**Seesaw: An Idea for [math4]**

I’ve been trying to come up with an idea for an application to write for the math4 program. I’ve mentioned this program before, and you can find more information at their wiki page: http://wiki.sugarlabs.org/go/Math4Team.

My idea is inspired by a leaning game we used to play in elementary school in 4th and 5th grade. We had these devices reminiscent of balance scales and we had to put different weights on one end to balance the weights on the other. The trick, of course, is that while the left side of the balance may have had a 10 gram weight, we could only balance it with a discrete number of non-10 gram weights on the other end. Mathematically, you might think of it like this:

10 = X_{1} + X_{2} + … + X_{i}

Where each X was some weight. The first idea of my Sugar activity was just to emulate this behavior with some basic drag-and-drop. I think that’s a good start, but then I wondered: can this be expanded to include variables?

I think the answer is that it can. Consider the polynomial (6X + 13). If we need to balance this on the right side of our scale, then we need two types of weights: weights of the form nX and weights of the form n. There’s really no way around this. This can be explained formally with linear algebra and vector spaces, but that would be beyond the scope of our 4th grade curriculum. On the other hand, grasping that concept in a more a priori way is something that I feel can be important to grasping the bigger idea of variables and equations.

That’s not that hard then. We can simply have a new class of weights which take the form nX. In fact, it could be easily expanded to include weights of the form nY, nZ, et cetera; once the kid gets the concept, they should be able to balance a polynomial of any order.

From there, we can probably do even more, but I don’t have any solid ideas yet. I just think that the framework of using a seesaw format like this has lots of applications for understand equality.

As I wrote that last sentence, I realized that we could have a dynamically changing equality sign that demonstrates how the equation is currently balanced (a >, <, or =). With that in mind, I’m off to start coding!

Posted in Science and Mathematics, Technology Tagged: Coding Projects, Mathematics, Technology