This post is long overdue. I knew I needed to write it last May and am finally making the time.

Way, way, waaaayyyyy back when I was doing my education degree, my senior (grade 10-13, yes, grade 13 existed back then) math instructor was amazing. He drove about an hour each way to teach us twice a week. He brought in graphing calculators and taught us how to use them and how to teach with them. This was pretty incredible as it was 1994 (I told you it was as long time ago!). This laid the foundation for me to become a national instructor for TI a few years later (I have since resigned - my heart belongs to Desmos). This instructor also had us create "backward problems". Instead of just asking a question, we started from the answer and turned the question around. He helped me think in a different way and really turned around (pun intended) my idea of what assessment questions can look like.

So a public merci! goes out to Rodrigue St-Jean for helping me start my career in a positive way. I am grateful and a better teacher today thanks to you.

## Wednesday, 25 January 2017

### Math Minute

Back in September, I decided to try a new way of sharing some of the cool stuff I hear about online with the math department at my school. I call it "Math Minute" and this is part of the original email I sent them:

This was followed by a short description and the first link that was all about Desmos card sorts.

Here is the link to the Google doc I am using to keep track of what I have shared.

This is a sample (since it had no link):

"Week #8:

Mary"

Although I have had little feedback from these Math Minutes <insert sad face>, I thought I would share what I've done in case someone else is looking for a way of sharing ideas.

"Hello fellow mathies,

I thought I would share some of the great things I come across on Twitter and on the blogs I read. It might be a cool activity or link to an article or blog post, but should only take a minute (or so) to read - hence the Math Minute title. I'll do my best to send a Math Minute out once a week, however please feel free to let me know if you would prefer not to receive them."

This was followed by a short description and the first link that was all about Desmos card sorts.

Here is the link to the Google doc I am using to keep track of what I have shared.

This is a sample (since it had no link):

"Week #8:

I have been using the box (area model) method for multiplying and dividing polynomials for a while now. I like it because there are no tricks involved and students can see (and hopefully understand!) why they are doing what they are doing.

Below is a sample of factoring a non-monic trinomials. There would normally only be one box, but I tried to make my steps understandable for you. I have to say that I love algebra and decomposition and I have been friends for a long time, but I love the box for these. Try it out!

Cheers,

Although I have had little feedback from these Math Minutes <insert sad face>, I thought I would share what I've done in case someone else is looking for a way of sharing ideas.

## Friday, 20 January 2017

### Little Things

Sometimes it's the little things that make a difference...

As I was writing names next to questions on the board last week I realized that I was getting uncomfortable. Let me back up. I was randomly choosing the student who would write the solution to each question by selecting a Popsicle stick from my (Starbucks tea) tin which contains one stick with each student's name on it. When I chose a student who often struggles to solve a tougher question, I got uncomfortable. And I realized how in the past I would purposely assign those questions to students that I knew could complete them. I'm not even sure I did this consciously, but I am sure I did it. Using a random method of choosing names forces me to give all my students the opportunity to rise to the challenge. Given that I always tell my students that I appreciate it when they make mistakes because everyone can learn from them (and I always give them the option of purposely including mistakes when they write solutions on the board), I have no reason to worry about what solution they write. Noticing that it bothered me was a good reminder of why I use Popsicle sticks in my classes.

Review day (before a test) is usually a day when I do stations with my students. I stick questions from a previous year's test up around the room, randomly pair up students and have them go around the room working on big whiteboards. Each pair gets an answer sheet, the right-most column of which is labelled "For Administrative Use". I could simply post the test answers/solutions somewhere in the room for students to self-check, but instead I have them come show me their answers. If an answer is correct, they receive a sticker in the right-most column and if it is incorrect I send them back to try again. If they return with another incorrect answer to the same question I may get them to try a third time or have a conversation with them about what they tried so that I can (hopefully) ask a question that will help redirect them. I ensure that they eventually get to the correct solution and receive that sticker. It may seem silly, but the motivation provided by those stickers is huge. My students are engaged in meaningful mathematical discussions which sometimes turn into arguments as they work through the station. They are talking about the math and helping each other understand the material in greater depth. They make mistakes and figure out where they went wrong before they take the test.

Thing 3:

When my students are working on a practice question as a class, I often walk around the room to check on their progress. I bring along my happy face stamp (or stickers) which I use if their solution is correct. They love this. I get a good sense of how they are doing by the number of stamps/stickers I have given out, but also get the opportunity to help those who are stuck by asking a question to get them unstuck. I'm still working on ensuring that my questions are not leading questions... It's a tiny bit of one-on-one time with each student that gives me a window into their thinking.

