A GIGABYTE OF MUSIC, HOW MUCH IS THAT?
Subject(s): Consumer Math, Math, Science
Time: One class period plus an assignment
In an effort to stem the illegal downloading of music and the resulting financial losses to performers and others in the music industry, the entertainment industry has filed over 250 lawsuits against individuals. Fines can be high and since students are frequent downloaders, this issue is a concern to teens, their parents, and the schools they attend.
The mathematical methods used in this lesson are relatively new; they make conversions easier and more fun for students.
will learn to:
1. Distribute the Online NewsHour story, "Entertainment Industry Targets Individual Downloaders" for students to read. Briefly discuss the story emphasizing how schools must protect their computer network and then focus on this paragraph from the story:
Ask, "How large is five gigabytes?" Mention that our main goal today will be to make less familiar units of measure more understandable by using a mathematical conversion technique.
2. Tell the students that we need the following conversions: (Write them on the board.)
We also need to remember that because "1 gigabyte = 1000 megabytes" the fractions "1 gigabyte / 1000 megabytes" and "1000 megabytes / 1 gigabyte" both equal one. Multiplying by one preserves identity (x * 1 = x), so multiplying a measurement by one of these fractions produces an equivalent measurement. Since (x*1*1*1 = 1) multiple changes can be made at once.
Write the problem on the board: "How many CDs does it take to hold 5 gigabytes
4. Students generally find that linking together the fractions is fun, but some people will have trouble deciding which fraction to use. Point out that we choose the first fraction so that its denominator matches the unit used in the measurement to be converted. The unit used in the numerator of the first fraction will appear in the denominator of the second fraction and so on. In general, the unit in the numerator of one fraction will match the unit in the denominator of the fraction immediately to its right. Remind students that a numerator cancels with a denominator.
5. Ask how this problem would change if we wanted to know how many songs fit in five gigabytes of files. Write these conversions on the board. Explain the information in the parenthesis as you write. Then solve the problem.
Solution: "How many songs fit in five gigabytes of files?"
6. Finally, remind students that rounding should occur only at the last step of any problem. A nice thing about these problems is that we can enter all the numbers into the calculator in such a way that the equal key is hit only once; there is only one chance to round.
7. Distribute worksheets and allow students to work in groups.
1. Show students that this technique is also useful in making rates more understandable. For example, some people understand rates of pay more easily if the rate is given in terms of "yearly pay" and some understand "hourly pay" better. (Remember "per" translates as division.)
per hour =
per year = ($50,000 / 1 year) * (1 year / 50 weeks) * (1 week / 5 days) * (1 day
/ 8 hours) = $25 / hour or $25 per hour.
Author Mary Klein is a mathematics teacher with experience at the high school, middle school, and junior high school level. She is the author of several Web-based lessons on mathematics and basketball. She lives with her husband and son in Urbana, Illinois.
To find out more about opportunities to contribute to this site, contact Leah Clapman at firstname.lastname@example.org.