Comparing Fractions

Students enjoy this game which we play in a group of three or four. While playing, I observed that a number of students were able to move from the algorithm to the conceptual in the process. I teach students to compare fractions by multiplying on the diagonal. In this new district, they use the shoelace method, which is a take off on the diagonal method. As kids played the game, I saw them using the algorithm as well as visualizing and analyzing. They were able to acquire a familiarity with the fractions and fractions concepts that sometimes takes a lot longer to get.

Each student has a small white board, marker, and a pair of dice. The dice can be shared with the group if necessary, but it works better if everyone has their own set. Players roll the dice and write their two numbers as a fraction with the smaller number rolled as the numerator and the larger number rolled as the denominator. The fraction is then written in lowest terms. Students then look at everyone's fraction and announce by turn if they want to keep their fraction or roll again. Those who wish to, roll the dice a second time and write their new fractin based on their second roll. After that, the group works together to arrange the fractions from least to greatest. The person with the greatest fraction gets three points(if there are four players they get four points) the next fraction gets one less point on down to the lowest fraction which gets one point. Students keep track of their own score. The game is over when the time period is up or when someone reaches 21 points.

Variations on this game include:
giving the highest points for the smallest fraction
putting the larger number as the numerator requiring the students to change the improper fraction to a mixed number