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Teaching integration with various shapes and boxes of ping balls is really fun. Then use smaller balls to get a better estimate. Physical, visceral and chaotic with balls bouncing everywhere. Even counting a hundred-ish balls is hard and methods have to be devised (good way to intro number bases).

Exercise can also be done in 2d with colored squares or circles. Which is a nice segue into guestimation. Cover the entire curve to be measured with a square, value can't be large that as the square totally covers it, ask them to find the lower bounds.

Then get them to make estimates with other things they have around (bananas, shoes, etc), someone will come up with rectangles. Introduce the trapezoidal rule!

Then we are off into history with Newton and Leibnitz and that shit is good drama enjoyable by any age.

None of what I have presented requires counting past 20 (which really most of us can't do anyway).




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