My provincial curriculum scatters trigonometry throughout several high school courses. Right-angled trig appears first as an isolated experience at the Grade 10 level. From there, the two pathways in Grade 11 cover the Sine and Cosine laws, but only one stream (Pre-calculus) continues into the idea of the unit circle and eventually the connections between the side ratios of right-angled triangles, the unit circle, the wave functions, and trigonometric identities. Since trig is doled out in piecemeal portions each semester, I often find that the hidden beauty of trig is masked by things like SOH CAH TOA. (Or, if you dare …

Continue reading »# Category: tasks

## Shoe Sale Remake

I transferred schools at the end of last year, so for the first time in seven years, every one of my students I meet on the first day of school will be a stranger. This means that the first hour I have with each of the four classes is not only their introduction to the course, but also their introduction to me. It won’t take long for them to make an impression of me, of mathematics, of their classmates, and how I expect us all to co-exist for the next five months or so. I have written on first day …

Continue reading »## Solid Fusing Task

The progression followed by most teachers and resources during the study of surface area and volume is identical. Like a intravenous drip, concepts are released gradually to the patients so as to not overdose them with complexity. Begin with the calculation of 2-dimensional areas, and then proceed to the calculation of surface area of familiar prisms. (I say prisms, so a parallel can be drawn to the common structure for finding the volume of said prisms. That is, [area of base x height]). In this way, surface area is conceptualized as nothing more than a dissection of 3-dimensional solids into …

Continue reading »## 100 Rolls Task

Most probability resources contain a familiar type of question: the two-dice probability distribution problem. Often times, it is accompanied with questions concerning the sums of the faces that appear on each dice. For example: Roll two fair, 6-sided dice. What possible sums can be made by adding the faces together? What is the probability that: a) the sum is 6 b) the sum is a multiple of 4 c) the sum is greater than 15? I think the obsession with this specific subdomain of probability questions stems from the elegant way in which a table of outcomes (pictured below) leads to a …

Continue reading »## TDC Math Fair 2016: A Summary

Background:On June 15th, my Grade 9 class and I hosted our second annual math fair. What started out as a small idea has grown into a capstone event of their semester. This year, we had 330 elementary school students visit our building to take part in the fair’s activities. Several people (following the hashtag #TDCMathFair2016) commented that they would like to do similar things with their student transitions. This post details the rationale behind the event, how we structured it, what stations we had, and feedback/advice from our exploits.Rationale:I pursued this opportunity with a two-pronged focus. First, I wanted to showcase a …

Continue reading »## 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 »## 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 »## 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 »## 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 »## Fraction Talks

Discussion is one of the organic ways through which human interaction occurs, but not all discussion is created equal in the math classroom. The tone of discussion relies on the mode of listening (Davis, 1996). Most classroom talk focuses on an evaluative mode of listening. Students are expected to share, compare, and contrast solutions to problems.I do think that justification of their solutions gets at some important points regarding mathematical reasoning, but would like to move the discussion to center around that exact feature–the reasoning. Rather than piecing together the pieces of isolated reasoning (which I still think has value), I want to see a collective …

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