Conceptual Building Blocks of Multiplication and Division

1. Conceptual Building Blocks of Multiplication and Division Day Two Training

2. Taking Time to Self-Reflect Adapted from Basic Facts Knowledge: A Staff Tutorial. http.nzmaths.com, 2010.

3. A Look Back at Day One

4. What to expect from today. • Examine alternative strategies for multiplication and division. • Relate the concepts of multiplication & division. • Assess student work and identify their misconceptions.

5. Fact Selection Multiplication and Division-Grade 3-Unit 2. Georgia Department of Education. 2007. p. 26.

6. Mastering Math Facts The problem with rote work comes when it is used exclusively for teaching math facts. Research shows that overemphasizing memorization and frequently administering timed tests is actually counter-productive, (National Research Council, 2001).  Van de Walle, J.A., & Lovin, L.H. (2006) Teaching Student Centered Mathematics Volume II (3-5), Boston: Pearson.

7. Let’s get rockin’ with SALUTE • Materials: • a deck of ten frame cards with wild cards removed. • three participants for each group Student Student CAPTAIN

8. How my students think!

9. A muffin recipe requires 2/3 of a cup of milk. Each recipe makes 12 muffins. How many muffins can be made using 6 cups of milk? Adapted from Multiplicative Thinking. Workshop 1. Properties of Multiplication and Division. http.nzmaths.com, 2010.

10. The Additive Thinker A muffin recipe requires 2/3 of a cup of milk. Each recipe makes 12 muffins. How many muffins can be made using 6 cups of milk?

11. 2 3 4 1 2 Each rectangle represents a third of a cup of milk.

12. A muffin recipe requires 2/3 of a cup of milk. Each recipe makes 12 muffins. How many muffins can be made using 6 cups of milk?

13. The Multiplicative Thinker • Works with a variety of numbers such as larger whole numbers, decimals, common fractions, etc. • Can solve a range of problems involving multiplication and division • Can communicate math findings in a variety of ways including words, diagrams, symbolic expressions and written algorithms.

14. Multiplicative Thinking-Workshop 1. Properties of Multiplication and Division. http.nzmaths.com, 2010.

15. A family has $96.00 to spend at the Wally World adventure park. Each ride at the park costs $4.00 per person. How many rides will the family be able to enjoy while there?

16. Time for a Break

17. Learning How Students Think

18. Why encourage multiplicative strategies if additive strategies can be used? “The Jones family has $396.00 to spend at the Wally World adventure park. Rides cost $4.00. How many rides will the family be able to enjoy?”

19. Writing about what you have seen. Reflection Time

20. Why is math vocabulary so difficult? Students must be provided adequate opportunities to learn this vocabulary in meaningful ways. Learners need experiences with constructing meaning from context as well as from direct teaching.

21. Reflection Time

22. Let’s Make 100 • Use the die to generate a number. Spin the spinner to get the multiplier. The person closest to 100 after 5 spins is the winner. • You have the option of “staying” after 3 spins. • Any number greater than 100 is a bust.

23. Reflection Time

24. Multiplication in KCAS

25. Multiplication 23 x16 138 230 368

26. Errors or Misconceptions? Ashlock, Robert. Error Patterns in Computation: Using Error Patterns to Help Each Student Learn-Tenth Edition, 2009. Covenant College p.15.

27. If you use it, you must understand why it works and be able to explain it. What About Alternative Strategies? John Van De Walle

28. Partial Products 38 78 x 19x 54 30 x 10 300 70 x 50 3500 30 x 9 270 70 x 4 280 8 x 10 80 8 x 50 400 8 x 9 + 72 8 x 4 + 32 722 4212

29. Partial Products (Area Model) 62 x 18 60 2 600 480 10 600 20 20 + 16 8 480 16 1116

30. 1500+350+120+28 =1998 54 x 37 = 50 4 1500 120 30 28 7 350

31. (2x + 5) (x + 6) x 6 5x 30 5 12x 2x 2x

32. Lattice Method 37 3 7 x 95 185 3330 3515 1 1 3 9 5 5 5 1

33. 4 6 46 × 37 3 7

34. 4 6 46 × 37 = 1702 2 1 1 3 1 2 8 2 4 7 8 2 7 0 2

35. Drop Notation 476 476 x 8x 38 354 354 268 268 times 8 3808 121 218 times 3 18088

36. CHINESE METHOD OF MULTIPLICATION

37. 400 140 12 552 12 400 140 CHINESE METHOD OF MULTIPLICATION 23 x 24 =

38. 31 x 43=

39. Reflection Time

40. Lies my teacher told me… • To multiply by ten just add a zero to the end of the whole number. • The product is always larger. 5 x 10 = 3245 x 10= 10 x 2 = .5 x 10= 3.245 x 10= 10 x .02=

41. So What About Division? How many of our students understand dividing a number by 3 is the same as multiplying the number by 1/3?

42. 169 ÷ 14 = To begin thinking about division, solve this problem using a strategy other than the conventional division algorithm. You may use symbols, diagrams, words, etc. Be prepared to show your strategy Hedges, Huinker and Steinmeyer. Unpacking Division to Build Teachers’ Mathematical Knowledge, Teaching Children Mathematics, November 2004, p. 4-8.

43. Hedges, Huinker and Steinmeyer. Unpacking Division to Build Teachers’ Mathematical Knowledge, Teaching Children Mathematics, November 2004, p. 4-8.

44. KCAS CONNECTION

45. Primary Resources: Maths: Multiplication and Division.www.primaryresources.co.uk.maths.mathsC2.htm

46. The Confusion of Division 24 ÷ 6 = How many times can 6 be subtracted from 24? 24 divided into 6 equal groups. 24 divided into equal groups of size 6. What number times 6 gives the product of 24?

47. 24 ÷ 6 24/6 24 6 24 The symbolism of division 6

48. Division Vocabulary Quotient Dividend Divisor

50. THE PARTITIVE PROBLEM