Lesson 14: Solving Percentage Problems

Let’s solve more percentage problems.

14.1: Number Talk: Multiplication with Decimals

Find the products mentally.

$6\boldcdot (0.8)\boldcdot 2$

$(4.5)\boldcdot (0.6)\boldcdot 4$

14.2: Coupons

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?
Coupons 5 Copyright Owner: Hobbies on a Budget License: CC BY 2.0 Via: Flickr
  1. Clare buys an item with a normal price of \$24, but saves \$6 by using a coupon. For what percentage off is this coupon?

14.3: Info Gap: Music Devices

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. Read your card silently and think about what you need to know to be able to answer the questions.

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

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

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

If your teacher gives you the data card:

  1. Read your card silently.

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

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

  3. Have them explain “Why do you need that information?” before telling them the information.

  4. After your partner solves the problem, ask them to explain their reasoning, even if you understand what they have done.

Both partners should record a solution to the problem.

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 $\frac14$ 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."

Practice Problems ▶