Connected Mathematics 3: Pedagogy Training

1. Connected Mathematics 3: Pedagogy Training Daniel Anderson, Senior Editor Marta Miko, Marketing Manager December 9, 2013

2. Introduction to CMP3 History: CMP curriculum development 1991-1997 CMP2 revision 2000-2006 CMP3 published in 2010-2013

3. CMP3 Authors

4. CMP3 Program Philosophy Core Beliefs: A focus on the big ideas and the connections among them Teaching through student-centered exploration of mathematically rich problems Using continuous assessment to inform instruction

5. CMP3 Program Philosophy Guiding Principles Problem-centered Big ideas in depth Coherence Conceptual + procedural Concepts + skills Inquiry-based Effective technology High expectations

6. CMP3 Program Philosophy Criteria for Mathematical Tasks: Embeds important, useful mathematics Promotes conceptual and procedural knowledge Builds on and connects to other important mathematical ideas Requires higher-level thinking, reasoning, and problem solving Engages students and promotes classroom discourse Allows for various solution strategies Creates an opportunity for teacher to assess student learning

7. CMP3: How Does It Work? Pedagogical Strategies: Effective Questioning Cooperative Groups Active Participation Situational Context Written Expression

8. CMP3: How Does It Work? • Instructional Phases: Three-Part Lesson • Launch: Present the Problem! • Explore: Solve the Problem! • Summarize: Discuss solutions to the Problem!

9. CMP3: Instructional Phases Launch: Connecting to Prior Knowledge: Clarify prior definitions Review old concepts Connect the Problem to students’ past experiences PREPARATION QUESTIONS: What prior knowledge do my students need to build on? How can I use that information to support this Problem?

10. Launch: Presenting the Challenge: Help students understand: the Problem setting the mathematical context the challenge PREPARATION QUESTIONS: What are students expected to do? What do the students need to know to understand the context of the story and the challenge of the Problem? What difficulties for students can I foresee? How can I help without giving away too much of the Problem solution? CMP3: Instructional Phases

11. Launch: Video CMP3: Instructional Phases

12. CMP3: Instructional Phases Explore: Providing for Individual Needs: Move about the classroom to Observe individual performance Encourage on-task behavior Ask appropriate questions Provide confirmation and redirection where needed Differentiated Learning: students who are struggling and Going Further

13. CMP3: Instructional Phases Explore: PREPARATION QUESTIONS: How will I organize the students to explore this Problem? Individuals, pairs, groups, whole class? What materials will students need? How should students record and report their work? What different strategies can I anticipate they might use? What questions can I ask to encourage student conversation, thinking, and learning? What questions can I ask to focus their thinking if they become frustrated or off-task? What questions can I ask to challenge students if the initial question is “answered?” What difficulties are students having? How can I help without giving away the solution? What strategies are students using? Are they correct? How will I use these strategies during the Summarize?

14. CMP3: Instructional Phases Explore: Planning for the Summarize: What evidence do I have from the Explore that can be used to support student understanding of the Focus Question during the Summarize? How will I organize the discussion? What will I do if I have insufficient evidence to support the Summarize?

15. CMP3: Instructional Phases Summarize: Orchestrating the Discussion: Guide students to reach the mathematical goals of the Problem Connect new understanding to prior mathematical goals Begin when most students have made sufficient progress Students present and discuss their solutions and strategies Help students enhance their conceptual understanding of the mathematics Students refine strategies into efficient, effective, generalizable problem-solving techniques or algorithms

16. CMP3: Instructional Phases Summarize: PREPARATION QUESTIONS : How can I help students make sense of and appreciate the variety of methods that may be used? How can I orchestrate the discussion so that students summarize their thinking about the Problem? What questions can guide the discussion? What concepts or strategies need to be emphasize? What ideas do not need closure at this time? What definitions or strategies do we need to generalize? What connections and extensions can be made? What new questions might arise and how do I handle them? What can I do to follow up, practice, or apply the ideas after the Summarize?

17. CMP3: Instructional Phases Summarize: Reflecting on Student Learning : What evidence do I have that students understand the Focus Question? Where did my students get stuck? What strategies did they use? What breakthroughs did my students have today? How will I use this to plan for tomorrow? For the next time I teach this lesson? Where will I have the opportunity to reinforce these ideas as I continue through this Unit? The next Unit?

18. CMP3: ACE The ACE Concept: Applications Connections Extensions Homework assignments Bell-ringer question Opener activity

19. CMP3 + Practice Standards

20. CMP3 + Practice Standards

21. CMP3 + Practice Standards

22. CMP3 + CCSSfMC Considerations for Revisions: Research and data feedback from CMP2 New content and moved content for CCSSM alignment Data feedback, field trials, and revisions of new CMP3 materials

23. CMP3 + CCSSfMC

24. CMP3 + CCSSfMC

25. CMP3 Grade 8 Algebra I CMP3offers two paths through Grade 8: Grade 8 and Grade 8 and Algebra I Grade 8 Content Standards • 8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. • 8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Algebra 1 Content Standards • A-REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve. • F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

26. CMP3 Grade 7 Accelerated How About the Accelerated Grade 7 Path? This is not a "recommended" use of CMP3 but rather information for customers who want to know which CMP3 content corresponds to the Appendix A 7th Grade Accelerated Pathway The 7th Grade Accelerated Pathway content is covered in the following Units and Investigations: All Grade 7 Units Grade 8 Looking for Pythagoras: Investigations 2, 3, and 4 Grade 8 Growing, Growing, Growing: Investigations 1 and 5 Grade 8 Say It With Symbols: Investigations 1, 2, and 3 Grade 8 Butterflies, Pinwheels, and Wallpaper: all Investigations

27. CMP3 Alternate Pathways WITH A REGULAR PROGRAM: Students stuck on a track after Grade 6 Grade 7 On-Level Grade 8 On-Level Grade 6 Grade 7 Accelerated Grade 8 Algebra 1

28. CMP3 Alternate Pathways THE “CMP3 RECOMMENDED PROGRAM ” : Students put on track after Grade 7 Grade 8 On-Level Grade 6 Grade 7 Grade 8 Algebra 1

29. CMP3 Alternate Pathways THE “CMP3 ACCELERATED TRACK” : Students grouped by ability after Grade 6 Then, students are re-assessed at the end of Grade 7 Grade 7 On-Level Grade 8 On-Level Grade 6 Grade 7 Accelerated Grade 8 Algebra 1

30. CMP3 vs CMP2 What did our customers LIKE about CMP2?

31. Built on feedback from teachers Common Core-aligned TOC No extraneous content Grade-level alignment with CCSS Reduced language load Carefully curated suite of digital tools CMP3 vs CMP2

32. CMP3 vs CMP2 • Technology Toolbox: • Teacher Place • Teachability Teacher Community • Student Place • Skills Practice with MathXL for School

33. CMP3 vs CMP2

34. CMP3 vs CMP2

35. CMP3 Pedagogy Training Your questions? daniel.anderson@pearson.com marta.miko@pearson.com