The games require students to roll a die to select fraction blocks to add or subtract. The game board consists of a 'one whole' piece on which they must build new layers to win. The first student to build or subtract 5 complete layers of one whole wins (the rules can always be changed for smaller amounts of time). Sometimes I set a timer for ten minutes and say, "...whoever gets the furthest when the timer goes off, is the winner!" The process of selecting pieces to add or subtract helps kids to see the fractions that are equivalent, or compatible. By compatible, I mean fractions that will actually work together to make exactly one whole. Fractions like 5th and halves, won't work.
Then, you can expand the exercise to ask the question, "If fifths and halves cannot make exactly one whole together, can they ever be combined to make a whole number? How many fifths and halves would you need, and what whole numbers are possible to make?"
Use fraction blocks to work out the problem. For example:
1/2 + 2/5 ≠ 1
1/2 + 3/5 ≠ 1
2/2 + 5/5 = 2 *** "Can we make 3 wholes using fifths and halves?" etc.
Have the kids look for patterns. Will the whole number always be even, or is it possible to make an odd number? This kind of exercise can also give 4th and 5th graders a foundation for operations like adding fractions with uncommon denominators, or multiplying fractions by whole numbers.
