Unit 4, Lesson 12
Solving Multi-step Percentage Problems
Grade 7
12.1
Warm-up
Which three go together? Why do they go together?
A
B
C
D
12.2
Activity
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
If your teacher gives you the problem card:
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Silently read your card, and think about what information you need to answer the question.
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Ask your partner for the specific information that you need. “Can you tell me ?”
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Explain to your partner how you are using the information to solve the problem. “I need to know because . . . .”
Continue to ask questions until you have enough information to solve the problem.
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Once you have enough information, share the problem card with your partner, and solve the problem independently.
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Read the data card, and discuss your reasoning.
If your teacher gives you the data card:
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Silently read your card. Wait for your partner to ask for information.
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Before telling your partner any information, ask, “Why do you need to know ?”
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Listen to your partner’s reasoning and ask clarifying questions. Only give information that is on your card. Do not figure out anything for your partner!
These steps may be repeated.
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Once your partner says they have enough information to solve the problem, read the problem card, and solve the problem independently.
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Share the data card, and discuss your reasoning.
12.3
Activity
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A salesperson sold a car for \$18,250, and their commission is \$693.50. What percentage of the sale price is their commission?
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The bill for a meal was \$33.75. The customer left \$40.00. What percentage of the bill was the tip?
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The original price of a bicycle was \$375. Now it is on sale for \$295. What percentage of the original price was the markdown?
Student Lesson Summary
To find a 30% increase over 50, we can find 130% of 50.
To find a 30% decrease from 50, we can find 70% of 50.
If we know the initial amount and the final amount, we can also find the percent increase or percent decrease. For example, a plant was 12 inches tall and grew to be 15 inches tall. What percent increase is this? Here are two ways to solve this problem:
The plant grew 3 inches, because . We can divide this growth by the original height: . So the height of the plant increased by 25%.
The plant’s new height is 125% of the original height, because . This means the height increased by 25%, because .
Consider this new example: A rope was 2.4 meters long. Someone cut it down to 1.9 meters. What percent decrease is this? Here are two ways to solve the problem:
The rope is now , or 0.5, meter shorter. We can divide this decrease by the original length: . So the length of the rope decreased by approximately 20.8%.
The rope’s new length is about 79.2% of the original length, because . The length decreased by approximately 20.8%, because .
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