Proportional
Relationships
(4 apples cost 80 cents; therefore, 1
apple = 20 cents)
Standard: 3.A.3.2
Solve problems involving proportional relationships
including unit pricing (e.g., four apples cost 80 cents;
therefore, one apple costs 20 cents).
Concept Skill:
Proportional Relationships ________________________
A Proportional relationship is a relationship between two
equal ratios.
For example, oranges are sold in a bag of 5 for $2. The ratio
of oranges to their cost is 5:2 or .
If I bought 20 oranges, I could set up a proportion to
determine my cost.
You can also solve this by figuring out how many bags of 5
you need to have 20 oranges. You would need 4 bags of 5
oranges to equal 20. Therefore, you would multiply $2 times
4 to get $8.
“Teacher Sample Questions”
Example: 1
Mary bought 3 boxes of pencils and ended up with 15
pencils. How many pencils would she have purchased
if she had bought 7 boxes of pencils?
Step 1: Here it is useful to find out how many pencils are in
one box (unit rate = 5 pencils/1 box)
Step 2: Now multiply this unit rate by the seven boxes of
pencils. (5 x 7 = 35)
One should note that the foregoing problem actually involves
two unit rates: 5 pencils/l box and (1/5 box)/1 pencil. In
solving missing-value problems only one unit rate is
appropriate. Students need experience interpreting each
possible unit rate so that they can determine which rate is
appropriate to the problem.
“Student Practice Materials”
Evelyn bought 4 packages of crayons and ended up
with 20 crayons. How many crayons would she have
if she would have bought 9 packages of crayons?
A.
B.
C.
D.
35
40
42
45
Bob has 3 nickels in his pocket which is .15 cents.
How much would he have if he had 8 nickels in his
pocket?
Use words, numbers or pictures to show how much
Bob would have.
Jacob decides to make 6 batches of the Nature Mix for
his class. Which number sentence should he use to
find out how many cups of oat cereal he will need?
A.
B.
C.
D.
6
6
6
6
+4=
x4=
÷4 =
–4=
Almonds and cashews are nuts. How many cups of
nuts are needed to make 2 batches?
A.
B.
C.
D.
3
4
6
2
Sara wants to make 6 batches of Nature Mix. She
says that she needs 15 cups of dried pineapple. Is she
correct? Explain how you know?
Smiley cookies come in two different packages.
Package A
Package B
Madison needs exactly 26 smiley cookies for her class.
Which combination of packages totals 26?
A.
B.
C.
D.
1
4
2
7
of
of
of
of
Package
Package
Package
Package
A
A
A
A
and
and
and
and
4
3
4
2
of
of
of
of
Package
Package
Package
Package
B
B
B
B
Show your work to explain how you got your answer.
“KEY”
Evelyn bought 4 packages of crayons and ended up
with 20 crayons. How many crayons would she have
if she would have bought 9 packages of crayons?
A. 35
B. 40
C. 42
*D. 45
Bob has 3 nickels in his pocket which is .15 cents.
How much would he have if he had 8 nickels in his
pocket?
Use words, numbers or pictures to show how much
Bob would have.
8 x 5 = 40
“KEY”
Jacob decides to make 6 batches of the Nature Mix for
his class. Which number sentence should he use to
find out how many cups of oat cereal he will need?
A. 6 + 4 =
*B. 6 x 4 =
C. 6 ÷4 =
D. 6 – 4 =
Almonds and cashews are nuts. How many cups of
nuts are needed to make 2 batches?
A. 3
B. 4
*C. 6
D. 2
Sara wants to make 6 batches of Nature Mix. She
says that she needs 15 cups of dried pineapple. Is she
correct? Explain how you know?
No, because each batch would need 3 cups of dried
pineapple. She would need 18 cups.
6x3=18
“KEY”
Smiley cookies come in two different packages.
Package A
Package B
Madison needs exactly 26 smiley cookies for her class.
Which combination of packages totals 26?
A. 1 of Package A and 4 of Package B
B. 4 of Package A and 3 of Package B
*C. 2 of Package A and 4 of Package B
D. 7 of Package A and 2 of Package B
Show your work to explain how you got your answer.
There are 3 cookies in Package A. 3 x 2=6
There are 5 cookies in Package B. 5 x 4=20
20+6=26