Math Roots

A Thought Exercise

Two ways to see the same problem.

A Thought Exercise is a prompt a room has to reason through together, with no procedure to retrieve and no back of the book. Here is one. Most people take the long way round the first time - and that is the part worth looking at, not the answer.

A Thought Exercise, for example

Which side is larger? Is 8(7) + 5 greater than, less than, or equal to √9 + 7 · 8? Answering is optional.

Nobody is being tested. How you would get there is the interesting part - and most people reach for the arithmetic first, because that is what school taught all of us to do.

One exercise. The partnership is a year of teachers doing this together.

Math Roots grows teachers as mathematicians first: in-person sessions to prepare them, then monthly support across the school year, with teachers meeting as a knowledge-building community in between.

Generative Math Learning Framework · ©2025 Moore and Lewis · exercise compare-expressions