a story of units overview

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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units

A Story of Units Overview


N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Units

Session Objectives

2

• Examine the rationale and alignment of A Story of Units to the CCLS, Learning Progressions, Instructional Shifts, Publishers’ Criteria, PARCC, Major Content Emphases, and the Pre-Post Math Standards.

• Explore the How to Implement A Story of Units document as a tool for facilitating effective implementation of the Common Core Math Standards aligned curriculum.

• Prepare for redelivery of this information to teachers and other colleagues by identifying key tools and resources provided.



3



The Shape of Math in A+ Countries

4

Mathematics

topics

intended at

each grade by

at least two-

thirds of A+

countries

Mathematics

topics intended

at each grade

by at least two-

thirds of 21 U.S.

states



5

“To meet the realities of the 21st century global economy and maintain America’s competitive edge into the future, we need students who are prepared to compete not only with their American peers, but with students from all across the globe for the jobs of tomorrow.”

“Benchmarking for Success: Ensuring U.S. Students Receive a World-Class Education”



AGENDA

6

Examine Alignment with the Instructional ShiftsExamine Alignment with the Mathematical PracticesExamine Alignment with the Publishers’ CriteriaExamine PARCC Type I, II, and III TasksExamine Alignment with the Major Content Emphases

and the Pre-Post Math StandardsWatch a Video Clip of A Story of Units in the Classroom



Instructional Shifts

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Turn and Talk

8

• What have your districts/schools found to be most engaging about CCLS and the Instructional Shifts?

• What have your schools done to move toward implementing the Instructional Shifts in the mathematics classroom?

• What is the general reaction from administrators, educators, and students?



Curriculum Map

9

Pre-Kindergarten Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5

Approx. test date

for grades 3-5

M1: Multiplication and Division with Factors of 2, 3,

4, 5, and 10(25 days)

M3: Multiplication and Division of up to a 4-Digit Number by up to a 1-Digit Number Using Place Value

(43 days)

*M2: Unit Conversions(7 days)

M1: Place Value, Rounding, Fluency with Addition and Subtraction Algorithms of

Whole Numbers(25 days)

M2: Problem Solving with Mass, Time, and Capacity

(25 days)

M6: Collecting and Displaying Data (10 days)

M1: Whole Number and Decimal Fraction Place Value

to the One-Thousandths(20 days)

M4: Addition and Subtraction of Angle

Measurements of Planar Figures

(20 days)

M5: Order and Operations with Fractions

(45 days)

M2: Multi-Digit Whole Number and Decimal Fraction Operations

(35 days)

M6: Decimal Fractions(20 days)

20 days

20 days

Test Date

9/6/12

10/10/12

M2: Addition and Subtraction with Length, Weight, Capacity, and Time

Measurements(20 days)

M3: Place Value, Counting, and Comparison of Numbers

to 1000(25 days)

M2: Analyze, Compare, Create, and Compose Shapes

(15 days)

M1: Analyze, Sort, Classify, and Count up to 5

(45 days)

M2: Identify and Describe Shapes (7 days)

M3: Comparison with Length, Weight, and Numbers to 10

(43 days)

M1: Addition and Subtraction of Numbers to 10 and Fluency

(45 days)

M3: Ordering and Expressing Length Measurements as

Numbers(15 days)

M2: Place Value, Comparison, Addition and

Subtraction of Numbers to 20(35 days)

11/8/12

12/11/12

*M1: Sums and Differences(10 days)

M3: Count and Answer "How Many" Questions up to 10

(50 days)

20 days

20 days

20 days

20 days

M1: Classify and Count Numbers to 10

(43 days)

M6: Graph Points on the Coordinate Plane to Solve

Problems(40 days)

M5: Addition and Multiplication with Volume

and Area(25 days)

M7: Exploring Multiplication(20 days)

M7: Word Problems with Geometry and Measurement

(40 days)

20 days

20 days

20 days

20 days

M5: Fractions as Numbers on the Number Line

(35 days)

M4: Multiplication and Area(20 days)

M3: Multiplication and Division with Factors of 6, 7,

8, and 9(25 days)

5/28/13

M4: Addition and Subtraction of Numbers to 1000

(35 days)

M5: Preparation for Multiplication and Division

Facts(40 days)

M5: Write Numerals to 5, Addition and Subtraction

Stories, Count to 20(35 days)

M6: Analyze, Compare, Create, and Compose Shapes

(10 days)

M4: Number Pairs, Addition and Subtraction of Numbers

to 10(47 days)

20 days

M4: Describe and Compare Length, Weight, and Capacity

(35 days)

