multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12...

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Multiplication terms 12 3 4 multiplier: 4 multiplicand: 3 product: 12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

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Page 1: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Multiplication terms

1234

multiplier: 4multiplicand: 3product: 12factors: 4 and 3 are factors of 12multiple: 12 is a multiple of 4

12 is a multiple of 3

Page 2: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Multiplication Models

• Repeated addition

• Area

• Cartesian product

3333

a1

a2

a3

Page 3: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Figure 3.13

Page 4: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Units

• For addition and subtraction3 hours plus 5 miles

• For multiplication

8 miles per hour for 5 hours:how many miles?8 mi • 5 hr = 40 mi

hr

Page 5: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Multiplication

Properties

• Identity

• Zero

• Commutative

• Associative

Page 6: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Multiplication

Properties continued:

Distributive property--

combines multiplication and addition or subtraction

Page 7: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

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 8: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

The area model and the standard multiplication algorithm

Page 9: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Figure 3.20

Page 10: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Figure 3.21

Page 11: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Figure 3.22

Page 12: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Expanded vs compacted

Expanded Compacted

Page 13: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Multiplication-the area model

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

Page 14: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

10 + 10 + 10 + 2

10

+

4

Page 15: Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

Understanding FOIL