1. Standards of Mathematical Practice

2. http://thinkmath.blog.monroe.edu/

3. Today’s Goals To explore the mathematical standards for Content and Practice To discuss and learn strategies for getting students engaged in the Standards of Mathematical Practice To explore how we can use existing resources to focus on the Practices

4. Common Core State Standards Mathematics Standards for Content Standards for Practice

5. Standards for Mathematical Practice Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning © Institute for Mathematics & Education 2011

6. SMP 1: Make sense of problems and persevere in solving them. © Institute for Mathematics & Education 2011 Gather Information Make a plan Anticipate possible solutions Continuously evaluate progress Check results Question sense of solutions

8. SMP 2: Reason abstractly and quantitatively Decontextualize Represent as symbols, abstract the situation Contextualize Pause as needed to refer back to situation x x P 5 ½ Mathematical Problem © Institute for Mathematics & Education 2011

10. SMP 3: Construct viable arguments and critique the reasoning of others Use assumptions, definitions, and previous results Make a conjecture Build a logical progression of statements to explore the conjecture Analyze situations by breaking them into cases Recognize and use counter examples Justify conclusions Respond to arguments Communicate conclusions Distinguish correct logic Explain flaws Ask clarifying questions © Institute for Mathematics & Education 2011

12. SMP 4: Model with mathematics Images: http://tandrageemaths.wordpress.com, asiabcs.com, ehow.com, judsonmagnet.org, life123.com, teamuptutors.com, enwikipedia.org, glennsasscer.comhttp://tandrageemaths.wordpress.com Problems in everyday life… …reasoned using mathematical methods © Institute for Mathematics & Education 2011

14. SMP 5: Use appropriate tools strategically © Institute for Mathematics & Education 2011

16. SMP 6: Attend to precision Comic: http://forums.xkcd.com/viewtopic.php?f=7&t=66819http://forums.xkcd.com/viewtopic.php?f=7&t=66819 © Institute for Mathematics & Education 2011

18. SMP 7: Look for and make use of structure © Institute for Mathematics & Education 2011

20. SMP 8: Look for and express regularity in repeated reasoning © Institute for Mathematics & Education 2011

22. Fraction Puzzles On your own, write a fraction addition or subtraction equation.

23. Fraction Puzzles On your own, write a fraction addition or subtraction equation. Rewrite your equation on an index card, replacing some numbers in the numerators or denominators with n or d.

24. Fraction Puzzles On your own, write a fraction addition or subtraction equation. Rewrite your equation on an index card, replacing some numbers in the numerators or denominators with n or d. Exchange with a partner to solve for the unknown numbers.

25. Fraction Puzzles

26. What Standards for Mathematical Practice were focused on in this task?

27. Build a Fraction

29. What Standards for Mathematical Practice were focused on in this task?

30. Subtraction with mixed numbers

32. What Standards for Mathematical Practice were focused on in this task?

35. Adding Unlike Fractions

37. What Standards for Mathematical Practice were focused on in this task?

38. Strategies for Implementing the Practices

39. Use Rich Tasks

40. Where to find rich tasks. http://www.insidemathematics.org/ http://www.rda.aps.edu/mathtaskbank/start.htm http://www.galileo.org/math/MathProblems.html http://balancedassessment.concord.org/tasksalpha.html http://illustrativemathematics.org/

41. Rich Problems Worksheet Read through the tasks on the Rich Problems worksheet With a partner discuss what similarities you see in these problems

42. Creating Open Ended Questions

44. Creating open ended questions With a partner choose an upcoming topic you will be teaching. Create 3 open ended questions to engage your students? For each questions what Math Practices would you expect your students to be engaged in?

45. Additional Strategies

46. Where do I find these opportunities in my resources?

49. With a partner, pick an upcoming lesson and discuss how you are going to integrate the standards of Mathematical Practice. Focus on 1 or 2 Practices What will you see the students doing if they are engaging in the Practices? How will you facilitate the Practices?