Design two spinner games. Math homework help
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.
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
1. Download the project
template and rename the file as GamePresentation_YourName.
This file will become your presentation.
2. Download the spreadsheet template and rename the file as Spreadsheet_YourName. You will use this file to help
you create your presentation.
Project Research
1. 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.
2. 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.
3. Open your presentation. On slide 1, type your name. On slide 2,
complete the table with prize information.
Project Writing
1. 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.
2. 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.
3. 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.
4. 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.
5. Open your presentation. On slide 3, type in the information about
your first spinner game.
6. 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.
7. 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.
8. 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.
9. Open your presentation. On slide 4, type in the information
about your second spinner game.
10. Complete slide 5 by predicting how much money the game owner,
will make after each spinner game is played 100, 500, and 1000 times.
11. 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.
12. 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
13. 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.
14. Open your presentation. On slide 6, type in the information
about your simulations and compare them to your predictions.
15. 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.
16. 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
17. 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.
18. Open your presentation. On slide 7, type in the information
about your simulations and compare them to your predictions.
Project Reflection
1. Join the online session set up for you and your classmates.
2. 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.
3. 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)
Submit your project to your teacher.I ADDED TWO REAL EXAMPLES YOU CAN JUST PARAPHRASE THEMprm_a_06_project_template.pptprm_a_06_sample_project.pptprm_a_06_spreadhseet_template.xlsproject_3_n.pptxproject3.pptx