Leap Frogs - Maths

Leap Frogs is a problem that we had to solve using algebra.  We had to find out how to swap three frogs from one side of the pond with three from the other side.  Once we figured out the pattern that would solve the problem, we applied that pattern to difference amounts of frogs - 2, 4, 10, etc.  We had to then work out how many moves it took for each amount of frogs and record that information using a table.  Then we had to work out the generalisation or rule that would allow us to work the number of moves a larger amount of frogs would make without actually using the 'frogs' (counters!) to work it out.  Tricky stuff!  Most of us worked out the pattern needed to move the frogs from one side to the other - there were rules that couldn't be broken!  It was a little bit harder to work out the rule that would apply to any number of frogs.  We need to do some more work using algebra and finding rules and generalisations.