Yes. Yes, yes, yes.
After solving a number of literal equations for variables yesterday, I gave my favorite problem to the group of students I was working with.
Solve for &: #(@ - &) = $/!
Along with the reassurance that "Yes, you do know how to do this," and, "No, it doesn't matter that there are no numbers or true 'variables' as you know them."
They discussed it together and figured out how to solve for the &. It was my most successful uses of that problem across a number of years. But the even better part came at the end.
One of the girls looked at me questioning if we were "doing math." I said, "Of course you're doing math. You just solved an equation. Isn't that one of the things we do in math?" So, perplexed, she said, "But there were no numbers or variables." Agreed. We chatted for a minute or so more before she looked at me and said, "So math isn't really about numbers, it's like problem solving." My goodness, if we can start Algebra 1 with that idea, there is no limit to how far you can go!
I love seeing this mindset of thinking, figuring out, and solving problems spread within our classroom, school, and beyond.
