Fraction Game

The object of the game is to get all of the markers to the right side of the game board, using as few cards as possible.

Click on the pile to turn over one card. This is your target fraction. Move the markers so that the sum of your moves is a fraction that is less than or equal to the target fraction.

For example, if the first card turned over is 4/5, you could move the fifths marker to 3/5 and the tenths marker to 2/10, because 3/5 + 2/10 = 3/5 + 1/5 = 4/5. These moves are shown below.

In addition, any of the following moves would also be acceptable:

• The fifths marker to 4/5.
• The tenths marker to 8/10, because 8/10 = 4/5.
• The thirds marker to 2/3, because 2/3 < 4/5.
• The fifths marker to 1/5 and the tenths marker to 6/10, because 1/5 + 6/10 = 1/5 + 3/5 = 4/5.
• The halves marker to 1/2, the sixths marker to 1/6, and the eighths marker to 1/8, because 1/2 + 1/6 + 1/8 = 12/24 + 4/24 + 3/24 = 19/24 < 4/5.

There are many other moves that would also be acceptable, as long as the sum of the moves is less than or equal to 4/5.

When you have finished your move(s), click on the pile to get a new card.

The Sound On button can be used to add some excitement!

Play the game several times.

1. Which are the best cards to get at the beginning of the game? That is, which ones are most helpful when you first start? What cards are better to get later in the game?
2. Should you move the markers for fractions with larger or smaller denominators first?
3. The deck contains every possible card with a denominator of 2, 3, 4, 5, 6, 8, or 10. Knowing this, what is the fewest number of cards needed to complete the game? Justify your answer.