**Learning Targets:**

- I understand that if two ratios have the same rate per 1, they are equivalent ratios.
- When measurements are expressed in different units, I can decide who is traveling faster or which item is the better deal by comparing “how much for 1” of the same unit.

**Related Pages**

Illustrative Math

Grade 6

Let’s compare some speeds and some prices.

Illustrative Math Unit 6.3, Lesson 5 (printable worksheets)

The following diagram shows how to use ratios to compare rates.

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.

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?

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?

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?

- 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?

a. 2

b. 3

c. 4

d. 5

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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