Frogs and Toads

by Chris

When I was in the Upper 6th at my secondary school we ran a program for Year 6 students from schools in the surrounding area.

One of the sessions focussed on sequences of number i.e. the Fibonacci numbers, the square numbers etc.

The kids would be given sets of 4 numbers and then try and work out the next two numbers in the series.

After they had done this for a while they were told to play a game which I think was called frogs or toads.

There would be equal numbers of frogs and toads (for example X frogs and X toads) and they would be sitting on a line of (2X + 1) lily pads (i.e. if there were two frogs and two toads then there would be five lily pads).

The frogs and toads were lined up at each end with a lily pad space between the two groups.

The frogs and toads could either shift one space to a free lily pad of leapfrog over a single occupied lily pad to an unoccupied one.

A single lily pad may only have one occupant. The aim of the game is to get all the frogs and all the toads to the other side of the line of lily pads in the least possible number of moves.

The kids were started off I think with two each of frogs and toads, and then when the least possible number of moves that are needed was decided the kids then had a go with three each and then four.

At the end of the exercise the kids had to try and work out the pattern/formula that related the number of frogs and toads to the least number of moves needed to get them all to the opposite sides.

It was a fun game as we got the groups of kids to line up chairs and play the game with each other as the frogs and toads.

It was also a very challenging exercise as I, at the time a further mathematician, managed to fail three times to work out the least number of moves needed for a particular number of the wretched amphibians.

It’s a lot of fun for the kids though to have to be swapping about on the chairs and pretending to be frogs.

It’s also possibly a good idea for any teacher that intensely dislikes their A-level maths set.

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