1. ©Marian Small, 2011 Big Ideas 4 - 6 Session 3

2. ©Marian Small, 2011 Continuing with.. Tonight we will finish our work with number operations and go on to patterns and relations and statistics and probability.

3. ©Marian Small, 2011 Alternate algorithms We ended last time talking about the value of alternate strategies (or algorithms).

4. ©Marian Small, 2011 Would you… calculate 532 – 99 the same way you would calculate 532 – 111? Use a √ for yes and an x for no.

5. ©Marian Small, 2011 Would you… calculate 532 – 99 the same way you would calculate 532 – 111? Use a √ for yes and an x for no. Should students?

6. ©Marian Small, 2011 22 x 13 Here are two ways to represent 22 x 13. 22 x13 66 +220 286 Which one do you prefer? Use √ for the left and x for the right. 20 2 10 3 20020 606

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

8. ©Marian Small, 2011 Which representation? Which picture best shows what 72 ÷ 3 means? (You will vote soon.)

9. ©Marian Small, 2011 Which representation? Which picture best shows what 72 ÷ 3 means? (You will vote soon.)

10. ©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.

11. ©Marian Small, 2011 And what procedure? What do each of the procedures on the next screen help a student see better than the other ones? Vote A,B or C to tell me which you are willing to talk about in terms of what is good about it. I will call on people in each category.

12. ©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

13. ©Marian Small, 2011 What about estimating? Let’s think about estimating questions. It’s no longer just about rounding rules. Consider these questions.

14. ©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? Type your numbers on next empty screen.

15. ©Marian Small, 2011

16. I subtracted… a number from 3000. The result had the digits 3 and 4 in it. What could the subtraction have been? Write some numbers on next empty screen.

17. ©Marian Small, 2011

18. The product is.. The product of two numbers is almost 400. What might the numbers be? Raise your hand to respond.

19. ©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.

20. ©Marian Small, 2011

21. Patterns

22. ©Marian Small, 2011 WNCP Pattern Outcomes Grade 4- focus on identifying patterns and relationships in tables and charts Grade 5- focus on pattern rule to predict Grade 6- focus on table of value relationships

23. ©Marian Small, 2011 Here is a multiplication table X0123456789 00000000000 10123456789 2024681012141618 30369121518212427 404812162024283236 5051015202530354045 6061218243036424854 7071421283542495663 8081624324048566472 9091827364554637281

24. ©Marian Small, 2011 Here is a multiplication table X0123456789 00000000000 10123456789 2024681012141618 30369121518212427 404812162024283236 5051015202530354045 6061218243036424854 7071421283542495663 8081624324048566472 9091827364554637281

25. ©Marian Small, 2011 Big Idea

26. ©Marian Small, 2011 Here is a multiplication table X0123456789 00000000000 10123456789 2024681012141618 30369121518212427 404812162024283236 5051015202530354045 6061218243036424854 7071421283542495663 8081624324048566472 9091827364554637281

27. ©Marian Small, 2011 Big idea

28. ©Marian Small, 2011 Look at this To show the final digits of the multiples of 8: 0 1 2 3 4 5 6 7 8 9

29. ©Marian Small, 2011 Look at this To show the final digits of the multiples of 6. Someone take the pen. 0 1 2 3 4 5 6 7 8 9

30. ©Marian Small, 2011 Another big idea

31. ©Marian Small, 2011 Or another pattern X0123456789 00000000000 10123456789 2024681012141618 30369121518212427 404812162024283236 5051015202530354045 6061218243036424854 7071421283542495663 8081624324048566472 9091827364554637281

32. ©Marian Small, 2011 1 x 2 + 2 x 31 x 3 + 2 x 3 3 x 1 + 4 x 23 x 2+ 4 x 1

33. ©Marian Small, 2011 Move objects to compare 3 x 3 + 4 x 4 to 3 x 4 + 4 x 3

34. ©Marian Small, 2011 Picture a 100 chart 12345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 51525354555657585960 61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100

35. ©Marian Small, 2011 Big Idea

36. ©Marian Small, 2011 How else could you… represent the pattern 2, 5, 8, 11,….

37. ©Marian Small, 2011 How else could you… represent the pattern 2, 5, 8, 11,….

38. ©Marian Small, 2011 How else could you… represent the pattern 2, 5, 8, 11,….

