting sequence.Understand and apply properties of operations and the relationship between addition and subtraction.

#1 Operations

#1 Operations

#1 Operations

#1 Operations

#2 Base Ten

#2 Base Ten

#2 Base Ten#3 Measurement

#3 Measurement

#3 Measurement

#4 Geometry

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Four critical areas in 2nd GradeIn Grade 2, instructional time should focus on four critical areas:

extending understanding of base-ten notation1.

building fluency with addition and subtraction2.

using standard units of measure3.

describing and analyzing shapes4.

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http; ://www.corestandards.org/the-standards/mathematics/grade-2/introduction/Page 17

Four critical areas in 3rd GradeIn Grade 3, instructional time should focus on four critical areas:

developing understanding of multiplication and division and strategies for multiplication and division within 1001.

developing understanding of fractions, especially unit fractions (fractions with numerator 1) 2.

developing understanding of the structure of rectangular arrays and of area3.

describing and analyzing two-dimensional shapes4.

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http; ://www.corestandards.org/the-standards/mathematics/grade-2/introduction/Page 21

Mathematics Progressions

Whole Numbers to Fractions in Grades 3-6

http://commoncoretools.files.wordpress.com/2012/02/ccss_progression_nf_35_2011_08_12.pdf

3-5 Number and Operations - Fractions

Common Core Progressions Project

http://youtu.be/w7h64xjN-PM

http://www.youtube.com/watch?v=w7h64xjN-PM&list=PLD7F4C7DE7CB3D2E6&index=7&feature=plpp_video

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Three critical areas in 4th GradeIn Grade 4, instructional time should focus on three critical areas:

developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends

1.

developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers

2.

understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

3.

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http://www.corestandards.org/the-standards/mathematics/grade-4/introduction

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Building Fluency

What is meant by fluency?

http://www.youtube.com/watch?v=ZFUAV00bTwA&list=PLD7F4C7DE7CB3D2E6&index=13&feature=plpp_video

http://youtu.be/ZFUAV00bTwA

Mathematics Fluency: A Balanced Approach (1:56)

Grade Standard Key FluencyK MACC.K.OA.1.5 Add/subtract within 51 MACC.1.OA.3.6 Add/subtract within 10

2 MACC.2.OA.2.2MACC.2.NBT.2.5

Add/subtract within 20Add/subtract within 100 (pencil and paper)

3 MACC.3.NBT.1.2MACC.3.OA.3.7

Add/subtract within 1,000Multiply/divide within 100

4MACC.4.2.4

Critical Area #1Add/subtract within 1,000,000 Develop fluency with efficient procedures for multiplying whole numbers

5MACC.5.NBT.2.5Critical Area #1

Multi-digit multiplicationDeveloping fluency with addition and subtraction of fractions

6 MACC.6.NS.2.2MACC.6.NS.2.3

Multi-digit divisionMulti-digit decimal operations

7 MACC.7.EE.2.4a Solve px + q = r, p(x + q) = r8 MACC.8.EE.3.8b Solve simple 22 systems by inspection

Key Fluencies Handout #3

34A-Z

Three critical areas in 5th GradeIn Grade 5, instructional time should focus on three critical areas:

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http://www.corestandards.org/the-standards/mathematics/grade-5/introduction

developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions)

1.

extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations

2.

developing understanding of volume3.

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Mathematics Progressions

The Importance of Mathematics Progressions

http://youtu.be/a-P9KQdhE0Uhttp://www.youtube.com/watch?v=a-P9KQdhE0U&feature=BFa&list=PLD7F4C7DE7CB3D2E6

Operations on Whole Number Progressions

Handout #4

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Mathematics Progressions Project•Kindergarten Counting and Cardinality

•Number and Operations in Base Ten

•Number and Operations—Fractions

•K–5 Operations and Algebraic Thinking

•Measurement and Data

•Geometry Progression (coming soon!)•Expressions and Equations•Ratios and Proportional Relationships

•Statistics and Probability, Grades 6–8

http://commoncoretools.me/category/progressions/ 37

Give me a lever long enoughand a fulcrum to place it on,and I can move the world. ‐‐Archimedes

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Reflective Thoughts

How will the Critical Areas and the Cluster headings help to inform your curriculum and guide your instruction?

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3 How will you use the Learning Progressions to inform your curriculum and guide your instruction?

How will you use the Common Core Standards for Mathematical Practices to inform your curriculum and guide your instruction?

1

Handout #5

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