Lesson 14Solving Percentage Problems

Learning Goal

Let’s solve more percentage problems.

Learning Targets

  • I can choose and create diagrams to help me solve problems about percentages.

Lesson Terms

  • percentage

Warm Up: Number Talk: Multiplication with Decimals

Problem 1

Find the products mentally.

Activity 1: Coupons

Problem 1

A photograph of a newspaper showing coupons and scissors resting on it.

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 a 10% off coupon. How much does he save by using the coupon?

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

Are you ready for more?

Problem 1

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

Activity 2: Info Gap: Music Devices

Problem 1

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:

  1. Silently read your card and think about what information you need to be able to answer the question.

  2. Ask your partner for the specific information that you need.

  3. Explain how you are using the information to solve the problem.

    Continue to ask questions until you have enough information to solve the problem.

  4. Share the problem card and solve the problem independently.

  5. Read the data card and discuss your reasoning.

If your teacher gives you the data card:

  1. Silently read your card.

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

    If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.

  3. Before sharing the information, ask “Why do you need that information?” Listen to your partner’s reasoning and ask clarifying questions.

  4. Read the problem card and solve the problem independently.

  5. Share the data card and discuss your reasoning.

Lesson Summary

A pot can hold 36 liters of water. What percentage of the pot is filled when it contains 9 liters of water?

Here are two different ways to solve this problem:

  • Using a double number line:

    A double number line with 5 evenly spaced tick marks. The top number line is labeled “volume, in liters” and starting with the first tick mark, 0, 9, 18, 27, and 36 are labeled. The bottom number line is not labeled and starting with the first tick mark 0, 25 percent, 50 percent, 75 percent, and 100 percent are labeled.

    We can divide the distance between 0 and 36 into four equal intervals, so 9 is of 36, or 9 is 25% of 36.

  • Using a table:

    A two column table with two rows of data. The first column has the heading “volume ,in liters” and the second column has the heading “percentage”. The data are as follows: Row one, 36, 100. Row two, 9, 25. Arrows on both sides of the table from row 1 to row 2 are labeled "multiply by one fourth."