20 days

1/17/13

2/15/13

3/22/13

4/29/13

M3: Addition and Subtraction of Fractions

(22 days)

M4: Multiplication and Division of Fractions

(38 days)

M5: Numbers 10-20, Counting to 100 by 1 and 10

(30 days)M6: Place Value,

Comparison, Addition and Subtraction of Numbers to

100(35 days)

M7: Recognizing Angles, Faces, and Vertices of

Shapes, Fractions of Shapes(20 days)

M6: Comparison, Addition and Subtraction with Length

and Money(30 days)

20 days

20 days

20 days

20 days

20 days

20 days

M5: Identify, Compose, and Partition Shapes

(15 days)

M4: Place Value, Comparison, Addition and

Subtraction of Numbers to 40(35 days)



A Story of Units Aligned to theLearning Progressions

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Coherence Across the GradesGrade 2: 3 tens or 3 units of 10 (Grade 2 OA Standards)Grade 3: 3 fours or 3 units of/groups of four (Grade 3 OA Standards)Grade 4: 3 fourths or 3 units of one-fourth (Grade 3 NF Standards)




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Coherence Across the GradesLearning 12 tens = 120 12 tenths = 1.2Learning 4 thirds 4/3 = 1 1/3 or even 4 threes = 12




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Grade 3 Grade 4 Grade 5Number and Operations in Base Ten Standards (NBT)

Counting up and down by ones, tens and hundreds,

both with the number line and place value chart are

essential from Grade 3 forward to rounding and

mental math.

Meaningful understanding of all operations with base-ten

whole numbers

Understanding place value’s extension into decimal fractions and

operations



Turn and Talk

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How do these examples of the Instructional Shifts in AStory of Units compare with evidence of coherence inyour current curriculum?



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Number Line Model

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Number Line Model

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Key Points:

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• A Story of Units is being written in alignment with the Instructional Shifts required by the CCLS.

• All standards for each grade have been carefully included in the module sequence.

• The P-5 modules are designed with deliberate coherence to capitalize on the learning progressions that are embedded in the CCLS.

• The activities promote a careful balance of fluency practice, conceptual understanding, and application, which aligns with the instructional shift, rigor.



AGENDA

18





Standards for Mathematical Practice

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1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning

of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.



Standards for Mathematical Practice

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“… describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.”



Focus Standards for Mathematical Practice

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Mathematical Practice Brought to Life

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Lessons 2 and 3 include examples of MP.7, “Look for and make use of structure,” because, in counting, students make use of the structure provided by multiples of ten and a hundred. Students think in terms of “getting to a ten” or “getting to a hundred.”



Mathematical Practice in Lessons

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Name this Math Practice

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“Giving students opportunities to practice counting using ones and bundles of tens and hundreds while asking them to identify benchmark numbers will cue them to the ease and efficiency of skip-counting.”

MP.7 – Look for and make use of structure.



Mathematical Practices

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• At your table count off from 1 to 8. • Take two minutes to read your math practice.• Highlight the key phrases of the math practice.• Share with your table examples of how each math

practice is integrated into the A Story of Units curriculum.



Table Talk

26

Share with members of your table, examples of how theStandards for Mathematical Practice are brought to lifein A Story of Units.

Person 1 shares MP.1, person 2 shares MP.2, etc.



Key Point

27

A Story of Units brings the Standards for Mathematical Practice to life. Although all practices are integrated throughout the curriculum, individual lessons may highlight one or two practices specifically to facilitate educators in developing these habits of mind in their students.



AGENDA

28





The Publishers’ Criteria

29

I. Focus, Coherence, and Rigor in the CCSSM II. Criteria for Materials and Tools Aligned to the

StandardsIII. Appendix: “The Structure is the Standards”



Focus, Coherence, and Rigor

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• At any given grade level 75% of the year should be spent on major areas of work.

• The first half of the year should predominantly cover major areas of work.



Criteria for Materials and Tools

31




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Examples of Student Reasoning in A Story of Units

Sally did some counting. Look at her work. Explain why you think Sally counted this

way.

177, 178, 178, 190, 200, 210, 211, 212, 213, 214




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Examples of Student Reasoning in A Story of Units

Whisper the numbers as you count:

a) Count by 1s from 367 to 375.

b) Skip-count by 10s from 422 to 492.

c) Skip-count by 100s from 156 to 856.

d) Count by 1s from 269 to 261.

e) Skip-count by 10s from 581 to 511.

f) Skip-count by 100s from 914 to 314.

I found letter ____ to be challenging, because ________.

