HCPSS Worthwhile Math Task
Deli Dilemma
Common Core Standard
7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare
probabilities from a model to observed frequencies; if the agreement is not good, explain
possible sources of the discrepancy.
b. Develop a probability model (which may not be uniform) by observing frequencies in data
generated from a chance process. For example, find the approximate probability that a spinning
penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes
for the spinning penny appear to be equally likely based on the observed frequencies?
7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and
simulation.
b. Represent sample spaces for compound events using methods such as organized lists, tables
and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”),
identify the outcomes in the sample space which compose the event.
MP1:
MP2:
MP3:
MP4:
MP6:
MP7:
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.
Look for and make use of structure.
The Task
Currently the deli where you work, Pete’s Deli, is offering the following promotion:
After you finish your meal, roll the dice to determine your discount.
 Roll a 3 or 4: 10% off
 Roll a 5: 20% off
 Roll a 1 or 6: 30% off
 Roll a 2: Free Meal
You are not convinced this promotion is in the best interest of the business. Your job is to
explain to your boss why this promotion is not the best in terms of the theoretical probability of
events. Then, you need to create a new promotion idea involving rolling two dice. Be sure your
new game is in the best interest of the business, but still allows customers a chance to win each
of the four prizes. You will need to make a poster of your new promotion and provide an
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
explanation why your deal would be better for business. Your explanation should include the
theoretical probability of a guest winning each of the prizes.
(This task was inspired from an activity found on http://insidemathematics.org)
Facilitator Notes
1. Have groups brainstorm why the current promotion is not the best. If they struggle with
this, try asking, “which of these prizes should be the easiest to win? Which should be the
hardest?” (A larger copy of the promotion list is attached) (Look for evidence of MP1,
MP2 and MP3.)
2. Once students are ready to create their own promotion, suggest they make a sample space
of all the possible outcomes when rolling two dice. (Look for evidence of MP2.)
3. For students who may need some additional guidance, a sample resource sheet has been
provided. (Look for evidence of MP4.)
4. For a possible extension, have students ‘play’ their promotion and record the results for a
specific number of customers. Then ask them to compare the theoretical probability to
the experimental probability. A sample resource sheet for this is also attached. (Look for
evidence of MP6 and MP7.)
5. After students create sample space, consider having them check in with you so you know
they will be determining the probability of events correctly.
Follow-Up Questions
1.
2.
3.
4.
5.
What strategies did you use to find you answer?
How are the strategies the groups used to solve similar?
How are the strategies the groups used to solve unique?
What connections did you make to the problem?
Why is this important?
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
Solutions
There are many different possible solutions for this activity. Here are two examples:
Example 1
 10% Discount: Roll a 6, 7, or 8
16
o
Approx 44% chance
36
 20% Discount: Roll a 5 or 9
8
o
Approx 22% chance
36

 30% Discount: Roll a 4 or 10
6
o
Approx 17% chance
36

 Free Meal: Roll an 11 or 12
3
o
Approx 8% chance
36


Example 2
10% Discount: Roll a 7
6
o
Approx 17% chance
36
 20% Discount: Roll an 8
5
o
Approx 14% chance
36
  30% Discount: Roll a 4
3
o
Approx 8% chance
36

 Free Meal: Roll a 2 or 12
2
o
Approx 6% chance
36



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.