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

Problem Statement: Given the following right triangle, find cosθ, sinθ, tanθ, secθ, cscθ, and cotθ. Do not approximate: Find exact answers. Show all of your work and explain steps as necessary. Prompt: Use the provided template to solve the trigonometric functions problem above, and illustrate your process by addressing each of the following elements: I. Establish a context for the problem by explaining in your own words the course principles that apply: What are the relationships between theta and the lengths of the sides of the triangle? Be sure to correctly use the appropriate terminology in your explanation. II. Apply the mathematical process to solve the problem: A. Use the Pythagorean theorem to find the third side of the triangle. B. Write out the six trigonometric functions related to theta in exact form. III. Clearly state the answer using appropriate precalculus notations.Rubric and Milestone Template Attached