## Thursday, 7 December 2017

### Rate of Change Graphs

In grade 12 advanced functions (pre-calculus) we look at rates of change of functions. Our students have been working with rates of change since grade 9, but we now look at instantaneous rates of change, or slopes of tangents to a graph, along with rates of change of slopes of tangents. This can all be rather confusing to students so I decided to make a game to help my students build up their skills and vocabulary.

I started by placing all the desks in pairs, facing each other. Each pair had 2 small whiteboards and markers. I randomly assigned the pairs and had them decide who would be person A and person B.

Here was their challenge -

They jumped right in and were asking each other good questions. I paused them at one point and we talked about the fact that, as they couldn't ask about the actual graph, the person drawing should be able to come up with the shape of the graph but there could be horizontal and vertical translations.

They soon discovered that the orange piles had more challenging graphs and actually chose those ones! Once they had each gone through a number of graphs, I suggested they could make their own. And, boy, did they! Here are some samples:

Along the way there were great conversations and many misconceptions came to light.

My colleague suggested having students create velocity-time and acceleration-time graphs based on the green and orange graphs (assuming they were position-time graphs). That produced even more misconceptions.

It was great to see them engaged and challenging each other in a really positive way.

Here are the graphs that I used - the first 6 were the green graphs and the last 6 were the orange graphs.

## Friday, 1 December 2017

### TMC 18

We are starting to gear up for TMC18, which will be at St. Ignatius High School in Cleveland, OH  (map is here) from July 19-22, 2018. We are looking forward to a great event! Part of what makes TMC special is the wonderful presentations we have from math teachers who are facing the same challenges that we all are.

To get an idea of what the community is interested in hearing about and/or learning about we set up a Google Doc (http://bit.ly/TMC18sessug). It’s a GDoc for people to list their interests and someone who might be good to present that topic. The form is still open for editing, so if you have an idea of what you’d like to see someone else present as you’re writing your own proposal, feel free to add it!

This conference is by teachers, for teachers. That means we need you to present. Yes, you! In the past nearly everyone who submitted on time was accepted, however, we cannot guarantee that will be the case. We do know that we need 10-12 morning sessions (these sessions are held 3 consecutive mornings for 2 hours each morning) and 12 sessions at each afternoon slot (12 half hour sessions that will be on Thursday, July 19 and 48 one hour sessions that will be either Thursday, July 19, Friday, July 20, or Saturday, July 21). That means we are looking for somewhere around 70 sessions for TMC18. We are requesting that if you are applying to speak for a 30 or 60 minute session that there are no more than 2 speakers and if you are applying for a morning session that there are no more than 3 speakers.

What can you share that you do in your classroom that others can learn from? Presentations can be anything from a strategy you use to how you organize your entire curriculum. Anything someone has ever asked you about is something worth sharing. And that thing that no one has asked about but you wish they would? That’s worth sharing too. Once you’ve decided on a topic, come up with a title and description and submit the form. The description you submit now is the one that will go into the program, so make sure it is clear and enticing. Please make sure that people can tell the difference between your session and one that may be similar. For example, is your session an Intro to Desmos session or one for power users? This helps us build a better schedule and helps you pick the sessions that will be most helpful to you!

If you have an idea for something short (between 5 and 15 minutes) to share, plan on doing a My Favorite. Those will be submitted at a later date.

The deadline for submitting your TMC Speaker Proposal is January 15, 2018 at 11:59 pm Eastern time. This is a firm deadline since we will reserve spots for all presenters before we begin to open registration on February 1st.