1. Algebraic Reasoning Institute Math & Science Collaborative at the Allegheny Intermediate Unit

2. Overview of the Institute Math & Science Collaborative at the Allegheny Intermediate Unit

3. Overview of the Institute Math & Science Collaborative at the Allegheny Intermediate Unit

4. Overview Insert conceptual flow and goals overview. Math & Science Collaborative at the Allegheny Intermediate Unit

7. Common Core State Standards Design Math & Science Collaborative at the Allegheny Intermediate Unit Building on the strength of current state standards, the CCSS are designed to be: Focused, coherent, clear and rigorous Internationally benchmarked Anchored in college and career readiness* Evidence and research based

8. Common Core Standards for Mathematics Math & Science Collaborative at the Allegheny Intermediate Unit

9. Standards for Mathematical Practice Math & Science Collaborative at the Allegheny Intermediate Unit

10. CCSS Mathematical Practices Math & Science Collaborative at the Allegheny Intermediate Unit

11. Underlying Frameworks 5 Process Standards Problem Solving Reasoning and Proof Communication Connections Representations Math & Science Collaborative at the Allegheny Intermediate Unit

12. Underlying Frameworks Math & Science Collaborative at the Allegheny Intermediate Unit

13. Underlying Frameworks Math & Science Collaborative at the Allegheny Intermediate Unit

14. Strands of Mathematical Proficiency Conceptual Understanding – comprehension of mathematical concepts, operations, and relations Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently and appropriately Strategic Competence – ability to formulate, represent,, and solve mathematical problems Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy Math & Science Collaborative at the Allegheny Intermediate Unit

15. The Standards for Mathematical Practice Math & Science Collaborative at the Allegheny Intermediate Unit

16. The Standards for Mathematical Practice Math & Science Collaborative at the Allegheny Intermediate Unit

17. The Standards for Mathematical Practice Math & Science Collaborative at the Allegheny Intermediate Unit

18. CCSS Mathematical Practices Math & Science Collaborative at the Allegheny Intermediate Unit

19. The Standards for Mathematical Practice Math & Science Collaborative at the Allegheny Intermediate Unit

20. The Standards for Mathematical Practice Math & Science Collaborative at the Allegheny Intermediate Unit

21. The Standards for Mathematical Practice Math & Science Collaborative at the Allegheny Intermediate Unit

22. Mathematical Practice #3: Construct viable arguments and critique the reasoning of others Math & Science Collaborative at the Allegheny Intermediate Unit

23. Mathematical Practice #3: Construct viable arguments and critique the reasoning of others Math & Science Collaborative at the Allegheny Intermediate Unit

24. Mathematical Practice #3: Construct viable arguments and critique the reasoning of others Math & Science Collaborative at the Allegheny Intermediate Unit

25. Mathematical Practice #3: Construct viable arguments and critique the reasoning of others Math & Science Collaborative at the Allegheny Intermediate Unit

26. Standards for Mathematical Practice Math & Science Collaborative at the Allegheny Intermediate Unit

27. Implementation Issue Math & Science Collaborative at the Allegheny Intermediate Unit

29. React to the Following Statements in Writing When you hear the word algebra what kinds of mathematical ideas come to mind? What, if anything, does algebra have to do with the content you teach? What might it mean to engage with children on algebraic ideas? Math & Science Collaborative at the Allegheny Intermediate Unit

30. Mathematical Themes Are two different definitions of even numbers equivalent? What comprises an argument that a statement is always true when you cannot check every number? What are generalizations about adding and multiplying odd and even numbers and how can they be proved? Math & Science Collaborative at the Allegheny Intermediate Unit

31. Hue and Julio scenario Math & Science Collaborative at the Allegheny Intermediate Unit

35. Math Practices in The Classroom Math & Science Collaborative at the Allegheny Intermediate Unit

36. Acknowledgement This material is based on work supported by the SW PA MSP 2010 funds administered through the USDOE under Grant No. Project #: RA- 075-10-0603. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the granting agency. Math & Science Collaborative at the Allegheny Intermediate Unit