Dan Anderson’s Dragon Curve program

The best way to start off on this project is to say that I wish we’d done better with this one. Not that it went terribly or anything, I just think that Dan’s program is a great thing to use to talk with kids about Dragon curves, fractals, programming, and probably lots of other stuff, too. We just scratched the surface.

With that off my chest . . . .

Earlier this week Dan Anderson posted a really cool program you can use to explore the Dragon Curve (you may have to click on the gif to start the animation):

The code and an interactive version of the program is here:

Dan Anderson’s cool Dragon Curve program

One of the reasons that I was excited to see Dan’s program is that I’d done a Dragon Curve project with the boys a little over 3 years ago. In fact, it was Family Math 8 – this project was Family Math 292!!

Today we started by just playing around with Dan’s program. The main idea here was to see if they remembered what Dragon Curves were and to let them see the basics of how Dan’s program worked:

Next I let the kids just play around with the program. They enjoyed varying the angles in the curve and seeing the resulting shape change from sort of simple looking, to crazy looking, and then *surprise* back to amazingly simple looking:

In the last part we decided to take a closer look at the situation when the angles in the curve produced equilateral triangles. Unfortunately, it proved to be a little more difficult than I thought to talk about the angles here because the clockwise vs counter-clockwise turns were a little confusing for the boys to see. Although they seemed to get to a pretty good understanding by the end of the talk, I wish I would have anticipated the difficulty with the angles here. I’m sure I could have explained what was going on much better if I would have understood ahead of time that understanding the angles would be confusing.

So, as I said in the beginning, there’s way more you can do with Dan’s program that we did in this project. Even just scratching the surface was fun, though. I hope I get to see someone use this program for a “hit it out of the park” math project with kids.

More AMC problem challenges

We had some more fun tonight working through three old AMC 8 and 10 problems that gave my kids a little difficulty.

First up, my younger son working on problem #4 from the 1989 AJHME (the predecessor to the AMC 8). The problem asks you to estimate the value of 401 / .205. This is a really nice estimation example.

His solution is interesting because he decides to simply the problem by multiplying the denominator by 1,000. That leads to some difficulty later on when we have to go from that number back to the solution to the original problem. Definitely some instructive difficulty, though.

I helpfully show him a different way to solve the problem that involves multiplying by 10 incorrectly . . . .

Next up was problem #6 from the 1989 AJHME. This is a problem about a number line that you can find here:

The 1989 AJHME – scroll down to problem 6

This is a classic “fence post” problem. I’m not sure what gave him trouble when he was working through it the first time around, but it sounds like he may have miscounted the fence posts. He doesn’t have much trouble this time around.

Last up was my younger son working on problem #18 from the 2007 AMC 10 B. The problem is a nice geometry problem. You can find it here:

The 2007 AMC 10b (scroll down to problem 18)

The arithmetic and algebra on this problem gave him some difficulty while he was working on the problem during the day. He manages to work through that algebra here, though, and presents a nice solution. We also get to talk about a nice alternate solution that he thought about early in the video before going in a different direction.

From my perspective, I found it very interesting to hear about the various choices that he thought he had along the way. For example, at one point he’s trying to decide whether or not to use the quadratic formula or taking the square root of both sides of an equation.