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 them to solve or put them on a sheet of paper and pass them out to everyone.
If a sign in the store says that bananas are 3 pounds for 99 cents, how much would 5 pounds cost?
The dog food in the store sells for $4.50 for 25 pounds. If smaller packages sell at the same rate, how much would a 10 pound package sell for?
If a marathon runner runs a at a pace of six miles in 32 minutes, how long will it take her to run 15 miles if she maintains that same pace?
While traveling from San Francisco to Los Angeles, you were able to go 165 miles in 3 hours. If you maintain that same rate of speed, how far will you have traveled after four hours?
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 to the problems.
- 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 . Have a volunteer come to the board to solve the problem for the class. Point out to the class how the cross product method was used in solving the problem.
Continue putting one problem up at a time. Have students read it and then solve it at their desks. After they have solved it, have someone volunteer to show how to do it to the class. Assign some more problems like the five above.
Wrap-Up and Assessment Hints
Stress throughout the lessons that the cross product method is based on 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. When assessing students, have them write down the proportions they are solving and all the work they do when solving them. Too often students don't write down their work, which makes it almost impossible to see where they might be making mistakes.