Satinder Singh, Director of Mathematics [email protected] Debbie Williams, Coordinator of Mathematics [email protected] San Joaquin County Office of Education,

TRANSITIONING TO THE COMMON COREDay I: Content and CurriculumJefferson K-2

Satinder Singh, Director of [email protected]

Debbie Williams, Coordinator of [email protected]

San Joaquin County Office of Education, Education Services

Shift in Approach“The most necessary task of civilization is to teach people how to think. It should be the primary purpose of our public schools…The trouble with our way of education is that it does not give elasticity to the mind. It casts the brain into a mold. It insists that the child must accept. It does not encourage original thought or reasoning, and lays more stress on memory than observation.”

_ Thomas A. Edison

2

OutcomesTo understand the background and rationale

for the Common Core State Standards for Mathematics

To become aware of the required shifts in Focus, Coherence, and Rigor

To deepen our understanding of the Common Core State Standards for MathematicsOrganization of the StandardsStandards of Mathematical PracticeSpecific Grade Level ExpectationsCoherence of Progressions

3

AgendaWelcome, OverviewBackground of the Common Core State StandardsInstructional Shifts for MathematicsStandards for Mathematical PracticeStandards for Mathematical ContentReflections, Closing

44

KWL ChartWhat I already KNOW about the Common Core State Standards

What I WOULD like to learn about the Common Core State Standards

What I LEARNED about the Common Core State Standards

55

Common Core Quiz- True or False?The Common Core State Standards …1. …are National/Federal Standards2. …were commissioned by Achieve in Washington, D.C. 3. …will be assessed in the spring of 2015 by two

assessment organizations4. …are K-12 standards that test

at every grade level 5. …are for Mathematics and English

Language Arts only

6

PISA 2009Overall Math Scale

Significantly Above OECD Average

Not Significantly Different

(OECD Average 496)

Significantly below OECD Average

1 Shanghai-China 600

2 Singapore 562

3 Hong Kong-China 555

4 Korea 546

6 Finland 541

9 Japan 529

10 Canada 527

11 Netherlands 526

13 New Zealand 519

15 Australia 514

16 Germany 513

22 France 497

28 United Kingdom 492

31 United States 487

32 Ireland 487

34 Spain 483

38Russian Federation

468

51 Mexico 419

57 Brazil 386

61 Indonesia 371

Why Common Core?

7

8achievethecore.org8

Why Common Core?

9

Nationwide, many students in two-year and four-year colleges need remediation in math.

Remedial classes lower the odds of finishing the degree or program.

Need to set the agenda in K-12 math programs to prepare more students for postsecondary education and training

achievethecore.org9

Why Common Core?

10

Background of the Common CoreThe National Governors Association (NGA) and Council of Chief State School Officers (CCSSO) commissioned the development of the Common Core standards with the following design principles:Fewer, higher and clearer standardsBased on solid research and practice evidenceResult in College and Career Readiness

achievethecore.org10

Benefits of the Common CoreClarity. Students understand what is expected of them.

Equity. Common set of expectations across the nation.

Competition. Internationally benchmarked.

Collaboration. States and district sharing resources.

Preparation. Students able to succeed after high school.

1111

States that Have Adopted the CCSS

1212

13

Instructional Shifts in Mathematics

13achievethecore.org

FocusFocus strongly where the standards focus.

CoherenceThink across grades and link to major topics.

RigorPursue conceptual understanding,procedural skill and fluency,and application.

14

Shift #1 Focus:

Focus Where the Standards Focus


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

The Shape of Math in A+ Countries

Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002). 15 15

Required Fluencies & Priorities

16

Gr Required Fluency Priorities

K Add/subtract within 5 (K.OA.5)

Addition and subtraction—concepts, skills, and problem solving

1 Add/subtract within 10 (1.OA.6)

2 Add/subtract within 20 (2.OA.2)Add/subtract within 100 (2.NBT.5)

What is Fluency?Fluency is much more than fact recall. It does not equate timed test or memorization.It is flexible use and understanding of numbers and quantities. It involves reasoning about numbers and operations. e.g. 5 + 7 + 8 Make quick tens 5 + (5 + 2) + 8

(5 + 5) + (2 + 8) 10 +10 = 20

17

Fluency continued…How do we develop fluency with understanding?

