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November 26, 2019

Grade 10s explored a leapfrog problem.

Using either this site, or a game board and frogs, we looked at the number of moves it takes to have the frogs swap sides. The frogs can slide one space or hop over another frog and each counts as one move.

We aimed to minimize the number of moves to have the frogs switch sides. We can vary the number of frogs, and then look for patterns. The goal was to be able to say how many moves it would take for any given number of frogs.

We saw a few ways to model the problem. Here’s a neat visual model.

Some used tables and used the equation with desmos to show that the equation was a good fit.

Once we figured out the equation for this situation, we were ready for a new challenge. What happens if there were 2 spaces between frogs at the start? What happens if there are different numbers of frogs on each side? How will this affect our equations?

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