Math Shifts FocusCoherenceRigor

What are the Shifts? Focus: focus strongly where the standards focus

Instructional Shift: What does focus mean for our instruction?

GRADEFOCUS (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?

PreKK HS Mathematical Practices Counting & Cardinality Number & Operations in Base Ten Ratios & Proportional Relationships Number & Quantity Number & Operations - Fractions The Number System Operations & Algebraic ThinkingExpressions & EquationsAlgebra Functions Geometry Measurement & DataStatistics & Probability 9 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. 15 Standards for Mathematical Practice

The Importance of the Standards for Mathematical Practices Video clip

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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! 27 Content & Practices

“A lack of understanding (of the content) effectively prevents a student from engaging in the Mathematical Practices.” Skip Fennell, former NCTM president 28 Content & Practices

Great Tasks Matter! 1.What is a great task? 2.Why is it important to use great tasks? 29

“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 30

“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 31

Dan Meyer Math class needs a makeover - YouTube.mp4 Dan Meyer: Math Class Needs a Makeover TED Talk 32

What is a Great Task? 33

Why use a Great Task? 34

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 Progression documents for the Common Core State Standards found online at

Smarter Balanced Assessment Consortium An Assessment System to Support Teaching and Learning

Item and Task Specifications and Sample Items Sample assessment items and tasks are included in item/task specifications: Live sample items and tasks:

Go to the Smarter Website Click on Smarter Balanced Assessment (top of page) 3.In drop down, scroll to Sample Items and Performance Tasks 4.In task bar, click on View More Sample Items 5.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 = 10 B. y - 2x = -5 C.-2y = 10x – 4 D.2y = - 4x - 10

The three different linear functions below are represented in three different ways, as shown. 2y + 3 = 3x X f(x) (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 Smarter Balanced Math Assessments How will Smarter Balanced decide when and 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 DuFour 4 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 expect as 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? dard-3

“…collaboration is a means to an end, not the end itself.” (Learning by Doing, Solution Tree 2006)

Resources Common Core State Standards Initiative Achieve the Core Illustrative Mathematics The Hunt Institute Videos WVDE Office of Instruction

Resources National Science Digital Library – Serving STEM Education University of Arizona – Progressions Documents for the CCSS – M Hawaii State Department of Education – Standards Database Council of Chief State School Officers iTunes Preview – CCSS Apps