Activity Icon - Frogs and Toads.png

Frogs & Toads

How it works

To play Frogs and Toads with 2 frogs and 2 toads, you need a 1 x 5 game board. You start by placing the frogs in the two squares on the left and the toads in the two squares on the right, with an empty square in the middle.

Frogs and toads can slide into empty squares, or they can jump over exactly one animal of the other species and into an empty square.

The goal is to reverse the positions of the frogs and the toads, so the frogs are on the right and the toads are on the left.

After students figure out how to reverse the positions of the frogs and toads when there are only 2 frogs and 2 toads, they then explore whether it is possible to do this when the frogs and toads aren’t allowed to move backwards, and, if so, how many moves it takes. They then move on to a version with 3 frogs and 3 toads, as well as versions with different numbers of frogs and toads.

Frogs & Toads datasheet
Video example of Frogs & Toads

Why we like this activity:

  • It’s fun! Students enjoy the puzzle and playing with the frogs and toads.

  • It helps to develop algorithmic reasoning.

  • It encourages data recording.

  • It requires students to engage in mathematical habits of mind:

    • Finding and using strategies to solve the game.

    • Making observations / looking for patterns / making and testing predictions / understanding and explaining when trying to figure out which situations lead to an impossible to win state and working backwards to avoid “getting stuck”.

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