Children’s Thinking Activity Part 1

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

Children’s Thinking Activity 1

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

Children’s Thinking Activity 1

• 1C.

• Can you see 5 • 5 + 2 • 5?

Children’s Thinking Activity Part 1

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

Children’s Thinking Activity Part 1

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

Children’s Thinking Activity Part 1

• 2C Can you see 10 • 6 + 2 • 6?

What skills and concepts did these students know?

• BASIC MULTIPLICATION FACTS!

• And… (give examples for each)

Link the pictorial models• Suppose I want to multiply 3 • 4.

Link the pictorial models• Suppose I want to multiply 3 • 40.• This is much harder to draw, but it can be

done.

Link the 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

Rectangular Area Model

• 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.

7

15

Rectangular Area Model• Look at this more closely:

• This is the same as 7 • 10 + 7 • 5

7

10 + 5

70 + 35

Rectangular Area Model• This idea works for more: 32 • 14

10 + 10 + 10 + 2

10

+

4

32 • 14Do you see 4 • 2? 4 • 30? 10 • 2? 10 • 30?

10 + 10 + 10 + 2

10

+

4

Rectangular Model• 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)

The area model and the standard multiplication

algorithm

34 X 56

34 X 56

34 X 56

Compare models• 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?

Ryshawn and Nicholas

20 • 4 + 9 • 4

25 • 4 + 4 • 4

Multiplication-the area model

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

Jemea

30 • 12 - 12

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

Understanding FOIL

Explain why…• 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 46 X 37 X 37

42 42 280

46X 37 2842

What is 280?

Is it 7 • 4 or 7 • 40?

What does the placeholder mean?

Where is the error? 46 46 X 37 X 37

42 42 280

46X 37 2842

What is 280?

Is it 7 • 4 or 7 • 40?

What does the placeholder mean?