Fall 2013

1. Putting the Mathematical Practices Into Action Fall 2013

2. Norms • Listen as an Ally • Value Differences • Maintain Professionalism • Participate Actively

3. Session Outcome • Understand the Standards for Mathematical Practice • Explore strategies for implementing the Standards effectively

5. What has been your biggest challenge with the implementation of The Standards for Mathematical Practice?

6. Overarching habits of mind of a productive Mathematical Thinker

7. Exploring Standard 1 Make Sense of Problems and Persevere in Solving them.

8. Understanding the Standard • What do we do each day in our classroom to build mathematical thinkers? • What do we do to keep our students actively engaged in solving problems? • How do we help our students develop positive attitudes and demonstrate perseverance during problem solving?

9. What questions could you ask? Shipley Aquarium Admission Cost Adults - $8.00 Children (ages 3 and over) - $6.50 Children (ages 2 and under) – Free

10. Traditional Problems vs. Rich Problems • We can ask questions that stifle learning by prompting a quick number response. • What is the answer to number 3 on your worksheet? • What is 5 x 4? • We can ask questions that promote discussion, thinking, and perseverance.

11. Sort the math questions. Check your arrangement on page 22

12. Exploring Standard 6 Attend to precision.

13. Understanding the Standard • Why is precision important in mathematics? • What does it mean to be precise? • What can we do in the classroom to promote precise communication in mathematics?

14. Estimate and Exact • Buying bags of candy to put in party treat bags • Measuring the dimensions of the doorway to install a screen door • Buying pizzas for a class party • Buying carpeting for a living room floor

15. Estimation Skills 5 x 8/9 1 5 10 7

16. Sort and Label

17. Exploring Standard 2 Reason abstractly and quantitatively.

18. Understanding the Standard • What can we do in our classrooms each day to help students build a strong understanding of numbers (quantities)? • How do we help students convert problems to abstract representations? • What can we do to help students understand what numbers stand for in a given situation?

19. How Do We Get There? • Translate the Symbol • Expression Webs • Pinch Cards

20. Expression Webs A > B

21. Translate the Symbol • 4 dollars and 10 cents is greater than 4 dollars and 5 cents • One-fourth of 16 is 4 • Doubling a number then adding six more

22. Translate the Symbol • 12 = 7 + 5 • 4 + x = 6 • 3 x 4 > 2 x 5

23. Which Is More Challenging? • 4 dollars and 10 cents is greater than 4 dollars and 5 cents • One-fourth of 16 is 4 • Doubling a number then adding six more • 12 = 7 + 5 • 4 + x = 6 • 3 x 4 > 2 x 5

24. Pinch Cards Pinch cards are an all-pupil response technique. There were 6 soccer teams in the league and 12 players on each team. How many players were in the league? The 4 members of the High Rollers Bowling Team scored 120, 136, 128, and 162. What was the team’s mean score? page 41

25. Pinch It There were 6 soccer teams in the league and 12 players on each team. How many players were in the league? The 4 members of the High Rollers Bowling Team scored 120, 136, 128, and 162. What was the team’s mean score?

26. Avoiding Key Words • Key words are misleading. • Many problems have no key words. • The key word strategy sends a terribly wrong message about doing mathematics. A sense making strategy will always work.Van de Walle & Lovin (2006)

27. Video of Key Words

28. Exploring Standard 3 Construct viable arguments and critique the reasoning of others.

29. How Do We Get There? • Eliminate It • Agree or Disagree?

30. Eliminate It! • As a group, decide on the concept that should be eliminated with reasoning or math data to back up your decision. • There may be more than one way to eliminate an item! • Create your own.

31. Agree or Disagree? • 75% is more than 2/3. • Tell why you agree or disagree.

32. Assertion vs. Argument • Assertion: a statement of what students want us to believe without support or reasoning. • The answer is correct “because it is,” “because I know it,” or “because I followed the steps.” • Argument: a statement that is backed up with facts, data, or mathematical reasons • Constructing viable arguments is not possible for students who lack an understanding of math skills and concepts.

33. Is this true? 19+6 = 20+5

34. Exploring Standard 4 Model with mathematics.

35. Assessment Tips • Tell me what your model represents. • Why did you choose this model? • Did creating a model help you any way? If so, how? • Did you get any insights by looking at your model? • Is there another way you might model this problem or idea? How? Page 75

36. Exploring Standard 5 Use appropriate tools strategically.

37. Which tool is more efficient? There is often more than one tool that will work for a task, but some tools are more efficient than others. • Paper & Pencil • Mental Math • Calculator

38. Solve using your assigned tool! • 5 x 6 • 23 x 15 • Estimate the cost of 2 pies @ $3.75 each Cereal @ $3.20 each Milk @ $1.79 gal Bananas @ 59 cents/lb • 236 x 0 x 341 • What comes next 3, 7, 15, 31, ___ • A local TV store had a sale on TV’s. They sold 7 for $1,699.95 each. They made a profit of $169.00 on each TV. What did the store pay for the 7 TVs? • $1,183.00 C. $13,082.65 • $10,716.65 D. $11,899.65

39. In My Head? (Mental Math) Do I use paper & pencil or do it in my head? • 734 x 82 • 63 x 4 • 1/4 + 2/8 • 930 ÷ 3 Students need to identify tools that increase their efficiency with math tasks.

40. What questions do you have?

41. For all you do for our students!