Ordered Fractions is a game that requires a thorough understanding of what a fraction means and represents. In order to win this game consistently, students will need to understand how to quickly and fluidly change their fractions to other equivalent fractions with different denominators. For kids who are just beginning their work with fractions you may want to limit the numbers for the denominators of the fractions. Keep it simple to start with so that you can diagnose exactly how much they understand about fractions. You may even want to begin with the simplest possibility, such as using a specific denominator that you give them and having them roll just for the numerator. This is a very challenging and exciting game but they'll get frustrated if their skill level can't keep pace with other players.
Once they've mastered the game with just one denominator, you may want them to use 6-sided dies for both the numerator and denominator. They'll need plenty of scratch paper to figure out: Which is larger 2/3 or 5/6? (just one denominator change); Which is larger 4/6 or 1/3? (just one denominator change); Which is larger 3/5 or 2/3? (two denominator changes). Once you see that they've become proficient at finding equivalent fractions and ordering them using the same denominators, you can move on to a 12-sided die for the numerators and a 6-sided die for the denominators. Don't rush the process. This is a fascinating game that will give them an incredibly thorough understanding of fractional equivalents. After they've mastered the denominators 1-6, it's time to step up the challenge and have them work with 12-sided dies for both the numerators and denominators.
In addition to the fluidity with which players need to go back and forth among equivalent fractions, there's an enormous amount of strategy needed for them to figure out where they should best place the numbers they are presented with when they roll the dies. There are lots of opportunities for them to see patterns within different groups of fractions, such as fractions that have even numbers as denominators or fractions whose denominators are multiples of each other.
After kids have played this game for an hour or more, it's a great idea to record the winning strings of fractions on a blackboard or somewhere where kids can look at them and review them.
Common Core Mathematical Standards
3.NF Develop understanding of fractions as numbers.
4.NF.1 Extend understanding of fraction equivalence and ordering.
4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols, >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
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