# Building Equations… Again

I’m teaching again! There’s so much that I can share about the start of my new job, but for now I just really want to blog about lesson ideas. So let’s do that.

In Geometry we’re going through our introductory review unit. I wanted to see what my students’ algebraic skills are, especially with solving equations. I decided to expand on an idea I used last year.

The original idea was that students could get a better understanding of the way equations work by constructing equations themselves. If students are going to be expected to “backtrack”, it makes sense that they should see how the equations go forwards in the first place.

So students choose a value to assign to a variable, then perform operations on that variable and value, step by step. They then exchange equations with each other, which they solve by finding the steps that created the equation in the first place.

My latest version has two main aspects. Firstly, it’s now an INB foldable.  And secondly, there’s a second part for creating problems with variables on both sides of the equation. This is a little more involved. I had students create two equations, starting with the same value and ending at the same result on the right-hand side of the equation. Then, they equated the left-hand sides of the equations to create the complete equation. A big difference with these equations, however, is that solving the equation doesn’t take the student through the same steps as the person who created it. But I think that’s a good thing, as it highlights that equations like these require a different approach to solve. I hoping my students will recognize that having variables on both sides means that just backtracking won’t get to the solution.  I realizing that one of my go-to ways to structure a lesson is having students construct their own problems for other students so solve. It really helps to “pull back the curtain” and show students what’s really going on with different problems. Math seems completely opaque to so many students, particularly when they’re only taught procedural methods. Instead, let’s work on making math transparent.