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Common Core State Standards K-5 Mathematics Kitty Rutherford and Amy Scrinzi

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Introductions 5/13/2015 page 2 Microsoft

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Parking Lot Technology Session Materials Breaks cc: Microsoft.com 5/13/2015 page 3

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Norms Listen as an Ally Value Differences Maintain Professionalism Participate Actively 5/13/2015 5/13/2015 page 4

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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. 5/13/2015 page 5

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Reflecting on Standards for Mathematical Practice 5/13/2015 page 6 Who can name 1 of the 8 Mathematical Practices?

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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 strategically 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Standards for Mathematical Practices 5/13/2015 page 7

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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. 5/13/2015 page 8

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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 strategically 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Standards for Mathematical Practices 5/13/2015 page 9

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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? 5/13/2015 page 10

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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 strategically 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Standards for Mathematical Practices 5/13/2015 page 11

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Students illustrate Mathematical Practices 5/13/2015 page 12

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Time to Reflect 5/13/2015 page 20 Summary

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Mathematics Claims The 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.

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Mathematics Claim #1 Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.

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Mathematics Claim #2 Students can frame and solve a range of complex problems in pure and applied mathematics.

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Mathematics Claim #3 Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

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Mathematics Claim #4 Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

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Grade 11 SUMMATIVE ASSESSMENT TARGETS Providing Evidence Supporting Claim #3- Communicating Reasoning The Number System 1. REASONING with RATIONAL-IRRATIONAL NUMBERS: Use understanding of rational and irrational numbers and properties of operations to confirm and justify an estimate or explain the reasonableness of a calculation, estimation, or proposed solution, using equations, diagrams, calculations, or other representations to determine (a) the accuracy of the solution, and (b) the reasoning behind the strategy used in order to provide justification for the best approach, the correct outcome, or flaws in the reasoning Standards: 8.NS-1, 8.NS-2 (DOK 2, DOK 3 if providing justification for or articulating the reasonableness of the solution, using evidence) Expressions and Equations 2. REASONING with PROPORTIONAL RELATIONSHIPS: Given one or two possible solutions to a multistep problem using proportional relationships (e.g., slope, linear equations, graphs, unit rates, similar triangles) use graphing, equations, diagrams, or other representations to determine (a) the accuracy of the solution(s), and (b) the reasoning behind the strategy used in order to provide justification for the best approach, the correct outcome, or flaws in the reasoning Standards: 8. EE.5, EE.6 (DOK 2, DOK 3 if providing justification for or articulating the reasonableness of the solution, using evidence)

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

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Teach-Then-Solve Paradigm Traditionally teachers taught the mathematics, the students practices it for a while, then they were expected to use the new skill or ideas in solving problems. 5/13/2015 page 34

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Teach-Then-Solve Paradigm Mathematical practices are separate from the learning process Students who expect teachers to tell them the rule are unlikely to solve problems requiring then to think through and find a strategy to solve a problem. 5/13/2015 page 35

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Effective Practices Begin where the students are, not where we are. Are a result of problem-solving experience rather then elements that must be taught before solving (Hiebert) Learning mathematics by doing mathematics! 5/13/2015 page 36

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The valve of teaching using the Mathematical Practices Mathematical practices….. Focuses student’s attention on ideas and sense making of mathematics. Develops the belief in students that they are capable of doing mathematics. Provides ongoing assessment data 5/13/2015 page 37

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Mathematical practices….. Develops and engages “mathematically powerful students”. Allows an entry point for a wide range of students. It is a lot of fun! 5/13/2015 page 38

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Task A Task engages students in making sense of key ideas you want them to learn. It has no prescribed or memorized rules or methods nor is there a perception by students that there is a spefici “correct” solution method. (Hiebert) 5/13/2015 page 39

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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 5/13/2015 page 40

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Types of Math Problems Presented

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How Teachers Implemented Making Connections Math Problems

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Lesson Comparison Japan 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 43

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Time to Reflect 5/13/2015 page 44 Summary

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Time to Reflect 5/13/2015 page 45 Summary

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Time to Reflect 5/13/2015 page 46 Summary

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Time to Reflect 5/13/2015 page 47 Summary

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