One pedagogical approach called Number Talk is ideal for developing it

18


19


3 Add/subtract within 100 (3.OA.7)Add/subtract within 1000 (3.NBT.2)

Multiplication and division of whole numbers and fractions—concepts, skills, and problem solving

4 Add/subtract within 1,000,000 (4.NBT.4)

5 Multi-digit multiplication (5.NBT.5)


20


6 Multi-digit division (6.NS.2)Multi-digit decimal operations (6.NS.3)

Ratios and proportional reasoningEarly expressions and equations

7 Solve equations of the form px + q = r and p(x + q) = r where p, q, and r are rational numbers (7.EE.4)

Ratios and proportional reasoningArithmetic of rational numbers

8 Linear algebra

9 Understand solving equations as a process of reasoning—master linear (A-REI.A)

21

Shift #2 Coherence:

Think Across Grades, Link Major Topics Within Grades


2 x 7 = 14

0 211472

7

Linear Model—Repeated Addition Area Model—Multiplication Array

17 x 12

0 362412 48 60 72 84 …

17

12

Shift #2 Coherence:


Base Tenblocks

0 362412 48 60 72 84 …

17

12

10

7

10 2

(17)(12)

(10 + 7)(10 + 2)

100 + 20 + 70 + 14

Distributive Property

Shift #2 Coherence:

Think Across Grades, Link Major Topics Within Grades17 x 12

100 20

1470

10

7

10 2

(17)(12)(10 + 7)(10 + 2)100 + 20 + 70 + 14

(x + 7)(x + 2)x2 + 2x + 7x + 14x2 + 9x + 14

x 2

x

7

Multiplying Binomials

Shift #2 Coherence:


Multiplying Binomials

(x + 7)(x + 2)x2 + 2x + 7x + 14

x2 + 9x + 14

x 2

x

7x

7

x 2

x2 2x

7x 14

Factoring Trinomials

x2 + 9x + 14(x + 7)(x + 2)

Shift #2 Coherence:



Rigor requires a balance of:Deep understandingComputational and procedural fluencyApplication of skills in problem

solving situationsPursuit of all three requires

equal intensity in time, activities,and resources

Shift #3 Rigor:

Pursue Conceptual Understanding,Procedural Fluency, and Application

RIGOR

Deep U

nders

tandin

g

Applica

tion

Flu

en

cy

27

Instructional Shifts in MathematicsCompare your current practice to the required shifts toward focus, coherence, and rigor.What are you currently doing well?What might be some areas in need of growth?

Share your thoughts with your table.

Standards for Mathematical Practice“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.”

National Governors Association Center for Best Practices and Council of Chief State School Officers (2010)Common Core State Standards for Mathematics

2828

College instructors rate the Mathematical Practices as being of higher value for students to master in order to succeed in their courses than any of the CCSS content standards.

Conley, Drummond, Gonzalez, Rooseboom, & Stout 2011

Standards for Mathematical Practice

29

30

Standards for Mathematical Practice

JIGSAW Divide up the Practices with members of your table group

so each person reads at least two. Read your assigned Practice.

• Underline key words or phrases.• What is this Practice about?

After reading, share one or twohighlights about the Practices you read.

30

Individually complete the task at your grade level.

Once the task is completed, discuss with your grade level:Which Standards for

Mathematical Practice did you use to solve the task?

How did you use the Practice? Be specific.

Mathematical Practices in Action

31

Examine the student work for the task you completed.

Determine which Standards for Mathematical Practice are represented.

Compare your work with the student work. How are the practices

similar? How are the practices

different?

Mathematical Practices in Action

32

Standards for Mathematical ContentDomains and Conceptual Categories

33

Findell & Foughty (2011)College and Career-Readiness through the Common Core State Standards for Mathematics

33

High School: Two Suggested Pathways

TRADITIONAL (Typical in U.S.)

2 Algebra courses, 1 Geometry course, with Probability and

Statistics interwoven

INTEGRATED(Typical outside of U.S.)

