Children s thinking activity part 1
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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.

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Children’s Thinking Activity Part 1

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Children s thinking activity part 1

Children’s Thinking Activity Part 1

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


Children s thinking activity 1

Children’s Thinking Activity 1

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


Children s thinking activity 11

Children’s Thinking Activity 1

  • 1C.

  • Can you see 5 • 5 + 2 • 5?


Children s thinking activity part 11

Children’s Thinking Activity Part 1

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


Children s thinking activity part 12

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 13

Children’s Thinking Activity Part 1

  • 2C Can you see 10 • 6 + 2 • 6?


What skills and concepts did these students know

What skills and concepts did these students know?

  • BASIC MULTIPLICATION FACTS!

  • And… (give examples for each)


Link the pictorial models

Link the pictorial models

  • Suppose I want to multiply 3 • 4.


Link the pictorial models1

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 models2

40

3

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:


Rectangular area model

15

7

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.


Rectangular area model1

10 + 5

7

70 + 35

Rectangular Area Model

  • Look at this more closely:

  • This is the same as 7 • 10 + 7 • 5


Rectangular area model2

10 + 10 + 10 + 2

10

+

4

Rectangular Area Model

  • This idea works for more: 32 • 14


32 14

10 + 10 + 10 + 2

10

+

4

32 • 14

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


Rectangular model

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

The area model and the standard multiplication algorithm


34 x 56

34 X 56


34 x 561

34 X 56


34 x 562

34 X 56


Compare models

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

25 • 4 + 4 • 4

Ryshawn and Nicholas

20 • 4+ 9 • 4


Multiplication the area model

Multiplication-the area model

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


Jemea

Jemea

30 • 12 - 12


Thomas

Thomas

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


Understanding foil

Understanding FOIL


Explain why

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


Children s thinking activity part 1

  • Ellen begins the following problem.

    46X 37 42

    Is Ellen correct or incorrect? Explain why.


Children s thinking activity part 1

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?


Where is the error

Where is the error?

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?


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