Counting Factors with Grade 7/8s

One of the great parts of my job as a split classroom teacher and division consultant is that I get to spend time in classrooms from grades six to twelve. This means I often need to be in one head space to teach my own Grade 12s and then switch gears to act with younger mathematicians. It also means that the classroom experiences are sporadic and involve teachers working in several different places in several different curricula. On this particular occasion, I was working with a 7/8 split class that had just finished a unit on perfect squares and divisibility …

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A Twist on Ordering Decimals

Every time I teach a unit on fractions, there are many students who insist that they’d rather use decimals, and I don’t blame them. The obvious parallels to the whole numbers make decimals a “friendly” extension from the integers into the rational numbers. Many of the things school math asks kids to do with rational numbers can be easily transferred into decimals with minimal stress on the algorithms. Such is not the case with fractions. Take addition for example.  When we add whole numbers, we combine collections of equal denomination until it is possible to collect, bind together, and count …

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Problem(s) with Triangles

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 …

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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 …

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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 …

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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 …

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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 …

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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 …

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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 …

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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 …

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