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“The Structure is the Standards”

You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will send one piece a day in an envelope for the next year…

Standards for a Grecian Urn

http://commoncoretools.me/wp-content/uploads/2012/02/jigsaw.jpg



Indicators of Quality in Instructional Materials and Tools for Mathematics

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• Problems in the materials are worth doing.

• Assignments aren’t haphazardly designed. Exercises are given to students in intentional sequences.

• The modules contain different types of problems that are presented in a simple to complex format. There is variety to what students produce in response to prompts.



Indicators of Quality in Instructional Materials and Tools for Mathematics

36

• There are separate teacher materials that support and reward teacher study.

• The use of manipulatives follows best-practices.

• The visual design isn’t distracting or chaotic.

• Support for English language learners and members of other special populations is provided.



Key Point

37

A Story of Units adheres to the guidelines established in the Publishers’ Criteria and benefits from on-going feedback from Student Achievement Partners throughout the writing process.



AGENDA

38





PARCC Type I Tasks

39

• Assess concepts, skills and procedures• Include a balance of conceptual understanding,

fluency, and application• Can involve any or all mathematical practice

standards• Are machine-scored including innovative, computer-

based formats



PARCC Type I Tasks

40



PARCC Type II Tasks

41

• Assess ability to express mathematical reasoning• Call for written arguments/justifications, critique of

reasoning, or precision in mathematical statements (MP.3, MP.6) and can involve other mathematical practice standards

• Are hand-scored, or machine-scored with innovative computer-based formats, or a combination



PARCC Type II Tasks

42



PARCC Type III Tasks

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• Assess modeling/applications • Call for modeling/application in a real-world context

or scenario (MP.4) and can also involve other mathematical practice standards

• Are hand-scored, machine-scored with innovative computer-based formats, or a combination



PARCC Type III Tasks

44

Sample Grade 4 ProblemJim has three times as much money as Sally. If Jim has$14 more than Sally, how much money do they havealtogether?



Turn and Talk

45

• How do the new PARCC assessments compare with current and previous assessments?



Key Point

46

• The problems woven throughout the modules, as well as the Mid-Module and End-of-Module Assessment Tasks, are aligned with the PARCC Type I, Type II, and Type III problems/tasks.



AGENDA

47





Major Content Emphases

48



49



50



Pre-Post Math Standards

51

• Select a testing grade and review the Standards that are expected to be taught before and after the state test.

• Which Standards will be addressed after the test?



Pre-Post Math Standards

52

Grade 3 Grade 4 Grade 53.MD.43.MD.83.G.1

4.NF.54.NF.64.NF.74.MD.14.MD.2

5.OA.35.G.15.G.2



Key Point

53

A Story of Units is being written in alignment with the Major Content Emphases. Each grade focuses only on the appropriate math and prioritizes the major work of the grade. For Grade 3 through Grade 5, the standards identified on the Pre-Post Math Standards as those which should be taught after the state test in April, have been intentionally aligned with the final modules of those grades.



AGENDA

54





Video Clip – Subtraction with Renaming

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Guiding Questions:• What resonates with you as it relates

to our transition to teaching the CCLS?• What do you notice about the

interaction between the students and the teacher?

• Where do you see evidence of the Instructional Shifts and the Standards of Mathematical Practice?




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This video is posted in the video library on EngageNY:

http://engageny.org/video-library






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Guiding Questions:• What resonates with you as it relates

to our transition to teaching the CCLS?• What do you notice about the

interaction between the students and the teacher?

• Where do you see evidence of the Instructional Shifts and the Standards of Mathematical Practice?



Key Points

58

• A Story of Units • aligns with the Instructional Shifts required by the CCLS. • brings the Standards for Mathematical Practice to life. • adheres to the Publishers’ Criteria. • includes PARCC Type I, Type II, and Type III problems/tasks.• aligns with Major Content Emphases and the Pre-Post Math

Standards.



Next Steps

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• What are your next steps in introducing components of this curriculum to your school(s)/district(s)?

• How can you use your expertise as a leader and as an educator of mathematics to share your support of this curriculum?


NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units

Overview Follow Up



Team Time – Major Content Emphases

61

• How are the major content emphases for your grade(s) reflected in the Curriculum Overview?

• How much time is devoted to the major content emphases?

• When are the ‘post’ standards addressed?



Team Time – Mathematical Models

62

• Which mathematical models are relevant for your grade(s)?

• In what ways will these models impact instruction?



Team Time – Publishers’ Criteria

63

• In what ways does A Story of Units meet the expectations established in the Publishers’ Criteria?

a story of units overview

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