Maryland CCRG Algebra Task Project
Discounting Tickets
Common Core Standard
F.BF.1 Students will write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
b. Combine standard function types using arithmetic operations. For example, build a function
that models the temperature of a cooling body by adding a constant function to a decaying
exponential, and relate these functions to the model.
Common Core Traditional Pathway: Algebra I, Unit 2
Common Core Integrated Pathway: Mathematics I, Unit 2
The Task
Today, you have been hired as a member of the sales team for the Math Rocks Theatre. The
only problem is that the tickets sales for the theatre have been very low for the past couple of
months. One of your first jobs with your teammates will be examine different promotions and
determine which plan will increase the tickets sales the most.
Now your boss tells you that he is horrible at math, but he has two promotion ideas to sell out the
tickets to the next show. The first deal is to discount the tickets $10 per week until they sell out.
The other deal is to discount the tickets 25% every week, until they are sold out.
Facilitator Notes
1. Ask students to explain what a promotion is and provide an example of a promotion they
have heard on the radio, television, or Internet.
2. Divide the class into their “teams” and explain that they will be working with their new
teammates to design the most successful promotion for ticket sales for the Math Rocks
Theatre.
3. Give the students 5-10 minutes to brainstorm pros and cons of offering a promotion at the
Math Rocks Theatre. Allow groups to share their charts. Make sure the students explain
“profit” and “discount” in their discussion.
4. Present students with the discount ticket options. Give students several minutes to discuss
their reactions to the scenario with their groups. Have them list questions they may still
have and have them brainstorm ideas about how to determine, which promotion would be
more successful.
5. After discussing the questions/ideas they developed, explain that each group will be
given a different show with a different original cost, but the boss still wants them to use
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Maryland CCRG Algebra Task Project
one of his two promotion ideas. Then, assign each group with one of the following ticket
shows:
 “Beauty and the Beast” Original Cost: $80
 “The Lion King” Original Cost: $200
 “Mamma Mia!” Original Cost: $120
 “Mary Poppins” Original Cost: $40
6. Select one of these optional activities for the class to complete:
 Ask them to represent the problem: graphically, numerically, algebraically, and
as a written description. (Note: Students may struggle with writing an equation
for the exponential function, but they should be able to recognize and translate
the linear equation.) Have them determine which plan would be the best
promotion given the original cost of the ticket. Have each group present their
proposal to the class and allow other groups to ask clarifying questions. While
groups present, have students chart the similarities and differences between the
solutions. *Important Note: While the equation and graphs they generate to
model the situation may be continuous, it is important to point out that the domain
needs to be restricted to represent the number of weeks on sale which would make
the graph a set of discrete points. It will be important to emphasize the equations
are generated to model the situation, but values will not change for half of a week.
 Have students develop a proposal for their boss illustrating which promotion is a
better for the company for their show. They should use graphs, charts, and
equations to justify their choice. Then, have students take a gallery walk around
the room to compare which promotion the other groups chose based on their
original cost. Have students travel with their team and develop a list of
similarities and differences between the proposals.
 Have students vote on the best presentation/proposal as a class.
Follow-Up Questions
1. Will the tickets ever cost the same amount? If so, when will this occur?
2. Will the tickets ever be free? Why or Why not?
3. How did the initial cost have an effect on the solution?
Extension Activities
Now that you have seen each group’s solution to the promotion, design a unique promotion for
your show that you think would be most effective. Create your own proposal for your boss that
you think would be the most effective way to boost ticket sales. Be sure to use tables, graphs,
numbers, algebraic expressions or equations, and/or, written descriptions in your proposal.
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Maryland CCRG Algebra Task Project
Solutions
While there are many approaches students may use to solve this task, here are a few
sample answers:
Cons
Pros
If the theatre does not bring in enough
customers, then the promotion may not
make a profit.
Customers could expect a promotion
every time they attend the Math Rocks
Theatre.
If the timing of the promotion is not
good or if they do not advertise well
enough, they may loose money.
(Example: If they offer a promotion in
the summer and many people are on
vacation, the sales may be low.)
Reduce ticket sales could bring in
more customers, which would yield a
greater profit.
If the promotion is successful, it could
lead to more returning customers, with
or without a second promotion.
The promotion could also increase
concession sales.
Promotion Pros and Cons:
Sample Brainstorm Questions:
 What is the initial cost of the tickets?
 How long do they have to sell the tickets?
 Does this mean the ticket price could eventually be zero?
 How many possible tickets can they sell?
