Games of chance are a fun way to learn arithmetic. Here are four games that I use to teach properties of factors, multiples, greatest common factors (GCFs), and least common multiples (LCMs). In each case, play the game a few times, and try to work with the other players to determine the best winning strategies. I want to emphasize this last point. If you are going to take the time to play these games, it's important to reflect on the mathematics underlying them. Understanding why the winning strategies are what they are will shed a lot of light on the nature of factors and multiples and the relationship between these two ideas.
Each game requires dice, pencil, and paper. If you don't have the required dice on hand, you could buy a 7-die standard set, and in the mean time, you can use a cut deck of playing cards, or even put numbers on scraps of paper and pull them from a hat.
Chose numbers from the factors of the numbers 1 through 12.
Repeats allowed.
For example, a game board can look like this:
1 1 1 2
2 2 3 3
4 5 6 7
8 9 11 12
Play: Roll 1D12 (in other words, roll one 12-sided die or pick a card from Ace to Queen). All players play the same roll on every round. Each player crosses out all of the factors of the roll that they have on their board. For example, if the roll is 9, each player crosses out one of each of 1, 3, and 9 on their board. In the board above, the player would cross out one 1 and one 3.
Goal: First player to cross out all numbers on their board wins.
Question: Which numbers come up most often?
Variation: Play with D20.
Choose number from the multiples of the numbers 1 through 6.
Repeats allowed.
For example, a game board can look like this:
1 2 3 4
5 6 6 6
10 12 14 15
16 25 30 30
Play: Roll 1D6.
Each player crosses out all of the multiples of the roll that they have on their board. For example, if the roll is 3, each player crosses out one of each multiple of 3 on their board. In the board above, the player would cross out 3, 6, 9, 12, 15, and 30.
Goal: First player to cross out all numbers on their board wins.
Question: How can you win the game in one roll?
Variation: Play with D10.
The numbers are chosen from the number of factors of the numbers from 1 through 20.
Repeats allowed.
For example, a game board can look like this:
1 2 2 3 5
Play: Roll D20 to make a number from 1 to 20.
Count the number of factors of that number. Each player crosses out that number if they it have on their board. For example, if the roll is 25, then 25 has 3 factors (1, 5, and 25). So, each player crosses out the number 3 on their board, if they have it. If the roll is 29, then each player can cross out a 2 because 29 is prime, and prime numbers have exactly 2 factors.
Goal: First player to cross out all numbers on their board wins.
Questions: How many rolls have 1 factor? What are all of the roles have an odd number of factors? How many rolls have 5 or more factors?
Variation: Play with 2D10 to make a number from 0 to 99. 0 = 0, 00 = 00
Find GCD(x,y) and LCM(x,y).
Multiply them to get your score.
Players alternate turns.
Bonus points: If GCD times LCM equals x times y, then take a bonus 99 points.
For example, if the rolls are 3 and 4. then GCD = 1 and LCM = 12. 1 times 12 equals 12, so the score is 12. Also 1 times 12 equals 3 times 4. So this roll gets a 99 bonus for a total of 111 points.
Goal: First player to 1000 points wins.
Question: Which rolls give the bonus points?
Variation: Play with 2D20.
Each game requires dice, pencil, and paper. If you don't have the required dice on hand, you could buy a 7-die standard set, and in the mean time, you can use a cut deck of playing cards, or even put numbers on scraps of paper and pull them from a hat.
1. Zonk Game:
Set up: Each player makes their own board of 16 numbers.Chose numbers from the factors of the numbers 1 through 12.
Repeats allowed.
For example, a game board can look like this:
1 1 1 2
2 2 3 3
4 5 6 7
8 9 11 12
Play: Roll 1D12 (in other words, roll one 12-sided die or pick a card from Ace to Queen). All players play the same roll on every round. Each player crosses out all of the factors of the roll that they have on their board. For example, if the roll is 9, each player crosses out one of each of 1, 3, and 9 on their board. In the board above, the player would cross out one 1 and one 3.
Goal: First player to cross out all numbers on their board wins.
Question: Which numbers come up most often?
Variation: Play with D20.
2. Zink Game:
Set up: Each player makes their own board of 16 numbers.Choose number from the multiples of the numbers 1 through 6.
Repeats allowed.
For example, a game board can look like this:
1 2 3 4
5 6 6 6
10 12 14 15
16 25 30 30
Play: Roll 1D6.
Each player crosses out all of the multiples of the roll that they have on their board. For example, if the roll is 3, each player crosses out one of each multiple of 3 on their board. In the board above, the player would cross out 3, 6, 9, 12, 15, and 30.
Goal: First player to cross out all numbers on their board wins.
Question: How can you win the game in one roll?
Variation: Play with D10.
3. Zonker Game:
Set up: Each player makes their own board of 5 numbers.The numbers are chosen from the number of factors of the numbers from 1 through 20.
Repeats allowed.
For example, a game board can look like this:
1 2 2 3 5
Play: Roll D20 to make a number from 1 to 20.
Count the number of factors of that number. Each player crosses out that number if they it have on their board. For example, if the roll is 25, then 25 has 3 factors (1, 5, and 25). So, each player crosses out the number 3 on their board, if they have it. If the roll is 29, then each player can cross out a 2 because 29 is prime, and prime numbers have exactly 2 factors.
Goal: First player to cross out all numbers on their board wins.
Questions: How many rolls have 1 factor? What are all of the roles have an odd number of factors? How many rolls have 5 or more factors?
Variation: Play with 2D10 to make a number from 0 to 99. 0 = 0, 00 = 00
4. GCD Times LCM Game:
Play: Roll 2D12 to get numbers x and y.Find GCD(x,y) and LCM(x,y).
Multiply them to get your score.
Players alternate turns.
Bonus points: If GCD times LCM equals x times y, then take a bonus 99 points.
For example, if the rolls are 3 and 4. then GCD = 1 and LCM = 12. 1 times 12 equals 12, so the score is 12. Also 1 times 12 equals 3 times 4. So this roll gets a 99 bonus for a total of 111 points.
Goal: First player to 1000 points wins.
Question: Which rolls give the bonus points?
Variation: Play with 2D20.
