Understanding Multiplication

Use the Base 4 blocks to find these products.

214 334

× 134 ×234

Find the following products in Alphabitia:

AB CD ×B0 ×DC

Find the following products in Base 8:

258 578

×138 ×648

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

Multiplication Models• Repeated addition

• Area

• Cartesian product

3333

a1

a2

a3

Figure 3.13

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

MultiplicationProperties

• Identity

• Zero

• Commutative

• Associative

Multiplication

Properties continued:Distributive property--

combines multiplication and addition or subtraction

The area model and the standard multiplication algorithm

Figure 3.20

Figure 3.21

Figure 3.22

Expanded vs compacted

Expanded Compacted

Multiplication-the area model

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

10 + 10 + 10 + 2

10

+

4

Understanding FOIL