We started today by finishing yesterday's lesson on the distance between two points.
At this point I realized that we should probably do an example using the formula. I crowd sourced values for the coordinates and this is what we got:
The issue of x1 - x2 versus x2 - x1 came up naturally and one pair of students said that it didn't make a difference as they had tried it both ways (yay!). So I asked why. It took a little digging but we got there eventually...
A student also said that their calculator gave a different answer which led me to talk about simplifying roots a little (this is in the grade 11 curriculum in Ontario).
Then we moved on to finding the midpoint.
It is amazing how "trained" our students are - we just worked out the distance formula, so I must need to use that! About half of the class worked out the distance between the two points and divided that by 2. I asked what they had found and whether that was the midpoint which caused them to stop and scrunch up their faces a little. I let them work on it a little longer before I put this up:
Some immediately made the connection to finding the axis of symmetry given the zeros of a parabola.
They worked through a simple example and a student wrote their solution on the board which we, as a class, improved. The mathematics was all correct, but it looked like magic numbers on a page. I stress the fact that solutions should be written such that anyone in their class can follow from the beginning all the way to the end.
Then they tried this one:
There were many different approaches used to solve this (two shown above) along with many students having no idea where to even begin. My response to them was "You have a midpoint formula - which parts of it do you know?" or something like that. We will definitely have to do a few more practice questions like this.
It was interesting to note that a number of students found the difference between the values and added/subtracted that to the midpoint to find the endpoint. I think I will try to incorporate that into a homework set somehow.
They got the last 10 minutes to work on this solving linear systems review in preparation for tomorrow's quiz. They also got this for homework.