Sides of a rectangle played out differently this year than last.

The question is tucked away in the Mathematics Assessment Project formative assessment lesson on Finding Equations of Parallel and Perpendicular Lines.

Line segment SP has equation *y*=2*x*+3. Find the equations of the line segments forming the other three sides of the rectangle.

Towards the end of our first day in our unit on Coordinate Geometry, I sent a Quick Poll to collect three equations from each student on which the other three sides of the rectangle might lie.

I was easily able to sort the results in the Portfolio Workspace by student so I could tell whether each student was successful.

For example, Chandler has two equations with a slope of 4, and upon further investigation, they represent the same line. He also has the given equation, y=2x+3 as one of the possibilities, although he has written it in an equivalent form.

Daniel’s submissions will work, but Eli has submitted a line that will not be perpendicular to the given line (his slope is ½ instead of –½.)

There were other issues as well. What do you notice about Kelsey’s equations (and several others, whose work I have not shown)?

Kelsey y=−1/2-4 09:57:58.322

Kelsey y=−1/2+4 09:57:58.322

Kelsey y=2*x-3 09:57:58.321

Last year I had my students enter their equations on a Graphs page. I was able to watch them correct their mistakes with Class Capture. I didn’t have to be the expert. This year, I sent a Quick Poll on the second day that was just a little different from the first. I have “Include a Graph Preview” checked, so as students entered the equations they had come up with the day before without graphing technology, the equations are graphed for them.

I watched using Class Capture.

Kelsey’s equations turned in to

Kelsey y=−1/2*x-6 09:42:41.031

Kelsey y=−1/2*x+4 09:42:41.031

Kelsey y=2*x-3 09:42:41.031

Chandler realized that graphing y=(4/2)x+(6/2) was the same as y=2x+3. He changed his submission to

Chandler y=2*x+7 09:45:08.199

Chandler y=−1/2*x+1 09:45:08.199

Chandler y=−1/2*x+9 09:45:08.199

Eli submitted

Eli y=−1/2*x+6 09:41:20.023

Eli y=2*x 09:41:33.813

Eli y=−1/2*x-2 09:41:33.813

I did want to have some whole class discussion on how students were working. And I realized later that I should have “allow resubmit” on the Quick Poll before I sent it so that students would be able to revise their answer after submission if needed. So I made a student the Live Presenter.

What do you notice about the equations? What kind of figure is formed? How can we correct the equations?

And then I made another student the Live Presenter.

What do you notice about the equations? What kind of figure is formed? How can we correct the equations?

And so the journey continues … providing opportunities for students to make sense of mathematics, often using technology to help them learn, even if the final assessment question might be calculator off.

Kristin

March 15, 2014 at 3:11 pm

I used that lesson this year, too. I love the technology you included.

Heidi Rudolph

March 15, 2014 at 7:30 pm

Love this one!

Travis

March 26, 2014 at 2:09 am

Keep this one in mind if/when others ask you for something simple, yet exemplary of what can be done with Nav/QuestionGraph/Capture.monitoring. It is great for all the things you mention.

Also, it might be helpful to add a note about how to ‘square’ the window with that split pane or else those last couple of minutes are spent in consternation by the students and a teacher new to this feature.

And another thought, using 2 as slope is much better than 1, lest students make some faulty generalizations.

Opposite slopes only and reciprocal slopes only both have structure worth probing/pushing.

jwilson828

March 26, 2014 at 10:47 am

Thanks, Travis. Good points about using Window/Zoom > Zoom – Square to be sure that the lines actually look perpendicular when they are. I always right-click on the grid to get that. And you do the same in the Review Workspace to square the displayed grid as well.

Kristin & Heidi, The Mathematics Assessment Project site is one of the best finds of implementing CCSS-M!

Travis

March 26, 2014 at 2:47 am

…and keeping the vertices on lattice points was fun while looking at the y-intercepts