This document provides instruction on factoring expressions using the greatest common factor (GCF) and the distributive property. It includes examples of factoring expressions with variables like 3f + 3g and 6x + 9y. Students are asked to identify the GCF of expressions and use it to write equivalent expressions. They are given exercises to factor expressions and evaluate equivalent expressions for given variable values. The document aims to teach students how to move between expanded and factored forms of expressions.

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Problem Set Lesson 10 Answers

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MODULE 4 Expressions and Equaons
Topic C: Replacing Leer and Numbers
Lesson 11 Factoring Expressions
Student Outcomes
§ Students model and write equivalent expressions using the distribuve property. They move from an
expanded form to a factored form of an expression.
Turn to the sprints so we can review
Greatest Common Factors

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Sprints Round 1

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Sprints Round 2

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Classwork
Example 1
a. Use the model to answer the following quesons.
How many fives are in the model?
How many threes are in the model?
What does the expression represent in words?
What expression could we write to represent the model?

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b. Use the new model and the previous model to answer the next set of quesons.
How many fives are in the model?
How many threes are in the model?
What does the expression represent in words?
What expression could we write to represent the model?
This is the correct model
for your notes.

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a. Is the model in part (a) equivalent to the model in part (b)?
b. What relaonship do we see happening on either side of the equal sign?
a.) b.)
2 x 5 + 2 x 3 (5+3)+(5+3) or 2(5 + 3)

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2 x 5 + 2 x 32(5 + 3) =
e. In 5th grade and in Module 2 of this year, you have used similar reasoning to
solve problems. What is the name of the property that is used to say that

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Example 2
Now, we will take a look at an example with variables.
What does the model represent in words?
What does 2a mean?
How many a’s are in the model?
How many b’s are in the model?
What expression could we write to represent
the model?
How many a’s are in the expression?
How many b’s are in the expression?
What expression could we write the
represent the model?
Are the two expressions equivalent?

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Example 3
Use GCF and the distribuve property to write equivalent expressions.
1. 3f + 3g
What is the queson asking us to do?
How would Problem 1 look if we expanded each term?
What is the GCF in Problem 1?
How can we use the GCF to rewrite this?

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2. 6x + 9y
What is the queson asking us to do?
How would Problem 2 look if we expanded each term?
What is the GCF in Problem 2?
How can we use the GCF to rewrite this?

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3. 3c + 11c
Is there a greatest common factor in Problem 3?
Rewrite the expression using the distribuve property.

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4. 24b + 8
Explain how you used GCF and the distribuve property to rewrite the expression in Problem 4.
Why is there a 1 in the parentheses?
How is this related to the first two examples?

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Exercises
1. Apply the distribuve property to write equivalent expressions.
a. 7x + 7y
b. 15g + 20 h
c. 18m + 42n
d. 30a + 39b
e. 11f + 15f
f. 18h + 13h
g. 55m + 11
h. 7 + 56y

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2. Evaluate each of the expressions below.
a. 6x + 21y and 3(2x + 7y) x = 3 and y = 4
b. 5g + 7g and g(5 + 7) g = 6

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c. 14x + 2 and 2(7x + 1) x = 10
d. Explain any paerns that you noce in the results to parts (a)–(c).
e. What would happen if other values were given for the variables?

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Closing
Please take out your exit ticket for Lesson 11, close your
binder, and complete the exit ticket. This will be collected.
How can use you use your knowledge of GCF and the distribuve property to write equivalent expressions?
Find the missing value that makes the two expressions equivalent.
Explain how you determine the missing number.
I would expand each term and determine the greatest common factor. The greatest common
factor is the number that is placed on the blank line.

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