Jason put up a very cool puzzle that is equivalent to solving a quadratic equation.

Somewhat spurred by a comment on that post, and partly out of my own confusion as to what was going on, I tried to make up my own variation^{1}:

The middle of the arcs are the products of the ends, the middle of a line segment is the sum of the ends.

Part of my motivation for this is that my students would just stop dead in their tracks If presented with Jasons problem.

So, they need some scaffolding. Start off with using it to actually create the polynomial from the product of two binomials:

Some of my students, once the understand the relationships between the boxes, can go straight to the end problem. Others may need this intermediate mega training wheel step”

Before ending up with the final version that Jason presented:

^{1} I hope that the improvements include: not relying on color or dashes, as well as showing which numbers go together for a binomial pair. Or I might have just made it too confusing. I can’t tell.

## { 4 } Comments

I should mention the scaffolding I was meaning to use (although I haven’t finished the worksheet yet) was to separate the puzzle from its factoring context entirely and have problems with only 3 or 4 circles, then 5, then 6, etc.

That is, have them be actual puzzles with arbitrary layouts.

I updated my original post so you can see a different puzzle using the same system.

Just wondering – what program did you use to draw these puzzles up? I could have done it myself, but not quickly.

I find this a really compelling way of illustrating just how much more complicated quadratics get when you let the coefficient of x2 be other than 1. Draw up a graph for x2 + 7x + 12 – it only has 4 circles (counting the 7 and the 12). The difference is huge!

I use a Mac package called EazyDraw. I’m fairly comfortable with it, so it took abut 10-15 minutes to come up with the final draft of that, and half of that was adjusting stuff to see which way I liked it better.