Common Core State Standards: The look and the structure

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Common Core State Standards: The look and the structure. KSDE/KATM Summer Academy ~ 2011 Several slides used from USD 259 Learning Services. 2011 KATM Fall Conference. October 3, 2011 Washburn Rural Middle School (Topeka) For more information, visit katm.org. Stand and Be Counted!.

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### Common Core State Standards:The look and the structure

KSDE/KATM Summer Academy ~ 2011

Several slides used from USD 259 Learning Services

2011 KATM Fall Conference
• October 3, 2011
• Washburn Rural Middle School (Topeka)
Stand and Be Counted!

Jennifer Weilert ~ Math in a Flash

WELCOME!

Give me five please.

• Norms

Active Listening

Equity of Voice

Take care of your own needs

• Y Chart
Why are we here?

Participants will:

• become familiar with the Common Core State Standards (CCSS).
• have opportunities to network with colleagues.
• formulate an implementation plan for your school/district.
Treasure Hunt
• Work with a

partner or a

small group to

explore the CCSS

document.

Standards for Mathematical Practice

• Everyone read the introduction on page 6.

Even Steven/Odd Todd Structure

• Steven reads even numbers
• Todd reads odd numbers.
• Everyone read the conclusion on page 8.

+ This is new information for me

• I already knew this

? I don’t understand

I think this is important

Share with your partner.

PSPB = Practice Standards Pocket Book
• Number each page 1-8.
• Paraphrase and/or write key words that capture the essence of each standard.
• Sketch a pictorial representation for that standard that is meaningful to you.
Teaching for Understanding
• Dan Meyer
• As you watch and listen, record or tally references to each Practice Standard as it relates to what he is demonstrating.

Requires:

• Teacher knowledge of mathematics language and content.
• Teacher knowledge of how to promote student involvement in mathematical practices.
• Shifting students’ focus from “answer getting” to solving problems.
• Establishing the classroom environment as a community of learners.
Say Something
• Question ~ “I wonder . . .What if. . ?”
• Connection ~ “This reminds me of. .”
• Opinion ~ “I think. . “
• Reaction ~ “Wow, I am excited about. . .”
Welcome Back!
• Feedback
• General Questions

What might the Standards for Mathematical Practice look like in a task addressing this content?

…divide decimals to hundredths, using concrete models or drawings and strategies based on place value…; relate the strategy to a written method and explain the reasoning used.

Your math partner turns to you and says:

I worked the problem 124 ÷ 8 on my paper

and got 15 r 4. But when I did it on my

calculator, it said 15.5. Which answer is right?

How would you respond to your

partner’s question?

Things to consider. . .
• Using the term “groups”, restate what 124 ÷ 8 means.
• In the context of the problem, are the quotients 15 r 4 and 15.5 the same or are they different?
• What do the quotients mean?
• What does it mean to have a remainder of 4 when you are dividing by 8?
• What does 0.5 mean?
• What could you do to convince your partner that the answers are the same or different?
Teacher Actions
• Each person needs a Practice Standards Sorting Mat and a set of Teacher Action Sorting Cards.
• Read each Action Card and match it

with the correct Practice Standard.

Make sense of problems and persevere in solving them.
• Ask clarifying questions, such as,
• “Which part do you agree or disagree with?
• Suggest starting points, such as, “What answer do YOU get when you do the division?”
• Provide appropriate tools for investigating the problem.
Reason abstractly and quantitatively.
• Ask questions that focus the student’s thinking on the operation, such as,
• “What does it mean to have a remainder of 4 when you are dividing by 8?”
• Ask questions that focus the student’s thinking on the meaning of the numbers, such as, “What does 0.5 mean?”
• Design tasks in a way that directly involves mathematical argumentation.
• Ask questions that model the desired
• thinking, such as, “Are you sure that the answers are different? Can you convince me that they are different? How can you explain to me what each answer means?”
Model with mathematics.
• Show students how to represent their thinking with symbols, for example:
• 0.5 = = and
• 4 out of 8 is =

5

1

10

2

4

1

8

2

Use appropriate tools strategically.
• Have a selection of tools (e.g. place value blocks, calculators, graph paper) readily available for students to use to represent their thinking.
• Ask students to use a drawing or a model to show what they mean.
• Have students critique the uses of tools by asking questions like, “What made the use of the calculator in this problem confusing for this student? When would using a calculator be helpful?”
Attend to precision.
• Ask students to describe the quotient and remainder in words.
• Ask students to describe the decimal quotient in words.
• Ask students to compare and contrast situations in which you might decide to use a decimal quotient instead of a remainder.
Look for and make use of structure.
• Ask questions that focus student thinking on the relationship of the remainder to the divisor, i.e. 4 is half of 8.
• Ask questions that focus student thinking on the values of the digits in the quotient, i.e. in 15.5, the 5 to the right of the decimal point means 5 tenths.
Look for and express regularity in repeated reasoning.
• Have students explore what happens with other numbers that when divided by 8 leave a remainder of 4, e.g. 12 ÷ 8
• 36 ÷ 8
• 804 ÷ 8
• Have students explore the remainders in other division problems that have a quotient that ends in .5, e.g. 9 divided by 6, 35 divided by 10, 126 divided by 12.

Requires:

• Teacher knowledge of mathematics language and content.
• Teacher knowledge of how to promote student involvement in mathematical practices.
• Shifting students’ focus from “answer getting” to solving problems.
• Establishing the classroom environment as a community of learners.

How are the standards organized?

High School

Conceptual Category

Domain

Cluster

Standards

K-8

Domain

Cluster

Standards

(There are no pre-K Common Core State Standards)

Format of Mathematics Content Standards

• Domains: overarching ideas and larger grouping of related standards
• Clusters: illustrate progression of increasing complexity from grade to grade; related standards within a domain
• Standards: define what students should know and be able to do at each grade level – part of a cluster

Critical Areas

Grade Level - Overview

Domains

Ratios and Proportional

Reasoning

The Number System

Expressions and Equations

Geometry

Statistics and Probability

Cluster Statements

Progression of Overviews

Highlight the domain title across grade levels.

Highlight the verbs found within the cluster content statements under the domain.

What are some things you notice as the domains transition from elementary to middle school and then into high school?

• What observations do you make as you look at the progression of skill level across the cluster statements?
• What connections do you see between cluster statements that may cross over into other domains?
Scope & Sequence
• Project Learning
• Illustrative Mathematics
Common Core Standards

Based on research, the following elements are critical and can be found within each standard:

• Inclusion of particular content
• Timing of when content should be introduced and the progression of that content
• Ensuring focus and coherence
• Organizing and formatting the standards
• Determining emphasis on particular topics in standards

Page 42

Domain

Standard

### Format of K-8 Standards

6.NS.1

Cluster

Cluster

Standard

Standard

Standard

Page 60

Conceptual Category Number & Quantity

Domain

Standard

Standard

### High School Format

Cluster

Cluster

Standard

Conceptual Category Number & Quantity

Domain

Standard

### Format of High School

Cluster

Standard

Standard

Domain

Modeling
• Read pages 72 & 73.
• Highlight helpful information.

Conceptual Category Number & Quantity

Domain

Standards

### High School Format

Cluster

Cluster

Standards

Reflections

3 points I want to remember about the CCSS

Ideas circling in my head.

Things that squares with my beliefs and the CCSS.

Please leave any feedback on the Y Chart before leaving.