### The fence question

So I assigned the classic fence-against-the-river question to my group (you have 200m of fencing, what's the largest rectangular area you can contain where one side is not needed against the river). We had just started quadratics so they have no real background in it at all. One student solved it thusly:
1) He made a table of values for a few fences:
Then, he turned to Maple. We had done a unit on linear systems and did a few questions on finding lines of best fit... so he used the Curve Fitting Tool to find the best fit parabola, then found the vertex of the parabola and hence the best area.
Then he found the vertex of the parabola by zooming:
Almost every other student did it the traditional way of setting up the equation, graphing and finding the vertex. I thought it was a nice bit of synthesis from the previous unit to approach it in this fashion!

### Teacher Professional Development and Microsoft OneNote

During the first three weeks of July, I have the amazing opportunity to work at the Park City Mathematics Institute.  It is, without exaggeration, the best professional development opportunity for teachers of mathematics.  Participants spend three weeks thinking deeply about mathematics and mathematics education.

There are three main aspects of PCMI:

learning mathematicsreflection on practice (RoP)becoming a resource to others.I'm part of the team for RoP and in charge of the third aspect, in which participants consider a gap in professional development back at their home districts and work in small groups to help fill that hole by developing a rich PD seminar on that topic.

It is not easy to develop professional development.  Teachers who haven't written PD have to patiently learn how to write (essentially) lesson plans for someone else.

This year, I used Microsoft OneNote to facilitate the process.  We have a central OneNote Notebook through which I lay out the daily schedule…

### Desmos, OneNote & Replay

So using Desmos activities are a great way to encourage exploration and discussion in math class -- if you haven't tried them, I encourage it.  They're collected at https://teacher.desmos.com/

But ... Desmos doesn't give you quite enough.  It doesn't have a way of capturing the work that the student does within their space, and it doesn't allow for annotation of class contributions as we come together to discuss.  Well, not surprisingly, OneNote comes to the rescue.
Using the Windows shortcut Windows-Shift-S it is really quick to snag the Desmos screen and pop it into a waiting OneNote page.  From there, we can grab our pen and (using wireless projection) talk about what all the different responses mean and where to go from there.
(An aside : one of the nice features of Desmos activities are the way you can hit PAUSE and it will pause all the screens of the students working.  I always give them a heads up "10 seconds to pause..." and it's refreshing…

### Five reasons to learn Math with OneNote

So, Alice Keeler - @alicekeeler- who is an amazing blogger and an incredible resource for those using Google products, posted 60 Ways Math Teachers can use Google Classroom last April.  It came across my desk the other day and, since school hadn't started yet, I thought it might be a good reflection for me on how one could do similar tasks with OneNote Class Notebook.

I went through the list and checked that I could accomplish them all with OneNote and re-wrote her post with those modifications ... but it was looking a little "plagiarism-y" so, just to check, I emailed Alice to see if she was okay with it.  She was not, but encouraged me to do my own brainstorming.
So... Math Teachers & OneNote (including OneNote Class Notebook).  My top five...
1) The Under-valued value of scribbles & notation
If you really want to be "paperless" (and that should never be a goal - you want to be digital so that content is no-cost) in a mathematics classroom, it's n…