NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Lesson 12
Lesson 12: Distributing Expressions
Date:
11/19/14
133
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
+
+
Lesson 12: Distributing Expressions
Student Outcomes
Students model and write equivalent expressions using the distributive property. They move from factored
form to expanded form of an expression.
Classwork
Opening Exercise (3 minutes)
Opening Exercise
a. Create a model to show × .
b. Create a model to show × , or .
Example 1 (8 minutes)
Example 1
Write an expression that is equivalent to ( + ).
In this example we have been given the factored form of the expression.
To answer this question we can create a model to represent 2( + ).
Let’s start by creating a model to represent ( + ).
Create a model to represent ( + ).
The expression ( + ) tells us that we have of the ( + )’s. Create a model that shows groups of ( + ).
+
MP.7
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Lesson 12
Lesson 12: Distributing Expressions
Date:
11/19/14
134
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
How many ’s and how many ’s do you see in the diagram?
There are ’s and ’s.
How would the model look if we grouped together the ’s, and then grouped together the ’s?
What expression could we write to represent the new diagram?
+
This expression is written in expanded form.
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.
Let = and = .
( + ) +
( + ) () + ()
() +
Note, if students do not believe yet that the two are equal, you can continue to plug in more values for and
until they are convinced.
What happens when we double ( + )?
We double , and we double .
Example 2 (5 minutes)
Example 2
Write an expression that is equivalent to double ( + ).
How can we rewrite double ( + )?
Double is the same as multiplying by two.
( + ) or +
Is this expression in factored form, expanded form, or neither?
MP.7
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Lesson 12
Lesson 12: Distributing Expressions
Date:
11/19/14
135
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
+
+
+
The first expression is in factored form, and the second expression is in expanded form.
Let’s start this problem the same way that we started the first example. What should we do?
We can make a model of + .
How can we change the model to show ( + )?
We can make two copies of the model.
Are there terms that we can combine in this example?
Yes, there are 's and 's.
So the model is showing + .
What is an equivalent expression that we can use to represent ( + )?
( + ) = +
This is the same as () + ().
Summarize how you would solve this question without the model.
When there is a number outside the parentheses, I would multiply it by all the terms on the inside of the parentheses.
Example 3 (3 minutes)
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 in expanded form?
() + ()
MP.7
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Lesson 12
Lesson 12: Distributing Expressions
Date:
11/19/14
136
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
+
Example 4 (3 minutes)
How can we use our work in the previous examples to write the following expression?
Example 4
Write an expression in expanded form that is equivalent to ( + ).
We will multiply × and × .
We would get + . So, ( + ) = + .
Exercises (15 minutes)
Exercises
Create a model for each expression below. Then, write another equivalent expression using the distributive property.
1. ( + )
+
2. ( + )
+
Apply the distributive property to write equivalent expressions in expanded form.
3. ( + )
+
+
+
+
+
+
+
+
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Lesson 12
Lesson 12: Distributing Expressions
Date:
11/19/14
137
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
4. ( + )
+
5. ( + )
+
6. ( + )
+
7.
+
8. ( + )
+
Closing (3 minutes)
State what the expression ( + ) represents.
groups of the quantity plus .
Explain in your own words how to write an equivalent expression in expanded form when given an expression
in the form of ( + ). Then, create your own example to show off what you know.
To write an equivalent expression, I would multiply times and times . Then, I would add the two
products together.
Examples will vary.
State what the equivalent expression in expanded form represents.
+ means groups of size plus groups of size .
Exit Ticket (5 minutes)
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Lesson 12
Lesson 12: Distributing Expressions
Date:
11/19/14
138
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Name Date
Lesson 12: Distributing Expressions
Exit Ticket
Use the distributive property to write the following expressions in expanded form.
1. 2( + )
2. 5(7ℎ + 3)
3. ( + )
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Lesson 12
Lesson 12: Distributing Expressions
Date:
11/19/14
139
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Exit Ticket Sample Solutions
Use the distributive property to write the following expressions in expanded form.
1. ( + )
+
2.
(
+
)
+
3. ( + )
+
Problem Set Sample Solutions
1. Use the distributive property to write the following expressions in expanded form.
a. ( + )
+
b. ( + )
+
c. ( + )
+
d. ( + )
+
e. ( + )
+
f. ( + )
+
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Lesson 12
Lesson 12: Distributing Expressions
Date:
11/19/14
140
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
+
+
2. Create a model to show that ( + ) = + .
