Name
Class
CHAPTER 2
Date
Problem Solving Connections
How Much Paint? Jody’s family has moved into
a new house, and Jody is going
to repaint her new bedroom.
Jody’s dad says that she first has
to calculate how much paint to
buy. How can Jody use algebraic
expressions to find the amount of
paint she will need?
CC.6.EE.1
CC.6.EE.2a, b, c
CC.6.EE.3
CC.6.EE.4
CC.6.EE.6
1 Write Expressions
A
Jody’s bedroom is rectangular. Let a represent the width (shorter side)
of the room, and let b represent the length (longer side). Let c represent
the height of each wall.
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The rectangular prism below can be used to model Jody’s bedroom.
Label a, b, and c on the prism.
B
Write an algebraic expression to represent the combined area
of the two larger walls of the room. Explain your thinking.
C
Write an algebraic expression to represent the combined area of the two
smaller walls. Explain your thinking.
D
Write an algebraic expression to represent the area of the ceiling.
E
Use your answers above to write an algebraic expression to represent
the total area of all four walls and the ceiling.
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Problem Solving Connections
2 Evaluate Expressions
A
Now Jody must measure her bedroom so she can substitute the
measurements into the algebraic expressions. First Jody measures the
height c of the walls and the length b of the longer wall. She finds that
c = 12 feet and b = 20 feet.
Rewrite the expression that represents the combined area of the two
larger walls. Then evaluate this expression using the values of b and c
that Jody found. What is the total area of these two walls?
B
Jody cannot reach high enough to measure the ceiling, so she measures
the floor instead. She already knows that the longer side of the floor b
measures 20 feet. She finds that the shorter side a measures 8 feet.
Rewrite the expression that represents the area of the ceiling. Then
evaluate this expression using the values of a and b that Jody found.
What is the area of the ceiling?
Does Jody need to measure anything else to find the area of the
two smaller walls? Why or why not?
D
Rewrite the expression that represents the combined area of the
two smaller walls. Then evaluate this expression using the appropriate
values. What is the total area of these two walls?
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Problem Solving Connections
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C
E
Find the total area of the four walls and the ceiling. Explain how you
found your answer.
F
“Now we can go to the paint store and buy the paint,” Jody says. “Wait!”
says Dad. “Some of the walls are not really rectangles. Your room has a
door and two square windows. You can paint the door if you want, but
you are definitely not going to paint the windows!” After thinking about
it, Jody decides that she will paint her door.
Both windows are the same size. Let s represent the side length of one
of the windows. Write an algebraic expression with an exponent to
represent the combined area of both windows. Explain your thinking.
G
Jody returns to her room to measure one of the windows. She measures
the window’s length as 4 feet.
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Rewrite the expression that represents the combined area of the two
windows. Then evaluate that expression using Jody’s measurement.
What is the total area of the two windows?
H
Explain how you used the order of operations to evaluate the expression
for the windows’ area.
I
What operation should Jody use to find the total area of the surfaces
she is going to paint?
Find the total area that Jody will paint.
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Problem Solving Connections
3 Answer the Question
A
Jody and her dad arrive at the paint store, where Jody chooses two paint
colors—light blue for the walls and white for the ceiling.
ft2
Look back to find the area of the ceiling and write it here:
How can Jody find the total area of just the four walls (not including
the ceiling)?
Find the area of only the four walls.
The label on each paint can reads “Covers 300 square feet.” Jody reasons
600
= 2 cans
that the area of the four walls is about 600 ft2, so she will need ___
300
of blue paint. Do you agree with Jody? Why or why not? If not, how many
cans of blue paint do you think Jody should buy?
C
How many cans of white paint does Jody need? Explain your thinking.
D
The paint store associate recommends that Jody put two coats on each
surface to completely cover the existing color. Does one can of white
paint contain enough paint for two coats on the ceiling? Explain.
Jody and her dad agree with the paint store associate and decide
to apply two coats. Jody says, “Then we need twice as much paint,
two cans of white paint and six cans of blue paint.” Is Jody
correct? Explain.
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Problem Solving Connections
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B