Rationale: Create a game that embeds the skills of adding and subtracting integers into a conceptual decision making structure.Objective: Insert a set of integers into a 4-by-4 grid so that the sums of the rows and columns is a minimum. Game Set-up:All the students need is the game board and the list of sixteen numbers. The board consists of sixteen boxes arranged in a four-by-four array. Space is left between the boxes to insert the addition and subtraction signs. You can give the students a blank board and have them all fill in the operations to match a board projected in …

Continue reading »## Fraction Task Testing

The testing of a task went horribly right. Background: Graham Fletcher (@gfletchy) tweeted an Open Middle (@OpenMiddle) prompt for comparing fractions. The thread debated whether or not a representation on a number line would be best. Many people liked the number line better, but I decided to stick with the inequality signs because: Students see this type of two-bounded inequality notation with domain and range. The number line gave the impression of a single, fixed answer (because the fractions appear a definite, scaled distance away from each other). I gave this question as a starter to a group of my grade …

Continue reading »## Dice Auction

Every student has a gut feeling when it comes to probability, and I feel like I have been too quick to theorize their gut instincts in the past. This year to introduce Grade 9 probability, I decided to exploit gut feelings to introduce the topic. To do this, I needed a semi-familiar situation, some friendly competition, and a time pressure to make decisions. To fit these criteria, I invented the Dice Auction.Premise:You are invited to an auction, and given a budget of $10. Everyone at this auction has an identical budget. You all are bidding on possible events when two …

Continue reading »## My Favourite Surface Area Question

Surface area is intuitive. Intuition is a natural hook into curiosity. When you think something might (or should) be the case, it begs the question, why? It just seems as though textbooks haven’t gotten wind of that.Perusing the surface area chapter of the assigned textbook for my Grade 9 math class offers a steady diet of colourful geometric solids all mashed together (at convenient right angles) in various arrangements. Without fail, the questions ask the same thing:Find the surface area of…Best case, students are asked to “create” a mimicked amalgam of standard solids and then calculate the surface area of …

Continue reading »## FractionTalks.com

I have been thinking about extending the Fraction Talk love ever since I wrote this initial post in June 2015. I have used them with my grade nine classes as the starter during units on rational numbers. I have taken the larger questions (such as “What possible fractions can be shaded using this diagram?”) as the prompt for entire lessons of student activity. I have used them to create great conversations with grade 7 and 8 students at our school’s annual math fair. I finally found the time (honestly, I found the tech guy… many thanks to @evandcole) to begin a collection …

Continue reading »## Candies, Pennies, and Inequalities

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

[Post Updated June, 2018] 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 …

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/ verb 1. 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 …

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 …

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