MPM2D - Days 68 & 69: Test (part II) and Equation of a Circle

Day 68
Yesterday was day 2 of the test. I don't really want to talk about it...

Day 69
We changed gears completely today and looked at the equation of a circle. This is one of those weird topics in our curriculum that doesn't really fit in. I do it as an application of the distance formula, but we only look at circles centered at the origin so I don't even get to make connections to the transformations we have done. Well, it's not part of the curriculum, but I usually have them explore circles that are not centered at the origin.

I started off with a little group activity. They had to plot 12 points and calculate the distance between each point and the origin. This is what it looked like:

They easily saw the pattern (all the answers were 5!) and that the points formed a circle. So then I asked them to define a circle. Here is what they said:

Pretty good, right? We went on to develop the equation of a circle.

Then they filled in a big table giving them different information (equation, radius, intercepts, graph).

Next, we looked at this question:

We hopped onto Desmos to see what this looked like. They could easily see if a point was inside, outside or on the circle, so they talked in their groups about how we could figure this out without the picture.

In our discussions, we talked more about radius that radius squared, so that is how we looked at the example that follows.

And then class ended early so students could go clean up their lockers. They were not sad about not getting homework.