Unit 3, Lesson 10: What Are Percentages?

10.1: Dollars and Cents (5 minutes)

Setup: Display questions for all to see.

Lesson GoalsUnderstand that a percentage is a rate per 100.Use a double number line with percentages on one line and corresponding valueson the other to find other values.State explicitly what one is finding a percentage of.

Required Materials••

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GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 10: What Are Percentages? 1

Student task statementFind each answer mentally.

1. A sticker costs 25 cents. How many dollars is that?

2. A pen costs 1.50 dollars. How many cents is that?

3. How many cents are in one dollar?

4. How many dollars are in one cent?

Possible responses

1. (or 0.25) of a dollar

2. 150 cents

3. 100 cents

4. (or 0.01) of a dollar

Anticipated misconceptions

In response to “how many dollars are inone cent,” students might say there areno dollars at all in one cent. Ask themwhat fraction of a dollar one centrepresents.

GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 10: What Are Percentages? 2

10.2: Coins (15 minutes)

Setup: Students in groups of 2. 3 minutes of quiet think time, followed by partner discussion and collaboration.

GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 10: What Are Percentages? 3

Student task statement1. Complete the table to show the values of these U.S. coins.

coin penny nickel dime quarter half dollar dollar

value (cents)

2. Write the name of the coin that matches each expression.

The value of a quarter is 25% of the value of adollar because there are 25 cents for every 100cents.

a. 25% of a dollar

b. 5% of a dollar

c. 1% of a dollar

d. 100% of a dollar

e. 10% of a dollar

f. 50% of a dollar

3. The value of 6 dimes is what percent of thevalue of a dollar?

4. The value of 6 quarters is what percent of thevalue of a dollar?

Possible responses

1. 1, 5, 10, 25, 50, 100

2. a. Quarter

b. Nickel

c. Penny

d. Dollar

e. Dime

f. Half-dollar

3. 60% of a dollar

4. 150% of a dollar

Anticipated misconceptions

Students may notice a patternparticular to this activity—that thepercent value is the same as that forcents—and carry that assumptionforward and apply it incorrectly to

GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 10: What Are Percentages? 4

situations in which 100% does notcorrespond to 100. This conversation isaddressed in the Activity Synthesis.

Are you ready for more?Find two different sets of coins that each make 120% of a dollar, where no type of coin is in both sets.

Possible Responses

Answers vary. Sample response:A dollar and two dimes, four quartersand four nickels

GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 10: What Are Percentages? 5

10.3: Coins on a Number Line (10 minutes)

Setup: Keep students in the same groups. 2–3 minutes of quiet think time, followed by a partner discussion.

Student task statementA $1 coin is worth 100% of the value of a dollar. Here is a double number line thatshows this.

1. The coins in Jada’s pocket are worth 75% of adollar. How much are they worth (in dollars)?

2. The coins in Diego’s pocket are worth 150% ofa dollar. How much are they worth (in dollars)?

3. Elena has 3 quarters and 5 dimes. Whatpercentage of a dollar does she have?

Possible responses

1. $0.75

2. $1.50

3. 125%

Anticipated misconceptions

Based on previous work with labelingnumber lines less than 1, students maylabel the tick marks with fractionsinstead of the decimal value of thecoins. This may not be helpful foranswering the first two questions, butprovides an opportunity to discussalternative ways to label the numberline given the context of the problem.Consider prompting them to writefractional values as cents or torewrite the cents as dollar values.

GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 10: What Are Percentages? 6

Lesson Synthesis (5 minutes)What is a percentage? How can we find percentages using a double number line?

10.4: Eight Dimes (Cool-down, 5 minutes)

Setup: None.

Student task statement1. Fill in the blank: The value of 8 dimes is ______% of the value of a dollar.

2. Name a combination of coins that is 130% of the value of a dollar.

Possible responses

1. 80%

2. Answers vary. Sample response: 5quarters and 1 nickel

Anticipated misconceptions

In the first question, students may writethat 8 dimes is 8% of the value of adollar because they account for thenumber of coins but not account theirvalue. In the second question, studentsmay put 125 cents as the answer, notdifferentiating between combination ofcoins and the value of the coins.

GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 10: What Are Percentages? 7