Unit 2, Lesson 8: How Much for One?

8.1: Number Talk: Remainders in Division (10 minutes)

Setup: Display the problem for all to see. 2 minutes of quiet think time, followed by a whole-class discussion.

Lesson GoalsUse double number lines to find equivalent ratios between prices and quantities.Use the word “per” to refer to cost of 1 item or unit of purchase.Understand what “at this rate” means in the context of unit prices.

Required Materialsrulerstools for creating a visual display

Student task statementFind the quotient mentally.

Possible responses

20.5

Anticipated misconceptions

Students may struggle to interpret theremainder as a decimal or fraction andmay instead write r 6.

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GRADE 6 MATHEMATICS

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Unit 2: Introducing Ratios, Lesson 8: How Much for One? 1

8.2: Grocery Shopping (10 minutes)

Setup: Access to rulers. Start with quiet think time, followed by a partner discussion.

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Unit 2: Introducing Ratios, Lesson 8: How Much for One? 2

Student task statementAnswer each question and explain or show your reasoning. If you get stuck, consider drawing a doublenumber line diagram.

3. A 10-pound sack of flour costs $8.

a. How much does 40 pounds of flour cost?

b. What is the cost per pound of flour?

1. Eight avocados cost $4.

a. How much do 16 avocados cost?

b. How much do 20 avocados cost?

c. How much do 9 avocados cost?

2. Twelve large bottles of water cost $9.

a. How many bottles can you buy for $3?

b. What is the cost per bottle of water?

c. How much would 7 bottles of water cost?

Possible responses

1. a. $8

b. $10

c. $4.50

2.a. 4 bottles for $3

b. $0.75

c. $5.25

3.a. $32

b. $0.80

Anticipated misconceptions

Some students may have difficulty withthe answers not being integers. Eitherfractions or decimals are acceptable.Fractions provide the most direct route,but decimals are common for working

GRADE 6 MATHEMATICS

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Unit 2: Introducing Ratios, Lesson 8: How Much for One? 3

with dollars and cents. Also, studentsmay use the larger numbers as thedividend, simply because they arelarger. Encourage students to check thereasonableness of their answers.

Are you ready for more?Is bigger always better? It is commonly thought that buying larger packages or containers, sometimes calledbuying in bulk, is a great way to save money. For example, a 6-pack of soda might cost $3 while a 12-pack of thesame brand costs $5.

Find 3 different cases where it is not true that buying in bulk saves money. You may use the internet or go to alocal grocery store and take photographs of the cases you find. Make sure the products are the same brand.For each example that you find, give the quantity or size of each, and describe how you know that the largersize is not a better deal.

Possible Responses

Answers vary.

GRADE 6 MATHEMATICS

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Unit 2: Introducing Ratios, Lesson 8: How Much for One? 4

8.3: More Shopping (15 minutes)

Setup: Students in groups of 3–4. Provide tools for creating a visual display and access to rulers. Discuss the meaning of “at this rate.”

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Unit 2: Introducing Ratios, Lesson 8: How Much for One? 5

Student task statement

3. Neon bracelets cost $1 for 4.

a. What is the cost per bracelet?

b. At this rate, how much will 11 neon bracelets cost?

Pause here so you teacher can review your work.

4. Your teacher will assign you one of the problems. Create a visual display that shows your solution to theproblem. Be prepared to share your solution with the class.

1. Four bags of chips cost $6.

a. What is the cost per bag?

b. At this rate, how much will 7 bags of chips cost?

2. At a used book sale, 5 books cost $15.

a. What is the cost per book?

b. At this rate, how many books can you buy for $21?

Possible responses

1. a. The cost per bag is $1.50.

b. Seven bags cost $10.50.

2. a. The cost per book is $3.

b. You can buy 7 books for $21.

3. a. The cost per bracelet is 25cents.

b. Eleven bracelets cost $2.75.

Anticipated misconceptions

The first and third questions involveusing decimals to represent cents. If thedecimal point is forgotten, remindstudents that the cost of the bracelet isless than one dollar, and the cost of thechips is in between one and two dollars.

Watch for students working in centsinstead of dollars for the bracelets.They may come up with an answer of

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Unit 2: Introducing Ratios, Lesson 8: How Much for One? 6

Lesson Synthesis (5 minutes)How do I find a unit price? Why is a unit price a useful thing to know?

8.4: Unit Price of Rice (Cool-down, 5 minutes)

Setup: None.

275 cents. For these students, writing25 cents as $0.25 should help, orconsider reminding them of theavocados from a previous activity,which had a unit price of $0.50.

Student task statementHere is a double number line showing that it costs $3 to buy 2 bags of rice:

1. At this rate, how many bags of rice can you buy with $12?

2. Find the cost per bag.

3. How much do 20 bags of rice cost?

Possible responses

1. 8 bags

2. $1.50

3. $30

GRADE 6 MATHEMATICS

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Unit 2: Introducing Ratios, Lesson 8: How Much for One? 7