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Maryland CCRG Algebra Task Project
Sample Answers ($80):
Graphically:
Promotion #2: Discount 25% per week
Promotion #1: Discount $10 per week
Numerically:
Promotion #1: Discount $10 per week
Promotion #2: Discount 25% per week
Number of Weeks
on Sale
Cost of the Ticket $
Number of Weeks
on Sale
Cost of the Ticket $
0
80
0
80
1
70
1
60
2
60
2
45
3
50
3
33.75
4
40
4
25.312
5
30
5
18.984375
6
20
6
14.23828125
7
10
7
10.67871094
8
0
8
8.009
As students complete the tables, they should recognize that promotion #2 would never reach $0.
Since the ticket price is always decreasing by 25% of the previous purchase, the y-value will
never reach 0. Students should also start to question how long the tickets would be on sale for,
because in the promotion #1 after 8 weeks, the cost will be $0. Does that mean that the theatre
will have to pay $10 per ticket if they go on sale for the 9th week? Should the company put a
limit on the number of weeks the promotion runs? All of these questions should be addresses
when students write and present their proposal to their boss. They should also notice that the
plans would cost the same at approximately 7 weeks.
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Maryland CCRG Algebra Task Project
Algebraically:
*Important Note: While the equation and graphs they generate to model the situation may be
continuous, it is important to point out that the domain needs to be restricted to represent the
number of weeks on sale which would make the graph a set of discrete points. It will be
important to emphasize the equations are generated to model the situation, but values will not
change for half of a week.
Promotion #1:
y  10x  80
Where y = the cost of the ticket, and x = the number of weeks the tickets have been on sale

Promotion #2:
y  801  .25
x
y  800.75
x
Where y = the cost of the ticket, and x = the number of weeks the tickets have been on sale

*Students may struggle when trying to write the exponential equation; however, it is not
necessary that all students be able to write this equation at this point in the curriculum. They will
need to recognize the difference between exponential and linear functions.
Written Description (Answers will vary):
The solution to this problem comes down to the students’ explanation. If they chose to go with
promotion #1, they could reason that the discount is less each week until the 7th week. They
could recommend that if the theatre runs the promotion for only a few weeks, they could
discount the tickets by a reasonable amount. If they continued the promotion past the 7th week,
then they would earn $0 for the tickets or without putting exclusions on the deal, they may even
be paying their customers to attend the show.
If the group chooses promotion #2, they may reason that this promotion will never actually sell
tickets for $0. However, it does discount the tickets more drastically than the first promotion.
This may be a good promotion for tickets on sale for only 3 weeks or so. After that, the
company may lose money for the show, since the tickets cost an unreasonably low amount.
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information on this license, refer to: http://creativecommons.org/licenses/by-nc/3.0/.
Maryland CCRG Algebra Task Project
MSDE has licensed this product under Creative Commons Non-Commercial. For more
information on this license, refer to: http://creativecommons.org/licenses/by-nc/3.0/.
Maryland CCRG Algebra Task Project
Follow Up Questions (Answers will vary):
1. Will the tickets ever cost the same amount? If so, when will this occur? Yes and no.
Both promotions are the same in the beginning, since both ticket prices start at $80 and
they are almost the same at 7 weeks, when they are both about $10. If the students found
the exact intersection is would be (6.9, 10.99); however this does not make sense in the
problem, since the promotion runs the same amount for the entire week. You could even
discuss with students that the promotion #1 could be a step function, since the amount of
money would remain the same from week 1 until it reaches week 2, where the function
would jump down to the next amount.
2. Will the tickets ever be free? Why or Why not?
In promotion #1, the ticket cost model shows that the tickets could be sold for $0 or they
could owe the customers money. Students may recommend putting a restriction on the
number of weeks the promotion can run. In the second promotion, students should
recognize that the function is approaching $0, however, it never will actually intersect the
x-axis. Even though the amount will eventually round to $0, it is never really $0. The
students that choose promotion number two could justify that their model never actually
cost $0, so their model will make more sense.
4. How did the initial cost have an effect on the solution?
Students will probably mention the initial cost effected how long the promotion would be
able to run. The higher the initial cost of the ticket, the greater the length of the
promotion. More simply, if the original cost of the tickets was higher the number of
weeks the promotion could run would be longer. In either case, the groups would come
to similar conclusions about which promotion they thought was best, regardless of the
original cost.
MSDE has licensed this product under Creative Commons Non-Commercial. For more
information on this license, refer to: http://creativecommons.org/licenses/by-nc/3.0/.