Lesson PlansBack to lesson plans archive March 13, 2013
How much is a gigabyte of music? – Lesson Plan
Author Mary Klein is a mathematics teacher in Urbana, Illinois
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.
Students will learn to:
- make unfamiliar units of measure more understandable by using a mathematical conversion technique;
- convert conversion equations to fractions;
- convert from one unit of measure to another;
- solve problems involving conversions.
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:
UC Berkeley is including an orientation session for incoming students that warns about the dangers of downloading copyrighted material. The university will also cut off students’ access if they transfer more than five gigabytes worth of files per week.
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.
3. Write the problem on the board: “How many CDs does it take to hold 5 gigabytes of files?”
Show the work explaining as you write:
5 gigabytes * (1000 megabytes / 1 gigabyte) * (1 CD / 700 megabytes) =(5 gigabytes /1) * (1000 megabytes / 1 gigabyte) * (1 CD / 700megabytes) =(Note: Draw a slash through the bolded units of measure to show canceling)
(5 * 1000* 1 CDs) / (1 * 700) = 5000 CDs / 700 = 7.142857… CDs
So it would take 8 CDs to hold 5 gigabytes of files.
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?”
(1 song / 2.5 min.) =5 gigabytes * (1000 megabytes / 1 gigabyte) * (1 CD / 700megabytes) * (80 min. / 1 CD) * (1 song / 2.5 min.) =(Note: Draw a slash through the bolded units of measure to show canceling)(5 * 1000 * 1 * 80 * 1 song) / (1* 700 * 1 * 2.5) = (400,000 songs / 1750) = about 228.571… songs or about 229 songs
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.)
$18 per hour =
$50,000 per year = ($50,000 / 1 year) * (1 year / 50 weeks) * (1 week / 5 days) * (1 day / 8 hours) = $25 / hour or $25 per hour.
2. Investigate your high school’s policy toward downloading music on school computers.
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.
The Materials You Need
Tooltip of materials
- NewsHour Extra article: Entertainment Industry Targets Individual Downloaders
- One calculator per student or group of students
- Student Worksheet
- Answer Key
- Chalkboard or overhead
Common Core Standards
Tooltip of standarts
Relevant National Standards:
- Recognize and apply mathematics in contexts outside mathematics
- Apply appropriate technique, tools, and formulas to determine measurements
- Use the language of mathematics to express mathematical ideas precisely
Correlation to National Teachers of
Tooltip of related stories
Tooltip of more video block
Tooltip of RSS content 3
Debating Our Destiny: Do Presidential Debates Matter? – Lesson Plan
The presidential debates have been an important part of the U.S. election process for decades, but how much do they really influence voters? In this lesson, students will watch video clips from PBS NewsHour’s “Debating Our Destiny” with Jim Lehrer, which includes famous debate moments as well as interviews with the candidates themselves. Continue readingCivicsdebatingDonald TrumpElection 2016Hillary ClintonJim LehrerLee Banvillepresidential debatesSocial Studies
Where do the presidential candidates stand on education?
As Election Day approached, the candidates running for president have made and effort to appeal to parents, teachers and students by showing them where they stand on education.CampaignDonald TrumpeducationElection 2016Hillary Clinton
Candidates cite security qualifications after weekend attacks
Following pipe bomb attacks over the weekend, the presidential candidates each took a moment to assure voters of their national security qualifications. Continue readingCampaignElection 2016extremismterrorist attacks
Clinton on bed rest and defensive over ‘deplorables’ remark
Hillary Clinton had to stay home in order to recover from pneumonia this week, but that didn’t stop her campaign.campaign 2016Donald TrumpElection 2016Hillary ClintonPolitics
Native American tribes band together to block oil pipeline
Unrest in North Dakota persists as the Standing Rock Sioux Tribe continues to protest the building of an oil pipeline that would threaten its culture and health. Continue readingArmy Corps of EngineersNative AmericansNorth DakotaoilpipelineSiouxsocial justiceSocial StudiesStanding Rock Sioux Tribe