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Lesson Plans and Worksheets for Grade 7

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 7

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

### 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.

Classwork

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.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Lesson Plans and Worksheets for Grade 7

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 7

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.

• 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.

• Writing sums as products is the backwards process of writing products as sums; so, instead of distributing and multiplying, the product is being factored.

Classwork

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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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