1. ©Marian Small, 2011 When you can hear and speak, please click on the If you cannot hear or speak, please click on the Microphone On/Off There are only two for this room – we will share them

2. ©Marian Small, 2011 If you are having audio issues, please go through these steps: 1.Check that mic is not muted or turned down often volume control is on plastic piece on headset wire, volume and mute may be separate controls 2.Check that headset and speaker prongs are in the correct holes in your computer 3.Make sure that you do not have separate external speakers plugged in If you do, please unplug them 4.Check that internal computer volume is not muted Start  control panel  sound & audio devices 5.Go through Audio set up wizard in Elluminate Tools  audio  audio set-up wizard 6.If your head set was plugged into front of computer, try plugging it into back of computer (or vice versa) and repeat Audio set-up Wizard 7.Throw computer out the window ( haha kidding!! )

3. ©Marian Small, 2011 Overview of Elluminate

4. ©Marian Small, 2011

9. Big Ideas for 4 – 6 Math Session 2 Developed by ERLC/ARPDC as a result of a grant from Alberta Education to support implementation

10. ©Marian Small, 2011 Introductions Please tell us …. 1.Where you are located 2.Which math courses/grades you are teaching 3.What is one thing you’d like to get out of today A = microphone B = chat box C = pass

11. ©Marian Small, 2011 Big Ideas 4 - 6 Session 2

12. ©Marian Small, 2011 Agenda We will continue talking about number tonight, mostly operations. I will stop early to give you time to share some of your stories. To help me know how early, please use a happy face now if you tried something and will be willing to share later.

13. ©Marian Small, 2011 More and less A fraction is slightly less than 1/2. What might it be? How do you know?

14. ©Marian Small, 2011 More and less A fraction is slightly less than 1/2. What might it be? How do you know? Type some possibilities on the next empty slide. I will ask a few of you how you know.

15. ©Marian Small, 2011

16. More and less

17. ©Marian Small, 2011 Or… Which do you think is the best way to compare 2/5 and 4/9? A: draw 2/5 and 4/9 of the same whole and compare B: rename 2/5 as 18/45 and 4/9 as 20/45 C: rename 2/3 as 4/10 Vote– Then I will ask for a few hand-raisers.

18. ©Marian Small, 2011 Comparing decimals Which is greater? How do you know? Is it 0.4 or 0.19?

19. ©Marian Small, 2011 Comparing decimals Which is greater? How do you know? Is it 0.4 or 0.19? Raise your hand to explain how you know.

20. ©Marian Small, 2011 Comparing decimals Which is greater? How do you know? Is it 0.4 or 0.19?

21. ©Marian Small, 2011 Number Operations We will focus on multiplication and division, but not exclusively.

22. ©Marian Small, 2011 A surprise Did you ever see this one? You want to solve 500 – 153.

23. ©Marian Small, 2011 A surprise So you think: 4999 + 1 -1532 3467 + 1 = 3468

24. ©Marian Small, 2011 Important “why”s We encourage students to use a variety of strategies, but we don’t always make sure they know why they work. For example….

25. ©Marian Small, 2011 Why is… 5 x 8 the same as 10 x 4 (double/half)? Draw a picture– you can use the shape tools or text tools.

26. ©Marian Small, 2011

27. Maybe

28. ©Marian Small, 2011 Maybe 0 4 8 12 16 20 24 28 32 36 40

29. ©Marian Small, 2011 But.. 10 ÷ 2 is not the same as 20 ÷ 1. It is the same as 5÷ 1 (half/half). Draw a picture to show why.

30. ©Marian Small, 2011

31. Maybe

32. ©Marian Small, 2011 Or… Why is 20 ÷ 5 the same as 15 ÷ 5 + 5 ÷ 5?

33. ©Marian Small, 2011 Or…

34. ©Marian Small, 2011 Let’s talk about alternatives Alternative meanings for the operations Alternative ways to calculate

35. ©Marian Small, 2011 Let’s try this Make up two story problems involving subtraction of two larger whole numbers (both are at least 1000). The stories need to be different. Can some of you type some of your stories using the text tool on the next slide?

36. ©Marian Small, 2011

37. Meanings of subtraction Subtraction can be about take away, can be about comparison and can be about “what do I have to add”.

38. ©Marian Small, 2011 Meanings of subtraction Subtraction can be about take away, can be about comparison and can be about “what do I have to add”.

39. ©Marian Small, 2011 Let’s vote Does this picture model multiplication or not? Use happy face for yes– thumbs down for no

40. ©Marian Small, 2011 Or multiplication Multiplication can describe Equal groups Areas Rate situations Combination situations

41. ©Marian Small, 2011 For example I have three kinds of sandwich breads and four fillings. On the next screen, draw a model to help me figure out how many different sandwiches I can make.

42. ©Marian Small, 2011 B1 B2 B3 F1 F2 F3 F4

43. ©Marian Small, 2011 And there are many procedures Many of you are increasingly focusing on student development of personal strategies. How might a student figure out what 3 x8 is? Imagine a student you teach. Which way would you like to see that student get the answer? Vote A, B,C or D.

44. ©Marian Small, 2011 3 x 8 A: Double 3 x 4. B: Subtract 16 from 5 x 8. C: Add 16 and 8. D: Draw a picture and count. Raise your hand to explain your vote.

45. ©Marian Small, 2011 Which algorithm We want students to use personal strategies, but how important do you think it is to ultimately have the more traditional strategy? Vote: A for very important B important for most C not important

46. ©Marian Small, 2011 Would you… calculate 532 – 99 the same way you would calculate 532 – 111?

47. ©Marian Small, 2011 22 x 13 Here are two ways to show it: 22 x13 66 +220 286 Which one do you prefer? Raise your hand. 20 2 10 3 20020 606

48. ©Marian Small, 2011 What about division? Let’s think about both what it means and how to calculate

49. ©Marian Small, 2011 Which representation? Which picture best shows what 72 ÷ 3 means?

50. ©Marian Small, 2011 Which representation? Which picture best shows what 72 ÷ 3 means?

51. ©Marian Small, 2011 Vote A for 1 st picture B for 2 nd picture C if you think they’re equally good D if you think neither is good I will ask a few people to explain their thinking.

52. ©Marian Small, 2011 And what procedure? What do each of these procedures help a student see better than the other ones?

53. ©Marian Small, 2011 115 ÷ 5 23 10 + 10 + 3 5 115 5 115 5 50 + 50 + 15 -100 - 50 10 15 65 - 15 - 50 10 0 15 - 15 3 0 23

54. ©Marian Small, 2011 I added…. 3 numbers. One is little. One is close to double the other. The sum is 5000. What could the numbers be?

55. ©Marian Small, 2011 I subtracted… a number from 3000. The result had the digits 3 and 4 in it. What could the subtraction have been?

56. ©Marian Small, 2011 The product is.. The product of two numbers is almost 400. What might the numbers be? Raise your hand to respond.

57. ©Marian Small, 2011 I wonder.. I divided []3[] by 4. The answer was a 3 digit number. Tell me anything about []3[] that you’re sure of. Raise your hand to respond.

58. ©Marian Small, 2011

59. Sharing Time I hope some of you have stories to share.

60. ©Marian Small, 2011 I am hoping that : you will try out one of the questions we discussed or, even better, your own question to bring out a big idea in number. We’ll talk about the results next time.