Homework Problems
Name
Team Name
Team Did Not Agree On
Questions…
Team Complete?
#’s
Quick Look
Today we learned how to compare rates. For example:
It costs $5.49 for a 28 ounce container of peanut butter, but it costs Jen
$0.90 to make 4 ounces of peanut butter. Which peanut butter is cheaper?
To compare rates, find an equivalent rate so that one of the units in both of the rates has the same
quantity. You can use common factors and common multiples to compare. In this example, 4 is the GCF
of 4 and 28.
Store-bought
÷7
$0.80
4 ounces
$5.60
28 ounces
Homemade
$0.60
4 ounces
÷7
$0.80 for 4 ounces > $0.60 for 4 ounces. Jen can make her own peanut butter for less than she can buy
the store-bought kind.
You can always use unit rates to compare because one of the units will have a quantity of 1. Let’s find
how much 1 ounce of peanut butter costs for each type.
Store-bought
$5.60
28 = $0.20
÷
28 ounces
28
ounce
Homemade
$0.60
$0.15
÷ 4 =
4
4 ounces
ounce
$0.20 per ounce > $0.15 an ounce. We got the same answer either way.
PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 5 Cycle 1 Lesson 4
Homework Problems
1
Directions for questions 1–6: Compare the two rates.
1) Ade and Rachel checked their heartbeats. Ade’s heart beat 37 times in 15 seconds and Rachel’s beat
124 times in 1 minute. Who had a faster heartbeat?
2) Team Cure ran 27 miles in 261 minutes. Team Speedster ran 13.5 miles in 117 minutes. Which team
ran at a faster speed?
3) Betty makes 80 donuts in one hour. Andre makes 64 donuts in 40 minutes. Who can make donuts at
a quicker rate? Explain your thinking.
4) A red game spinner makes 32 revolutions in 19 seconds. A blue game spinner makes 24 revolutions
in 13 seconds. Which color spinner is faster?
5) A 6-ounce steak costs $5.58 and a 10-ounce steak costs $8.90. Which steak is the better buy?
Explain your thinking.
6) 3 slices of sausage pizza cost $3.90 and 4 slices of vegetable pizza cost $4.50. Which type of pizza
costs less per slice?
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 5 Cycle 1 Lesson 4
Homework Problems
Mixed Practice
7) Subtract.
8.209 – 4.13 =
9) Divide.
5
8
÷
=
24
15
8) Convert to an improper fraction:
2
4
=
6
10) Order these numbers from least to greatest:
2
6
, 2.09, 2.538
15
Word Problem
11) Harper’s family eats 5 boxes of cereal in 3 days. Owen’s family eats 9 boxes of cereal in 5 days.
Which family will need to buy more cereal in one month? Explain your thinking.
PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 5 Cycle 1 Lesson 4
Homework Problems
3
For the Guide on the Side
Today we learned how to compare rates. To compare rates, one of the units in both of the rates needs to
have the same quantity. If Selena drives 10 miles in 25 minutes and Avis drives 15 miles in 30 minutes, it
is difficult to see who travels at a faster speed. If we find equivalent rates we can see it takes Avis a
shorter amount of time to travel the same distance as Selena, so Avis travels at a faster speed.
Selena:
10 miles = 30 miles
25 minutes 75 minutes
Avis:
15 miles = 30 miles
30 minutes
60 minutes
Students can use what they already know about equivalent ratios to compare. This is similar to finding
common denominators to compare fractions.
Your student should be able to answer these questions about comparing rates:
How did you compare these rates?
How do you know these rates are equivalent?
Is there another way you could have compared these rates?
Here are some ideas to work with comparing rates with your student:
1) Sometimes, grocery and convenience stores do not give you the unit price to help compare the price of
their products. Compare products that do not give the unit prices to find which one is cheaper per
volume and/or weight.
2) Guess how fast your heart beats in 60 seconds. Then place two fingers on your wrist or neck and
count how many beats you feel in 10 seconds. Was your guess faster or slower than the heartbeat you
measured?
3) Use Khan Academy to review finding the unit price and unit rate.
http://www.khanacademy.org/math/arithmetic/basic-ratios-proportions/v/finding-unit-rates
http://www.khanacademy.org/math/arithmetic/basic-ratios-proportions/v/finding-unit-prices
4
PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 5 Cycle 1 Lesson 4
Homework Problems
Homework Answers
1) Ade has a faster heartbeat.
2) Team Speedster ran faster.
3) Andre can make donuts at a quicker rate.
Possible explanation: 10 is a factor of 60 and 40, so I used it to compare the rates.
6
Betty: 80 donuts ÷ = 13.3 donuts
Andre: 64 donuts ÷ 4 = 16 donuts
60 minutes
6
10 minutes
40 minutes
4
10 minutes
16 donuts > 13.3 donuts, so Andre makes donuts faster.
4) The blue spinner is faster.
5) The 10-ounce steak is the better buy.
6) The vegetable pizza costs less per slice.
Possible explanation: I found the unit cost of 1 slice of pizza to compare the rates.
$3.90
$1.30
$4.50
$1.13
Sausage:
÷ 3=
Vegetable:
÷ 4 =
3 slices 3
slice
4 slices
4
slice
$1.13 < $1.30, so the vegetable pizza costs less per slice.
Mixed Practice
7) 4.079
9)
25
64
8)
8
3
10) 2.09, 2
6
, 2.538
15
Word Problem
11) Owen’s family will need to buy more cereal in one month.
Possible explanation: First, I made equivalent ratios with 15 in the denominator because it is
the LCM of 3 and 5.
5 boxes 5 25 boxes
9 boxes 3 27 boxes
Harper’s Family:
× =
Owen’s Family:
× =
3 days
15 days
5 days
15 days
5
3
Then, I compared the number of boxes eaten in 15 days. 27 boxes is more cereal eaten than
25 boxes, so Owens’ family eats boxes of cereal at a faster rate. If his family eats more cereal
than Harper’s family in 15 days, his family will still eat more than Harper’s in a month.
PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 5 Cycle 1 Lesson 4
Homework Problems
5