A Day In… Honors Algebra 1

Actually, 100% of the guesses were less than 59 seconds (the time of the student) and greater than ~30 seconds (half the time of the student). With the visual/tangible introduction, students seemed to grasp the idea that the tag team should finish faster than either person working alone, but that my contribution wouldn’t be quite as helpful as having two students team up (that’s where the 30 seconds comes into play).

After we measure the tag team time, students did wonder if finding the difference of the two times (100 – 59 = 39) would always provide a good estimate. “Suppose two students, each with a time of 59 seconds, worked together. Would their tag team time be 59 – 59 = 0?” That question allowed students to reason that the difference is not the way to go, and was just coincidence here.

One semi-disappointing and unintended consequence that showed up about a week after the lesson: One student applied our “efficient” strategies (those developed on the second handout) to a different type of problem, demonstrating that she doesn’t really understand what’s going on in either scenario, and she’s just relying on mimicry. So the work never ends. But that’s what I signed up for, and a significant part of why I like my job.

Thanks for sharing your comment and question! I hope your colleagues enjoy using some aspect of the lesson. If they have feedback (whether positive, or things they would improve), send it my way.

A lovely lesson here. I am pleased to hear that no one simply added your times. How many simply took the average of your times? This is obviously a bad estimate and I think we can talk kids out of that with examples like yours. However, I wonder about the persistence of an idea like this one (similar to the exponent conversation that Christopher Danielson has picked up on) I can imagine that kids would focus on some aspect of the average difference in your times and try to shoehorn that into this situation.
I have passed this along to my Algebra I colleagues. Thanks!