1. Office of Curriculum, Instruction and School Support 2012 Mathematical Practice 3: Construct Viable Arguments and Critique the Reasoning of Others Mathematics Implementation Module 1

2. Module Objectives CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS After today’s module on Mathematics Practice 3, teachers will have an understanding of how students should CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS in the mathematics classroom (TLF 3b: Using Questioning and Discussion Techniques) 2

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 FOCUS in grade level/department groups, engage in on- going dialogues regarding FOCUS areas for mathematics FOCUS begin reviewing current curricular materials to determine where it aligns to the critical areas of FOCUS 3

4. The Intersection of Mathematical Standards Standards for Mathematical Practice The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. Standards for Mathematical Content The Standards for Mathematical Content are a balanced combination of procedure and understanding. They define what students should understand and be able to do in their study of mathematics 4

5. Hip to be … 5 MARS Task

6. Activity 6 Structure strategy: Guided sharing: Private, Partner, Public Private: Time to think and work on the problem Take 3 minutes to solve the problem on your own. Partner: Time to discuss our pathways and solutions. Need for a discussion prompt: Say a Second Sentence Ask your partner: How do you know that your answer makes sense? Tell me more. Public: Select students to participate strategically based on work samples Select a pair of students/participants who had different approaches.

7. Hip to be … 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. 7

8. Standards for Mathematical Practice 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 8 Priority for 2012-13

9. Mathematical Practice 3 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 discussion of the polygon problem?  What made for stronger arguments? Weaker arguments? 9

10. Common Core Content Connections Standards for Mathematical Practice Anchor Standards for ELA and Content Literacy MP3: Construct viable arguments and critique the reasoning of others 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. 10

11. Ties to the Teaching and Learning Framework 11

12. Mathematical Practice 3: Activity: In grade level groups, using Handouts 4 and 5, discuss:  What do language standards look like and sound like for our students?  How do we share these expectations with students?  What actions should we be doing as teachers? How do we model this practice for 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? 12

13. Implementation Strategy Questioning-Putting MP3 into Practice Say a Second Sentence 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. 13

14. 14 “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

15. Summary Engaged in a mathematical problem intersecting content and practice standards C ONSTRUCT VIABLE ARGUMENTS AND CRITIQUE 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 links to the Teaching and Learning Framework through questioning and discussion techniques 15

16. Next Steps C ONSTRUCT V IABLE A RGUMENTS AND C RITIQUE THE R EASONING OF O THERS Engage all students in using Mathematical Practice #3: C ONSTRUCT V IABLE A RGUMENTS AND C RITIQUE THE R EASONING OF O THERS utilizing strategies from this session 16

17. Math Module 2: FOCUS focusing the content Understanding of the design principle of FOCUS as an instructional shift for mathematics and how focusing the content will affect the look and sound of the classroom 17