Fraction Capture with Cube Dice

After exploring dividing a circle into equal sectors and shading in all equivalent fractions, we are now playing the ultimate fraction game: Fraction Capture.

My objective is to have the children not only know how to shade fraction parts but to choose between the larger and smaller fraction and to split them up into strategic parts. Let’s play.

Player one rolls two dice and makes a fraction with the numbers that come up on the dice. The number on either die can be the numerator and the other die, the denominator. A fraction equal to a whole number is NOT allowed. For example, if a player rolls a 3 and a 6, the fraction cannot be 6/3 because that is a whole number, 2; however, it can be 3/6 which is also 2/4 or 1/2. Other fractions that are not allowed include: 6/2, 4/2, 6/1, 5/1, 4/1, 3/1, and 2/1. Also, if a player rolls doubles like 5/5, that is a whole number but switching the dice do not give you a non-whole number so that player rolls again.

Each player chooses a color. The player who rolls, colors in sections of one or more game board squares to show the fraction rolled on the dice. For example, if a player rolls a 5 and a 6, she can choose 5/6 or 6/5. It will almost always be advantageous to choose the improper fraction, 6/5 (the numerator is greater than the denominator; the fraction has a value greater than one). However, near the end of the game, it may be more beneficial to choose the proper fraction 5/6 (the numerator is less than the denominator; the fraction has a value between 0 and 1) to fill in specific fractions. 

A player captures a square when it has claimed more than one half of the square. The minimum number of fractions to capture a square is 2/2, 2/3, 3/4, 3/5, and 4/6. Do not claim more than the minimum or that would be a wasted move.

So in the example above, choosing 6/5, that player can capture two squares with 3/5 on one and 3/5 on another.

Also, equivalent fractions can be claimed. If a player rolls the best roll on the board, 5/2, it can also do 10/4 or 15/6. Also, it can split up the fraction to 1 + 1 + 1/2 and turn the 1 into any fraction like 5/5 or 4/4. Note that a player must use all of the sections of his fraction or he forfeits a turn. For example, if all of the sections on the 1/6 squares are filled in and he rolls a 1 and a 6, there is nowhere to go so that player forfeits his next turn.

A square is considered blocked when it is filled in 1/2 by each player or, if there are three players, filled in 1/3 by each player so no player can capture more than a half.

The winner is the player that has captured the most squares after time is up or all squares have been captured or blocked. 

Strategically, you should use the 1/6 squares before the 1/5 and the 1/5 before the 1/4 and so on. Why? because after you have captured 1/2, you only need a smaller fraction to capture the square. Consider a player who already has captured 1/2 of the 1/2 square and 3/6 of the 1/6 square. That player has to roll a 1/2 to win on the 1/2 square but only needs to roll a 1/6 to win the 1/6 square.

Also, the best moves on the board in order are as follows: 5/2, 5/3, 6/4 and 3/2, 4/3, 5/4, and finally, 6/5. All other moves are proper fractions with a value of less than one. The worst rolls in order are 1/6, 1/5, 1/4, 1/3 or 2/6, 1/2 or 2/4 or 3/6.