A GIGABYTE OF MUSIC, HOW MUCH IS THAT?
Using Mathematical Conversions to Better Understand Numbers in the News

 

AUTHOR: Shawn Piasecki

LESSON SOURCE: http://www.pbs.org/newshour/extra/teachers/lessonplans/math/download_10-2.html

DATE LESSON TO BE TAUGHT: 3rd and 4th days of the 4 week unit.

GRADE LEVEL: 10-12

CONCEPT(S): The purpose of this lesson is to teach the students a new kind of thinking through dimensional analysis.  This not only allows them to not only solve problems which there is no given formula, but also gives them the higher cognitive skills which are necessary to solving real world problems.

OBJECTIVES:

SWBAT

·        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.

TEKS: §112.45. Chemistry. (2)  Scientific processes. The student uses scientific methods during field and laboratory investigations. The student is expected to: (A)  plan and implement investigative procedures including asking questions, formulating testable hypotheses, and selecting equipment and technology; (B)  make measurements with precision; (C)  express and manipulate chemical quantities using scientific conventions and mathematical procedures such as dimensional analysis; (D)  organize, analyze, evaluate, make inferences, and predict trends from data; and (E)  communicate valid conclusions.

MATERIALS LIST and ADVANCED PREPARATIONS:

Per student

SAFETY:

No safety issues posed.

 

ENGAGEMENT
 
 

 


What the Teacher Will Do

Eliciting Questions

Formative Assessment

Student Responses

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."

- How large is five gigabytes?

 

- Our main goal today will be to make less familiar units of measure more understandable by using a mathematical conversion technique called “dimensional analysis.”

-Some students might have an idea of about how big it is.

 

EXPLORATION
 
 

 


What the Teacher Will Do

Eliciting Questions

Formative Assessment

Student Responses

 

-We need the following conversions: (Write them on the board.)

1 gigabyte = 1000 megabytes

1 CD = 700 megabytes    (from a CD package)

 

 

- 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.

 

-Since this is one of the first times for a student to work this problem, the teacher explains though this example problem.

-How many CDs does it take to hold 5 gigabytes of files?

 

5 gigabytes * (1000 megabytes / 1 gigabyte) * (1 CD / 700 megabytes) =

 

(5 gigabytes /1) * (1000 megabytes / 1 gigabyte) * (1 CD / 700 megabytes) =

 

(5 * 1000* 1 CDs) / (1 * 700) = 5000 CDs / 700 = 7.142857... CDs

 

So it would take 8 CDs to hold 5 gigabytes of files.

 

Since some students will have trouble picking which fractions to use, point out that the rule of thumb is always: “What you want goes on top.”

 

 

Give the students a problem to work out in groups.

-How would this problem change if we wanted to know how many songs fit in five gigabytes of files?

 

-Information to know:

 

1 CD = 80 minutes of playing time (copied from the label of a package of CDs)

1 song = 2.5 minutes of music (on average)

 

 

 

-Students break into groups of about 3 to solve this problem.

EXPLANATION

 

 
 

 

                                               

What the Teacher Will Do

Eliciting Questions

Formative Assessment

Student Responses

 

-So, How many songs fit in five gigabytes of files?

-Students have a representative of their group write the solution on the board (it should look something like this):

 

5 gigabytes * (1000 megabytes / 1 gigabyte) * (1 CD / 700 megabytes) * (80 min. / 1 CD) *
(1 song / 2.5 min.) =

 

5 gigabytes * (1000 megabytes / 1 gigabyte) * (1 CD / 700 megabytes) * (80 min. / 1 CD) * (1 song / 2.5 min.) =

 

(5 * 1000 * 1 * 80 * 1 song) / (1* 700 * 1 * 2.5) = (400,000 songs / 1750) = about 228.571... songs or about 229 songs

           

ELABORATION

 

 
 
 

 

 


What the Teacher Will Do

Eliciting Questions

Formative Assessment

Student Responses

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.

 

 

Distribute worksheets and allow students to work in groups.

 

 

 

EVALUATION
 
 

 


What the Teacher Will Do

Eliciting Questions

Summative Assessment

Student Responses

Homework problems:

1. If you were paid $18.00 per hour, and you worked full time (40 hours a week), how much yearly salary would you make?

 

2. If someone tells you that they make $50,000 per year and they work full time (40 hours a week), how much do they earn per hour?