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Title of Project:
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Willy Dropitt
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Team Members: |
Russ Bishop, Melissa Cooper, Niki Scyoc, and Sue Shoemaker
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Grade Level
and/or Course: |
Grades 9-12
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Concept(s) used: |
Simple
Probability, Permutations, Sample Space, Outcomes, Experimental
Probability, Theoretical Probability, Compound Probability, and Event
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PA Standard(s) Addressed: |
- 2.2.11A
- 2.5.11C
- 2.7.11C
- 2.7.11D
- 2.7.11E
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NCTM Standard(s) Addressed: |
Numbers and Operations, Data Analysis and
Probability, Connections, Representations, Problem Solving, and
Communications
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Introduction / Applications: |
Willy Dropitt, a waiter
at the Greasy Spoon, is having a rough day. So far he has dropped a
milkshake on his boss’s wife’s lap and bumped into a waitress carrying a
tray of spaghetti. With his job on the line and under the watchful eye
of his boss, Willy rushes over to table four (4) forgetting his order
pad. Willing to risk it, he successfully memorizes the orders. However,
when Willy goes to deliver the meals, he can’t recall who ordered what?
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Question: |
What is
the chance that all four guests receive the correct meal? Only one guest
receives the correct meal? Exactly 2 guests receive the correct meal?
Exactly 3 guests receive the correct meal?
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Model: |
Students will use simulations to
arrive at experimental probability leading to the calculation of
theoretical probability.
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Resources and
Materials
(estimated cost): |
- 4 placemats ($4)
- paper plates ($2.50)
- magazine(s) containing food items (that will be glued onto the
plates) ($5)
- brown grocery bags (free at a local grocery store)
- glue ($1)
- student worksheet (below)
- a marker ($1.29)
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Procedures &
Activities
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Procedures: |
- In groups of 5 (4 guests and Willy the waiter) students will
simulate the event 50 times. The simulation will involve Willy
randomly pulling one plate at a time out of the paper bag and placing
it on the placemat of the first guest to his left and continuing
clockwise until all four plates are distributed.
- After all four guests have a meal; students should record the
number of guests receiving the correct meal. A tally chart is an
option for recording the 50 outcomes.
- Using the data, calculate the experimental probabilities that 0,
1, 2, 3, and all 4 guests received the correct meal.
- List all possible permutations of the four meals.
- For each permutation determine the number of guests receiving the
correct meal. Then use that information to determine the theoretical
probabilities.
- Compare the theoretical and experimental probabilities in order to
discuss the connection.
- Extension: Take into consideration that all four guests have
ordered beverages. What are the probabilities that Willy gives each
guest the correct meal and beverage?
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Solutions: |
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#
correct |
 |
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#
correct |
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#
correct |
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#
correct |
| 1 2 3 4 |
4 |
2 1 3 4 |
2 |
3 1 2 4 |
1 |
4 1 2 3 |
0 |
| 1 2 4 3 |
2 |
2 1 4 3 |
0 |
3 1 4 2 |
0 |
4 1 3 2 |
1 |
| 1 3 2 4 |
2 |
2 3 1 4 |
1 |
3 2 1 4 |
2 |
4 2 1 3 |
1 |
| 1 3 4 2 |
1 |
2 3 4 1 |
0 |
3 2 4 1 |
1 |
4 2 3 1 |
2 |
| 1 4 2 3 |
1 |
2 4 1 3 |
0 |
3 4 1 2 |
0 |
4 3 1 2 |
0 |
| 1 4 3 2 |
2 |
2 4 3 1 |
1 |
3 4 2 1 |
0 |
4 3 2 1 |
0 |
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| P(0 correct) = 9/24 |
P(2 correct) = 6/24 |
P(4 correct) = 1/24 |
| P(1 correct) = 8/24 |
P(3 correct) = 0/24 |
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Accommodations/Adaptations
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ESL: |
Provide reading assistance as
needed
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Special Needs: |
Allow students to complete
the activity with only three guests (reducing the number of
permutations)
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Enrichment: |
Find the theoretical
probabilities associated with more than four guests.
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Willy
Dropitt WorkspaceWilly
Dropitt, a waiter at the Greasy Spoon, is having a rough day. So far
he has dropped a milkshake on his boss’s wife’s lap and bumped into
a waitress carrying a tray of spaghetti. With his job on the line
and under the watchful eye of his boss, Willy rushes over to table
four (4) forgetting his order pad. Willing to risk it he
successfully memorizes the orders. However, when Willy goes to
deliver the meals he can’t recall who ordered what?
What is the chance that all four guests receive the correct meal?
Only one guest receives the correct meal? Exactly 2 guests receive
the correct meal? Exactly 3 guests receive the correct meal?
Tally Space:
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# Correct
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Tally |
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0 |
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1 |
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2 |
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3 |
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4 |
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Experimental Probabilities:
P(0 correct) =
P(2 correct) =
P(4 correct) =
P(1 correct) =
P(3 correct) =
Theoretical Probabilities:
P(0 correct) =
P(2 correct) =
P(4 correct) =
P(1 correct) =
P(3 correct) =
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