Sometime back in late 2011 or early 2012, I remember reading the Common Core state standards for the first time. At the time I was teaching Freshman Algebra and saw that high school students would be solving systems of equations containing a linear and quadratic equation in two variables. I laughed at the idea that, due to freshman solving those types of equations, systems of equations with two linear equations and two variables would be solved by eighth graders. Who would have thought that, by the end of the school year, my position would be cut, I would be transferred to eighth grade, and I would be teaching linear systems of equations to eighth graders the following year.

This past week the cold, yet again, took two teaching days from me, so we started graphing systems of equations on Wednesday. My plan was to graph for the three days I had left, teach substitution for about a week, elimination for a week, and then start doing all types of applications of systems. After Wednesday and Thursday, I knew it was time to move on to substitution. The students had mastered graphing and were becoming bored. I sold students on substitution by showing the limitations of graphing, as far as graph size, fractional and decimal intercepts and slopes, and decimal and fraction solutions. Many students have told me they don’t like graphing because “it takes too long.”

I put the first problem up and discussed students the procedure when I have a substitute teacher as far as me leaving and someone else replacing me, doing the same job I do. Once I showed students how this translated to the problem, many took off and found the first variable. For those that had it right away, I showed them how to find the second variable and let them go. With other students, I had to reteach the concepts of distributive property, combining like terms, and solving multi-step equations. I was shocked and excited by how many students understood the second problem immediately and just ran with it. It was one of those moments that teachers teach for. Most of the students who are still struggling with substitution are not struggling because of the concept of substitution, they are struggling with the concepts of multiplying with negatives, arithmetic, and inverse operations. I hope that after some more practice and using calculators, they will be able to have some success with substitution.

This week just reinforced something I noticed earlier this year. For most of my years teaching, I have been afraid to present too much of a challenge to students because they may fail. This year, I’ve learned that some students are going to struggle, no matter where I set the bar. I’ve really cheated the top students by not pushing them harder. I’m hoping to differentiate my lessons more this unit as to push the top students, but give the lower students an opportunity to still have success and maybe even enjoy the mathematics as well.

This next week brings us a snow storm Tuesday to Wednesday and a really cold day Thursday. I’m not sure how many days I’ll be at school this week, but, if I am there Wednesday, we have a half-day in service with the people from Pearson. Have a great week everyone!