Math Games
by Mike Thompson, 2/2/2013
This winter I volunteered as a teacher in the Washington Alliance for Better Schools program. Working with two other Boeing volunteers, we're leading hour-long, after-school math enrichment classes for 4th Graders at Fernwood Elementary School. Below are some of the fun, math-oriented games that we're using.
Twenty-Four
Remove the Jokers from a deck of playing cards. Deal four cards face-up. Try to reach a total of 24 by combining any/all of the four cards using addition, subtraction, multiplication, and/or division. Aces and face cards have the following values.
- Ace=1
- Jack=11
- Queen=12
- King=13
Below are some sample four-card hands that you might be dealt, followed by solutions.
7,9,K,8: 7 + 9 + 8 = 24
8,2,J,3: 8 x 3 = 24
5,7,A,6: (5 x 6) - (7 - 1) = 24
Target Number
Remove the Jokers, face cards, and 10s from a deck of playing cards. Deal four cards to each player, face-down. Then deal two cards face-up, the first card becoming the tens digit and the second card becoming the ones digit of the target number. The goal is to organize the four cards dealt face-down into a two-digit subtraction problem whose result is as close to the target number as possible.
For example, if the two cards dealt face-up are a 3 followed by a 1, then the target number is 31. If the cards dealt face-down are 4, 9, 3, and 2, they could be combined in many different ways to form two-digit subtraction problems, including the following.
- 94 - 32 = 62
- 49 - 32 = 17
- 49 - 23 = 26
Of these possible arrangements of the four cards, 49 - 23 = 26 yields the result that's closest to 31, the target number, making it the best choice. Since the difference between the result, 26, and the target number, 31, is 5, the player would score 5 points for this hand. The goal is to minimize your score by forming the best two-digit subtraction problem possible with the hand you're dealt.
One Hundred
Starting from zero, using one die, try to get to exactly 100 using addition or multiplication with each roll. If you go over 100, go back to zero and start again. In the sample game shown below, the player rolled the following sequence of numbers: 3, 5, 6, 4, and 4.
0 +3 -- 3 x5 -- 15 +6 -- 21 +4 -- 25 x4 -- 100
It's easy to adjust the rules of this game to suit different purposes. For example, you can allow subtraction and division as well as addition and multiplication. You can allow players to overshoot 100 without having to go back to 0, as long as they can use subtraction and/or division to back up with.
The game within the game is to come up with the strategy that yields the highest probability of reaching 100 in as few rolls as possible. As a tool for providing practice in arithmetic, this game works well for elementary school students. As a tool for evaluating the probabilities for success of different strategies, it could work in an introductory statistics course.