Friday, 24 June 2016

Grade 10 Applied Math, February - June 2016

At some point during this semester I said I would blog about what I did with my grade 10 applied class. I have spiralled this course for a number of years now and felt that it was time to change things up a bit. Here is my attempt to remember what I did and why. Firstly though, here is the Google sheet that I used to plan and record what I would be doing during each cycle. There are pictures of the cycles included below.

The first big change I made this time around was to start with trig. I have found that starting with 26-squares did not pose enough of a challenge to some students who decided right away that they didn't need to do any work in this course and behaviour issues ensued. Trig, being new to all students, was a great way to see how they learned and dealt with new content. I also introduced sine, cosine and tangent right away. I used to wait until cycle 3, but found that students tried to pick it up and then forgot how to use the tables. I taught with both trig tables and SOH-CAH-TOA the entire way through the course, and students generally chose one way and stuck with it.

Another change I made had to do with warm-ups. I still did them daily, but I created them as we worked through the course so that they would connect more with the content, either as practice for what we were doing or as lagged practice for a topic that we hadn't looked at for a bit. Here are this semester's warmups. There are no warmups for weeks 6 and 12 because I was testing those weeks.

Here is a look at cycle 2:

Here is a look at cycle 3:

And end-of-year stuff:

I didn't make any other major changes, but did try to spend a bit longer on each topic in cycle 2. I am sure I added a few new things but when you wait several days or weeks to blog about them, you forget. Well, at least I do. If there is anything that you want to know more about, please get in touch!

Monday, 20 June 2016

Things to Remember

Teaching can be a tough job. But it is also the most rewarding. This blog post is something I hope to remember to read on the difficult days.

I find the end of the school year hard. I am so happy to see what amazing people my grade 12 students have become, and for them to go off and make their mark on the world. But this is always accompanied by a sense of loss. I have spent at least 5 months in their company, and for some it has been 4 years, on and off. The connections built over that time are meaningful to me. This is why I write cards to each of my grade 12 students each year - I say something good about each of them and how they have impressed me along with good wishes for the future. Each message is different, as is each student. They also each get a lollipop which is a symbol of achievement in my class - a great result or a marked improvement earns a lollipop on a returned test. So it always fills my heart to receive some thank you cards from my students - I hope they have learned that a small gesture can mean a lot. Their words make me proud of who they are and what we have accomplished together. Here are a few excerpts:

"Thank you for actually making me like math and giving me back some confidence I lost a long time ago about my capabilities in math. You are the nicest teacher I have ever had and I really do appreciate everything you have done for me this year. Thanks for letting me know it's ok to make mistakes and giving me the time and all the effort you have put in to let me grow. I hope no matter what I accomplish in the future, I achieve it by hard work, and with all the kindness, empathy and dignity you have taught me."

"Your style of teaching and attitude towards math is so inspiring to me. It feels like you genuinely care about getting your students interested and getting them to succeed. I am honestly amazed you are able to keep up such a positive attitude and it honestly inspires me so much. ... If I grow up to become half as passionate as you about something, I would be so happy."

"I know I didn't get the greatest marks, however you not giving up on me and continuing to demand my best work will always be something I'm grateful for."

"I want to sincerely thank you for everything you've done for our class this semester. Thank you for being more than a calculus & vectors teacher, thank you for being patient, kind, supportive and always having a smile on your face."

"You are one of those teachers who truly cares about her students, and I'm so thankful for that."

"You have been incredibly inspiring to me and have greatly affected me. I admire your passion for math and especially learning. Your love for math is nerdy and contagious and you are the best teacher I've ever had because of it. ... I wish one day I can be half as lovely and caring as you."

Knowing your content is important. Being passionate about it is far more so. And the relationships we foster in our classrooms help inspire students to be their best selves. We do make a difference and our students notice what is important to us. And every so often we will hear a gem like "Your love for math is nerdy and contagious" - it doesn't get much better than that!

Wednesday, 1 June 2016

What's Your Best Question?