39. ©Marian Small, 2011 How else could you… What pattern do you see? Term number Term value 12 25 38 411

40. ©Marian Small, 2011 How else could you… What pattern do you see? Term number Term value Related pattern 123 256 389 41112

41. ©Marian Small, 2011 Variables and equations Grade 4- problems as equations with unknowns; solve one-step equations Grade 5- single-variable, one-step equations Grade 6- generalizations written using variables; model equality preservation

42. ©Marian Small, 2011 Algebra big ideas

43. ©Marian Small, 2011 Try this What situation might 2w describe? Type some possibilities on the next screen.

44. ©Marian Small, 2011

45. Try this Jeff got $12 in allowance every week. What does 6 x w tell about the situation? A: his allowance B: his allowance in w weeks C: his allowance in 2 xw weeks D: his allowance in w ÷ 2 weeks

46. ©Marian Small, 2011 Try this Jeff got $12 in allowance every week. What does 12w tell about the situation? What equation would you solve to find out how many weeks until he had $156?

47. ©Marian Small, 2011 The solution is… The solution to an equation is x = 2. What might the equation have been? Type some possibilities on the next screen.

48. ©Marian Small, 2011

49. Respond by raising your hand

50. ©Marian Small, 2011 Data Grade 4- many-to-one correspondence for pictographs and bar graphs Grade 5- double bar graphs Grade 6- line graphs

51. ©Marian Small, 2011 What’s going on? Vote for A or B in terms of which makes it easier for you to tell what’s going on?

52. ©Marian Small, 2011 A Kids who like chocolate chip cookies most: Jane, Kyle, Ravi, Shilpa, Elaine, Jar-Ye, Sindy, Amy, Liam Kids who like oatmeal cookies most: Aaron, Amanda, Diana, Carolyn, Geoffrey, Suhana, Jeremy, Terry-Lynn

53. ©Marian Small, 2011 B Chocolate Chip Oatmeal

54. ©Marian Small, 2011 B Chocolate Chip Oatmeal

55. ©Marian Small, 2011 Which graph would you use? Vote: A for bar graph with scale of 2 B for bar graph with scale of 5 C for pictograph with scale of 2 D for pictograph with scale of 5

56. ©Marian Small, 2011 Let’s compare bar graphs Do the two graphs on the next two slides give you the same impression about the following data? Use √ for yes and x for no. Favourite Pets Dog20 Cat15 Rat2

57. ©Marian Small, 2011 You choose

58. ©Marian Small, 2011 You choose

59. ©Marian Small, 2011 You choose

60. ©Marian Small, 2011 How do these differ in the impression they give? Raise your hand.

61. ©Marian Small, 2011 What will happen I will show you a graph. I will mention some things you might think it shows well. If you think it is easy to see, click a happy face. If not, click a thumbs down.

62. ©Marian Small, 2011 What does this graph about how I divide my day show?

63. ©Marian Small, 2011 The big idea

64. ©Marian Small, 2011 Other important big ideas Pictographs and bar graphs are particularly useful for comparing frequency of data in different categories. Line graphs are particularly useful for showing relationships between quantities and trends.

65. ©Marian Small, 2011 Probability Grade 5- verbal comparisons of likelihood Grade 6- experimental/theoretical probability

66. ©Marian Small, 2011 Using probability language Choose which is most likely about a new kid joining a Grade 5 class: A: It’s a boy. B: The student is the same age as lots of other kids in the class. C: The student lives in the area. D: The student is human.

67. ©Marian Small, 2011 Now… You write a phrase that is: Almost certain Impossible Very likely Very unlikely

68. ©Marian Small, 2011 A Big Idea

69. ©Marian Small, 2011 You just flipped a coin and… You got H H H H H H H H H Vote: √ if you think a H next time X if you think a T next time

70. ©Marian Small, 2011 Experimental probability You are going to create an experiment using ONE die. The result you want should happen about three-fourths of the time. What would you choose for your result? Some choices are on the next screen.

71. ©Marian Small, 2011 Choices A: an even number B: a number more than 2 C: anything but 1 D: a number less than 5

72. ©Marian Small, 2011 Big Ideas

73. ©Marian Small, 2011 Sharing Time I hope some of you have stories to share.

74. ©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.