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Children’s Thinking Activity Part 1

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- 1A. Do you see 5 boxes each with 7 turtles?

- 1B. Do you see 5, 10, 15, 20, 25, and then 10 more?

- 1C.
- Can you see 5 • 5 + 2 • 5?

- 2A. Do you see 12 bags with 6 candies in each?

- 2B. Do you see 10 bags, with 60, and then 2 more bags 2 • 6 = 12?

- 2C Can you see 10 • 6 + 2 • 6?

- BASIC MULTIPLICATION FACTS!
- And… (give examples for each)

- Suppose I want to multiply 3 • 4.

- Suppose I want to multiply 3 • 40.
- This is much harder to draw, but it can be done.

40

3

- As the numbers get bigger, it is harder to draw in all the little dots. But the area model will work well: 3 • 40:

15

7

- Let’s look a little closer:
Let this be a unit square--that is, a square that measures 1 unit on each side.

Then, this is a representation for 7 • 15.

10 + 5

7

70 + 35

- Look at this more closely:
- This is the same as 7 • 10 + 7 • 5

10 + 10 + 10 + 2

10

+

4

- This idea works for more: 32 • 14

10 + 10 + 10 + 2

10

+

4

Do you see 4 • 2? 4 • 30? 10 • 2? 10 • 30?

- You try: 46 • 23 Use the base 10 blocks or draw a picture.
- Now, can you explain where these products are in the diagram?
46 • 23 = (46 • 20) + (46 • 3) or

= (23 • 40) + (23 • 6)

- Can you explain how this is related to the lattice multiplication model you did for Exploration 3.13?
- Can you explain how this rectangular model is related to the standard multiplication algorithm?
- Can you explain how this rectangular model is related to the four students’ models?

25 • 4 + 4 • 4

20 • 4+ 9 • 4

- How could Jemea’s strategy be represented using the rectangular area model?

30 • 12 - 12

17 • 36 = ((17 • 10) • 3)+ (6 • 10) + (6 • 7)

- Can you show, using pictures or base-10 blocks, why 3 • 14 = 14 • 3?
- Can you show or explain why? Give a reason? Draw a picture?
- 2 • (3 • 14) = (2 • 3) • 14?
- 2 • (3 • 14) = (3 • 2) • 14?
- 2 • (3 • 14) = 3 • (2 • 14)
- 2 • (3 • 14) = 14 • (2 • 3)
- 2 • (3 • 14) = 3 • 14 + 3 • 14
- 2 • (3 • 14) ≠ 2 • 3 + 2 • 14

- Ellen begins the following problem.
46X 37 42

Is Ellen correct or incorrect? Explain why.

46 46X 37X 37 42 42 280

46X 37 2842

What is 280?

Is it 7 • 4 or 7 • 40?

What does the placeholder mean?

46 46X 37X 37 42 42 280

46X 37 2842

What is 280?

Is it 7 • 4 or 7 • 40?

What does the placeholder mean?