Common Core State StandardsK-5 Mathematics

Kitty Rutherford and Amy Scrinzi

Introductions

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Microsoft

Parking Lot

TechnologySession Materials

Breaks

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Norms

• Listen as an Ally

• Value Differences

• Maintain Professionalism

• Participate Actively

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Our Goals for today• Recognize how Standards for

Practice mandate better ways of managing instruction.

• Recognize what makes a good task.• Understand the complexity of place

value.• Recognize the relationship between

multiplication and division.

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Reflecting on Standards for Mathematical Practice

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Who can name 1 of the 8 Mathematical Practices?

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 strategically6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

Standards for Mathematical Practices

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Representation of Practices

• In your group, use pictures, numbers and words to illustrate your assigned mathematical practice.– Be sure to write the name of the practice on

the chart paper.

• Be prepared to share your illustration with the whole group.

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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 strategically6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

Standards for Mathematical Practices

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Mathematical practices describe the habits of mind of mathematically proficient students…

• Who is doing the talking?

•Who is doing the thinking?

• Who is doing the math?

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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 strategically6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

Standards for Mathematical Practices

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Students illustrate Mathematical Practices

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Time to Reflect

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Summary

Mathematics ClaimsThe Smarter Balanced Assessment

Consortium has released a document outlining four claims about what mathematically proficient students can do.

The claims are a synthesis of the Standards for Mathematical Practice, and form the guiding principles to be used in creating assessments.

Mathematics Claim #1

Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.

Mathematics Claim #2

Students can frame and solve a range of complex problems in pure and applied mathematics.

Mathematics Claim #3

Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

Mathematics Claim #4

Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

http://www.k12.wa.us/smarter/

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When planning, ask

“What task can I give that will build student

understanding?”rather than

“How can I explain clearly so they will understand?”

Grayson Wheatley, NCCTM, 2002

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Types of Math Problems Presented

How Teachers Implemented Making Connections Math Problems

Lesson ComparisonJapan and United States

The emphasis on skill acquisition is evident in the steps most common in U.S. classrooms

The emphasis on understanding is evident in the steps of a typical Japanese lesson

•Teacher instructs students in concept or skill

•Teacher solves example problems with class

•Students practice on their own while teacher assists individual students

•Teacher poses a thought provoking problem

•Students and teachers explore the problem

•Various students present ideas or solutions to the class

•Teacher summarizes the class solutions

•Students solve similar problems

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Time to Reflect

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Summary

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