Spinner Games, project help
Unit Project:
Spinner Games
Review
the requirements for completing the Graded Assignment.
Goals
You will
be faced with many situations involving uncertainty throughout your
life, and many of those situations will involve money. Whether you
are choosing to buy an insurance policy, a warranty on a printer, or
a chance to win a stuffed teddy bear in a spinner game, it is
important that you understand the mathematics behind these costs.
During
this unit, you will design two spinner games.
First
you’ll learn about spinner games and choose the prizes. Then you’ll
use expected values to design your games to make a profit and
simulate playing those games to see if they make the profit amount
you expected.
Schedule of
Completion
Suggested Time to
Complete and What to Turn In
Project
Research: 2 days. No submittals.
Project
Writing: 2 days. Submit Lesson Checkpoint: Expected Value. Submit
your completed project to your teacher.
Project
Reflection: 1 day. Participate in a discussion with fellow students,
if directed by your teacher.
Project
Instructions
Before
beginning, review the sample project so that you understand what
you’ll be creating.
Project Files
You will
use the following documents and tools for this project:
Project
Overview:
PRM_A_06_project_overview.doc
Sample
Project:
PRM_A_06_sample_project.ppt
Project
Template:
PRM_A_06_project_template.ppt
Spreadsheet
Template:
PRM_A_06_spreadsheet_template.xls
Spinner
Tool: Access
the Spinner Tool though Student
Resources: Links.
Template
Download
the project template and rename the file as
GamePresentation_YourName.
This file will become your presentation.
Download
the spreadsheet template and rename the file as Spreadsheet_YourName.
You will use this file to help you create your presentation.
Project Research
Decide
on the prize for your first spinner.
Look
on the Internet to find an item that sells for less
than $5.
Prize ideas include, but are not limited to, small stuffed animals,
posters, T-shirts, goldfish, and small puzzles. Assume that the site
you find is the site where the prizes would be purchased from. If the
prizes are sold in bulk (such as a dozen to a pack), figure out the
cost per single prize. Do
not use the same item that the sample project uses.
Decide
on the prize for your second spinner.
Look
on the Internet to find an item that sells for between
$10 and $30.
Prize ideas include, but are not limited to, large stuffed animals,
sports caps, board games, and backpacks. Assume that the site you
find is the site where the prizes would be purchased from. Do
not use the same item that the sample project uses.
Open
your presentation. On slide 1, type your name. On slide 2, complete
the table with prize information.
Project Writing
Complete
Lesson Checkpoint: Expected Value, an online, ungraded assessment.
You’ll practice finding and interpreting expected value for a game
of chance—a skill essential to completing your project. Reach out
to your teacher with any questions you have after taking this
assessment.
Design
a draft of your first spinner game (the game with the less expensive
prize.)
Determine
how many sectors the spinner will have. Choose between 2 and 12
sectors.
Choose
the cost to play the game.
Tip:
You want to make your game appealing to the public. You can achieve
this with a greater probability of winning and/or a lower cost to
play.
Open
your spreadsheet and use the first table in the Expected
Values tab to
find the expected value of your game. (Tabs are located at the bottom
of the page.)
Use
the value of your prize to determine the outcomes. Type the outcomes
in cells B5 and C5.
Use
the number of sectors in your spinner to determine the probabilities.
Type the probabilities in cells B6 and C6.
The
expected value will appear below the table in cell B8. Note:
There is a formula in cell B8. Do not type over it.
Think
about the expected value shown. Remember, the goal is to make a
profitable game that people will want to play. Modify your game until
you think you have achieved this. You can change the cost to play the
game and/or you can change the number of sectors in your spinner. If
you choose to change your prize, be sure to update the information on
slide 2 in your presentation. Update the values in cells B5, B6, C5,
and C6 as needed. Save your work when you are finished.
Open
your presentation. On slide 3, type in the information about your
first spinner game.
Design a
draft of your second spinner game (the game with the more expensive
prize.)
Determine
how many sectors the spinner will have. Choose between 2 and 12
sectors.
Choose
the cost to play the game.
Tip:
This game has a greater prize value than your first game. To make the
game profitable, you may need to charge more to play the game, and/or
decrease the probability of winning.
Open
your spreadsheet and use the second table in the Expected Values
tab to find the expected value of your game.
Use
the value of your prize to determine the outcomes. Type the outcomes
in cells B13 and C13.
Use
the number of sectors in your spinner to determine the probabilities.
Type the probabilities in cells B14 and C14.
The
expected value will appear below the table in cell B16. Note:
There is a formula in cell B16. Do not type over it.
Think
about the expected value shown. Remember, the goal is to make a
profitable game that people will want to play. Modify your game until
you think you have achieved this. You can change the cost to play the
game and/or you can change the number of sectors in your spinner. If
you choose to change your prize, be sure to update the information on
slide 2 in your presentation. Update the values in cells B13, B14,
C13, and C14 as needed. Save your work when you are finished.
