When you can hear and speak , please click on the

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

2. If you are having audio issues, please go through these steps: 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 Check that headset and speaker prongs are in the correct holes in your computer Make sure that you do not have separate external speakers plugged in If you do, please unplug them Check that internal computer volume is not muted Start control panel  sound & audio devices Go through Audio set up wizard in Elluminate Tools  audio  audio set-up wizard 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 Throw computer out the window (haha kidding!!)

3. Overview of Elluminate

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

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

11. Big Ideas 4 - 6Session 2

12. 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. More and less A fraction is slightly less than 1/2. What might it be? How do you know?

14. 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.

16. More and less

17. 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. Comparing decimals Which is greater? How do you know? Is it 0.4 or 0.19?

19. 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. Comparing decimals Which is greater? How do you know? Is it 0.4 or 0.19?

21. Number Operations We will focus on multiplication and division, but not exclusively.

22. A surprise Did you ever see this one? You want to solve 500 – 153.

23. A surprise • So you think: 4999 + 1 -1532 3467 + 1 = 3468

24. 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. 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.

27. Maybe

28. Maybe 0 4 8 12 16 20 24 28 32 36 40

29. 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.

31. Maybe

32. Or… Why is 20 ÷ 5 the same as 15 ÷ 5 + 5 ÷ 5?

33. Or…

34. Let’s talk about alternatives Alternative meanings for the operations Alternative ways to calculate

35. 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?

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

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

40. Or multiplication Multiplication can describe • Equal groups • Areas • Rate situations • Combination situations

41. 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. B1 B2 B3 F1 F2 F3 F4

43. 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. 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. 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. Would you… calculate 532 – 99 the same way you would calculate 532 – 111?

47. 22 x 13 20 2 10 3 200 20 60 6 • Here are two ways to show it: 22 x13 66 +220 286 Which one do you prefer? Raise your hand.

48. What about division? Let’s think about both • what it means and • how to calculate

49. Which representation? Which picture best shows what 72 ÷ 3 means?

50. Which representation? Which picture best shows what 72 ÷ 3 means?