Carnivale Royale

Here we go...time to make our own game.  At this point you should have done some thinking about your game and now be ready to start finalizing your design, testing your game, and building it.  We have three days to do this.  Here is what you will need:

• INSTRUCTIONS
• PLANNING/REPORTING PAGE - make your own copy and put it in your math shared folder
• RUBRIC

Remember to look at some of the examples from the previous posting.

Here is a brief timeline that you should use for your planning purposes

BLOCK #1 (May 25)

• Get partners
• Look over project documents (above)
• Decide on theme
• Decide on game mechanics
• Determine Theoretical Probability of Winning
• Start Designing Poster

BLOCK #2 (May 27)

• Determine Payout
• Determine Expected Profit
• Simulate Your Game (physical or digital)
• Start Reflecting on Theo vs. Exp
• Start Building Game
• Finish Designing Poster

BLOCK #3 (May 29)

• Bring Poster
• Finish Theo vs. Exp reflection
• Finish Building Game

If you have any questions, ask them via this blog post so that there is a running record of them for others to look at.

Final Reflection and Game Planning

Yahoo...you just finished your final formal summative assessment.  All that is left is to design and build your carnival game.

Task #1: End of Year Reflection

After each unit, you have completed a Learning Behaviour Reflection.  Now I would like you to reflect on your entire year and think about the level of responsibility, organization, collaboration, and reflection that you have demonstrated as a math learner. Complete the survey below:



Task #2: Start Thinking About Your Game

Next class, we are going to start building our games. Before that time, you should start thinking about some ideas.  Remember that you are going to be with a partner so you will need to come up with a compromise.

Here are some things to consider:

• Think about what game elements you want to use - coins, dice, spinners, cards, or marbles.
• Your game should have two different actions to it. For example, you might flip a coin and spin a spinner OR you might pick 2 marbles from the same bag of marbles.
• You should have a cool name and/or theme for your game.

Check out these examples of games that have met expectations and have been exemplary to give you some ideas of what students have done in the past:

Advanced Sample Spaces

Focus Questions:

• How can we analyze compound events in a more efficient way?
• What effect does replacement have on probability

Do Now:

To win this game, you must pick a green marble out of each bucket.  What is the probability of winning this game? Use a sample space to show your work.

Part 1: A Question of Replacement

In this part of the lesson, we will explore what effect replacing the first block chosen from a bag has on the probability of getting a matching pair of red blocks.  Here is what you will need:

• A bag with four blocks - 2 RED, 1 BLUE, and 1 YELLOW

Game #1:

• Pick 1 block from the bag, put it back in the bag, and then draw a second block.
• If both blocks are RED - you win.
• Repeat this 20 times and record how many times you win.

Game #2:

• Pick 1 block from the bag, do NOT put it back in the bag, and then draw a second block.
• If both blocks are RED - you win.
• Repeat this 20 times and record how many times you win.

Record your results in this form.

Part 2: Advanced Sample Spaces

In this part of the lesson, we will look at how we can use a more advanced form of tables and tree diagrams to help us analyze a greater variety of events with more efficiency.  Here is what you will need to do:

• Create a SAMPLE SPACE to show all of the outcomes for both experiment #1 and experiment #2.  Be careful with experiment #2 - it is tricky.

NOTE TAKING - What we want to do is be able to use a more efficient version of our sample spaces that focuses on the relative frequency of each different type of outcome as opposed to representing each "equally likely" outcome.  We will try some of these together as a class.  Here is an example of a more advanced "table" and a more advanced "tree diagram":

Part 3: Making Money

In this part of the money we will begin to take a look at how to decide whether a game will make money at a carnival. We will continue to explore this next class.

Here is another version of making purple. Do you expect the school to make money playing this game? Justify your answer.

Here is what you MUST do before next class:

• ACE (1-4, 8)

3.1 Designing Another Spinner

Focus Question:
How can we use a probability simulation to make predictions?

Part 1: Looking At Spinners

Part 2: Analyzing a Spinner

Kalvin decides to use the spinner shown below:

1. What is the theoretical probability that the spinner will land on each time?
2. Based on the theoretical probabilities, if Kalvin spins the spinner 64 times, about how many times can he expect to go to bed at each time? Explain. Why do you think I chose 64 times?

Part 3: Testing the Spinner

1. Go to the following website: Spinner Site (you will probably need to use Firefox or Safari)
2. Click on "Change Spinner"
3. Design your spinner.
4. What was the experimental probability that the spinner landed on each time?
5. How many times did you "spin" the spinner? How did you decide that you had enough trials?
6. How do your experimental results compare to your theoretical probabilities?

Part 4: Designing a New Spinner

Pretend that you are Kalvin's father.  Design a new spinner where it is "most likely" that Kalvin will go to bed at 9:00. Your spinner must have at least three different times and four different sections.

1. Test your spinner to be sure that it meets the criteria.
2. Take a screen shot and post it on your blog along with the theoretical probability of Kalvin going to bed at each time.

Scratching Spots:

• How might we design a simulation to test the probability of winning this contest?
• Try to use one of the probability tools to design a simulation for this situation. Be prepared to share your idea with others.

1. Based on your simulation, what is the experimental probability of winning this game?
2. Build a sample space to try and determine the theoretical probability of winning this game?
3. Is it worth it to spend $1000 at Tawanda's Toys to try and win video games?  Explain.

