## Saturday, July 04, 2015

### An Introductory Exercise for Equations with Two Variables

I was planning to blog this Fourth of July something about Independent variables, given the nature of the day, but something else came up.

I was reading Twitter, which I do way more often than is probably healthy, and I saw another image posted (or reposted) by Jo Morgan (@mathsjem), which was a simple puzzle with 7 circles, arranged in 2 columns of three and an extra circle in the middle, such that there were three lines of numbers. The center circle was filled in with a number and you had to fill in the blank circles with certain numbers so that everything totaled a given amount.

With a little modification, I produced the following image. It's a first draft, and already I see one teaching mistake. If this is the first time we're approaching problems with two variables, then it isn't likely that I've discussed the concept of ordered pairs before, so that will likely change to just pairs.

The two takeaways I would want to see from this: first, that the students could create an equation with x and y and a constant equaling another constant (with Standard form being an extension); second, will they notice that as one number gets larger, the other, by necessity, must get smaller.

You can also keep asking for different possibilities until they "run out" or someone thinks to use a negative number or a fraction. (At that point, the jig is up! You can quit the exercise, unless you want to circle the room one full time to get an answer from everyone.

Here is the image I posted on twitter in response to the first one. Again, the instructions need to be updated/corrected, but I like the exercise itself.

What do you think? On the right track? Waste of time?