Support Materials --

Math for All-Plus

Is It Fair?

During this math program you will:
help your children investigate whether a game is "fair" or "unfair"
help your children understand that a winning strategy involves making informed decisions
have fun with your children as you practice "mathematical thinking" by playing games
Things to ask your children: Is a good strategy as important or more important than chance? Which do you like to play more, games that involve strategy or games that involve chance? Does winning depend on strategy or chance?

Activity #1
Fair or Unfair Flip?
Materials:
One coin for flipping
30 pennies or chips for players
Paper and pencil

In this game each player will need fifteen pennies or chips. Decide who will be "heads" and who will be "tails." Flip the coin; if it shows heads, the player who chose heads places a penny on the table; if the coin shows tails, the other player places a penny on the table. The first player to place all of his/her pennies or chips on the table is the winner. Play this game three or four times, keeping track of who wins each time.
In mathematics, a game is "fair" if all players have an equal chance of winning. in this game, did the same person win each time? Did each player win about the same number of times? Do you think this game is fair?

Additional Activities
Choose a game you enjoy and that you have at home, such as checkers, monopoly, dominoes, etc. Play the game four or five times, keeping track of who wins. Does winning depend on strategy or chance? Which do you like more, games that involve strategy or games that involve chance? Why?

Activity #2
To Reduce or Not To Reduce?
Materials:
2 random number generators (dice)
Paper
Pencil
Fraction calculator (optional)

The object of this game is to recognize fractions that can be simplified (reduced). Decide which player will be "A" and which will be "B." Roll two random number generators (dice) at the same time. Use the smaller number as the numerator of the fraction and larger as the denominator. When both numbers are equal, the numerator and denominator will be the same. If the fraction can be simplified, i.e., 3/3 = 1, 2/6 = 1/3, player A scores 1 point; otherwise player B scores 1 point. Play 12 times, taking turns tossing the dice. The winner is the player with the most points.
Does each player have an equal chance of winning. Is it better to be player A or player B? Repeat the game 3 or 4 times, keeping track of who wins. Do you think this is a fair game?
Additional Activities:
This game involves strategy! To start the game, place 20 counters - chips, coins or toothpicks - on the table. Decide who will go first. Each player takes turns removing either one or two objects. The player who removes the last object is the winner. Play this game three more times, keeping track of who wins. Do you think this is a fair game? What strategy, if any, is used in playing this game? Play the game again, only this time the player who picks up the last piece loses. Is this version of the game fair? Why or why not? Is your stategy different? Is there a way for the starting player to always win?

Activity #3
Spin to Win!
Materials:
Two pencils
One large Paper clip
Paper

You will be playing this game with a spinner. To make your own spinner, you need a large paper clip, two pencils and paper. Place a pencil point inside at one end of a large paper clip; keep this pencil stationary. This will be the middle point of your spinner. Place another pencil tip at the other end of the paper clip and rotate it around, keeping the paper clip pulled taut so that you draw a circle. Draw a line across the circle through the center. In mathematics we call this line a diameter. Draw another line from the center to the edge of the circle so it divides one half equally. In mathematics a line from the center to the edge of a circle is called a radius.
Keeping the spinner in place with pencil #1, players A and B take turns spinning the paper clip. If the spinner lands on 3, the player gets 3 points, on 2 it is 2 points and on 1 it is 1 point. Take turns spinning ten times, keeping track of each player's points. Does this game seem fair? Play the game several more times. Did one player win more often? Is this a fair game?