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## Angle of Elevation and Depression

A few weeks ago, I was asked to go out to a school and teach a demo lesson.  The entire math department was released for the afternoon and they watched the lesson in period 3, and we met to talk about it in period 4.  I was given a Math 10 Applied class (non-academic 10th graders), and instructed to teach a lesson on Angles of Elevation and Depression.  My goal was to present the lesson in a manner that is consistent with the pedagogy of Alberta’s revised program of studies.  As much as possible, I wanted the students active and constructing their own meaning.

To introduce angle of elevation and depression, I first introduced the concept of “horizontal”.  I had the students use tape measures to measure the heights of their eyes.  Then I asked them to circulate around the room and find an object that was at the exact same height as their eyes and label a picture that looked like this:

After that, they were instructed to make a list of objects in the room that they would have to look up to see (elevation),

and objects that they would have to look down to see (depression).

Next, I stole a page from Dan Meyer’s playbook.  I took the class down to the atrium in the middle of the school and asked them to estimate how high above the main floor the railing around the second floor was.  As a motivator, I promised a prize for whichever team of three had the closest estimate to the actual height.

We returned to the classroom, and each group recorded its guess on the SMART board.  Then I had the students construct clinometers similar to this one.   I asked them to return to the atrium and use the clinometer and a tape measure to find the actual height of the railing.  At this point, I made a major pedagogical error.  Instead of letting them go to the atrium and figure out which measurements they needed and how to get them, I diagrammed it all for them on the board.  I helped too much.  I think I did it because the entire math department was there watching and I didn’t want the lesson to flop.  I also didn’t know the kids since it wasn’t my class, and I wasn’t sure how much they would be able to handle on their own.  I should have found out by letting them struggle.

Once the kids had made their measurements, they returned to the classroom to make the calculations.  Each group recorded its calculated height on the SMART board next to the estimate.  One group even self corrected when they realized they were several meters out because they had added the height of the measurer’s eyes in feet to the height of the railing in meters.  The correct answer was revealed, and the group with the best estimate and the group with the best calculated value each got cookies.  I tried to discuss sources of error with them, but it was getting late in a class taught in a different manner than they were accustomed to, so that discussion was not well focused.

Overall, the lesson went well, and I believe the students learned angle of elevation and angle of depression in a more compelling manner than it is normally presented.  I gave exit slips to check this theory, but I forgot to bring them with me when I left.  I would have rushed back to get them, but one of the perks of being a consultant is that I don’t have to mark anymore.