Also yesterday, I had one of the best days in terms of student learning, thinking and application. We've been learning how to solve systems of equations. Two days ago I gave my honors students the following problems:
ax + b = y
x + c = y
ax + by + c = 0
ax + cy + b = 0
They were to solve both problems for x and y in terms of a, b and c. This is very abstract. Higher level thinking and application of what I've been teaching them. It blew their minds. They hated me for a solid 10 minutes until the bell rang. The next day, I let them know they weren't off the hook. We talked about how ax - x = (a -1)x. And then I gave them back their papers, mostly blank still. I told them to work with their groups to solve these and that they counted as today's quiz grade. Several of them ROCKED it! Many of them got off to a good start. There was lots of talking about math and solving math. Sigh. I'm so proud!