Tag Archives: equations

## Lessons Learned on 2 Step Equations

16 Sep

This past week I taught my 7th graders how to solve 2-step equations. But did they actually learn how? Just graded their quizzes, and the mean score was about 75%. Arghhh!

I’ve been teaching this topic for years, and this year I did a few things differently. I think a few ideas were  good, and others still need work.

The good:

• I introduced 2-step equations and how to solve them with a demonstration.  I showed the students 3 cups. I told them that the cups hold exactly the same number of paper clips. The number of paper clips in those cups along with the 6 in my hand total 18 paper clips. How many paper clips in each cup? This was awesome; in each class, the student I called on to explain their thinking on solving the problem, solved the problems exactly how we normally solve 2-step equations: “First I subtracted 6 from 18 and got 12. Then I divided by 3 since there are 3 cups. So each cup has 4 paper clips.” Sweet. I then went and explained their thinking using the variable, c, for cup and so on…  Where did I get the idea for this demonstration? In the most unlikely place: their Holt texbook. Ha, who would have thunk?
• After we concluded that a good way to solve an equation was to zero-out the constant term that is on the same side as the variable, and then to make the coefficient 1, we created a flow map (thinking map) for their notes. I think this is a great time to emphasize the vocabulary: constant, coefficeint, and term.
• I had students come to the board and work out the homework problems twice this week. Students love it, and I get to see where they are having problems.

Things needing work:

• Many students are having a difficult time with equations like 2m-3=-9.  They are not seeing the 3 as negative, so they are subtracting 3. Previous years I would have them immediately change the subtraction sign to adding the opposite. This year I was trying to get them to use inverse operations instead. Instead of subtracting 3, lets add 3.  I *thought* they were getting it, and I think they sort of did. But this is where most of the mistakes were made on the quiz. More practice with this on Monday!
• I had my students check their work, by substituting their answer into the variable. We practiced this again and again. However, I am still seeing students work where they get the answer incorrect, and then they check their work, and they rush to believe that their check is true. I somehow want them to slow down and do the check as objectively as possible…yah right.  This is  driving their teacher crazy.  Maybe some multiple choice problems would help here.