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.