Open Middle Style Activity for Equations with One/No/Infinite Solution(s)

Two summers ago, I created some open middle style problems that have been a hit in my classroom. Both problems use a reusable set of tiles that have the numbers from -4 to +4 printed on them. These tiles are laminated which has helped them hold up to use over multiple years.

The first problem I created reviewed the concept of function/not a function. Students had to create three relations that were functions. Then, they had to create three relations that were not functions. I shared the file for this activity here.

I followed up the creation of that activity with an evaluating functions problem that can be downloaded here.

This year, I’m placing a big emphasis on solving equations with variables on both sides. Though I covered this last year, my emphasis on word problems meant I didn’t do a good job of introducing my students to the concepts of no solution and infinite solutions. This year’s solving equations/inequalities unit hasn’t gone perfectly, but I know it
never will. I will always have room for improvement as a teacher.

I decided to see if I could make an open middle style problem for creating equations with one solution, no solution, and infinite solutions.

First, I did a bit of trial and error on a scrap of paper.

My husband had to bail me out because I accidentally created two problems with infinite solutions. Shaun reminded me that I had a lot of wiggle room because the tiles in the one solution problem could be moved around a lot.

Then, I took advantage of the fact that my freshman students went on a field trip leaving me with almost no students for an entire day to actually type up the activity.

After typing it up, I realized that I only had 8 boxes for my 9 tiles to fit in. Luckily, I just had to make a tiny tweak to the bottom equation.

Students have to place the tiles in the appropriate boxes so an equation is formed that matches each equation type. My students found it pretty easy to get one of the equations correct. They found it much harder to get all three of the equations correct using the exact number tiles provided.

Here are some action shots from my classroom: