Distributing Expressions

Videos and solutions to help Grade 6 students model and write equivalent expressions using the distributive property. They move from a factored form to an expanded form of an expression.

New York State Common Core Math Grade 6, Module 4, Lesson 12

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Learn how to use distributive property to recognize equivalent expressions

Lesson 12 Opening Exercise
a. Create a model to show 2 x 5
b. Create a model to show 2 x b or 2b

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?
How would the model look if we grouped together the a’s, and then grouped together the b’b’s?
What expression could we write to represent the new diagram?
What conclusion can we draw from the models about equivalent expressions?
To prove that these two forms are equivalent, let’s plug in some values for and and see what happens.

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

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?

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

Exercises
Create a model for each expression below. Then write another equivalent expression using the distributive property.

1. 3(x + y)
2. 4(2h + g)
   Apply the distributive property to write equivalent expressions.
3. 8(h + 3)
4. 3(2h + 7)
5. 5(3x + 9y)
6. 4(11h + 3g)
7. a(9b + 13)

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Write an expression that is equivalent to double (3x + 4y).

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Rewrite an 2(9 +5k) and 5(3m+2) using the distributive property.

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Rewrite 12a+8b using the distributive property.

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Lesson 12 Exit Ticket

Use the distributive property to expand the following expressions.

1. 2(b + c)
2. 5(7h + 3m)
3. e(f + g)

Lesson 12 Problem Set

1. Use the distributive property to write the following expressions in expanded form.
   a. 4(x + y)
   b. 8(a + 3b)
   c. 3(2x + 11y)
   d. 9(7a + 6b)
   e. c(3a + b)
   f. y(2x + 11z)
2. Create a model to show that 2(2x + 3y) = 4x + 6y

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