Open
your presentation. On slide 4, type in the information about your
second spinner game.
Complete
slide 5 by predicting how much money the game owner, will make after
each spinner game is played 100, 500, and 1000 times.
Go to
the online spinner. Set it up to model your first spinner.
Click
Change Spinner. Click the up and down arrows to adjust the number of
sectors to equal the number of sectors in your first spinner. When
finished, click Apply.
Simulate
playing the game 100, 500, and 1000 times.
Predict
where the arrow will land. Consider this sector the winning sector
for all plays.
With
the Number of Spins set to 100, click Go. Find the number of times,
f, the arrow landed in your chosen sector. Record this as the
number of wins in the table below. Calculate the number of losses by
subtracting the number of wins from 100.
Change
the number of spins to 400 and click Go. There are now a total of 500
spins. Find the number of times, f, the arrow landed in your
chosen sector. Record this as the number of wins in the table below.
Calculate the number of losses by subtracting the number of wins from
500.
Change
the number of spins to 500 and click Go. There are now a total of
1000 spins. Find the number of times, f, the arrow landed in
your chosen sector. Record this as the number of wins in the table
below. Calculate the number of losses by subtracting the number of
wins from 1000.
Number of plays
Win
Lose
100
500
1000
Open
your spreadsheet and use the first row of tables in the Simulations
tab to calculate the game owner’s profits from the simulation.
Notice that cells for the outcomes are already populated.
Use
the values from your table in Step 12 for the frequencies of the
outcomes. Type the frequencies in cells B6 and C6, F6 and G6, and J6
and K6.
The
profits for the simulations will appear below the tables in cells B8,
F8, and J8. Note:
There are formulas in cells B8, F8, and J8. Do not type over them.
Open
your presentation. On slide 6, type in the information about your
simulations and compare them to your predictions.
Go back
to the online spinner. Set it up to model your second spinner.
Click
Change Spinner. Click the up and down arrows to adjust the number of
sectors to equal the number of sectors in your first spinner. When
finished, click Apply.
Simulate
playing the game 100, 500, and 1000 times.
Predict
where the arrow will land. Consider this sector the winning sector
for all plays.
With
the Number of Spins set to 100, click Go. Find the number of times,
f, the arrow landed in your chosen sector. Record this as the number
of wins in the table below. Calculate the number of losses by
subtracting the number of wins from 100.
Change
the number of spins to 400 and click Go. There are now a total of 500
spins. Find the number of times, f, the arrow landed in your chosen
sector. Record this as the number of wins in the table below.
Calculate the number of losses by subtracting the number of wins from
500.
Change
the number of spins to 500 and click Go. There are now a total of
1000 spins. Find the number of times, f, the arrow landed in your
chosen sector. Record this as the number of wins in the table below.
Calculate the number of losses by subtracting the number of wins from
1000.
Number of
plays
Win
Lose
100
500
1000
Open
your spreadsheet and use the second row of tables in the Simulations
tab to calculate the game owner’s profits from the simulation.
Notice that cells for the outcomes are already populated.
Use
the values from your table in Step 16 for the frequencies of the
outcomes. Type the frequencies in cells B14 and C14, F14 and G14, and
J14 and K14.
The
profits for the simulations will appear below the tables in cells
B16, F16, and J16. Note:
There are formulas in cells B16, F16, and J16. Do not type over them.
Open
your presentation. On slide 7, type in the information about your
simulations and compare them to your predictions.
Project Reflection
Join
the online session set up for you and your classmates.
Write a
response to any of the following.
Would
you be more likely to play a game with a greater chance of winning a
small prize amount or a game with a lesser chance of winning a large
prize amount? Explain.
Knowing
that games of chance are designed for the customers to lose, on
average, would you save your money and never play these types of
games? Why or why not?
What
do you think about consumers buying short-term warranties for
brand-new items? Would you be likely to buy one? Explain.
Comment
on at least one other student’s post.
Alternate
Reflection Assignment
If your
teacher excuses you from the online discussion, then add a slide
(slide 8) to the end of your presentation. On the slide, explain
whether, if given the opportunity in the real world, you would play
either of the two games you created, or if you would save your money
and walk away. Also, if you had to choose between the two games,
which one would you play and why?
Submission
Confirm
that your presentation contains all your work:
Prize
information for each spinner game
Facts,
probability distribution tables, expected values, and expected value
explanations for each spinner game
Predicted
profits after 100, 500, and 1000 plays of each game
Simulation
results (frequency distribution tables and profits) for each game
with accompanying discussion
Alternate
reflection assignment slide (ONLY if you did not participate in the
online discussion)