Homework:

• Design a Spinner Challenge Task
• ACE (13,14)
  
  
• Complete these Khan Academy activities:
  
  Probability Space
  Probability 1

Analyzing Compound Events

Focus Questions:

• How can you decide if a game is fair or not?
• How can we determine the theoretical probability of a compound event?

New Vocabulary:

• Fair Game - a game where the winning and losing are "equally likely"
• Sample Space - a list of all of the possible outcomes for an event.
• Tree Diagram - One type of "sample space" that is useful for events that have more than two parts.
• Compound Event - An event that has two or more parts or actions

Part 1: The Coin Game

Here are the rules of this game:

• You will toss three coins.
• If all three of the coins match, you get a point (and some money).
• If all three of the coins do NOT match, I get a point.
• Everybody gets one turn.
• At the end, the team (students or teacher) with the most points wins.

Part 2: Analzying the Game

1. What is the "experimental probability" of having all three coins match?
2. How many outcomes are there in this game?
3. Draw a sample space to determine all of the outcomes. (which type of sample space should you draw?)
4. Is this a "fair game"? Explain why or why not.

Part 3: The Bonus Prize

You are a contestant on Gee Whiz Everybody Wins and have made it to the final "Bonus Round".  In the Bonus Round you get to choose one of two games to play.

Game #1

• How to Play - Choose a block from Bag #1 THEN Choose from Bag #2
• How to Win - If you correctly predict the color of block that you will choose from each bag, you win.

Game #2

• How to Play - Choose a block from Bag #1 AND Bag #2 at the same time.
• How to Win - If you correctly predict the color combination that you will choose, you win.

Which game should you play?  Justify your decision with experimental and theoretical probabilities.

Part 4: Playing The Game

Task A:

• Run each experiment 18 times.  Record the results in your table.  Please remember to treat the bags kindly as they need to be used in multiple classes.
• After you have completed your experiment, fill out the forms below to contribute to class data.
• Game #1
• Game #2
• Here are the results from our class data: 

Part 5: Analyzing the Experiment

Answer the following questions in your squarebook:

1. What is the "experimental probability" of choosing each outcome for Game #1? Game #2?
2. What is the "theoretical probability" of choosing each outcome for Game #1? Game #2?
3. Are all of the outcomes "equally likely" for Game #1? Game #2?
4. How do the "experimental probabilities" and the"theoretical probabilities" compare for Game #1? Game #2?
5. Which Game should you choose to play? What should you predict if you play this game?

By the end of this lesson, you should be able to do the following:

• Determine whether a game is "fair".
• Describe how a "compound event" is different from a "simple event"
• Determine the "sample space" for a compound event using a probability tool such as a tree diagram or table

Homework:

1. ACE (9,11,12) (26) (*38)
2. Mid-Unit Summative on Investigations 1 and 2 next class.

Battle of the Sums

Focus Questions:

What does it mean for a game to be “fair”?

How can we determine whether a game is in fact “fair”

Part 1: Battle of the Sums (30 min)

For this lesson we are going to be playing a couple of different games and then analyzing the games.  The first game that we are going to play is called “Battle of the Sums”

After the game is played, make a tally of how many times Player A won vs Player B. Do you think that this is a "Fair Game"?

Part 2: Rolling Dice

For this part of the lesson, we are going to explore the "relative frequency" for each sum when we roll two dice. You will need to make the following table in your squarebook.

	2	3	4	5	6	7	8	9	10	11	12
Tally
Total

Now, roll a pair of dice 36 times and keep track of how many times each sum is rolled. record this in the table.

When you are finished, add your data to this form

Check out the results here:

Part 3: Redesign the Game. (10 min)

Have students propose a more “fair” version of the game they just played.  There are a lot of ways to do it.  Some will try to say things like (roll only one die, ignore sums of 7 etc.)  Tell students that they challenge is to assign EVERY possible sum to one of the players.

Part 4: Sample Spaces. (10 min)
Watch the video below on "sample spaces". This will be a major focus of what we do next class as a way to "represent" probability.

Homework:

• Students may need to finish the game at home.
• Give students the “Sample Spaces” handout and tell them to watch the video at home.

Choosing Marbles

Focus Question: 

How do we determine the theoretical probability of some slightly more complex situations.

New Vocabulary:

• AND - All conditions described must be met.
• OR - Only one of the conditions described need to be met.
• NOT - The conditions listed must NOT occur.

Part 1: More Kalvin

For this part of the lesson you are going to do a quick formative assessment to see how well you understand the main focus questions from last week's lessons on probability.

You will do the assessment independently and can use calculators if you think that you need them.

Part 2: Simple Events

In this part of the lesson you will watch a video describing some of the basics around finding the theoretical probability of an outcome for a given event.  We have already talked about this a little bit, so this should be mostly a reinforcement of prior knowledge.

When you have finished watching the video, make sure that you complete the "On Your Own" questions.  Show your teacher when you have finished the questions.

Part 3: Choosing Marbles - Determining Theoretical Probabilities

The main part of this lesson is for you to now practice applying the concept of theoretical probability.  This is also in your textbook on page 30.

By the end of this problem you should be able to do the following:

• Determine the theoretical probability for a series of outcomes that contain the "OR", "AND", and "NOT" conditions.
• Develop a probability situation based on theoretical probabilities.

Homework:

1. ACE (p. 36) (6-7) (18-25)