I’m teaching a summer physics course. One thing I’m doing differently this year is having students do at-home experiments with friends or family. Part of their reporting back involves having to share the ideas of their friend or family member. Here are a few quotes from students discussing what happened when they dropped a book, a piece of paper, and crumpled up piece of paper.

I think the most interesting thing for the physics teacher is people's explanations of why things happened.

I'm trying to think of topics in my math classes that students could share with friends and family. I'll be teaching pre-calculus, calculus I, and calculus II in the fall. But I'm interested in algebra questions that can be shared at home, too. The first criteria is ease of understanding, but there's also the aha! factor, when something doesn't turn out like you expected. I know lots of cool mathy experiments that students could easily share, like making a mobius strip, but I'm not sure I know any related to calculus...

Can you help me, dear readers?

Probability is always fun. Maybe the students can show their friends and family the Monty Hall problem?

ReplyDeleteAlternatively, the 7 Bridges Problem is good to share, although the friends, family, etc... may find it slightly frustrating.

For algebra, I like paradox-ish things too. For instance, the classic question about how to share the cost when three people meet on the road bringing different amounts of stuff? I can't find a link to the details of that one at the moment.

ReplyDeleteFor calculus, mini-projects like estimating the surface area and volume of a pear might be fun things to do with family.

For precalculus, get them to explain exponential growth, maybe with something purely calculational like "how big a piece of graph paper would you need to graph y = e^x from x = 0 to 20, with each unit being 1 cm? How about if you want to go up to x = 30? How big a range of x would you need to reach the Andromeda Galaxy, 2000000 light-years away?" or stuff like that, or alternatively with something more real-world like the difference in your $ at retirement if you invest $1000 per year starting at age 25 vs at age 35, assuming some average stock-market growth rate like 7%.

Could they show approximations for area under a curve?

ReplyDeleteMaybe even explaining the FoxTrot comic strip where Jason does simple arithmetic area problems using calculus?

Josh, you reminded me of the one I do asking which way they'd rather be paid: Plan 1: day1=$100, day2=$200, day3=$300, ... day30=$3000, or Plan 2: day1=1 cent, day 2=2 cents, day 3 = 4 cents, day4=8 cents,...

ReplyDeleteI think they and their families would have fun together with that one.

Jo in OKC, I love the idea of having them explain comics! I'll have to find the one you mentioned. I'm not sure I've seen it.

ReplyDeleteMy fave for algebra is where Paige is hating on her math homework and Peter rephrases the question in terms of shopping. She answers him, and says she still doesn't get the math problem.

Sue -

ReplyDeleteHere's a link to the comic I was talking about:

http://www.pleacher.com/handley/humor/comics/calculus/area.html

Thanks!

ReplyDeletePerhaps the students could find their own way to explain the deltas (x, dx/dt, dv/dt) and vary it until they were able to explain it to a couple of different people.

ReplyDeleteFor me the "aha" moment in calculus came when I saw the relationship between location, space, and time in terms of motion. Point in space vs. change in space over time (velocity) and (this was the big one) change in velocity over time. For some reason I didn't get it until some one used a car are a reference - car in garage, car on town road at constant speed, car on on-ramp to free way. Then it all made sense and I could use that in other applications.

Another calculus idea: Maybe something like Don Cohen does in "Calculus by and for Young People".

ReplyDeleteFor infinite series, you can always do cookie sharing. Don has lots of write-ups on his site about how he does this.

I'd better check his site out more carefully as part of my prep for calc!

ReplyDelete