Download - 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?
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Children’s Thinking Activity 1
• 1B. Do you see 5, 10, 15, 20, 25, and then 10 more?
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Children’s Thinking Activity 1
• 1C.
• Can you see 5 • 5 + 2 • 5?
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Children’s Thinking Activity Part 1
• 2A. Do you see 12 bags with 6 candies in each?
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Children’s Thinking Activity Part 1
• 2B. Do you see 10 bags, with 60, and then 2 more bags 2 • 6 = 12?
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Children’s Thinking Activity Part 1
• 2C Can you see 10 • 6 + 2 • 6?
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What skills and concepts did these students know?
• BASIC MULTIPLICATION FACTS!
• And… (give examples for each)
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Link the pictorial models• Suppose I want to multiply 3 • 4.
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Link the pictorial models• Suppose I want to multiply 3 • 40.• This is much harder to draw, but it can be
done.
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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
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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
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Rectangular Area Model• Look at this more closely:
• This is the same as 7 • 10 + 7 • 5
7
10 + 5
70 + 35
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Rectangular Area Model• This idea works for more: 32 • 14
10 + 10 + 10 + 2
10
+
4
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32 • 14Do you see 4 • 2? 4 • 30? 10 • 2? 10 • 30?
10 + 10 + 10 + 2
10
+
4
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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)
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The area model and the standard multiplication
algorithm
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34 X 56
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34 X 56
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34 X 56
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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?
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Ryshawn and Nicholas
20 • 4 + 9 • 4
25 • 4 + 4 • 4
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Multiplication-the area model
• How could Jemea’s strategy be represented using the rectangular area model?
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Jemea
30 • 12 - 12
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Thomas17 • 36 = ((17 • 10) • 3)+ (6 • 10) + (6 • 7)
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Understanding FOIL
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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
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• Ellen begins the following problem.
46X 37 42
Is Ellen correct or incorrect? Explain why.
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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?
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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?