Whats wrong

1

• Whats wrong?
• 49 12
• 49 1 is 50, so do 50 12, which is 600, and
  then minus 1, and get 599.

2
Childrens Thinking Activity Part 1

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

3
Childrens Thinking Activity 1

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

4
Childrens Thinking Activity 1

• 1C.
• Can you see 5 5 2 5?

5
Childrens Thinking Activity Part 1

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

6
Childrens Thinking Activity Part 1

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

7
Childrens Thinking Activity Part 1

• 2C Can you see 10 6 2 6?

8
What skills and concepts did these students know?

• BASIC MULTIPLICATION FACTS!
• And (give examples for each)

9
Link the pictorial models

• Suppose I want to multiply 3 4.

10
Link the pictorial models

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

11
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

12
Rectangular Area Model

• Lets 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.

13
Rectangular Area Model

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

14
Rectangular Area Model

• This idea works for more 32 14

15
32 14

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

16
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)

17
The area model and the standard multiplication
algorithm
18
34 X 56
19
34 X 56
20
34 X 56
21
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?

22
Ryshawn and Nicholas

• 20 4 9 4

23
Multiplication-the area model

• How could Jemeas strategy be represented using
  the rectangular area model?

24
Jemea

• 30 12 - 12

25
Thomas

• 17 36 ((17 10) 3) (6 10) (6 7)

26
Understanding FOIL
27
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

28

• Ellen begins the following problem.
• 46 X 37 42
• Is Ellen correct or incorrect? Explain why.

29

• 46 46 X 37 X
  37 42 42
  280
• 46 X 37 2842

What is 280? Is it 7 4 or 7 40? What does
the placeholder mean?
30
Where is the error?

• 46 46 X 37 X
  37 42 42
  280
• 46 X 37 2842

What is 280? Is it 7 4 or 7 40? What does
the placeholder mean?