Illustrative Mathematics | v.360 Curriculum

8.1

Warm-up

Find the value of each product mentally.

8.2

Activity

Select all the expressions that represent the area of the large, outer rectangle in Figure A. Explain your reasoning.
A
One rectangle diagram. Labeled A. Large outer rectangle partitioned into 2 smaller rectangles, vertical side 6. First rectangle bottom side length 3. Second rectangle bottom side length 2.
Select all the expressions that represent the area of the shaded rectangle on the left side of Figure B. Explain your reasoning.
B
One rectangle diagram. Labeled B. Large rectangle with bottom side length 7, partitioned into 2 smaller rectangles. First rectangle vertical side 4, bottom side length blank, area shaded blue. Second rectangle vertical side 4, bottom side length 2.

8.3

Activity

Complete the table. If you get stuck, consider skipping an entry and coming back to it, or drawing a diagram of two rectangles that share a side.

column 1	column 2	column 3	column 4	value

Student Lesson Summary

When we need to do mental calculations, we often come up with ways to make the calculation easier to do mentally.

Suppose we are grocery shopping and need to know how much it will cost to buy 5 cans of beans at 79 cents a can. We may calculate mentally in this way:

When we think, “79 is the same as . I can just multiply and and add the products together” we are using the distributive property.

In general, when we multiply two factors, we can break up one of the factors into parts, multiply each part by the other factor, and then add the products. The result will be the same as the product of the two original factors. When we break up one of the factors and multiply the parts we are using the distributive property of multiplication.

The distributive property also works with subtraction. Here is another way to find :

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The Distributive Property, Part 1

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Lesson 8

The Distributive Property, Part 1

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