nine - a lesson on slope-intercept form

I had a really good class last week. It just clicked. It was our second meeting of the school year, and yet it was as if they had been my students for months.

At the end of each semester, I give my students an evaluation form on which they evaluate the course and me as their teacher. Two pieces of feedback that I received last year from my math students was that they wanted more group work and wanted me to better integrate word problems into the course on a day to day basis. So, I'm trying out ways of doing these two things this semester.

It was a simple lesson on slope-intercept form of linear equations. I didn't have high hopes for this class to be a stellar one. The material can be boring because it is review for every single student in the room as they have all taken Algebra 1 before. It's not ground-breaking and quite frankly, linear equations just aren't that interesting. I mean, who likes to be linear? :)

I began class by creating six groups of two or three students; they remained with these partners for the rest of the seventy-five minute class period. First, they went over the homework assignment with their group members. They compared answers and tried to account for and correct any discrepancies. As they did this, I circulated around the room, making certain that every student had fully completed the homework, and I engaged each student in a conversation about what they found easy and difficult. Once the groups had all finished, I answered a few general questions on the board that several students asked. Then, I started reviewing how to write equations in slope-intercept form from a variety of given information.

(For those of you reading who need a bit of a refresher, slope-intercept form looks like this: y = mx + b where m is the slope of the line, b is the point at which the graph intersects the y-axis, and (x,y) represents any coordinate point on the line.)

For each example problem that I put on the board, I had the students work with their partners to solve the problem and then I would call on a group to either come up to the SmartBoard to write their solution or to provide the solution verbally as I wrote the steps. I also included five word problems spaced throughout the lesson for the class to work on in their groups. I did not walk them through any example problems first. I just gave them the problem and let them figure it out together. If there was a problem on which the whole class was stuck after a few minutes, I would talk them through it step by step.

I got really lucky on this day. For one, the groups that I randomly created the night before worked together extremely well - so well, in fact, that I think I will have them keep these groups for at least the next one to two weeks before I switch them up again. I was able to pace the class such that I had about 10-15 minutes of extra material in case I needed it, but I still was able to cover each point that I intended to during my planning without using my extra material. I felt that the students were engaged with the material even though it was review, and I felt that each student left the class having learned something new - whether it was about how to work with a classmate, how to pull information out of a word problem, how to read function notation, or how to write an equation in slope-intercept form.

Although this may seem like a straightforward and very simple lesson, there are so many things that could have gone wrong. I could have run out of time and not been able to cover all the material I had planned. I could have not prepared enough material and then had extra time to fill at the end of the class. I could have given a homework assignment that was either too easy or too hard the previous class, thus resulting in students that complained about the homework or asked too many or too few questions about it. I could have put students into groups that failed completely - students who were introverted and preferred to work alone, students who were too chatty to focus on their work, students whose math level was too disparate so that one student completely dominated the discussion while the other sat passively. I could have written word problems that were too easy or too difficult, leaving the students bored or frustrated. I could have failed to teach them about slope-intercept form. I could have failed to teach them anything at all.

Yep, I got lucky. I hit on a class in which the kids and I were clicking, and I felt that we were all engaged with both the material and each other. Of course, after six years of teaching, I know that I shouldn't get used to this. Contentment and laurel resting are dangerous things. Plus, the unpredictability of teenagers leaves no room for such self-indulgences.

However, leaving school on Thursday with the feeling of "wow…that was a really good class" was a great way to start the new school year.