## Wednesday 26 November 2014

### Sine Law

Jennifer Wilson wrote a post about productive struggle that you can find here. I did my usual trick of sending myself the link. I have a filter on my school email that automatically labels emails from me and files them away under "Twitter" so that I never actually see these emails. Thankfully I keep vague recollections of what I have tagged and earlier this week I knew to search my "Twitter" label for something interesting relating to sine law.

I stole this from Jennifer's post, having first shown my students the picture of the riverbank and surveyor and the diagram without any numbers. Straight from Jennifer's post.

Students worked in groups on their big whiteboards to find the width of the river. There was definitely some productive struggle going on and a lot of good mistakes were made along the way. I love that students try to use other mathematics they know, in this case Pythagorean theorem and right angle trigonometry. There were some good conversations around when those apply and why they don't in this case (with the triangle as drawn here). One group split up the 107° angle into a 90° and and a 17° angle (below). They struggled a lot and did some good math along the way. When they realized that they needed to create an altitude instead, they were quick to solve the whole thing.

Groups, one by one, figured out that they needed to add the altitude from S2. Some made mistakes along the way...

But they eventually got there!

Once they had found the width of the river, they had to work with an oblique triangle that did not have any numbers on it (again stolen from Jennifer's post):

Find an expression that represents the length of side c, I said. I got a lot of, uh, interesting looks. Most did not want to work without numbers. Didn't know where to start. They struggled in their groups for a bit then I told them to finish it for homework. That was their only homework.

The next day, we worked through the development of the sine law together and it went fairly well - better than in previous years, I think.

Working in groups on the big whiteboards has really made a difference to the culture of my classroom. Students are willing to try things and make mistakes and they persevere. That makes me happy.

As a side note, none of my students thought of solving it the way Jennifer showed on her blog here. I will have to make sure I work that in next time around.