MFM2P - Day 40 (Similar Triangles & Trig)

We did today's warm-up quickly as we had a lot I wanted to get done. Here it is:

I was surprised at how poorly some students understood what the numbers meant. A number of them divided the diameter by the number of slices and compared the results. I actually had to draw a circle, then the diameter and divide it up to help them make sense of what they had just calculated. Eventually they understood that we needed to compare areas. Here is one student's solution (he figured it all out on his own):

And my consolidation:

After the warm-up we talked about similar triangles. I asked what they knew about similar triangles. They said that they were the same only different sizes. Someone mentioned scale factor. I asked what the scale factor told you about the triangles. They replied that it was how much bigger the larger one was (I know it could go the other way). We moved on to doing a couple of practice questions (links to handouts are below). Here is the first one:

We went back to colour-coding corresponding sides which really does help some students. We found the scale factor, made sure everyone understood what that number meant then used it to find the missing side. The second example involved angle of incidence and angle of reflection, which they have learned about in science class.

They worked out the height of the statue after I demonstrated the process using a mirror. I then put them into random groups and set them on their way to collect data for two objects with inaccessible heights within the school. Some groups needed more guidance to correctly collect their data. They worked out the missing heights when they came back to class, although for many, their work ethic did not seem to make it back to class (the perils of letting them "loose"). Once done, they started to work on a trig practice sheet involving finding angles. I was pleased that they remembered to start by labeling the sides with "opposite", "adjacent" and "hypotenuse".

Here is the mirror activity handout and here is the practice worksheet for solving for an angle using trig. More trig on deck for tomorrow.