Math Background

Lesson: Proportions
Developing the Concept

In this lesson, you'll introduce your students to some of the many kinds of problems that can be solved with proportions. Today, have volunteers illustrate their work on the board up front for all the students to see.

Materials: Prepare an overhead transparency with the following problems for students to solve or write the problems on a sheet of paper and give a copy to each student.

  1. If a sign in the store states that bananas are 3 pounds for 99 cents, how much would 5 pounds cost?
  2. The store sells 25 pounds of dog food for $4.50. If smaller packages sell at the same rate, how much would a 10-pound package sell for?
  3. If a marathon runner runs 6 miles in 32 minutes, how long will it take her to run 15 miles if she maintains that same speed?
  4. While traveling from San Francisco to Los Angeles, you were able to drive 165 miles in 3 hours. If you maintain that same speed, how far will you have traveled after 4 hours?
  5. On the planet Mathdom, a month is 45 days, and there are 5 weeks in a month. How many days are there in 2 weeks?
  • Say: Today we are going to solve some problems involving proportions. Who can remind us how to solve a proportion?
    Make sure students remember how to set up and solve a proportion before continuing.
  • Ask: Would someone please read the first problem for us? How could we solve this problem?
    After reading the problem, someone may suggest setting up the proportion Three pounds over ninety-nine cents equals five pounds over n cents, or three over ninety nine equals five over n. Have a volunteer come to the board to solve the problem for the class. Point out to the class how the cross-product method can be used in solving the problem.

    Continue putting one problem on the board at a time. Have students read the problem and then solve it at their desks. After they have solved it, have someone volunteer to show the solution to the class. Assign some more problems like the five listed above.

Wrap-Up and Assessment Hints
Stress throughout the lessons that the cross-product method is a shortcut for multiplying both sides of the equation by the product of the two denominators. Be sure to have students check to see that their answers make sense in terms of the original problem. To assess students' understanding, have them write the proportions they are solving and show all their work. Too often, students don't show their work, which makes it almost impossible to see where they might be making mistakes.

Houghton Mifflin Math Grade 6