I want students to solve systems out of necessity. I want them to feel the interconnectedness of the two (or three) equations. In the past, I’ve asked small groups to build a functional 4×4 magic square. Soon they realize that changing a single number has multiple effects; this is the nature of the system. Unfortunately, abstracting the connections results in more than two variables. This year, I wanted to create the same feeling with only two variables. (The familiar x & y). Enter: Alex Overwijk.We blitzed through a task of his for systems of equations when I participated in a …

Continue reading »## Desmos Art Project

This semester I gave my Grade 12s a term project to practice function transformations. I began by sourcing the #MTBoS to see who had ventured down this road before. Luckily, several had and they had great advice regarding how to structure the task. I use Desmos regularly in class, so it was not a huge stretch for them to pick up the tool. I did show them how to restrict domain and range (although most of them stuck exclusively to domain). I gave them the project as we began to talk about function transformations, and they had 3.5 months to …

Continue reading »## Desmosification: Building Custom Parabolas

After an emoji was named 2015 Oxford Dictionary word of the year, I am holding out hope for next years’ candidate:des-mo-si-fy/dez-MOH-suh-fahy/verb1. to transform the condition, nature, or character of a classroom activity using Desmos.Starting with a Dan Meyer post, the art of infusing dynamic software into student activities changes the ways that students encounter abstract, functional relationships in mathematics. Desmos’ activity builder gives teachers an extremely user friendly platform to create tasks that move students through semi-structured lines of inquiry. I decided to start with a task that I already liked.Before:I like to spend a few days at the beginning of …

Continue reading »## Counting Circles Brainstorm

Let it be known that Sadie Estrella is a Hawaiian treasure.She made her way north for SUM2015 in Saskatoon and I got the opportunity to learn from her about counting circles (as well as share an eventful dinner). It is probably good to understand her work on counting circles before reading a couple of ideas I had during her session. I went to her blog and searched for #countingcircle, and the results can be read here. *****Use this time to read Sadie’s work*****A couple things struck me while she was talking: She is so honestly passionate. You can tell that she cares when she talks. I immediately …

Continue reading »## Clothesline Series

I joined a middle years math community organized by my school division. I have a growing interest in the transition of students from middle school to high school because many of the tasks I use or create get at middle years content. I’m wondering what knowledge students come to my room with and what atmosphere it was learned in. Both have huge impacts on how students operate in my room.I was surprised to hear that middle years teachers lamented that students could not use number lines. I use number lines as a support in my high school classes because I …

Continue reading »## WODB: Polynomial Functions

If you haven’t experienced the conversation stemming from Which One Doesn’t Belong? activities, you are missing out. As far as I can decipher (#MTBoS feel free to correct me), this all began with Christopher Danielson’s Shape Book centered around this structure. From there, a crew of tweeps (headed up by Mary Bourassa) established WODB.ca (YES! Canadian) to curate a collection of problems of this format. My unit on polynomial functions (either in Foundations of Mathematics 30 or Pre-calculus 30) requires students to decipher attributes of polynomial functions from their graph and vice versa. These include end behaviour, sign of …

Continue reading »## Central Tendency: 10 Burning Questions

My intern just started a unit on statistics with my favourite starter question of all time. (First blogged near the end of this post in 2011…)The question is simple: floor is very low, and ceiling is very high. Create a data set with the following characteristics: Mean = 3 Mode = 3 Median = 3 During the teacher rotation between groups, I picked up on some lines of reasoning. (Not being directly responsible for the teaching of the lesson, allows me to sit back, be inspired, and follow the lines of inspiration). Student justifications for their data sets were very …

Continue reading »## Navigating Collectivity: Grade 9 Fractions

“I hate fractions” – Everyone Today an amazing thing happened; students put aside the endemic disdain for rational numbers and had a conversation. I’d go further, they weren’t discussing their views on fractions, they were collectively conjecturing–the moves of the room enacted each other. I don’t think that a written document can capture the movement of the body of learners, but I have to try something. Think of it as less of a remembering and more of a re-membering, a reconstruction of a living learning event from the past. My intern and I have worked at fostering a spirit of collectivity …

Continue reading »## Integer War

Math 9 poses the specific challenge of pre-assessment. The wave of administrative details (lockers, fees, photos, textbooks, tryouts, etc.) creates a logistical whirlwind for teachers. On top of that, you have no clue who (most) of these new students are, or what their mathematical history is. Our department gives a short pre-skills exam to help with this process, but I like to use the first week to work on integer tasks to really see how the newbies move mathematically–beyond a number on an exam. One such task was stolen (read: borrowed) from Timon Piccini. I decided to place focus on the idea of …

Continue reading »## Classroom Clean-Up

No more students for this year. I’ve spent a full day cleaning up and re-arranging my space for my incoming intern (for whom I’m very excited for). Amidst the broken calculators and stray linking cubes, I found a note that a student wrote me from my first year of teaching. It served as a brief reminder of why I attempt to curate a community of mathematical action with my students. It isn’t the easiest way to teach, but has a limitless ceiling. Dear Mr. Banting, You called me a “genius” in math class once, and that night I went …

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