Hi Dan, my HS son suddenly is interested in the length of various segments of a parabola (and other curves). He is currently studying precalculus and introductory physics.
I don’t want to blow this opportunity to have him ease himself into the calculus, so I was hoping that you have a choice link or two that can help me point the way: I’m struggling not to get bogged down in the algebra.
Thanks in advance

In general the lengths of curves are very tricky things. It is often easier to work out something slightly different – for example, it’s much easier to figure out the time taken to travel along a parabola than its actual length.

Of course, physicists come up against things that are tough to calculate all the time. Their usual approach isn’t to make their head explode trying to learn new maths – it’s to approximate. We can do the same here.

I’ve spent three or four minutes putting together a spreadsheet which approximates a particular bit of a parabola. A particularly persistent high school student (with his dad’s help and a good knowledge of spreadsheets) might be able to see how it works and extend it to other curves.

On the other hand if you thing it will intimidate him rather than challenge him – feel free to ignore.

https://spreadsheets.google.com/ccc?key=0AorIV213RTSEdEZTLW45NmZoSVNCeVFscHFVZ2lvT2c&hl=en&authkey=CLfYrKYJ

Wow, that’s great! This is the sort of thing I can use in my classroom at little “cost”

I don’t have to worry about losing a whole day, or kids shutting down. Its a three-minute activity that really hits and reinforces a single math idea.

THANKS. Will be using it in just a couple of months.

1. Very cool idea accompanied by a simple, elegant delivery. An awesome exposition into one idea and review of a couple others.

2. Just out of curiosity- why did you use a video where your shot was wildly short? A Jedi-mind trick to engage them more? Did it have less complicated production than a shot that went in? The aesthetics are so crisp, but kids who love hoops are going to wonder why the six foot seven dude doesn’t reach the rim.

3. Also, and unrelated: you tweeted about a Jo Boaler visit to one of your lectures. Goosebumps, man. Did she illuminate any of the fogginess of pseudocontext? I think what’s especially interesting of late is the how you’ve delineated pseudocontext vs. actual-context-but-just-bad-problems. Which is worse?

I’m with Sean on wondering why you would feature the video with a sad, sad air ball. I’m sure there is a good pedagogical reason why you would invite good-natured heckling.

Bowen — Good idea. By layering, students could see that more than one solution exists as well since varying shot paths can have the same result!

Hands-down one of the coolest math opportunities I’ve ever seen.

This is great, although a bit of a pseudo-context. When did you see spectators or basketball-players actually calculate whether the basketball would hit the hoop or not?

Great lesson! My students loved it. I took your half pics and set them as a background on the TI-Navigator and then had students find symbolic rules that would match the pattern. Students had some great ideas as to where to place the vertex. Lots of terrific conversation took place. Thanks for your hard work and for sharing!

Dan,

I have been mulling through your stuff as usual, playing with Geogebra, and trying to learn all this stuff that you are giving the world, and I thought of a fun (yet maybe impossible) extension to this one.

Remember the cheesy teen comedies of the 90’s (Saved by the Bell being the best example), and whenever they played basketball things just always seemed to work. I was thinking of testing some of these out if they work, if they make true parabolas or if they are fake. I don’t know how it would work, but in my mind it would be a hoot (maybe out of context for the students these days, but I am sure there is a cheesy comedy out there with basketball shots).

Hello,

On your Youtube video of parabolas using a basketball shot as one of your examples, there was a tool you used to manipulate your parabola through stretching and compressing. This tool actually found the equation of your line. Do you happen to know where i could get that tool ??

Dear Dan,

Thanks so much for posting these excellent resources. Your approach is clear and engaging.

I teach math in Community College and will use these in my algebra classes.

Thanks!

–Ben

Did this task with my Use of Maths class. We had a lot of fun!