I have to plan a mockup maths lesson where the "main topic" should be river reactivation. The given suggestion is to focus on computing cross-sectional areas of rivers using basic geometry and for more advanced classes (only high school) maybe integrals or introducing Simpson's rule - which to me is a very uncreative idea and a very boring task.
Hence, I want to do something less trivial related to river reactivation (as you can see, already the suggestion is not too related to it, so I have quite a bit of freedom). I don't want to do something purely physical (as it's not a physics lesson) either. I have been thinking about doing something nice with complex numbers but I can't come up with a way to use them in a natural way.
Any ideas how I could do that or what else I could do?
Edit: Reading the comments to the question I realised that I read 'river recreation' and interpreted it as any 'playful' approach to mathematics that has to do with rivers. So effectively my answer doesn't address the question at all, does it?
Not sure if this what you have in mind, but I always liked the life-guard example for optimisation problems:
A life-guard is supposed to safe a drowning person in the river. Obviously the guard is faster on land than in the water, so it might make sense to first run a bit to get on a similar height as the person and then jump into the water. However entering the river at a 90 degree angle would make the actual distance that is traveled longer. Given the speed of the life-guard on land and in the water and the distance of the drowning person from the river bank, there is a unique optimal angle in which to enter the water.
Edit: The distance of the person from the bank turns out to be irrelvant because certain triangles are similar. This might come as a surprise.
Second idea (also to do with swimming): You want to swim from one side of the river to the exact opposite side of the river. However the river has a current which pushes you down the river. Given the speed of the current and you speed, at which angle do you actually have to swim, to end up with a straight line? How fast will you effectively be?
Question one does assume that there is no current, one could use ideas from question two to modify the first one.