My geometry class has started investigating shapes on coordinate grids. Doing this reminded them that they knew how to use the Pythagorean Theorem and how to find the slope of a line segment. Here’s an example of what they worked on:
In looking at the slopes of side AB and side BC, which I wrote on the board as slope of AB = 
Contemplating the situation, one of my students asked, “If you combine those two slopes, will you get the slope of the other side?” I’m thinking that by “combine” he means “add” and of course you cannot add these two slopes to get the slope of the other side. But instead of saying that I asked him, “What do you mean by ‘combine’?” He responded by explaining that if you add the numerators and denominators separately, it seemed like you would get the slope of the other side. He was thinking about this:
(+3) + (+3) = (+6) and (-3) + (+5) = (+2) which leads to a slope of 
Imagine what would have happened if I had asked the wrong question, or just replied without asking the question that I did.
We had two days of orientation last week – organized by students, with adult assistance – and they were really great. The first day was once again at Fort Williams Park and the weather, though quite hot, was sunny. Three years in a row. How can we be so lucky? The difference this year was that 9th and 10th graders were organized by paired advisory groups. Each group had a couple of juniors with them, as mentors, and their adult advisors, of course. The team-building activities were facilitated by juniors with adult assistance. The senior class was off on their own, team building at a ropes course nearby. They joined us at the end of the day, so we had most of the school together, out there under the trees, to debrief the activities of the day.
rawsonmath 