I have to say that my preparation for today turned out to be less than stellar. I chose to use the investigation I have used with my MPM2D class before and a handout that I use with my grade 10 applied class. I should have thought through this a little more and consolidated the two into one as there was considerable overlap. So noted for next time. Meanwhile, my students were measuring angles and side lengths, and trying to draw some conclusions about what makes shapes similar.
It didn't take long for there to be consensus that all the corresponding angles were equal. However, I have these set up so that it could look like there is some additive property between the sides if you don't check all the lengths. It took a bit more work to sort out that each side of the smaller shape is in fact multiplied by a constant to get the length of the corresponding side in the similar shape. I stopped there with this investigation (some had already been working on the flip side). Before switching over to this handout, we went over how sides and angles are names in triangles, along with a few pertinent facts.
Then they once again measured side lengths and angles - I suggested they split up the work within their groups and this is what we found:
They seemed to understand that the 1.7 means that the larger triangle is 1.7 time larger than the smaller one. We gave the number a name and talked about how you can tell if triangles are similar. I am not emphasizing proving similarity during this cycle - I will do that in cycle 2 or 3.
I loved it when a student suggested multiplying 12 by 1.5 to get the length of x. We tried and decided that 18 didn't make sense for the small triangle and therefore needed a different strategy.
We will continue with more similar triangle work tomorrow. Here is today's homework set.