Family Mathematics Problem Solving
Sponsored by
The Somerville Mathematics Fund

The Family Mathematics problems are written for adults and children to work on together. They are not meant as another homework, instead it is an opportunity for you to work together to solve a mathematical problem. This Month’s Family Mathematics Problems are games for you to play and analyze. People play games all the time, not all games are fair, here are two games for you to decide whether they are fair or not. We hope you will enjoy playing together.

The Somerville Mathematics Fund was founded in 2000 to celebrate and encourage mathematics achievement in the city of Somerville. We offer scholarships to students and grants to teachers.
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From March 2002    
Grades 4, 5, and 6
Grades 7 and 8


Family Mathematics Problem Solving: Grades 4, 5, and 6
It’s a different game of “War”
Play the game:
This is a game for two players.
For this activity you need a deck of cards with all the jacks, queens, and kings removed. This is a game for two players, A and B.
Shuffle the deck of cards and deal all the cards equally to the two players. The cards should remain face down in two stacks.
Each player turns over the top card.
Find the product of the two numbers showing (count the ace as “1”).
If the product is even, A gets the cards.
If the product is odd, B gets the cards.
Place the cards at the bottom of the player’s stack and continue playing until one player has all of the cards.
Talk about the game:
Who won the game?
If you played again, do you think the same person will win again? Why or why not?
Would you rather be A or B?
Is this a fair game (every player has an equal chance of winning)? Why or why not?
If it isn’t fair, how would you change the game so it will be fair for each player?

 
Family Mathematics Problem Solving: Grades 7 and 8

One, Two, Three Show!
Play the game:
This is a game for three people.
The hand motions are similar to the game “rock, paper, scissors.”
Together, everyone counts and moves one hand (closed fist) up and down to “One, Two, Three” and then says “show!”
On the word “Show” each person simultaneously holds out 1, 2, or 3 fingers.
Person A gets 1 point if no one shows the same number of fingers.
Person B gets 1 point if two people show the same number of fingers.
Person C gets 1 point if all three people show the same number of fingers.
The person who has the most points after 27 rounds, wins the game.
Talk about the game:
Who won the game?
If you played again, do you think the same person will win again? Why or why not?
Would you rather be A , B, or C?
Is this a fair game (every player has an equal chance of winning)? Why or why not?
If it isn’t fair, how could you change the game so it will be fair for each
 
Other Problem Solving Sources:
http://mathforum.org/pow/
http://www.figurethis.org/index40.htm
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