Factor Game: Aliquot is a strategy game involving factors, subtraction, number sense and strategy. It is an excellent game for promoting mathematical thinking.
Game In a Nutshell:
The first question when starting this game is always "What is an aliquot?" It's certainly an unusual word!
An 'aliquot part' is any whole factor of a number other than itself.
e.g. The aliquot parts of 28 would be 14, 7, 4, 2 & 1. However 28 is not an aliquot part because a number cannot be its own aliquot part.
Player 1 chooses a number from the game board that has two or more factors, then places a counter on it. Players then take turns moving the counter towards zero by the aliquot parts of the number chosen and then the number landed on with each move.
Teacher Tip: It's not essential that students know the word "aliquot," though it's of course a really cool word! There are neat words for most everything in Math, like the line between the numerator and denominator (vinculum) or the proper name for the symbol for Division (obelus). While they aren't super important, these terms are still nice to know!
What You Need:
1 game counter
1 Aliquot game board
How to Play:
1. Player 1 chooses a number on the board with multiple factors e.g. 32.
2. Player 1 places the counter on the number 32 then states the number's aliquot parts i.e.16, 2, 4, 8 & 1
4. Player 2 now chooses one of the aliquot parts and moves the counter towards zero by that many spaces e.g. If Player 2 chooses 4 they move the counter from 32 to 28.
5. Play continues in this fashion until one of the players is forced to land on 1.
- Define and investigate factors.
- Explore the factors of given numbers
- Explore factor trees.
- Investigate 'factor rainbows'.
- Ask students to explain how they arrive at the factors for a given number.
- Explore strategies for working out a number's factors.
During the Game:
- Observe how students work out factors to inform your future lessons and tutorial groups.
- Encourage students to devise strategies to help them do well in the game.
How to Win:
A player wins when all other players are forced to land on the number one.
Possible Reflection Questions:
- What did you learn about factors?
- How does the game 'Aliquot' help you learn about factors?
- What questions do you still have about factors?
- On a scale from 1 to 10, how would you rate your ability to find the factors of a number? Explain your reasoning.
When you land on the number 1, the game is over (i.e. ONE has no aliquot parts). Why do you think this is the case given you've been able to use one throughout the game?
Hint 1: The answer has something to do with the definition of an aliquot.
Hint 2: "Itself" is one. How could this fact help you understand why one is the game ender?
Included in this Download:
1 Aliquot Game Board
1 Powerpoint File so you can discuss the game.