## Tuesday 5 January 2016

### MPM2D - Day 72: Cosine Law (day 1)

As with yesterday's class, I started today by asking them to find the side length of a triangle.

They tried various strategies but they could not determine the value of x. When I asked why they said they didn't have enough information, which we then turned into not having the right information for the tools they had. We then developed the cosine law.

I was surprised where the hurdles appeared in this process. This was the first one:

I assumed that they would all write the ratio without any difficulty, but student after student (that I chose using popsicle sticks) could not come up with this. There were strange combinations of trig and the Pythagorean theorem, proportions involving trig somewhere along the way, and other convoluted (incorrect) answers. I gave them a few minutes to discuss what was being asked after which we got to the equation we needed.

The second hurdle came when I asked them to expand and simplify (a - x)². The errors didn't bother me so much as the lack of confidence working this out. We worked through it on the whiteboard and then moved on.

Seeing that you could substitute expressions from the left side into the right side proved to not be an issue which also surprised me.

They talked about the patterns they saw in the equations before we tackled our first example. I love that the student who wrote this solution made the mistake you see below. So many forget, or miss, the order of operations when they write out all the steps, which leads them to the wrong answer. I suggested that they should just put the entire expression in their calculator and let it do the work. I also reminded them that using the ANS key on their calculators can be really helpful.

I worked on one more example that was a little less straightforward and was their first attempt at solving for an angle using the cosine law.

We will do more work with the cosine law tomorrow and talk about when to use what in trig.

Here is today's homework.