For the last little while we've been studying Trigonometry. Honestly, the students are doing very well with the idea of angles and side lengths. We took extra time to make sure that everyone understood the big idea that Sine, Cosine and Tangent were RATIOS and they were able to make connections with our work on proportions (affectionately known as the "P-word") from the first unit. We did a quiz and it seemed that most of them were getting it.
As it turns out, "application" of these concepts was going to be a challenge. After making clinometers out of protractors and drinking straws, we went for a walk to look at ways we could use our trigonometry knowledge. We identified the peak of the roof of the school and I asked them measure the angle and distance. Upon returning to class, we did not have time to complete the problem so I put it off until the next day.
At the beginning of the next class I decided that we'd start the day where we had left off so I put this problem on the board:
|Darla is standing 15 m from the base of a building and using a clinometer she measures the angle of elevation to be 37°. If her eyes are 1.65 m above ground level, find the height of the building.|
Puzzled looks and some anxious comments followed: "I hate word problems", "You never taught us this", "What's a clinometer"...
I quickly surmised that our trip outside on the previous day was not as "sticky" as I had thought. I needed to ease the tension and provide some sort of success -- quickly -- so I said, "Why don't you try to draw a picture?...Imagine the scene and try to sketch it."
Two girls immediately pulled out their coloured markers and started making a full page drawing of Darla -- eye lashes, coiffed hair, nails, the works. Ooops. I didn't expect that!
I don't think I reacted very well when I saw that NO ONE DREW A TRIANGLE!!! Dammit, we'd been studying triangles for two weeks, and I didn't see this coming at all. I am sure I sounded slightly exasperated when I said, "Can somebody please draw a triangle?"
It is amazing the number of ways we learn what our students need and how we respond. We've been setting up ladders, measuring flag poles, ramps, drawing pictures and solving problems for a week.
Yet, on Friday, one of the students who'd missed 3 days drew the picture below. The edventure continues....