1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM The Number System Crafting Teaching Sequences for Extended Interventions Grades 6-9

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions The Rhind Mathematical Papyrus

3. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Why do Teaching Sequences Matter? #958536 (C) Mat Hayward / Fotolia

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions The Basic Cycle Teach Plan Analyze Assess

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Interventions Instant Short-term Extended

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Process Evaluate student work using MP protocol Analyze foundational teaching sequence Construct a sequence of questions Navigate and study the curriculum Craft an intervention sequence Create 2 nd chance assessment

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Part 1 Short-term intervention

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Analyze student work… …using the MP Protocol

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Construct a Sequence of Questions

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Review the sequence of the module

11. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Craft a short-term intervention By Ildar Sagdejev (Specious) (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5- 2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons Target the gap(s) you aim to address Read the module overview Read the topic overviews Read the lessons, looking for the sequences within each lesson Craft the short term intervention

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Craft 2 nd chance assessments Second Chance Assessment: What is the decimal expansion of the number 99/3? Is the number 99/3 rational or irrational? Explain.

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Part 2 Extended intervention

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Bingo

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Analyze student work… …using the MP Protocol

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Construct a Sequence of Questions

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Review the sequence of the module

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Review the sequence from prior modules

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Craft an extended teaching sequence By Ildar Sagdejev (Specious) (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Make a poster to display the extended teaching sequence

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Second chance assessments! Second Chance Assessment: What is the decimal expansion of the number 2/9? Is the number 2/9 rational or irrational? Explain.

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Reflection How might “studying teaching materials” 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 mathematics?