I was walking with my wife along the River Corrib in Galway last weekend when we got into an argument that lasted the rest of the walk. I’ll present our two arguments and some illustrative video. Then I’d like you or your students to help sort us out.
Argument A: It would be much harder to swim to the other side of the river in the fast-moving water as in still water.
Argument B: It would be just as easy to swim to the other side of the river in the fast-moving water as in still water.
I hope this gets as out of hand for you and your students as it did for me and my wife.
This excellent question exhibits a quality that is not found often in math curricula: it has the “specificity sweet spot”: it is specific enough for a student to answer, but non-specific enough for every kid to agree on the answer. Students making different assumptions will have different responses, thus creating a real mathematical argument.