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Write Products as Sums and Sums as Products

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Common Core For Grade 7

Examples, videos, and solutions to help Grade 7 students learn how to use an area model to write products as sums and sums as products.

New York State Common Core Math Grade 7, Module 3, Lesson 4

Download worksheets for Grade 7, Module 3, Lesson 4

Lesson 4 Student Outcomes

• Students use an area model to write products as sums and sums as products.
• Students use the fact that the opposite of a number is the same as multiplying by to write the opposite of a sum in standard form.
• Students recognize that rewriting an expression in a different form can shed light on the problem and how the quantities in it are related.

Lesson 4 Closing

• The term or factor is multiplied by -1. In using the distributive property, every term inside the parentheses is multiplied by -1.
• Writing sums as products is the backwards process of writing products as sums; so, instead of distributing and multiplying, the product is being factored.


Exercise 1
1. Rewrite the expressions as a product of two factors.
a. 72t + 8
b. 55a + 11
c. 36z + 72
d. 144q - 15
e. 3r + 3s

Exercise 2
a. Write the product and sum of the expressions being represented in the rectangular array.
b. Factor 48j + 60k + 24 by finding the greatest common factor of the terms.

Example 3
For each expression, write each sum as a product of two factors. Emphasize the importance of the distributive property. Use various equivalent expressions to justify equivalency.

Example 4
A new miniature golf and arcade opened up in town. For convenient ordering, a play package is available to purchase. It includes two rounds of golf and 20 arcade tokens, plus three dollars off. There is a group of six friends purchasing this package. Let g represent the cost of a round of golf and let t represent the cost of a token. Write two different expressions that represent the total amount this group spent. Explain how each expression describes the situation in a different way.

Exercise 5
a. What is the opposite of (-6v + 1)?
b. Using the distributive property, write an equivalent expression for part (a).

Example 6
Rewrite 5a - (a - 3b) in standard form. Justify each step applying the rules for subtracting and the distributive property.

Exercise 6
Expand each expression and collect like terms.

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