Lesson 9The Distributive Property, Part 1

Let's use the distributive property to make calculating easier.

Learning Targets:

I can use a diagram of a rectangle split into two smaller rectangles to write different expressions representing its area.
I can use the distributive property to help do computations in my head.

9.1 Number Talk: Ways to Multiply

Find each product mentally.

9.2 Ways to Represent Area of a Rectangle

Select all the expressions that represent the area of the large, outer rectangle in figure A. Explain your reasoning.
Select all the expressions that represent the area of the shaded rectangle on the left side of figure B. Explain your reasoning.

9.3 Distributive Practice

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

column 1	column 2	column 3	column 4	value
				490

Are you ready for more?

Use the distributive property to write two expressions that equal 360. (There are many correct ways to do this.)
Is it possible to write an expression like that equals 360 where is a fraction? Either write such an expression, or explain why it is impossible.
Is it possible to write an expression like that equals 360? Either write such an expression, or explain why it is impossible.
How many ways do you think there are to make 360 using the distributive property?

Lesson 9 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:

In general, when we multiply two numbers (or 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.

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

Lesson 9 Practice Problems

Select all the expressions that represent the area of the large, outer rectangle.
Draw and label diagrams that show these two methods for calculating .
First find and then add .
First find and then take away 50.
Complete each calculation using the distributive property.
A group of 8 friends go to the movies. A bag of popcorn costs $2.99. How much will it cost to get one bag of popcorn for each friend? Explain how you can calculate this amount mentally.
1. On graph paper, draw diagrams of and when is 1, 2, and 3. What do you notice?
2. Do and have the same value for any value of ? Explain how you know.
120% of is equal to 78.
Write an equation that shows the relationship of 120%, , and 78.
Use your equation to find . Show your reasoning.
Kiran’s aunt is 17 years older than Kiran.
1. How old will Kiran’s aunt be when Kiran is:
  
  15 years old?
  
  30 years old?
  
  years old?
2. How old will Kiran be when his aunt is 60 years old?