How Many Solutions?

Before Christmas Break I started solving systems of substitution. We had just finished finding solutions of systems and solving systems by graphing. I introduced substitution by doing index card substitution. The students dutifully followed along but I don't think they had any idea what was going on. I was absent the next two days and left them a worksheet with two examples worked out and instructions for the two students who seemed to understand to help everyone. I came back and it was our School Spirit Assembly. The next week we studied and took finals. Fast forward to this week, starting back to school. Time to pick up where we left off.

I started on Monday with what I thought was a really great lesson. I made a graphic organizer type thing with arrows and each box had instructions. I did this because in the past, I realized my work on the board was so messy and scattered that theirs probably looked the same. They were all over the place. I couldn't even figure out what the common errors were because so many people were doing weird things. I was frustrated because they were so needy- expecting me to spoon feed them every little direction. They would just sit there, staring into the distance. When I asked what there question was, it was "I don't know where to start." It was hard for me to not be sarcastic when pointing out, "How about step 1?" But let's chalk that up to first day back.

Second day. We go over the homework and a number of students decided to not even try. So frustrating. I tried to do a 'speed dating' activity so that they could practice solving. By the time we did the warm up and went over their homework, they didn't even get their own problem done that they were supposed to be the expert on. And I'm not kidding. Three out of ten students got their problem finished so they just traded cards with each other and worked the new problem.

Day three. Starting to feel nervous at the lack of understanding. We move on, kind of, to finding how many solutions a system has. I love this lesson. I did it last year and my student's hearing impaired teacher complimented me on how well I break things down and attach it to a visual. I made some minor tweaks and did it again this year. I like to introduce how to solve systems first so that it's easier to understand why we are finding solutions and why there can be more than one.

Success. I really felt like my students were catching on. The next day almost everyone did their homework and said it was either easy or medium. No one said it was hard! I had them get up and check their answers and everyone did well. So proud!

I don't know if the students just got better as the week went on or if my little pep talk about putting forth effort inspired them or if this lesson just really ties it together in their minds, but I ended the week on a positive note and feeling positive about their understanding. This week it's on to word problems and elimination.