I am certain that all teachers have a multitude of little things that they do which make their classroom unique and better. I would love to hear some of yours in the comments.

__Thing 1__:As I was writing names next to questions on the board last week I realized that I was getting uncomfortable. Let me back up. I was randomly choosing the student who would write the solution to each question by selecting a Popsicle stick from my (Starbucks tea) tin which contains one stick with each student's name on it. When I chose a student who often struggles to solve a tougher question, I got uncomfortable. And I realized how in the past I would purposely assign those questions to students that I knew could complete them. I'm not even sure I did this consciously, but I am sure I did it. Using a random method of choosing names forces me to give all my students the opportunity to rise to the challenge. Given that I always tell my students that I appreciate it when they make mistakes because everyone can learn from them (and I always give them the option of purposely including mistakes when they write solutions on the board), I have no reason to worry about what solution they write. Noticing that it bothered me was a good reminder of why I use Popsicle sticks in my classes.

__Thing 2__:Review day (before a test) is usually a day when I do stations with my students. I stick questions from a previous year's test up around the room, randomly pair up students and have them go around the room working on big whiteboards. Each pair gets an answer sheet, the right-most column of which is labelled "For Administrative Use". I could simply post the test answers/solutions somewhere in the room for students to self-check, but instead I have them come show me their answers. If an answer is correct, they receive a sticker in the right-most column and if it is incorrect I send them back to try again. If they return with another incorrect answer to the same question I may get them to try a third time or have a conversation with them about what they tried so that I can (hopefully) ask a question that will help redirect them. I ensure that they eventually get to the correct solution and receive that sticker. It may seem silly, but the motivation provided by those stickers is huge. My students are engaged in meaningful mathematical discussions which sometimes turn into arguments as they work through the station. They are talking about the math and helping each other understand the material in greater depth. They make mistakes and figure out where they went wrong before they take the test.

Thing 3:

When my students are working on a practice question as a class, I often walk around the room to check on their progress. I bring along my happy face stamp (or stickers) which I use if their solution is correct. They love this. I get a good sense of how they are doing by the number of stamps/stickers I have given out, but also get the opportunity to help those who are stuck by asking a question to get them unstuck. I'm still working on ensuring that my questions are not leading questions... It's a tiny bit of one-on-one time with each student that gives me a window into their thinking.

I am certain that all teachers have a multitude of little things that they do which make their classroom unique and better. I would love to hear some of yours in the comments.

## Thursday, 19 January 2017

### Spiralled MPM2D Update

This semester I taught two sections of grade 10 academic math, both of which I spiralled. Although I have taught this course for many years, this was my second time spiralling it. I blogged my way though last year's journey, starting here. I thought it might be worth sharing what I did this time around as the changes resulted from my reflections the first time through the course.

The one big change was doing more quadratics earlier in the course. About half the course is quadratics so I tried to devote about half of each cycle to quadratics. We factored starting in cycle 1; the rationale being that factoring doesn't always stick so multiple exposures to it (and lots of practice) should help students better retain how to factor.

Cycle 1:

Cycle 2:

Cycle 3:

Not-really-a-cycle Cycle 4:

We managed to finish the content on December 22 so when we returned from the break there was a sufficient amount of time to review each strand and have an optional test for each strand. These tests covered 9 of the 10 curriculum expectations and each expectation was optional. Each student could choose which expectation they wanted to show - some did none while others did all 9.

I modified some of the homework sets from last year, but continued to spiral the homework as well. I tailored it to include questions that I know many students needed to practice, but always kept it to one page.

I'm sure there were other differences that I cannot recall at the moment. If you have questions I would be happy to answer them in the comments.

The one big change was doing more quadratics earlier in the course. About half the course is quadratics so I tried to devote about half of each cycle to quadratics. We factored starting in cycle 1; the rationale being that factoring doesn't always stick so multiple exposures to it (and lots of practice) should help students better retain how to factor.

Cycle 1:

Cycle 2:

Cycle 3:

Not-really-a-cycle Cycle 4:

We managed to finish the content on December 22 so when we returned from the break there was a sufficient amount of time to review each strand and have an optional test for each strand. These tests covered 9 of the 10 curriculum expectations and each expectation was optional. Each student could choose which expectation they wanted to show - some did none while others did all 9.

I modified some of the homework sets from last year, but continued to spiral the homework as well. I tailored it to include questions that I know many students needed to practice, but always kept it to one page.

I'm sure there were other differences that I cannot recall at the moment. If you have questions I would be happy to answer them in the comments.

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