Math ShiftsFocus

CoherenceRigor

What are the Shifts?• Focus:

focus strongly where the standards focus

Instructional Shift: What does focus mean for our

instruction?

GRADE FOCUS (and expectation of FLUENCY and CONCEPTUAL UNDERSTANDING)

K-2 Addition and subtraction – concept, skills and problem solving

3-5 Multiplication of whole numbers and fractions – concepts, skills and problem solving

6 Ratios and proportional relationships; early expressions and equations

7 Ratios and proportional relationships; arithmetic of rational numbers

8 Linear Algebra

What are the Shifts?• Focus:

focus strongly where the standards focus • Coherence:

think across grades, and link to major topics in each grade

Instructional Shift:

What does coherence mean for our instruction?

PreK K 1 2 3 4 5 6 7 8 HS

Mathematical Practices

Counting & Cardinality

Number & Operations in Base TenRatios &

Proportional Relationships

Number &

QuantityNumber & Operations - Fractions

The Number System

Operations & Algebraic Thinking Expressions & Equations Algebra

Functions

Geometry

Measurement & Data Statistics & Probability

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Next Generation Mathematics Content Standards and Objectives

What are the Shifts?• Focus:

focus strongly where the standards focus • Coherence:

think across grades, and link to major topics in each grade

• Rigor: in major topics, pursue with equal intensity

— conceptual understanding— procedural skill and fluency— applications

Instructional Shift:

What does rigor mean for our instruction?

Center of the Classroom Culture

Standards for Mathematical Practice

Overview of session

Eight Standards for

Mathematical Practice

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

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

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Standards for Mathematical Practice

The Importance of the Standards for Mathematical Practices

Video clip

r

e

t

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Connecting the Standard for Mathematical Practice with the

Content Standards

Standards that begin with “understand” are good

opportunities to connect the Practices to the Content!

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Content & Practices

“A lack of understanding (of the content) effectively prevents a student from engaging in the Mathematical Practices.”

Skip Fennell, former NCTM president

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Content & Practices

Great Tasks Matter!

1.What is a great task?2.Why is it important to use

great tasks?

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“If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level, cognitively complex tasks.”

Stein & Lane, 1996

Tasks Matter

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“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”

Stein, Smith, Henningsen, & Silber, 2000

Thinkmath.edc.org

Tasks Matter

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Dan Meyer Math class needs a makeover - YouTube.mp4

Dan Meyer: Math Class Needs a Makeover

TED Talk

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What is a Great Task?

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Why use a Great Task?

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Center of the Classroom Culture

Standards for Mathematical Practice

Phil Daro Video clip

Getting Into the Grade Level Content Standards

Day Two

Grade Level Emphasis

Other Resources for Understanding the Grade Level Standards

Learning Progressiondocuments for the Common Core State Standards found

online at http://ime.math.arizona.edu/progressions/

Smarter Balanced Assessment ConsortiumAn Assessment System to Support Teaching and Learning

Item and Task Specifications and Sample Items

Sample assessment items and tasks areincluded in item/task specifications:www.smarterbalanced.org/itemspecs

Live sample items and tasks:www.sampleitems.smarterbalanced.org

Go to the Smarter Website

1. http://www.smarterbalanced.org2. Click on Smarter Balanced Assessment (top

of page)3. In drop down, scroll to Sample Items and

Performance Tasks4. In task bar, click on View More Sample Items5. In drop down, click on Choose 6-8 or High

School

ADE is inside ABCD. Point E is halfway between points B and C on the rectangle. Side AB is 8 cm and side AD is 7 cm.

Part A: What is the area of ADE?Part B: What is the ratio of the area of ABE to the area of ADE?Part C: What is the ratio of the area of DCE to the area of ABCD?

A 20-gallon container is filled with 6 gallons of gasoline. What fractions of the container is filled with gasoline?

.

Which equation is represented by the graph?

A.2y + x = 10B. y - 2x = -5C. -2y = 10x – 4D.2y = - 4x - 10

The three different linear functions below are represented in three different ways, as shown.

2y + 3 = 3x X f(x)

-3 -9 3 3 6 9

(I) (II)(III)

Which function has the greatest rate of change? Does any pair of functions have the same rate of change? Justify your answer.

The diagram on the right shows a pillow Chris wants to cover with fabric.

•What is the total surface area of the pillow? Round your answer to the nearest hundredth.

Show your work:

Answer _________ square inches

•If Chris shortens the length of the pillow from 15 in to 12 in, how much less fabric will she need? Round your answer to the nearest hundredth.

Show your work:

Answer _______square inches

Calculator Use on the SmarterBalanced Math Assessments

How will Smarter Balanced decide whenand how to allow calculators?

Grades 6-HS

• Calculators are available for a small proportion of grade 6 items and gradually increase in availability as students progress toward high school.

• Calculators will be available for most or all of the high school math items.

Powerful Collaboration

PLCs at Work

Teacher collaboration is the key to improving instruction and reaching all students.

Education Trust, 2005; Kersaint, 2007

Critical Questions of Learning

1. What is it we expect them to learn?2. How will we know when they have

learned it?3. How will we respond when they don’t

learn?4. How will we respond when they already

know it?

Rebecca DuFour4 Critical Questions of a PLC

Video Clip

There is such a

thing as group IQ.

What is Collaboration?

What is a Professional

Learning Community?

Remember the URN!

What should you expectas you begin collaboration

within your PLC?

Solution-Tree.com

Working Together to Analyze Instruction

Peer Review and Discussion

What does instruction for mathematical practices look like?

http://www.insidemathematics.org/index.php/standard-3

“…collaboration is a means to an end, not

the end itself.” (Learning by Doing, Solution Tree 2006)

Resources• Common Core State Standards Initiative

http://www.corestandards.org/Math

• Achieve the Core http://www.achievethecore.org/

• Illustrative Mathematics http://www.illustrativemathematics.org/

• The Hunt Institute Videos http://www.youtube.com/user/TheHuntInstitute?feature=watch

• WVDE Office of Instruction http://wvde.state.wv.us/instruction/math.html

Resources• National Science Digital Library – Serving STEM Education

http://nsdl.org/search/standards/D10003FB

• University of Arizona – Progressions Documents for the CCSS – M http://ime.math.arizona.edu/progressions/

• Hawaii State Department of Education – Standards Database http://wetserver.net/hcpsv3_staging/cc/common-core.jsp

• Council of Chief State School Officers http://spaces.ccsso.org/CCSSO/Home

• iTunes Preview – CCSS Apps https://itunes.apple.com/us/app/common-core-standards/id439424555