# For Teachers: Advanced Multi-Step Equation Analysis

I was inspired by an activity created by Robert Kaplinsky that I used with all of my Pre-Algebra students with a great deal of success.  It involved maximizing/minimizing solutions of multi-step equations.  See the worksheet on Open Middle here:  http://www.openmiddle.com/two-step-equations/ (Look to the far right to access the worksheet).

I wanted to try something a step more challenging with my Advanced Pre-Algebra students.  There’s a chance that this activity exists out there somewhere and I’m not aware of it — if so, comment below and I’ll insert a link to the “original”.  I came up with this on my own, and thought I’d share it…

I had students roll a die/dice to determine different values found in an equation, and the overall answer to an equation.  They then had to find the “missing number” that would make the equation have the given answer.

Here’s an example question:

The students would roll die/dice to obtain the values for a, b, c, and d.  They would then have to find the value for the dark box that makes the equation true for the result “d”.

I was impressed with their techniques.  These students had no input from me in figuring out how to approach these problems.  Here are a couple of different approaches:

This student kept x as an unknown for the first step, then replaced x with it’s known solution to find the value for the box.

This student found her answer intuitively (after a little bit of algebra) then checked her answer by plugging in the known value for x.

This student replaced x with its known value immediately.

I was pleasantly surprised at the number of different approaches that I saw.  The students discussed with each other their methods and seemed “OK” with the differing strategies.

A couple of students completed the worksheet ahead of time so I gave them a challenge problem, re-arranging the unknown box so that it was found within a set of parentheses:

This student rolled the dice and got the values found in the blue equation. How would you find the value of the unknown box that makes the equation equal to -9?

An example solution.

I think this was a pretty good activity to give my students highly conceptualized practice in multi-step equations while really emphasizing understanding.

You can have a copy of the worksheet I created here:  Multi Step Equations Dice Activity

If you use it, let me know how it goes!

To find more activities to use in class, click on the Tags/Categories at the bottom of this post (#MTBoS)