## Saturday, August 21, 2010

### Toy Cars

Prompt:  How far would you have to pull the car back in order to get it to go 100'?

Materials:  Toy cars, meter sticks.

Hand them the cars, ask the question and get out of the way.

Question #1
But Mr. Cox, the farthest we can get the car to go is around 10'.  We can only pull it back so far until it starts clicking.

Right.  So if you could build a car that could be pulled back farther, how far would you need in order for the car to go 100'?

Question #2
Mr Cox, what do we do if our car keeps turning?

Yeah, I'm a cheapskate a father of 5 on a single teacher's income.  Give a guy a break will ya? very thrifty. So what can we do to estimate the distance the car travels?

The two groups that had problems with the car came up with two different solutions. One group decided to tie a piece of string to the spoiler and measured the amount of string the car pulled past the starting line and the other group simply estimated by breaking the curve down into short line segments. (Oh man, do you guys just realized you set me up for a lesson plan in May?  Can you say calculus?)

Question #3

Mr. Cox, if I pull the car back 3", it goes 30", but if she pulls it back 3", it goes 36".  Why?

Turns out that one kid pushed down on the car harder than the other which kept the tires from sliding.

Our Findings
I'm not sure if it is supposed to be or not, but the data was pretty linear.  One student wondered why it would be linear since the car takes time to speed up and slow down and the shorter distance it travels, the more energy it is using to simply get up to speed.

I tweet some pics of the activity and Frank asks me if I'm going to have a contest to see which group can get their car closest to the line.

*ahem* Of course I'm going to have a contest at the end to see who can best predict the distance their car travels.

Three groups were able to get within 1.5". (Two of them were the groups whose cars turned).  The best was this:

Shawn Cornally said...

Fabulous. Consider the closest to the line contest stolen, I mean, reiterated.

Anonymous said...

Love it! Thanks for taking the time to share. I'm also surprised it's linear. (Does it go through origin?) Will have to think about this some more. (More likely ask those who are more knowledgeable than me.)

David Cox said...

Hey, I stole the idea from Frank anyway.

My intuition says it shouldn't be linear either. Maybe it was the cars I bought, the tile floor, user error in measurements or whatever. Either way, it made for a good activity.

untilnextstop said...

Sounds fabulous. Thanks for sharing! I may have to steal this. Out of curiosity, did the turning radius end up affecting some of the kids' ability to get close to the finish line?

untilnextstop said...

Hey, I tried this with my kids, but it didn't go as well as I had hoped. I encountered these problems in my class, and was wondering if you had any suggestions:

* cars turning (even smashing into the side when we were doing the "closest to the line" contest). I think this can be fixed in the future by having narrower tracks. (I had built a track for the contest, but it was sort of wide and defeated the purpose.)

* The y-intercept for most groups was negative! Why?? The kids felt that was very non-intuitive, and so did I.

* Measuring accurately the distances was difficult for most groups, with the cars curving and all. So was releasing it consistently (applying the same pressure) each time. It made me feel that their data was fairly unreliable.

Thoughts?? The kids had fun, but I wasn't too happy with the way the math worked out. :(

Thanks!
Mimi

David Cox said...

Yeah, we ran into the same thing with measuring the cars that turned. But the kid in the video found a way to compensate. Honestly, I don't know if the data is supposed to be linear or not. Ours turned out to be which made things easier.

If the data turned out to be non-intuitive, that possibly could open up for a discussion for what was intuitive and why? The mathematical models usually only take us so far anyway.

I'll do the activity again next year, for sure, but I'm going to be prepared for things not to work out so nicely.
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}