Illustrative Mathematics Unit 6.3, Lesson 7: Equivalent Ratios Have the Same Unit Rates

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Illustrative Math
Grade 6

Lesson 7: Equivalent Ratios Have the Same Unit Rates

Let’s revisit equivalent ratios.

Illustrative Math Unit 6.3, Lesson 7 (printable worksheets)

Lesson 7 Summary

The following diagram shows that equivalent ratios will have equal unit rates.

Lesson 7.1 Which One Doesn’t Belong: Comparing Speeds

Which one doesn’t belong? Be prepared to explain your reasoning.

1. 5 miles in 15 minutes
2. 3 minutes per mile
3. 20 miles per hour
4. 32 kilometers per hour
   

• See Video for Whole Lesson

Scroll down the page for the answers to the questions in the “Are you ready for more?” section.

Lesson 7.2 Price of Burritos

1. Two burritos cost $14.00. Complete the table to show the cost for 4, 5, and 10 burritos at that rate. Next, find the cost for a single burrito in each case.
2. What do you notice about the values in this table?
   

number of burritos	cost in dollars	unit price (dollars per burrito)
2	14.00
4
5
10
b

3. Noah bought b burritos and paid c dollars. Lin bought twice as many burritos as Noah and paid twice the cost he did. How much did Lin pay per burrito?

	number of burritos	cost in dollars	unit price (dollars per burrito)
Noah	b	c	c/b
Lin	2 · b	2 · c

4. Explain why, if you can buy b burritos for c dollars, or buy 2 · b burritos for 2 · c dollars, the cost per item is the same in either case.

Lesson 7.3 - Making Bracelets

1. Complete the table. Then, explain the strategy you used to do so.
   

time in hours	number of bracelets	speed (bracelets per hour)
2		6
5		6
7		6
	66	6
	100	6

2. Here is a partially filled table from an earlier activity. Use the same strategy you used for the bracelet problem to complete this table.

number of burritos	cost in dollars	unit price (dollars per burrito)
	14.00	7.00
5	28.00	7.00
5		7.00
10		7.00

3. Next, compare your results with those in the first table in the previous activity. Do they match? Explain why or why not.

Lesson 7.4 - How Much Applesauce?

It takes 4 pounds of apples to make 6 cups of applesauce.

pounds of apples	cups of applesauce
4	6
7
10
	9
	20

1. At this rate, how much applesauce can you make with:
a. 7 pounds of apples?
b. 10 pounds of apples?
2. How many pounds of apples would you need to make:
a. 9 cups of applesauce?
b. 20 cups of applesauce?

Are you ready for more?

1. Jada eats 2 scoops of ice cream in 5 minutes. Noah eats 3 scoops of ice cream in 5 minutes. How long does it take them to eat 1 scoop of ice cream working together (if they continue eating ice cream at the same rate they do individually)?
   • Show Answer

     Together, Jada and Noah ate 5 scoops of ice-cream in 5 minutes.
     They would then eat 1 scoop of ice-cream in 1 minute.

2. The garden hose at Andre’s house can fill a 5-gallon bucket in 2 minutes. The hose at his next-door neighbor’s house can fill a 10-gallon bucket in 8 minutes. If they use both their garden hoses at the same time, and the hoses continue working at the same rate they did when filling a bucket, how long will it take to fill a 750-gallon pool?
   • Show Answer

     Andre’s garden hose could fill 20 gallons in 8 minutes.
     Together, the two hoses could fill 30 gallon in 8 minutes which is 1 gallon in 8/30 minutes.
     It would then take 750 • 8/30 = 200 minutes to fill the pool.

Lesson 7 Practice Problems

1. A car travels 55 miles per hour for 2 hours. Complete the table.
   

time (hours)	distance (miles)	miles per hour
1	55	55
1/2
1 1/2
	110

2. The table shows the amounts of onions and tomatoes in different-sized batches of a salsa recipe.
   Elena notices that if she takes the number in the tomatoes column and divides it by the corresponding number in the onions column, she always gets the same result.
   What is the meaning of the number that Elena has calculated?
   

onions (ounces)	tomatoes (ounces)
2	16
4	32
6	48

3. A restaurant is offering 2 specials: 10 burritos for $12, or 6 burritos for $7.50. Noah needs 60 burritos for his party. Should he buy 6 orders of the 10-burrito special or 10 orders of the 6-burrito special? Explain your reasoning.
   
4. Complete the table so that the cost per banana remains the same.

number of bananas	cost in dollars	unit price (dollars per banana)
4		0.50
6		0.50
7		0.50
10		0.50
	10.00	0.50
	16.50	0.50

5. Two planes travel at a constant speed. Plane A travels 2,800 miles in 5 hours. Plane B travels 3,885 miles in 7 hours. Which plane is faster? Explain your reasoning.
   
6. A car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses of a gallon of gas to go 1 mile.
   a. How far can the car travel with 15 gallons? Show your reasoning.
   b. How much gas does the car use to go 100 miles? Show your reasoning.
   A box of cereal weighs 600 grams. How much is this weight in pounds? Explain or show your reasoning. (Note: 1 kilogram = 2.2 pounds)
   
7. A box of cereal weighs 600 grams. How much is this weight in pounds? Explain or show your reasoning. (Note: 1 kilogram = 2.2 pounds)
   

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