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# Observations on Plotting Points in Pre-Algebra

Disclaimer:  Some of this might seem very, very obvious.  But sometimes it’s good to state the obvious, right?

This semester I decided to teach plotting points differently than I have in the past.

I started the lesson by handing each student a piece of graph paper and a ruler.  Yes, I know college students should probably be accountable for bringing their own supplies to class. However, in this particular class we spend a grand total of 2 class periods discussing graphing.  I do not believe it is worth it for these students to buy a pack of 100 sheets of graph paper when we do not do 100 sheets worth of graphing in this class.

The first thing I had the students do is draw a vertical line and horizontal line down the middle of their papers.  I did not even bother mentioning the terms x-axis and y-axis at this point, as my major focus was on the drawing itself.  From observing my students, I found out that it is not OK to assume that they can draw straight lines, even when they do have a ruler.

Next, I had the students label the positive x-axis, negative x-axis, positive y-axis, and negative y-axis (in this order).  From observing my students, I found out that it is not OK to assume that they can properly number a number line, even though this is a skill that we also discuss in the chapters on whole numbers, integers, fractions, and decimals.  For the x-axis, which I was still calling the horizontal axis at this point, many of my students had trouble figuring out if the positive numbers should be to the right or to the left of the negative numbers.  Interestingly enough, they were better with labeling the y-axis.

After every student had their graph drawn properly, we started labeling the Quadrants, the x-axis, and the y-axis.  Then I talked about x being positive and y being positive in Quadrant I.  I had the students determine the direction of x- and y- in the other three Quadrants on their own.  Then we plotted one point in each of the four quadrants.

It seemed as if it was much easier for the students to plot points on a graph that they created themselves.  They seemed to have taken ownership of their graph at this point.  This is a stark contrast to how I have taught plotting points in the past.  My previous method was to either have the students construct a graph without graph paper, or give the students a pre-labeled grid.  I found out that neither of these methods is OK and I will never do either of them again.

I continued the lesson from here by having student plot the coordinates of a sailboat.  I did not tell the students that we were going to plot a sailboat.  Instead, I told the students that we were going to plot one point at a time, drawing a straight line connecting the points as we go.  Many students were resistant to connect the points as we went, causing for chaos in constructing their sailboats.  What I found out is that some of my students did not want to connect the points until they knew whether or not they were plotting the correct points.  Once they realized that we were plotting one point at a time so that I could walk around and make sure they were plotting it in the correct position, their nerves were calmed a little.

Finally, I had the students plot the coordinates of a coffee mug on their own.  This seemed to be a good reinforcement activity to clear up some of the odds and ends.  Of course since they were now ‘on their own’ and not being guided by me, some students went back to not connecting the points as they went.  And some students got (0,1) confused with (1,0).  However, since I was walking around the classroom, I was able to correct the majority of those issues before the students got too far into the drawing of the coffee mug.

Overall, I must say that this was a half-an-hour of very well-spent time.  I would definitely use this particular progression of steps to teach this lesson to students again in the future.