Next unit up – dealing with negative numbers. For some reason, other math teachers at my level call this “integer rules”, even though the stuff applies to all real numbers.
My previously most successful attempt teaching adding and subtracting them used the concept of dinosaurs and people. People are positive (of course) and dinosaurs are negative. After a dinosaur eats a person, the get tired and take a nap. The answer is either how many people or hungry dinosaurs you have left. It gets a bit trickier with teaching subtraction, where you need to introduce additional pairs in order to be able to take away one part of it, but it’s still doable. There is less dissonance when using the squares from algebra tiles, but those aren’t as gruesomely appealing.
The thing is, this only addresses the mechanics. It doesn’t convey the idea of a continuum, where negative numbers are where you end up after you keep reducing positive numbers.
Things I’m thinking of that might work, but haven’t inspired me yet:
On the other hand, these are all just variations of the number line. What I really need is some way to tie the two concepts together. A game? Using cards (red negative and black positive) and number lines?
And what that really needs is some story to hold it all together. It seems a natural for a good vs. evil struggle, in a comic book kind of way. Some battle involving tokenized karma?
This is just the beginning of a brain storm. It seems that every time you try to come up with a new way of teaching something, it gets harder. I suppose that’s obvious, because you’ve already taken the easy pickings before. Still, it’s kinda neat to record this stage of the process – 98% of what I’m coming up with is crap – but figuring out how I turn that into something decent will certainly help next time around.