HCPSS Worthwhile Math Task
Music Dilemma
Common Core Standard
8.F.A.2 Compare properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions).
MP1:
MP2:
MP3:
MP4:
MP6:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Attend to precision.
The Task
Katie was just rewarded with a new MP3 player for making Honor Roll. She is doing research
to determine which Internet based company she should use to download her music. She has
found two different companies to choose from, Music Media Mania and Totally Tubular Tunes.
Music Media Mania does not have a joining fee and charges $2.25 per song purchased. Totally
Tubular Tunes has a one time joining fee of $15 and charges $1.50 per song purchased. Which
company should she choose? Why?
Facilitator Notes
1. Encourage students to use a variety of representations to compare the two companies,
including tables, graphs, equations, and other models. Depending on the model students
use to represent the scenarios, it may be necessary to talk about using a linear model to
represent the scenario. (Look for evidence of MP1 and MP4.) This scenario should be
represented as a set of distinct data points, rather than as a continuous function. To help
students understand, it is important to point out that it is not possible to purchase one-half
of a song. However, a linear model can be used to make predictions.
2. Solution 1 models a table being with 0 songs and progressing to a cost of 4 songs for
$9.00 and then counts by 4 songs to modeling a table strategy. The second table for
Solution 1 does not jump due to the initial $15 fee. Consider discussing the skip
counting strategy with students.
3. If your students are having a difficult time getting started, consider offering a starting
point. For example, ask the question: “How much will it cost her to buy 5, 10, 15, 20
songs?”
4. Engage in a discussion about extending each table, only as far as you need to in order to
determine the better deal. (Look for evidence of MP2 and MP4.)
5. Discuss with students the reasonableness of the value of x. Is it possible to buy a
negative value of x (a negative number of songs)?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
6. It is also important to discuss that any equation generated is a model for the situation, but
the actual scenario is a set a discrete points. To help emphasize this, ask if it is possible
to pay for 1.5 songs? Does this make sense? (Look for evidence of MP2.)
Follow-Up Question
1. Are there restraints that could effect Katie’s decision?
2. Is there a point where both music companies would cost the same amount? Why is this
important for a consumer to know? (Look for evidence of MP3 and MP6.)
3. What considerations need to go into Katie’s decision?
4. What strategies did you use to find you answer?
5. How are the strategies the groups used to solve similar? (Look for evidence of MP3.)
6. How are the strategies the groups used to solve unique? (Look for evidence of MP3.)
7. What connections did you make to the problem?
Solutions
Solution 1: Tables
Music Media Mania
# of songs Cost $
0
0
1
2.25
2
4.50
3
6.75
4
9.00
8
18.00
12
27.00
16
36.00
20
45.00
24
28
54.00
63.00
Totally Tubular Tunes
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
# of songs
0
1
HCPSS Worthwhile Math Task
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Students should notice when using the table that
16
cost is the same at $45.00. However, if Katie
17
purchase more than 20 songs, it is cheap to
18
Tubular Tunes. If she wants to purchase less than
19
cheaper to choose Music Media Mania.
20
Solution 2: Representing with Equations,
Check
Music Media Mania
y  2.25x
Totally Tubular Tunes
y  1.5x 15


21
22
23
24
Cost $
15
16.50
18.00
19.50
21.00
22.50
24.00
25.50
27.00
28.50
30.00
31.50
33.00
34.50
36.00
37.50
39.00
40.50
42.00
43.50
at 20 songs the
wants to
choose Totally
20 songs, it is
45.00
46.50
48.00
49.50
51.00
Guess &
Once students determine the equations they can plug in different values for x (number of songs)
to get total cost. Students should use the same values for both equations to compare the costs of
the two companies.
Students may use values for x such as: 0,5,10,15,20,25
Solution 3: Solving a System of Equations
Music Media Mania
y  2.25x



Totally Tubular Tunes
y  1.5x 15
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
2.25x  1.5x 15
.75x 15

.75x .75
x  20

Using this solution students will find where the cost is the same for both companies when Katie’s
purchases 20 songs.
Then students will have to look back to the equations and determine that Totally Tubular Tunes
will be cheaper after 20 songs because it only cost $1.50 per song compared to Music Media
Mania which charges $2.25 per song.
Solution 4: Graphing
Where the lines intersect at (20,45) represents where companies cost the same for the same
amount of songs. Since the line that represents Totally Tubular Tunes is lower than the line the
represents Music Media Mania it cheaper to belong to if Katie is purchasing more than 20 songs.
Solution 5: Graphing Calculator
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Students may also select to graph the functions on the graphing calculator. Using the graphing
calculator, students can examine the table of values as well as find the intersection of the two
models to represent the situation.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.