Yesterday, before class, I tweeted this out:

And, as usual, the #MTBoS came through. Here are just some of the replies I received:

I answered the question thanks to the great replies I got. But it was not until a student asked me how to solve the question that I realized that, despite knowing that many students would struggle with this question, I did not plan out what I would say when they asked for help. My answers ended up being just like those given to me on Twitter - "this is how you start it" which really took some of the fun out of solving this "puzzle". So I am now wondering what a good question would be to help move my students' thinking forward without giving away the solution. I should have at least asked "What do you notice?", but am not sure that would have been enough to get them going. Please tell me if I am wrong! This is the question I came up with in the van ride to take my kids to Jiu-Jitsu:

I am wondering what you would ask - what would your best question be? Please let me know in the comments!

Friday, 13 May 2016

OAME 2016

You know that feeling when you are trying really hard to get caught up on everything, but the "finish line" keeps moving? That's been me this week. I'm woefully behind on replying to emails, apparently have 9 comments awaiting moderation on my blog that I don't even remember getting notifications about (?!?) and I arrived home yesterday to a flooded upstairs bathroom which, of course, had spread to the downstairs bathroom, hallway and bedrooms while I was at school. When it rains, it pours! (sorry - couldn't help myself) 

However, I am attempting to work my way through my to-do list and owe David Petro my slide decks from OAME 2016. So, here they are:

WODB Session

Spiralling Panel Session
(this was with Bruce McLaurin, Jon Orr, Alex Overwijk & Sheri Walker)

Rethinking Grade 10 Math Double Session


Sunday, 1 May 2016


Last Thursday and Friday I had the privilege of working with some great math teachers from the Niagara region. I was invited to be part of the mini-conference for their OAME chapter (Golden Section) and got to meet so many wonderful teachers. The following morning I worked with a great group of teachers, most of whom have been spiralling through the curriculum this year. I want to thank Elizabeth Pattison and Liisa Suurtamm for giving me this opportunity. I have never before felt like my work has been so valued and cannot adequately express what a great experience this was.

And, as requested, here are my slides.
Spiralling Session

Sunday, 24 April 2016

Quadratic Visual Patterns

You all know how much I love Fawn Nguyen's Visual Patterns site. I use them a LOT. They have been part of my warm-ups for years now and have been some of the best moments of my class each week. I have been recreating my warm-ups for my grade 10 applied class this semester (no, I can't leave things alone). I decided to do this so they align more with the curriculum expectations we are working on or provide lagged practice for other expectations. The warm-ups have included quadratic visual patterns for a few weeks now and I decided to step it up a little this past week with with a couple of patterns from Michael Fenton. If you haven't tried these ones before, I encourage you to do so before you scroll down.

We didn't actually work with the colour-coding, instead looked at the squares that overlapped by 1 each time. We worked with the number of circles first, established that this is a quadratic relationship and then found the rule by comparing the "side length" of each square to the step number.

I really also wanted to look at this pattern using the colours as a guide so we started over and found that we ended up with the same simplified rule.

I am totally impressed that some of my students can do these as they are not easy, especially for students who have struggled a lot with math and have trouble making connections. They have shown incredible progress and I love how willing they are to try.

Here is the next one we did:

 There is a lot going on with this pattern, but the colours really help show the squares emerging.

I should note that these "warm-ups" took about 45 minutes to work through. It was definitely time well spent. 

Wednesday, 24 February 2016

Linking Cube Towers

I am not doing a daily blog about my grade 10 applied class this semester. This is not because everything is the same as last year or eve last semester. In fact, I have changed almost everything so far in this first cycle. I have different warm-ups, am doing topics in a different order and have made some new resources, too. If I'm not happy with things, I cannot leave them alone. I have thought about sharing what I have done at the end of each cycle - if that's of interest to you, please let me know.

Last year during a lesson study process we looked at an activity that involved students creating towers out of linking cubes and competing to see who could get the tallest tower. This is what I mean by linking cubes (also known as cube-a-links and unifix cubes):

I believe the students all had cards that told them how many cubes to begin with and how many to add each time. It went fairly well, but once a student was "out" (because their tower fell), they were no longer really engaged. Anyway, that is what inspired today's activity which will be my students first look at solving systems of linear equations. I am trying to have them really understand how the starting value and rate of change will affect their towers (and corresponding graphs). We have done a few visual patterns and solved some equations with a variable on both sides, so I think they will be ready for this.

Here is the file. I would love feedback. I will add a postscript if it's a disaster ;)