Thursday, 1 December 2016

TMC17 Speaker Proposals

We are starting to gear up for TMC17, which will be at Holy Innocents’ Episcopal School  in Atlanta, GA (map is here) from July 27-30, 2017. 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 ( 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 everyone who submitted on time was accepted, however, this year we cannot guarantee that everyone who submits a proposal will be accepted. 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 27 and 48 one hour sessions that will be either Thursday, July 27Friday, July 28, or Saturday, July 29). That means we are looking for somewhere around 70 sessions for TMC17.
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 16, 2017 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.
Thank you for your interest!
Team TMC17 – Lisa Henry, Lead Organizer, Mary Bourassa, Tina Cardone, James Cleveland, Daniel Forrester, Megan Hayes-Golding, Cortni Muir, Jami Packer, Sam Shah, and Glenn Waddell

Monday, 14 November 2016

Median, Altitude, Perpendicular Bisector Warm-Up

My grade 10 academic students have spent the last couple of classes working on finding the equations of medians, altitudes and perpendicular bisectors. Some did a lot of work and some, well, let's just say that some did less. As we move into looking at properties of quadrilaterals, I wanted to ensure that everyone has at least a basic level of comfort with the prior work. So, I came up with a warm-up that I thought I would share.

It incorporates collaboration and finding mistakes (there is no way that all groups will do this correctly on the first try). I suspect some will struggle finding the group with the same question as them, but they will learn to follow instructions better (hopefully).

Here are the questions, linked here, that I will cut into strips for them.

I have 28 students, so 14 pairs which means that I needed 7 questions in order for each question to be repeated. Two groups will eventually find the centroid (via equations of medians), two will find an orthocentre and three will find a circumcentre.

If you can think of ways of improving this, please let me know in the comments!

Wednesday, 9 November 2016

Centroid of a Triangle

Yesterday, my grade 10 classes learned about triangle centres. They each had a triangle awaiting them on their desk as they walked in (I copy them onto thicker-than-normal paper). 

I gave instructions along these lines:
- cut out the triangle
- figure out how to balance it on your pencil
- make note of the balance point
- figure out how the balance point relates to the coordinates of the vertices of the triangle
- when you think you know, create your own coordinates for a triangle ABC, write them on the board along with their balance point

That last part was new. Its inspiration is Joel Bezaire's Variable Analysis Game which you can learn more about here. It helped some students see the pattern (especially the last line that I added to make it a little more obvious) and kept those who had found it early engaged as they were checking that other student's coordinates and balance points worked.

It was a fun way to start the class so I thought I would share... Thanks, Joel!

Monday, 31 October 2016

Student-Created WODB

Once your students have done a number of Which One Doesn't Belong, they should be able to create their own. I described what I do with my calculus classes here, but thought I should take the time to outline my creating process.

Thanks to Chris Hunter, both when I am vetting or creating a WODB, I use a table like this where there are 4 criteria/characteristics labelled along the top.

I consider it a strong WODB if 3 of the items share a characteristic that is not present in the 4th. For example:

The criteria used for Shape 5 could be:

I find that working through one like this with students is a really important step for them to understand that "It's the only one that's pink" is not the depth that we are looking for (unless you are looking at colours!).

I also strongly encourage you to do some Incomplete Sets before your students create their own. Here is an example:

I love that there are many different options for the missing number here. And students (may) quickly see how helpful the table is to ensure a strong WODB.

What have I missed? Let me know in the comments!

Tuesday, 25 October 2016

The Box Method for Factoring Trinomials

I love using the box method (area model without appropriately sized side lengths) to help students learn how to multiply polynomials. I love, love, love to use the box method to divide polynomials. But I only started using it to factor non-monic trinomials last year and I did a horrible job of it. Really horrible. I'm sure none of my students understood it because I didn't really get it. I am happy to report that I now LOVE using the box method for factoring non-monic trinomials. I shared this with the other math teachers at my school (I send out a weekly "Math Minute" - a link to a cool activity, a blog post, an idea that is worth sharing... and this was what I sent this week). I tried to colour code it to make it easier to follow and made a second box to better show the steps.

Here is an attempt at an explanation in case the example is not clear. Start by finding two numbers that multiply to the product of 'a' and 'c' (here -120) and add to 'b' (here -2). In this case the number are 10 and -12. The box represents the area (trinomial) and we are looking for the length and width (binomials). I always put the x^2-term top left, the constant term bottom right and the x-terms along the remaining diagonal. The number we found are used as the coefficients of x so 10x and -12x go in the boxes along the diagonal. Then I common factor the first row and the first column (that's where the 2x and 4x come from). This would normally all happen with one box, but now jump down to the second box. Figure out what multiplied by 2x will produce 10x and what multiplied by 4x will produce -12x. Those complete the factors and you can check that it all works out with the constant term (does -3 times 5 equal -15?). There you go. I love this because it is not a trick - it makes sense and has built-in error checking. I find it really fast, too.

