I did a really fun half-lesson today involving Dan's cup stacking idea, and I really let the kids try to struggle with it for a bit to figure out what they would measure, and how. It worked brilliantly! Especially having come after already several other exercises (see previous posts) where we had discussed the meanings of slope and y-intercept, I really thought that this one tied it all nicely together.
(I didn't use my own height; I picked a kid from each class, which was pretty funny for them, and I got to be the judge of when the stack of cups reached the top of their head.)
We also discussed why it's not as good an idea to measure only one cup, even though you could visually see roughly where the "stacking rim" starts and where the "extra part" ends on that cup. (If you're off by even just 1 mm in measuring the rim, that's really easy to do, but when you account for the fact that you're stacking tens or maybe a hundred cups all together, that margin of error will really add up!) We also discussed again that x is the cause, and y is the effect between the two quantities. In one class, their predictions were right on -- several groups were off by 1 cup only. That's pretty amazing, considering that each additional cup only contributes a couple of centimeters in height.
What a lovely activity!
And, in our precalculus class, we finally did the final testing for the catapult launches. They went really well, and most groups had M&M's that landed right around their targets (using the catapults that they themselves had built earlier)! :) How super cool. There was actually one group whose 3 launches out of 4 had landed right in the (pretty small) landing pad that they had placed on the floor. AWESOME consistency!
I also recycled those M&M's for Kate's estimation activity that introduced absolute values. Now my kids are spoiled because they got to eat M&M's for three days in a row. :)
This is why I love math teacher blogs!!
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