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Common Core State Standards in Mathematics For Cluster 2 Network Leaders and Teams Prepared and presented by Louise Antoine, Kerry Cunningham, Linda Curtis-Bey, George Georgilakis, Carol Mosesson-Teig, Rose Shteynberg, Suzanne Werner 9/21/10

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What are Standards? Standards define what students should understand and be able to do. Standards must be a promise to students of the mathematics they can take with them.

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CCSS Mathematical Practices The Common Core proposes a set of Mathematical Practices that all teachers should develop in their students. These practices are similar to the mathematical processes that NCTM addresses in the Process Standards in Principles and Standards for School Mathematics.

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CCSS Mathematical Practices The Common Core proposes a set of Mathematical Practices that all teachers should develop with their students. These practices are similar to the mathematical processes that NCTM addresses in the Process Standards in Principles and Standards for School Mathematics and informed by the Strands of Proficiency from Adding it Up from the National Research Council.

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CCSS 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 strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

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Common Core Format High School Conceptual Category Domain Cluster Standards K-8 Grade Domain Cluster Standards (There are no Pre-K Standards)

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Grade Level Overview

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Critical Area Cross- Cutting Themes

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Format of K-8 Standards StandardStandard ClusterCluster ClusterCluster StandardStandard

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Format of High School Standards StandardStandard ClusterCluster DomainDomain

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Common Core - Domain Overarching big ideas that connect topics across the grades Descriptions of the mathematical content to be learned, elaborated through clusters and standards

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Common Core - Standards Content statements Progressions of increasing complexity from grade to grade

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High School Conceptual Categories The big ideas that connect mathematics across high school A progression of increasing complexity Description of the mathematical content to be learned, elaborated through domains, clusters, and standards

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High School Conceptual Categories Number & Quantity Algebra Functions Modeling Geometry Statistics & Probability

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High School Pathways The CCSS Model Pathways are NOT required. The two sequences are examples, not mandates Two models that organize the CCSS into coherent, rigorous courses Four years of mathematics: One course in each of the first two years Followed by two options for year 3 and a variety of relevant courses for year 4 Course descriptions Define what is covered in a course Not prescriptions for the curriculum or pedagogy

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High School Pathways Pathway A: Consists of two algebra courses and a geometry course, with some data, probability, and statistics infused throughout each (traditional) Pathway B: Typically seen internationally, consisting of a sequence of 3 courses, each of which treats aspects of algebra; geometry; and data, probability, and statistics.

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Answer Getting vs. Learning Mathematics United States How can I teach my kids to get the answer to this problem? Use mathematics they already know. Easy, reliable, works with bottom half, good for classroom management. Japan How can I use this problem to teach mathematics they dont already know?

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How might a fourth grader solve these problems? = =

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Students Ideas About Math D. Schifter and M. Riddle Read pages 28, 29, 30. STOP at Dig into Content Go back to Mathematical Practices in the Standards Find evidence for students use of some of the Practices described in the CCSS document.

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Domain Trace: Number and Operations in Base Ten: Grade 2 Use place value understanding and properties of operations to add and subtract 5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

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Domain Trace Number and Operations in Base Ten Grade 3 Use place value understanding and properties of operations to perform multi- digit arithmetic. 2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

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Trail Mix Problem At your tables, begin solving the problem on your own. Discuss and share solutions and strategies at your table. Choose one solution to share. Put it on chart paper.

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Take a BREAK Take a BREAK

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Sharing Strategies Listen Connect Compare

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Looking at Student Work: Trail Mix Problem Look at samples of student work Analyze for evidence of understanding through the CCSS Mathematical Practices

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LUNCH

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Using Video to Examine Teacher Practice

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Framework for Viewing What does the teacher do to foster learning? What is the impact on student learning?

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What Are Mathematical Tasks? Mathematical tasks are a set of problems or a single complex problem the purpose of which is to focus students attention on a particular mathematical idea.

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Why Focus on Mathematical Tasks? Tasks form the basis for students opportunities to learn what mathematics is and how one does it; Tasks influence learners by directing their attention to particular aspects of content and by specifying ways to process information;

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Why Focus on Mathematical Tasks? The level and kind of thinking required by mathematical instructional tasks influences what students learn; and Differences in the level and kind of thinking of tasks used by different teachers, schools, and districts, is a major source of inequity in students opportunities to learn mathematics.

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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, & Silver, 2000 The level and kind of thinking in which students engage determines what they will learn. Hiebert et al., 1997

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The Cognitive Level of Tasks Lower-Level Tasks Memorization Procedures without connections Higher-Level Tasks Procedures with connections Doing mathematics

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Task Analysis Guide Read over the Task Analysis Guide and highlight important words, phrases or ideas for each level. Discuss at your table. What type of task was the Trail Mix problem? Why?

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Adapt-a-Task Activity Choose a standard from the 4 th Grade or from the 8 th Grade CCSS in Mathematics. As a group, write a low-level demand task on a large post-it note. Discuss why the task is low-level demand using the Task Analysis Guide.

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Adapt-a-Task Three Stay-One Stray Designate one person as the Traveler. The Traveler takes the groups low-level demand task and moves to the next table. The rest of the group stays. The Traveler explains why the task is a low- level demand task to the new group.

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Adapt-a-Task The new group creates a high-level demand task from the low-level demand task using the Task Analysis Guide and the CCSS Standards for Mathematical Practices and writes their new task on chart paper. Facilitator Walk Facilitators move the charted tasks from table to table.

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Facilitator Walk (continued) Table groups evaluate the cognitive level of each task presented by the facilitator using the criteria from the Task Analysis Guide and writes the demand level (M, PwoC, PwC, DM) on a post-it note. The facilitator moves from table to table adding the post-it notes from each group to their charts. The facilitators discuss feedback on the tasks with the whole group.

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Reflection Review of the CCSS in Mathematics Article - Students Ideas About Math Trail Mix Problem Looking at Student Work Using Video to Examine Teacher Practice Adapt-a-Task (Low and High Level Tasks)

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A Sample Plan for Year 1 Explore and integrate at least one Mathematical Practice, into your students repertoire of doing mathematics. Integrate a Mathematical Practice into an existing unit of study in your curriculum map. Explore and collect mathematical tasks that will support students use of the CCSS Mathematical Practices. Collect student work and integrate looking at student work into your schools inquiry team work. Use classroom talk to support the CCSS Mathematical Practices. Develop one Domain strand trace covering the grade spans of your school (e.g. K-5, K-8, 6-8, 6-12, etc)

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