HCPSS Worthwhile Math Task
Music Dilemma
Common Core Standard
8.F.2 Compare properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions). For example, given a linear
function represented by a table of values and a linear function represented by an algebraic
expression, determine which function has the greater rate of change.
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?
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. 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.
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?
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?
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?
6. How are the strategies the groups used to solve unique?
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
Students should notice when using the table that
11
cost is the same at $45.00. However, if Katie
12
purchase more than 20 songs, it is cheap to
13
Tubular Tunes. If she wants to purchase less than 14
cheaper to choose Music Media Mania.
15
16
17
Solution 2: Representing with Equations,
18
Check
19
Music Media Mania
y  2.25x
Totally Tubular Tunes
y  1.5x 15


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
20
45.00
21
22
23
24
46.50
48.00
49.50
51.00
at 20 songs the
wants to
choose Totally
20 songs, it is
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
2.25x  1.5x 15
.75x 15

.75x .75
x  20
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
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
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.