# The Forty Frogs Game

## Learn to Find Fractions of Sets!

Note: If teachers suspect that some students may 'get stuck' while playing the Forty Frogs Game, they should consider allowing students to play the game in pairs.

Why Should Students Learn This?

In elementary school, students are expected to learn the most fundamental of math concepts. Since these fundamentals will act as the foundation upon which all future math learning occurs, it is important that students gain a solid conceptual understanding—and not simply a formulaic understanding—of basic math topics. Therefore, although much advanced-level math relies almost entirely on formulas, one should not underestimate the importance of conceptualizing early mathematical learning.

Early fraction instruction typically focuses on fractions of a whole (fractions of the number 1). However, as early as the fourth grade, many fraction problems (if not most) deal with fractions of numbers greater than 1. Therefore, students’ ability to extend their understanding of fractions to numbers greater than 1 is essential toward their development of a comprehensive understanding of fractions in general.

Generally, visualizing a concept is one of the best ways to understand it conceptually. Since it is arguably easier to visualize fractions of a whole than to visualize fractions of a set, The Forty Frogs Game attempts to merge the visualization of the two. The entire game is based on a 8 x 5 array of 40 objects. By keeping this array constant, students are able to break apart the set in a manner similar to breaking apart a solid whole. Thus, by building upon students’ previous understanding of fractions, the game overcomes the limitations of the more common method of using loose objects to teach about fractions of a set.

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