1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Creating Teaching Sequences for Extended Interventions

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Solve A) 28 + 56 = ___ B) 17 × 25 = ___ C) g ° = ___ h ° = ___ i ° = ___

3. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Think of a sequence of problems. Step 1: Choose 1 of the problems: 28 + 56, 17 × 25, or the missing angle problem. Step 2: Take 3 minutes to think of a sequence of few related math problems that would lead like a “ladder” to your chosen problem. Step 3: Share your sequence of problems with a partner or larger group. Step 4: Reflect on what you did to develop your sequence.

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Why do small and large sequences matter? Read, “Two Beliefs.” Use the following protocol: “Save the last word for me” 1.Put a star to mark a statement from the reading that stands out to you for whatever reason. 2.One member reads a starred statement. 3.The members of the triad (not the writer) comment on the statement. 4.Lastly, the person who chose the statement shares why the statement was impactful. 5.Repeat the process with the other members of the group.

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Objective: Create an extended sequence for intervention. Analyze incorrect student work and define the error by asking additional questions. Find and analyze coherent teaching sequences within A Story of Units to address student knowledge gaps. Teach Plan Analyze Assess Use the coherence of A Story of Units to plan an extended teaching sequence for intervention. Clarify a continuous cycle which allows us to unify assessment, analysis, planning, and teaching.

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Teach Plan Analyze Assess

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda Analyze student work using a protocol based on the Mathematical Practices. Define the student error. Study and analyze foundational teaching sequences in A Story of Units relevant to the assessment’s objective. Derive an extended teaching sequence to bridge the gap between the student’s current level and the objective. Make an illustrated poster to share the sequence. Create “second chance” assessment questions. Professional Reading and Closure.

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze the student work. Define the error(s).

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units What is the logic of the sequence, the “storyline”? Another way of asking the same question: What are the “rungs” in the “ladder” to the objective targeted by the assessment question? Does the student work reflect the work of the the module? What might that tell us about the student’s learning experience?

11. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze student work and the teaching sequence within the assessment’s module.

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units What is the logic of the sequence, the “storyline”? Another way of asking the same question: What are the “rungs” in the “ladder” to the objective targeted by the assessment question? Does the student work reflect the work of the the module? What might that tell us about the student’s learning experience?

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze student work using a protocol based on the Mathematical Practice standards.. Study and analyze foundational teaching sequences relevant to the assessment’s objective. Develop and share an extended teaching sequence to bridge the gap between the student’s current level and the objective. Make an illustrated poster to share the sequence. Create “second chance” assessment questions. Professional Reading and Closure. Agenda

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units To find and analyze the teaching sequences before the module, we must adeptly navigate in A Story of Units.

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Which modules are coherently linked to the objective?

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units While studying, think about: the “rungs,” the logic of the sequence, the “storyline” connections to and coherence with the grade level objective. the lessons/instructional strategies you think will most help the student.

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze the relevant teaching sequences of prior grade levels.

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units While studying, think about: the “rungs,” the logic of the sequence, the “storyline.” connections to and coherence with the grade level objective. the lessons/instructional strategies you think will most help the student.

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Collaboratively: Analyze student work using a protocol based on the Mathematical Practice standards.. Study and analyze foundational teaching sequences relevant to the assessment’s objective. Develop and share an extended teaching sequence to bridge the gap between the student’s current level and the objective. Make an illustrated poster to share the sequence. Create “second chance” assessment questions. Professional Reading and Closure. Agenda

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Build a ladder from the point of strength to the objective.

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Plan your extended teaching sequence for intervention.

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Build a ladder from the point of strength to the objective. G2 M7 Topics C & E  Create a ruler. Find missing units on a number line. G3 M2 Topics A-C  The clock and the number line. The graduated cylinder. Unit form. Rounding on the vertical number line to the nearest 10 and 100. G4 M1 Topics A –B Number comparison in unit form Rounding on the vertical number line.

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze student work using a protocol based on the Mathematical Practice standards.. Study and analyze foundational teaching sequences relevant to the assessment’s objective. Develop and share an extended teaching sequence to bridge the gap between the student’s current level and the objective. Make an illustrated poster to share the sequence. Create “second chance” assessment questions. Professional Reading and Closure. Agenda

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Make a poster to display the extended teaching sequence.

25. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Note: For today, please stay within the curriculum’s lessons rather than pulling from outside material or previously taught lessons. Sketch a “concrete/pictorial/abstract” or “pictorial/abstract” component at each step. Include the Grade Level, Module, and Lesson references for each rung of the ladder. Briefly describe the logic of each step. Include the pacing of each step. (Suggestion: 20 minute sessions with no more than 15 such sessions.)

26. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze student work using a protocol based on the Mathematical Practice standards.. Study and analyze foundational teaching sequences relevant to the assessment’s objective. Develop and share an extended teaching sequence to bridge the gap between the student’s current level and the objective. Make an illustrated poster to share the sequence. Create “second chance” assessment questions. Professional Reading and Closure. Agenda

27. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Engage students in their own growth.

28. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Second Chance Assessments!

29. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze student work using a protocol based on the Mathematical Practice standards.. Study and analyze foundational teaching sequences relevant to the assessment’s objective. Develop and share an extended teaching sequence to bridge the gap between the student’s current level and the objective. Make an illustrated poster to share the sequence. Create “second chance” assessment questions. Professional Reading and Closure. Agenda

30. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Reflection How might “studying teaching materials” (zuanyan jiaocai) be instrumental in educators becoming the “taxi drivers” whose cabs we would want to catch when late to the airport? How might studying, creating, and sharing extended teaching sequences support teachers in more deeply understanding elementary mathematics?

31. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units The Flow of our Work