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Workshop 3 Multiplication and Division

Workshop 3 Multiplication and Division. Nā te hiahia kia titiro, ā, ka kite ai tātou te mutunga. You must understand the beginning if you wish to see the end. Sharing Time. Focusing Questions – What has been working well? What are the difficulties? What is your next step?

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Workshop 3 Multiplication and Division

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  1. Workshop 3Multiplication and Division

  2. Nā te hiahia kia titiro, ā, ka kite ai tātou te mutunga. You must understand the beginning if you wish to see the end.

  3. Sharing Time Focusing Questions – • What has been working well? • What are the difficulties? • What is your next step? Place difficulties on stickers and place them on chart at front of the room. Homework 1) Shifts in development: Journey 2) Use Planning Sheets for Add & Sub

  4. Loopy Teacher Multiplication and Division Loopy – what are they learning at each stage? Discussion time - What underpins multiplication and division development? • Repeated addition / subtraction • Sets of … • Division as halves • Two ways of dividing • Patterns for times tables • Estimation

  5. Mult and Div Scenarios In a small group discuss the scenarios and stage

  6. Two students are solving this problem: A family has $96.00 to spend at the adventure park. Each ride costs $4.00. How many rides can the family go on?

  7. Discuss each student’s strategy. Are they both thinking multiplicatively? They think They record I need to find out how many times I can take $4.00 away from $96.00 • 96 • -4 • 92 • -4 • 88 • -4 • 84 • etc. • … Frank There are 25 lots of $4.00 in $100, $96.00 is $4.00 less, so… • 25 x 4 = 100 • 100 – 4 = 96 • So • 24 x 4 = 100 • … Awhina

  8. There was a qualitative difference in the way these two students solved the problem. Frank’s strategy was additive (rather strange when he was subtracting). Awhina’s strategy was multiplicative (rather strange since the problem was about division).

  9. Discuss what strategies you use to solve this problem: • Each carton holds 36 cans of spaghetti. There are 5 cartons. How many cans of spaghetti is that? How would this be solved using the commutative property From: GloSS Form C

  10. ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten 5 x 30 = 150 150 30 180 5 x 36 = + 5 x 6 = 180 + 30 Here is a strategy that you might have used along with an equipment representation:

  11. The first strategy involved the distributive property. This meant that one of the factors was split additively. 5 x 36 = 5 x 30 + 5 x 6 The 36 was split (distributed) into 30 + 6.

  12. 180 ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten ten Another strategy you may have used on the spaghetti can problem used the commutative property in conjunction with the associative property. = 18 x 10 = 180 36 x 5 5 x 36 = 180

  13. The associative property is about regrouping the factors. So in 36 x 5 the 36 was split multiplicatively: 36 x 5 = (18 x 2) x 5 = 18 x (2 x 5) = 18 x 10 = 180

  14. Here’s another example of the associative property: • How many small cubes make up this model? Any way in which you group the factors multiplicatively leaves the product invariant (unchanged).

  15. 5 4 3 What if the question changed to this? Give the dimensions of another cuboid with the same volume as this one?

  16. Example 1: What equation could be used to represent this model of division?(There are twelve containers)

  17. Example 2: What equation could be used to represent this model of division?

  18. Both of the stories you made up for the animations can be recorded as 12 ÷ 3 = 4, but the numbers refer to quite different things. The first animation showed 12 ÷ 3 as “twelve shared among three.” In this case the answer, four, tells how many are in each share. This is called partitive division (sharing).

  19. There are two kinds of division partitive and quotitive. The second animation showed 12 ÷ 3 as “twelve separated (measured) into sets of three.” In this case the answer four tells the number of sets that could be made. This is called quotitive division (measurement).

  20. Equipment Animations – NZmaths • Happy Hundred • Ice Cream Containers • Multiplication arrays 2 • Multilink cubes

  21. Lesson Modelling Fun with Five pg 28 Book 6 (book structure) Powerful Numbers pg 73 Book 6 (book structure)

  22. Play and Stage 1) Play the activity 2) Stage the activity (use book 1 to help) 3) Think about possible adaptations for other stages

  23. Follow up tasks Check which Basic Facts your students know and target the ones they do not know. Read the start of Bk 6

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