3 courses that attend to Algebra, Geometry, and Probability and Statistics

each year 34

HS Algebra I Mathematics I

Geometry Mathematics II

Algebra II Mathematics III

Courses in higher level mathematics: Precalculus, Calculus*, Advanced Statistics, Discrete Mathematics, Advanced Quantitative Reasoning, or courses designed for career

technical programs of study.

adapted from 2011 © CA County Superintendents Educational Services Association34

Standards Across the Grades

Perc

ent o

f Sta

ndar

ds a

t Eac

h G

rade

Lev

el

K 1 2 3 4 5 6 7 8 HS0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Alg & FuncGeometryMeas-Data-Stat-ProbNumber

35

Critical AreasTurn to the Introduction for your grade level.Review the critical areas.With your grade level team, create a graphic

representation to illustrate the critical areas.May include a few words for clarity

or emphasisMust include several drawings or

diagrams illustrating what studentsmust know and be able to do

36

Grade Level

Overview

37

Domains:Overarching

ideas that connect topics

across the grades

Clusters:Illustrate the

progression of increasing

complexity from grade to grade

37

Domain

ClusterHeading

Standard

Reading the Standards

38

Grade . Domain Level Code

California Addition

39

Domain AnalysisRead the Content Standards for your grade

level.Complete the Domain Analysis Tool,

identifying:What is familiar to us in the Content Standard

Clusters?What expectations appear to be new or

challenging?Compare your findings with a grade level

or course partner.

Unpacked Standards available at

http://tinyurl.com/nc1ccss



40

Base Ten Place Value Chart

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48

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Symmetry with Respect to the Ones Place

49

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100

30

10

3Fractional Notation

1

1

10

1

100

1

1000

1

1

1000

1

100

1

10

50


50

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0.6262

100Decimal Notation

1000 100 10 1 0.1 0.01 0.001

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51

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Ten

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103 102 101

100

Exponential Notation 1000 = 103 0.001 = 1.0 x 10-3

10-1 10-2 10-3


52

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ExponentialNotation

103 102 101 100

10-1 10-2 10-3


1000. 100. 10. 1. 0.1 0.01 0.001

DecimalNotation

FractionalNotation

1

1

10

1

100

1

1000

1

1

1000

1

100

1

10

Standards Progression

Within and Across DomainsGrades K - 3

Number and Operations in Base Ten

54

Number & Operations in Base Ten Progression (K-5)

Standard K.OA.3 and K.NBT.1“Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation(e.g., 5 = 2 + 3 and 5 = 4 + 1).”Activity: Bobby Bear “Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation ( e.g.,18 = 10 + 8)…”Activity: Tens and Ones using Unifix Cubes 55

Multiple RepresentationsVisualizing Number Combinations

https://www.teachingchannel.org/videos/visualizing-number-combinations?fd=1

“Count to 120, starting at any number less than 120.…”

“Compare two digit numbers basedon meanings of tens and ones digits…”

Activity: Ordering Numbers

57


Standards 1.NBT.1 and 1.NBT.3

“Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones; e.g. 706 equals 7 hundreds,0 tens, and 6 ones…”

Activity: Making 124

58


Standard 2.NBT.1

101 and OutPlace Value Game

59

http://soc.li/yT1gEqX

“Use place value understanding to round to whole numbers to the nearest 10 or 100.”

Activity: Rounding to 50 or 500

60


Standard 3.NBT.1

Progression Activities1. Bobby Bear Buttons (K)2. Tens and Ones Using Unifix Cubes (K &

1st)3. 101 and Out (K-2)4. Ordering Numbers ) ( 1st)5. Making 124 (2nd)

6. Rounding to 50 or 500 (3rd)

61

Connecting to Current Practice

62

Think-Pair-ShareCoherence: What connections do you see

between these various grade level activities?

Rigor:Deep understandingFluencyApplication?

In what ways did the activities illustrate rigor?

Reflection: KWL ChartLocate the KWL chart you

began earlier in the training.Complete the third column:

What I Learned about the CCSS

Partner up with someone at your table and share your favorite “aha” from today’s session.

6363

Feedback/ClosingPlease complete the feedback form before

leaving.Bring your CCSS booklet, folder, and

Teacher’s Edition to the next session.

64

Documents

Satinder Singh, Director of Mathematics [email protected] Debbie Williams, Coordinator of Mathematics [email protected] San Joaquin County Office of Education,