How I would have done it
- Play the video of the man building the helter skelter. Either play the whole thing or pause it half way, depending on how good the data comes out.
- Ask "How long would it take to build it twice as high/complete it?" or possibly a better motivator for a formula, " How long would it take to add another 100 sections?"
- Someone will probably say "twice as long". A bright spark may or may not notice that it will take him longer to walk up it each time as it's getting longer.
- At this point we take guesses and discuss how to solve it. Pretty soon we will be collecting data and plotting it. If we just plot the time as he completes each section, we end up with a curve, which is hard to extrapolate from, but splitting it into amount of time taken for each individual section we get a nice straight line. Pretty soon we're finding the sum of an arithmetic sequence.
My heart sank when it came out. Its just a bit rubbish really; a totally unconvincing line that just doesn't reward us for all that hard work. As painful as it was too see it go wrong, I feel that I've learned alot from trying to work out how to pitch this in the class and I'm still pleased with the initial idea.
I guess now I leave this idea to die, until the fair next comes to town.