So this is from a Formative Assessment Lesson from MARS site a couple of weeks ago.

As I think back, the pre-assessments were very lacking, some even left blank or only minimal scribbles. Their post-assessments were much better. They were more confident in manipulating equations to a similar form so they could more easily compare, picking those that were parallel and those perpendicular.

However, a handful really struggled with the given graph in the lesson. It had 3 lines without the x- & y-axes.

Part of the task asked them to place & label the axes on the graph. Some actually drew the graph and all lines forming the rectangle outside the given graph, then transferred their work to the graph. Interesting. It seemed easier for them to graph the entire thing than to simply add the missing information. I wonder why?

Several a-ha’s were noted throughout the lesson. Students thinking opposite slopes would be perpendicular, how to find the x-intercept, in the beginning naming equations like y+4x=3 and y= 4x+5 as parallel. It was definitely a task where I had to bite my tongue, let them struggle a little, then ask questions without telling them how I did it.

As I look over the first sort, I recall several having trouble getting started simply because the equations were in different forms. Once they realized putting them in similar forms would allow for easier comparisons. I gave them the categories for the sort, but I wonder how they would have sorted them had I chosen an open sort? One reason I chose to use the lesson’s headings was because a couple served as quick reviews of checking to see if a point was on the line and how to find the x-intercept.

Would a better assessment be to create equations (not in slope-intercept form) to fit it given categories?

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I did this last year with my Geometry students; I followed the MARS instructions exactly – gave the kids the worksheet as homework, collected it and wrote feedback ON EVERY SINGLE ONE IN 24 HOURS (102 papers), did the other activity in pairs, and then gave them back the worksheet with a request for them to revise it. They were able to sort the equations in class fairly easily, but even with that and the feedback comments, many were still not able to accurately place the axes in the exercise. Were you able to make progress with your students on that?

I just posted some thoughts your comments brought about…

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Introducing this concept with my 7th graders I have given pairs of students a couple of equations each, a vis-a-vis marker (each group a different color) & overhead graph paper. They graph their equations at their desks & then we layer them on the overhead (I’m sure more sophisticated technology would work as well). This generates a discussion about similarities and differences in the graphs and the equations that created them. Then I let them test their predictions.

Hi Mallory. Anytime you can get students talking/sharing -is a good thing! I love that you have them test their predictions.