I have taught the second half of a Math 9 Enriched course for the last three years. The students generally finish two-thirds of the curricular outcomes during the first semester (with an different teacher). This alleviates the perpetual nemesis of time, and leaves me with no excuse to stretch the boundaries of what is possible in a classroom. I spend most of the time developing a classroom ecology focused around conjecture, community, and curiosity. The result is a constant focus on problem shaping, solving, and re-posing. At the end of the semester, I ask students to respond to a simple …

Continue reading »# Author: natbanting

## MVPs and Fair Teams

You will not catch me claiming that problems need to be real world in order to be relevant. I would much rather think of classroom materials as either mind numbing or thought provoking. This continuum can be applied to hypothetical, practical, or genuine scenarios (a classification system neatly summarized in a chart in this article). I see the greatest potential in scenarios that provide elegant entrance to mathematical reasoning. If it happens to contain a real world context, fantastic. Either way, it needs to be thought provoking. Take a look at the chart below: If you don’t follow the NBA …

Continue reading »## (Min + Max) imize: A Classroom Game for Basic Facts

**this post was elaborated on in the May 2016 issue of The Variable from the SMTS.This is a game that was adapted from a colleague in my department. He can’t quite remember where it came from, but knows there was some influence from his undergraduate days. Nonetheless, he reinvented it to play with his Grade 9s, and this post represents yet another reinvention. The game has a simple mechanism (dice rolling), and endless extensions to elaborate on and play with. These are both keys to a great classroom game (for me anyway). (Min + Max) imize practices basic operations …

Continue reading »## Limbo: An Integers Game

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 …

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