Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of...

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Test 1 • Explain why as well as how. • Neatness and organization matter. • “consecutive” • Examples of good answers.
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Transcript of Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of...

Page 1: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Test 1

• Explain why as well as how.

• Neatness and organization matter.

• “consecutive”

• Examples of good answers.

Page 2: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Class Notes--Vidoes• In general, watch the videos, and try to

notice:a) what is the child doing?b) mathematically, what is going on?c) mathematically, why is it correct or incorrect.

Page 3: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Children’s Thinking Activity Part 1

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

Page 4: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Children’s Thinking Activity 1

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

Page 5: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Children’s Thinking Activity 1

• 1C.

• Can you see 5 • 5 + 2 • 5?

Page 6: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Children’s Thinking Activity Part 1

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

Page 7: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Children’s Thinking Activity Part 1

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

Page 8: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Children’s Thinking Activity Part 1

• 2C Can you see 10 • 6 + 2 • 6?

Page 9: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

What skills and concepts did these students know?

• BASIC MULTIPLICATION FACTS!

• And… (give examples for each)

Page 10: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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

Page 11: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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

done.

Page 12: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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

Page 13: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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

Page 14: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Rectangular Area Model• Look at this more closely:

• This is the same as 7 • 10 + 7 • 5

7

10 + 5

70 + 35

Page 15: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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

10 + 10 + 10 + 2

10

+

4

Page 16: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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

10 + 10 + 10 + 2

10

+

4

Page 17: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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)

Page 18: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

The area model and the standard multiplication

algorithm

Page 19: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

34 X 56

Page 20: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

34 X 56

Page 21: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

34 X 56

Page 22: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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?

Page 23: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Ryshawn and Nicholas

20 • 4 + 9 • 4

25 • 4 + 4 • 4

Page 24: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Multiplication-the area model

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

Page 25: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Jemea

30 • 12 - 12

Page 26: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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

Page 27: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

Understanding FOIL

Page 28: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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

Page 29: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

• Ellen begins the following problem.

46X 37 42

Is Ellen correct or incorrect? Explain why.

Page 30: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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?

Page 31: Test 1 Explain why as well as how. Neatness and organization matter. “consecutive” Examples of good answers.

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?