Solving in One Variable

First and foremost... this lesson is not orginally mine!!
Remember when I told you how much I loved this blog? When I was first starting INBs last year, I clung to a few blogs for ideas and tips. Sarah's was definitely one of them! HERE is Sarah's original post of this lesson.

I started with the scales just like she recommended. Your copy is here if you want it.

Students worked for a few minutes individually and then discussed ideas with a partner. Of course #3 and #6 really caused some problems... they don't have a solution! I encouraged students that if they got stuck on any particular problem to skip it and come back. Inevidably #3 and #6 were left til the end!

We discussed all six as a class and wrote the solution types. Our notes looked something like this when we were done.

We talked about one solution, no solution, and infinitely many solutions at this point. This was the first time most of my students had heard these ideas so we talked them through quite a bit. And yes...we wrote them algebraically. At first they moaned and groaned, espeically at the all real numbers, but by the end of the year, after coming back to these ideas repeatedly, they really felt acomplished. They would brag about being able to write things like "real mathematicians." I love math nerds!!! :)

Then we made a foldable, including one of each type of solution set.
**From here on the pictures are tiny. GRRRR. If you click they will enlarge. 

We talked about how the algebraic process of solving relates to the scale. For example, in the equation where the only solution is x=3, when we subtracted 2x from each side the resulting 2x=6 could be seen on the scale where two boxes line up to the 6 box. This really helped students grasp what was happening as they solve equations.

 How have you taught this idea? Got any great foldables or activities to share??