Probability WebQuest

Introduction

"Heads, you go first; tails, I do." "I need to roll a seven to win." "If I
can spin and land on a green slot the jackpot is mine."

How many times have you played a game and hoped to win? What is the probability of winning?
Probability is a part every person's life sooner or later. We might wonder who will be elected class president or student council, or how many people will vote in the next presidential election in the United States. Probability and statistics are used to help predict what is going to happen in these types of events.
Very young children might use probability and statistics to figure out what toy might be pulled out of the toy box next, or what snack will be given to them next (even if they don’t understand the mathematics of it all). Older and wiser students use these methods to figure out things like the statistics of their baseball player. Adults might use these methods to figure out statistics and probability dealing with the stock market or perhaps the lottery.

The Quest
The purpose of this WebQuest is to allow you to experiment with probability and to learn about some outcomes. At the conclusion of the WebQuest you will be able to explain why some choices are better than others.

The Task
In this Webquest, the class will be divided into two-member teams. Each team will follow the Webquest to each web site and complete the task given there. They will answer the Webquest questions in a journal that they keep of their work. When finished each individual from the class will reflect on how the Webquest helped them better understand probability overall.
Use the Internet links provided at each step to answer the basic questions that are listed for each task. These questions should remind you of discussions and activities that we have worked on in class. Consider everything that you have already learned as you work to answer the task-related questions.

The Process
Phase 1 – Examining Probability
INSTRUCTIONS:

1. Visit each of the Websites below and answer the questions from each section.
2. Write your team’s answers to each question on notebook paper. All answers should be carefully and neatly written using complete sentences, and your best spelling, grammar, and punctuation. Use diagrams, graphs, charts, and sample problems as necessary to illustrate your answers. Your team’s answers will need to be turned in when your work on the Webquest is complete.
3. At each website that your team visits, you will find different activities that you can explore in order to help you understand various concepts related to probability. In many of these activities, there are data fields that can be adjusted (or changed). These will probably need to be adjusted several times for you to be able to look at the difference that it makes in the outcomes of each task. Do not hesitate to attempt various different approaches at each site so that you understand exactly what happens with different combinations of data. Remember, with probability, sometimes you need to make many trials in order to see what is actually happening.

Understand Experimental Probability and Theoretical Probability – Spinners and Race Cars (5 activities)

· Understanding Experimental Probability - Choose a spinner to use, click the 'SPIN' and check the results. You can choose from different spinners as well as a number cube to roll.
· Racing Game With One Die – This is a simulated racing game where a car moves depending on which number is rolled on the dice. Every option can be adjusted in this simulation. Make sure you explore thoroughly.
· Racing Game With Two Dice – You can choose a 'lucky player' to move one more step than everyone else during the race. You can choose the number of players and the length of the race.
· Experimental and Theoretical Probability – You will be able to set up your own spinner and also choose how many spins you want to use. You should look at the results and compare between experimental and theoretical probabilities. You can change the size of the spinner and the number of spins.
· Adjustable Spinner Experiment - You can change the size of the sections within the spinner, and this will change the theoretical probability. You can also adjust the number of sections on the spinner as well as the number of spins.

Questions specifically related to understanding experimental probability and theoretical probability:

1. What happens when the arrangement of the spaces on the spinners are changed?
2. What happens when the number of spins change?

3. What happens when the race segments are dropped to two?
4. How does changing the field of which car moves affect the outcomes?
5. What happens when the number of runs is increased?

6. Compare and contrast the experimental and theoretical probabilities when the different fields are changed in different ways.

Understand Independent and Dependent Events – The Monty Hall Paradox

"Would you make a deal to trade up to five hundred dollars in cash for one of
these three doors, knowing behind one of them is $3,254 in cash or valuable
merchandise? Several people may have to make that decision during the next
few
minutes as we bring you the Marketplace of America.... Let's Make a
Deal! And now, here's America's top trader, TV's Big Dealer, Monty
Hall! - Opening Spiel 1963-1969

The well-known Monty Hall probability problem is based on a television show of the 1960's and 1970's called Let's Make a Deal. Show host, Monty Hall would ask a contestant to pick one of three doors. Behind one of the three doors was a large prize. Behind the other two doors were lesser prizes, sometimes a group of goats grazing on fresh hay. Once the contestant picked a door, Monty would open one of the remaining two doors that did not have a prize. Then, he would offer the contestant a chance to switch doors.
To learn about dependent and independent probability, your team will work with two Monty Hall simulation games. Before playing, predict whether or not it is better to switch door selections after one is revealed. Track your results carefully so that you can discuss what happens in your journal.
· Monty Hall Simulation (simple) – You will choose one of three doors behind which is a prize. After you choose, you will be shown what is behind a second door. At this point you have the option to either switch your choice, or stay with your choice. The simulation will keep track of the number of times you win and lose. You should try both switching and staying enough times to determine whether it makes any difference which strategy you choose.
· Monty Hall Game (with explanation) – This version of the game is similar to the first one you played. Work with it in the same way you did the first one. When you have finished, you should look at the explanation given for the outcomes.

Questions specifically related to understanding dependent and independent events in probability:
1. What happens when you stay with your original (first) choice of door?
2. What happens when you choose to switch doors?
3. Does it matter, in terms of winning, whether you stay or switch?
4. How can you explain your results in this activity?

Phase 2 – Real World Applications
Now that you and your partner have completed the explorations from this Webquest, use what you have learned to create a game that demonstrates some of what you understand about probability.
Design a game of probability using either a spinner or dice. Be sure to include the following elements:
· Title of your game
· Game components (parts and pieces)
· Directions so others can play
· List of rules
· Explanation of why your game is fair
Be prepared to share your game with the class.

Phase 3 – Personal Reflection
You have finished your WebQuest. You worked with a partner throughout the project, but you, as an individual learned what you learned. So, take time now to consider what it is that you gained as you worked on this project. Write your reflection on notebook paper using your best handwriting, spelling, and grammar.

• Discuss the specifics of the math.
• Did you understand anything differently or better?
• Did you enjoy the project?
• Did you feel you contributed to your team in particular ways?
• How would you change this project?
• What did you like?
• What did you not like?
• What was the most challenging part of this work for you?
• What would you tell someone else about this project?
  

Evaluation
Your work will be graded using the following rubric. All categories may earn up to ten points.

· Explanation (answers to questions are complete with detailed explanations)
· Use Of Illustrations (illustrations such as diagrams, graphs, charts, and tables are used to help describe and clarify explanations and answer questions)
· Mechanics (work is mathematically accurate and grammatically correct)
· Demonstrated Knowledge (shows complete understanding of the mathematical ideas, concepts, processes, and questions)
· Requirements (fulfills all the requirements of this assignment)

Conclusion
Did you complete all the activities, answer all the questions, and meet all the requirements for your game? Congratulations! You and your partner should understand probability much better now.