1. Instructional Shift in Math ESC NORTH Network Principal Meeting January, 2013

2. Objectives Identify the MAJOR, SUPPORTING, and ADDITIONAL CLUSTERS for a given grade level Understand how students should CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS in the mathematics classroom (TLF 3b: Using Questioning and Discussion Techniques) Connect work to the TEACHING AND LEARNING FRAMEWORK (Standards 1d4, 3b1, and 3b2) and to MATH PRACTICE 3 (Constructing viable arguments and critiquing reasoning of others)

3. CCSS District-wide Goals By May 2013, at a minimum, teachers will be expected to: Engage all students in using Mathematical Practice 3: C ONSTRUCT V IABLE A RGUMENTS AND C RITIQUE THE R EASONING OF O THERS In grade level/department groups, engage in on-going dialogues regarding FOCUS areas for mathematics Begin reviewing current curricular materials to determine where it aligns to the critical areas of FOCUS

4. Common Core Standards

5. Standards for Math Content These DOMAINS connect topics and content between and among grade levels. DOMAINS Each grade level consists of a set of DOMAINS which are large groups of related standards.

6.  Each domain consists of a set of CLUSTERS.  These CLUSTERS are smaller sets of related standards within the domain.  The CLUSTERS identify the primary ideas to be learned within the domain.

7. High School Arranged by cluster (NOT COURSE) Number and Quantity Algebra Functions Modeling Geometry Probability and Statistics

8. The Major Work of the Grade  Some clusters require greater emphasis or FOCUS than others based on the depth of the ideas, the time that they take to master, and/or the demands of college and career readiness.  In addition, an intense FOCUS on the most critical material at each grade level allows depth in learning, which is carried out through the Standards for Mathematical Practice.

9. The Major Work of the Grade The list of standards for each grade level is not a flat, one-dimensional checklist. To make these emphases more transparent and useful, MAJOR, SUPPORTING, and ADDITIONAL clusters have been identified by the CCSS authors.

10. Activity – Part 1 On Your Own: Read the instructions and critical areas of the grade level Mark each bulleted cluster with an M, S, or A to the best of your ability. (Notice the hint…) Use the Individual column for your answers As you mark each cluster, highlight key words in the text that supports your answer You will have 5 to 8 minutes for this INDIVIDUAL activity Handout 1

11. Activity – Part 2 With Your Partner: Compare your answers and mark the clusters where you disagree in the Partner column For each cluster where you and your partner disagree, one of you will make an argument defending the answer siting specific evidence from the text (Handout 1) to justify your answer The other partner listens without interruption. Switch roles and let the other partner present while the first partner listens After the second partner is finished, both partners continue to discuss and try to reach consensus until the facilitator indicates time is up

12. Answer Key Grade 7 Grade Level Focus Areas  Major Cluster □ Supporting Cluster Additional Cluster All Major Clusters

13. Answer Key Grade 7 Grade Level Focus Areas  Major Cluster □ Supporting Cluster Additional Cluster Additional Clusters Supporting Clusters

14. Implementation Strategy: Defending and Critiquing Arguments Students increase their understanding through creating explanations/arguments and listening to/critiquing the reasoning of others

15. Hip to be Square Activity: Take 2 minutes to begin working on this problem on your own. For the next 5 minutes, with a partner, continue to solve the questions. Challenge one another— How did you get that answer? How do you know that your answer makes sense? How are our solutions the same? Different?

16. Hip to be Square… Domain: Geometry (7 th grade) Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume Standard 6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

17. Standards for Mathematical Practice Priority for 2012-13 Standard 1: Make sense of problems and persevere in solving them Standard 2: Reason abstractly and quantitatively Standard 3: Construct viable arguments and critique the reasoning of others Standard 4: Model with mathematics Standard 5: Use appropriate tools strategically Standard 6: Attend to precision Standard 7: Look for and make use of structure Standard 8: Look for and express regularity in repeated reasoning

18. Mathematical Practice 3 MP3: Construct viable arguments and critique the reasoning of others Activity: Do a close read of Handout 2 With a partner, discuss— What parts of MP3 do you believe you and your partner used in your solution and discussion of the square problem? What made for strong arguments? Weaker arguments? What are students expected to know and be able to do? Handout 2

19. Common Core Content Connections Standards for Mathematical Practice MP3: Construct viable arguments and critique the reasoning of others Anchor Standards for ELA and Content Literacy Reading 1: Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text. Speaking and Listening 1: Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively.

20. Ties to the Teaching and Learning Framework

21. Mathematical Practice 3: Construct viable arguments and critique the reasoning of others Activity: In grade level groups, using Handouts 4 and 5, discuss: What does language sound like when constructing viable arguments and critiquing the reasoning of others look like for the age group and ELD levels of students we currently teach? What student actions/interactions should we see? How do we share these expectations with teachers/students? What actions should we be doing as principals/teachers? How do we model this practice for teachers/students? How do we begin to integrate Math Practice 3 into our lessons and classrooms now? What commitments will we make to see this happen?

22. Implementation Strategy “ Correct answers are essential…but they’re part of the process, they’re not the product. The product is the mathematics the kids walk away with in their heads…” - Phil Daro, co-author of CCSSM, 2012 Questioning-Putting MP3 into Practice Ask students to explain how they arrived at an answer to a given math problem. Listen for student understanding not for answer-getting. Ask a student to say a second sentence to explain their thinking.

23. Summary Spending more time on fewer topics allows for deeper learning and understanding All CCSS math content standards are important and to be taught, some have greater emphasis and should have more time devoted to them Students increase their understanding through creating explanations/arguments and listening to/critiquing the reasoning of others Discussed the meaning of Mathematical Practice 3: C ONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS and how to engage students in using this practice Made connections to the Teaching and Learning Framework Rubrics through questioning and discussion techniques

24. Next Steps With your grade level/department team: Engage students in using Mathematical Practice 3 Ask students to explain how they arrived at an answer to a given math problem. Listen for student understanding not for answer-getting. Ask a student to say a second sentence to explain their thinking. Have faculty review the MAJOR, SUPPORTING, and ADDITIONAL clusters for the grade they teach In future grade level/department team meetings, begin reviewing your current curricular resources looking for where current units of study correspond to the CCSS areas of emphasis In future meetings, begin aligning current units of study to what is emphasized in the CCSS and to what degree it is emphasized