While educators and policymakers debate whether 8th graders can be readied to learn algebra, Sigrid B. Frawley sits in front of her kindergartners with a magic bag. She puts three tokens in the bag ...

There is a direct proportion between two values when one is a multiple of the other. For example, \(1\text{cm} = 10\text{mm}.\) To convert \(\text{cm}\) to \(\text{mm}\), the multiplier is always 10.

She’s right—using simultaneous equations does get really complicated, and if you’d like to send me your work for the solution, I’d love to see it. But the system is also kind of a trick. Like a sudoku ...