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 variation1:
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.