I should note that I also show my students how to factor using decomposition and give them the choice of which method to use. So far more are choosing to use the box method. I can't wait to show this crew how to divide polynomials in a couple of years!

Rethinking Factoring Special Quadratics

Have you ever had a day when a lesson you took the time to rethink actually worked noticeably better? Let's be honest - I don't have the time (and sometimes not the motivation either) to rethink all my lessons. "What worked well enough last year is good enough for this year" happens far more frequently than I'd like to admit. I try to make notes if something really doesn't work or if I have a brilliant idea after the fact. And I do my best to act on those notes to my future self. Occasionally, if I teach more than one section of a course, I will make changes on the fly as I teach the second class. But the reality of teaching full-time and raising a family is that every lesson may not be as good as it could be. This is a difficult reality for me.

The change I made to yesterday's lesson was a simple one - I did the opposite of what has been done in the past. Let me back up for a minute (and I apologize if you've heard this all before)... The math teachers at my school all share lessons for all courses. I am the renegade who sometimes does things differently. I have been spiralling my grade 10 applied classes for several years and I spiralled my grade 10 academic class for the first time last year. I put a lot of thought into the order of topics and how each would be approached and blogged daily. This year I am tweaking what I did last year - the biggest change being that I am introducing more quadratics concepts earlier in the course. I am trying to be intentional when I look at past lessons and ask myself whether this is the best way to approach the topic. I looked at the "department lesson" on factoring special quadratics (at this point I have no idea who created it - it could have been me???) and just wasn't happy with it.

The old:

... followed by exclusively difference of squares practice questions. Then:

... followed by exclusively perfect square trinomial practice questions.

The new:

As I wrote above, I got students to do the opposite of the old lesson. Instead of expanding, they factored. This was good practice for them and they could see that there was a shortcut within the patterns. We had a whole-class discussion, talk with the people at your table, test your conjecture(s), come back to whole-class discussion kind of thing going, but we got there. They came up with the patterns (I didn't tell them) and they saw the value in what we were doing (I think). I think the old lesson tended to fall flat because they didn't see a need for more ways to factor - it was just confusing. They didn't see these special cases as being helpful. I hope this year's students do. They also know that they can also successfully factor them as they would any other trinomial if they don't notice that they are dealing with a special case. (Confession: Until I started teaching grade 10 applied, I did not think of a difference of squares being a trinomial where the x-term has a coefficient of 0. Factoring these with algebra tiles was a revelation!)

One of the things I love about spiralling is that it freed me from common test days. When my students need more time on a topic, I give them that time. So tomorrow we are factoring a little more. A few students are really solid with all types of factoring, but most have a more tenuous grasp of what to do when. My room is currently all set up for some factoring speed dating. Tomorrow should be a fun-filled day of factoring!

Monday, 3 October 2016

Distance Between Two Points with Tacos & Zombies

I thought it was about time to dust off my blog. I am spiralling my two grade 10 academic classes this semester (I also have a section of grade 12 Advanced Functions). It is really nice to have last year's plan and homework sets to work from and tweak. I recently saw what Nathan Kraft did to a cool Desmos Activity Builder activity created by Andrew Stadel and knew that I wanted to adapt it for my class. Their activity focused on horizontal and vertical distances between two points. I needed to include the distance between any two points. Due to the size of the activity (so many images!) Desmos struggled to keep up with my changes and I ended up having to hard code the points I used rather than having them referenced with variables. Using variables would have made it easy to move the points, but I will have to save that for another time. I think I'm getting ahead of myself here though. I should back up for a minute and start at the beginning of today's class. We started with Dan Meyer's Taco Cart 3-Act found here

After setting the scene with the Act 1 video, I asked what information they needed to know. They requested distances and speeds so they got this:

Next, they worked on big whiteboards in their table groups to determine whether Dan or Ben would get to the taco cart first. We talked a little about the Pythagorean theorem along the way.

Then, I played the Act 3 video to confirm their answers (all groups said that Dan would arrive at the taco cart first).

It was now time for the zombies! I used my Popsicle sticks to select random pairs and handed out Chromebooks. The link to the activity is here.

Despite the activity not running as smoothly as I would have liked (points were not showing up for some students and overall it was very slow), students seemed to learn what I wanted them to. After working out the distance between four sets of points on this screen, they understood the process and were ready to generalize. (Screen 13 was planned as an extension - I really wanted to ensure that everyone completed screen 8.)

We consolidated to close the lesson and did one quick practice question.