Unit 3, Lesson 14: Solving Percentage Problems

14.1: Number Talk: Multiplication with Decimals (10 minutes)

Setup: Display one problem at a time. 1 minute of quiet think time per problem, followed by a whole-class discussion.

Lesson GoalsGiven that of is , find , , or given the other two values and withoutscaffolding.Understand double number lines as a strategy for solving percent problems.

Required Materialspre-printed slips, cut from copies ofthe blackline master

Student task statementFind the products mentally.

Possible responses

1. 9.6

2. 10.8

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•

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GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 14: Solving Percentage Problems 1

14.2: Coupons (10 minutes)

Setup: Quiet think time to complete the activity, followed by a partner discussion.

Student task statement

2. Clare buys an item with a normal price of $24, but saves $6 by using a coupon. For what percentage off isthis coupon?

Han and Clare go shopping, and they each have a coupon.Answer each question and show your reasoning.

1. Han buys an item with a normal price of $15, and uses a10% off coupon. How much does he save by using thecoupon?

Possible responses

1. $1.50

2. 25%

Anticipated misconceptions

Since the first question asks students tofind the dollar amount, some studentsmay think that $6 is the answer to thesecond question and not realize that itis asking them to find the percentage.Also, some students may try to find thesale price on the first question and thepercentage of the sale price on thesecond question, instead of thediscount and the percentage of thediscount. Encourage them to revisit thequestions or clarify what the questionsask.

GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 14: Solving Percentage Problems 2

Are you ready for more?Clare paid full price for an item. Han bought the same item for 80% of the full price. Clare said, “I can’t believe Ipaid 125% of what you paid, Han!” Is what she said true? Explain.

Possible Responses

Yes. Han paid 80% or what Clare

paid. So Clare paid or 125% of what

Han paid.

GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 14: Solving Percentage Problems 3

14.3: Info Gap: Music Devices (20 minutes)

Setup: Students in groups of 2. Distribute problem cards and data cards.

Student task statementYour teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

Both partners should record a solution to the problem.

If your teacher gives you the problem card:

1. Read your card silently and think about whatyou need to know to be able to answer thequestions.

2. Ask your partner for the specific informationthat you need.

3. Explain how you are using the information tosolve the problem.

4. Solve the problem and show your reasoning toyour partner.

If your teacher gives you the data card:

1. Read your card silently.

2. Ask your partner “What specific information doyou need?” and wait for them to ask forinformation.

If your partner asks you for information that isnot on the card, do not do the calculations forthem. Tell them you don't have thatinformation.

3. Have them explain “Why do you need thatinformation?” before telling them theinformation.

4. After your partner solves the problem, askthem to explain their reasoning, even if youunderstand what they have done.

Possible responses

Problem Card 1:

1. Device A, only

2. 96%

Problem Card 2: $60

GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 14: Solving Percentage Problems 4

Lesson Synthesis (5 minutes)If of is , how do we find given and ? How do we find given and ? How do we find given and ?

14.4: Walking to School (Cool-down, 5 minutes)

Setup: None.

Student task statementIt takes Jada 20 minutes to walk to school. It takes Andre 80% as long to walk to school.

How long does it take Andre to walk to school?

Possible responses

16 minutes

GRADE 6 MATHEMATICS

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Unit 3: Unit Rates and Percentages, Lesson 14: Solving Percentage Problems 5