We started off our unit about systems of linear equations this week with a definition and a discussion of what a solution means. We learned how to check to see if a set of values was a solution or not in two ways – manually substituting values in (with parentheses!) or storing values in a TI-83 Plus.

I thought I would bring a little bit of a competitive aspect into their practice for this, since just checking potential solution points over and over is not super fun!

I wrote a set of 16 systems of equations that all had solutions whose x-values and y-values were both between 1 and 6 (aka, able to be rolled on a standard die). Each student received a set of cards with these 16 systems on it, a die, and this template in a dry erase pocket:

They drew a system of equations card and placed it in its spot, then rolled their die twice for an x and a y value. They then could check their solution however they chose, and I walked around and checked in on them as they worked.

The competition part is that I had them raise their hand anytime they found a solution to a system, and if it was a true solution, that student earned a point!

A few minutes into them working, I announced that if they found a point that *wasn’t* a solution, but they thought they knew what the solution *should be*, that they could change their values to that point and check to see. Keep in mind that they haven’t learned anything about how to solve systems yet, just how to check to see if a certain point is a solution or not. This had the result I was hoping it would, that many students started to really reason with what the equations were telling them and trying to logically figure out how to adjust a false solution to find one that would work! One or two students abandoned the dice all together and were trying to just find the solution from the beginning, which was awesome!

Here’s some pictures of my students in action on this activity:

I laughed a lot at how frustrated the students got when they kept not finding solutions. We talked about how small of a chance there was of rolling the correct solution (a 1 in 6 chance for x and for y…).

Students started yelling things out like, “Miss Mastalio, 8 is NOT equal to 17 and I’m really mad about it!”

or

“This point works in the first equation and I’m going to THROW A FIT if it doesn’t work in the second one!”

Overall I had excellent engagement for this activity, and I think a lot of students really got a deep understanding of what these solutions mean.

Here is the file for both the dry erase template and the systems cards, as an editable Publisher file and as a PDF.