This document contains a lesson on distributing expressions. It includes examples of distributing multiplication over addition in expressions like 2(a + b) and 3(7d + 4e). Students are asked to write equivalent expressions using the distributive property, both with and without models. They practice this by creating models and distributing expressions for problems like 3(x + y) and 4(11h + 3g). The lesson aims to teach students how to move between factored and expanded forms of expressions.

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Problem Set Lesson 11 Answers

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MODULE 4 Expressions and Equaons
Topic C: Replacing Leer and Numbers
Lesson 12: Distribung Expressions
Student Outcomes
§ Students model and write equivalent expressions using the distribuve property. They move from a factored
form to an expanded form of an expression.

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Classwork
Opening Exercise
a. Create a model to show 2 x 5.
b. Create a model to show 2 x b, or 2b.

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Example 1
Write an expression that is equivalent to 2(a + b)
Create a model to represent (a + b).
The expression 2(a + b) tells us that we have 2 of the (a + b)’s. Create a model that
shows 2 groups of (a + b)
How many a’s and how many b’s do you see in the diagram?

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How would the model look if we grouped together the a’s and then grouped
together the b’s?
What expression could we write to represent the new diagram?
What conclusion can we draw from the models about equivalent expressions?

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2(a + b) 2a + 2b Let a = 3 and b = 4
What happens when we double ( a + b)?
To prove that these two forms are equivalent, let’s plug in some
values for a and b and see what happens.

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Example 2
Write an expression that is equivalent to double (3x + 4y).
How can we rewrite double (3x + 4y)?
Is this expression in factored form, expanded form, or neither?

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Let’s start this problem the same way that we started the first example. What
should we do?
How can we change the model to show 2(3x + 4y)?
Are there terms that we can combine in this example?

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What is an equivalent expression that we can use to represent 2(3x + 4y)?
Summarize how you would solve this queson without the model.

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Example 3
Write an expression in expanded form that is equivalent to the model below.
What factored expression is represented in the model?
How can we rewrite this expression?

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Example 4
Write an expression that is equivalent to 3(7d + 4e).

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Exercises
Create a model for each expression below. Then write another equivalent
expression using the distribuve property.
1. 3 (x + y)

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2. 4(2h + g)
Create a model for each expression below. Then write another equivalent expression
using the distribuve property.

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Apply the distribuve property to write an equivalent expression.
3. 8(h+3)
4. 3(2h + 7)
5. 5(3x + 9y)
6. 4(11h + 3g)
7.
8. a(9b + 13)

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Closing
Please take out your exit ticket for Lesson 12, close your
binder, and complete the exit ticket. This will be collected.

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