# Finally, some good things…

It has felt like I’ve been really digging down deep to find the good things. Although today wasn’t spectacular by any means, there were some really nice moments.

(1) In math club today, our first one of the year, although we didn’t get a huge turnout, the student leaders did a solid job of facilitating the meeting. They used Estimation 180 to start it off, and then used

(2) In my Precalculus classes, I heard some awesome conversations coming from the groups. And a few “whoa!” and “crazy!” from a few kids if they got to a particular part of the questions that were being asked of them. Mainly, I was impressed that they were all searching for why. They were not content to just hear the answer from one group member and move on.

(3) Today I got an email about the USAMTS math competition, which I forwarded to people at my school who might be interested.  In my last precalculus class, I started telling them about this competition, and then I started talking about continued fractions because they were involved with a problem I remember being proud solving from the competition ages ago when I took it… and then… well… you know, I got to spend 6 minutes on an interesting diversion. They were eating out of the palms of my hands. I could have just done that the whole period. But I had to stop myself and get back to the lesson.

(4) After school, I helped a student see something. I saw the answer to the problem we were working on as $_nC_2+n$ and she saw the answer was $n+(n-1)+(n-2)+...+2+1$. I confirmed that her that her answer was correct — she suspected her answer worked but wasn’t sure why.  We talked about why her answer was correct. I then showed her my answer was correct. And then we rewrote $_nC_2+n$ using factorials, then simplified, and got $\frac{n(n+1)}{2}$. Thus that must mean that $n+(n-1)+(n-2)+..+2+1$ is the same thing! Something we will prove in a different way in a week or two. Awesome!

That’s all for now!