Lesson 5: Comparing Speeds and Prices
Let’s compare some speeds and some prices.
Illustrative Math Unit 6.3, Lesson 5 (printable worksheets)
Lesson 5 Summary
The following diagram shows how to use ratios to compare rates.
Lesson 5.1 Closest Quotient
Is the value of each expression closer to ½, 1, 1½
- 20 ÷ 18
- 9 ÷ 20
- 7 ÷ 5
Scroll down the page for the answer to the question about Tyler and Kiran.
Lesson 5.2 More Treadmills
Some students did treadmill workouts, each one running at a constant speed. Answer the questions about their workouts. Explain or show your reasoning.
- Tyler ran 4,200 meters in 30 minutes.
- Kiran ran 6,300 meters in ½ hour.
- Mai ran 6.3 kilometers in 45 minutes.
- What is the same about the workouts done by:
a. Tyler and Kiran?
b. Kiran and Mai?
c. Mai and Tyler?
- At what rate did each of them run?
- How far did Mai run in her first 30 minutes on the treadmill?
Are you ready for more?
Tyler and Kiran each started running at a constant speed at the same time. Tyler ran 4,200 meters in 30 minutes and Kiran ran 6,300 meters in ½ hour. Eventually, Kiran ran 1 kilometer more than Tyler. How much time did it take for this to happen?
Lesson 5.3 - The Best Deal on Beans
Four different stores posted ads about special sales on 15-oz cans of baked beans.
- Which store is offering the best deal? Explain your reasoning.Which store is offering the best deal? Explain your reasoning.
- The last store listed is also selling 28-oz cans of baked beans for $1.40 each. How does that price compare to the other prices?
Lesson 5 Practice Problems
- Mai and Priya were on scooters. Mai traveled 15 meters in 6 seconds. Priya travels 22 meters in 10 seconds. Who was moving faster? Explain your reasoning.
- Here are the prices for cans of juice that are the same brand and the same size at different stores. Which store offers the best deal? Explain your reasoning.
Store X: 4 cans for $2.48
Store Y: 5 cans for $3.00
Store Z: 59 cents per can
- Costs of homes can be very different in different parts of the United States.
a. A 450-square-foot apartment in New York City costs $540,000. What is the price per square foot? Explain or show your reasoning.
b. A 2,100-square-foot home in Cheyenne, Wyoming, costs $110 per square foot. How much does this home cost? Explain or show your reasoning.
- There are 33.8 fluid ounces in a liter. There are 128 fluid ounces in a gallon. About how many liters are in a gallon?
Is your estimate larger or smaller than the actual number of liters in a gallon? Explain how you know.
- Diego is 165 cm tall. Andre is 1.7 m tall. Who is taller, Diego or Andre? Explain your reasoning.
- Name an object that could be about the same length as each measurement.
a. 4 inches
b. 6 feet
c. 1 meter
d. 5 yards
e. 6 centimeters
f. 2 millimeters
g. 3 kilometers
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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