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February 24, 2009

http://www.multiplication.com/interactive_games.htm

Games to help kids learn multiplication facts

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February 24, 2009

• Section 3.3 – finish up multiplication

• Exploration 3.8

• Homework

• Bring Class Notes again on Thursday

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3.3 (cont’d)

Extend our pictorial models:

Suppose I want to multiply 3 • 4.

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3.3 (cont’d)

Extending pictorial models:

Suppose I want to multiply 3 • 40.

This is much harder to draw, but it can be done.

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3.3 (cont’d)

Extending pictorial models:

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

3

40

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3.3 (cont’d)

Let’s look a little closer at the area model: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:

7

15

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3.3 (cont’d)

Area Model:

This is the same as 7 • 10 + 7 • 5

7 • 10 and 7 • 5 are “partial products”.

7

10 + 5

70 + 35

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3.3 (cont’d)

Area Model:

This idea works for larger numbers: 32 • 14

10

+

4

10 + 10 + 10 + 2

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32 • 14Do you see 4 • 2? 4 • 30? 10 • 2? 10 • 30?Add the partial products.

3.3 (cont’d)

10

+

4

10 + 10 + 10 + 2

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3.3 (cont’d)

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)

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Can you explain how this is related to the lattice multiplication model you did for Exploration 3.13?

Can you explain how this area model is related to the standard multiplication algorithm?

Can you explain how this area model is related to the four students’ models? (Ryshawn, Nicholas, Jemea and Thomas)

3.3 (cont’d)

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3.3 (cont’d)

25 • 4 + 4 • 4

20 • 4 + 9 • 4

Ryshawn and Nicholas

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Jemea30 • 12 - 12

3.3 (cont’d)

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Thomas17 • 36 = ((17 • 10) • 3)+ (6 • 10) + (6 • 7)

3.3 (cont’d)

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3.3 (cont’d)

Exploration 3.8

Part 2: Circle clocks

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3.3 (cont’d)Which property or properties make these statements true?

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) = 2 • 3 + 2 • 14

2 • (3 • 14) ≠ 2 • 3 • 2 • 14

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Homework

Due Thursday, 2/26:

Link to online homework list