My Algebra 1 students this year are struggling with graphing linear functions. Every time we have to graph a line, it’s like they’ve never done it before ever. So now we’re doing systems of equations and we’re looking at graphing them and I knew they would need a TON of support to do that.
I’ve been trying to emphasize that graphing gives us an approximate solution to the system, and that we can’t be sure that it’s the correct solution until we check it in the equations, since that’s how the language of standard A.REI.6 reads and therefore how our SBG rubric reads. So to kind of boost their confidence graphing lines and focus on the “checking the approximate intersection point in the equations” component, I created this activity.
I chose 5 systems of equations, and put the letters in a 5-letter word at each of their solutions on the graph. Then I put some other red herring letters at coordinates where they might think the intersections were if they did things like used a positive slope instead of a negative slope or other common mistakes.
I put the activity in a sheet protector, so students could graph the systems using dry erase markers and erase after each system. I asked them to put on paper the letter of the solution, the coordinates of the solution, and evidence that they checked their solution.
This ended up reinforcing a lot of good things. They knew that their lines needed to go through at least some of the letters, and some of them started just assuming that the first letter their first line went through was the solution. When one of the lines went through two letters, they panicked. This led them to a better understanding that with a system of equations, we need to know how two lines interact. It also helped them to understand that if the point they got originally did not check out with the equations, they needed to regraph their lines and try again, not just say it didn’t work, because they needed the right letter to form their word.
Many of my students didn’t end up getting all the way to the word by the end of class because they were struggling so much with the graphing, but I still felt it was productive work even without that end result of ending up with a word.