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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Fraction War Task

A while ago I wrote a post on embedding atomic skills into tasks so that the basic skills are developed and used as tools of mathematics rather than the ultimate goal of mathematics. I try to develop tasks that follow this framework. I want the student to choose a pathway of thought that enables them to use basic skills, but doesn’t focus entirely on them.Recently, I was reading Young Children Reinvent Arithmetic: Implications of Piaget’s Theory by Constance Kamii and came across one of her games that she plays with first graders in her game-driven curriculum.The game was called double …

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The Guess Who Conundrum

Every so often, an idea comes out of left field. I woke up with this on my mind–must have been a dream. Back in the day, my family had a dilapidated copy of the game “Guess Who?” My siblings and I would take turns playing this game of deduction. You essentially narrowed a search for an opponent’s person by picking out characteristics of their appearance. http://www.flickr.com/photos/unloveable/2398625902/ I vividly remember playing with my younger sister one time at a family cottage. She–foolishly–chose a female person for me to identify. Anyone who has played the game before knows that the males far …

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Bike Trail Task

There is two hour parking all around University of Saskatchewan. I once went to move my car (to avoid a ticket) and found that the parking attendant had marked–in chalk–the top of my tire. I wanted to erase the mark so began driving through as many puddles as possible. I then convinced myself to find a puddle longer than the circumference of my tire–to guarantee a clean slate and a fresh two hours.  As I walked back to campus, I got thinking about the pattern left behind by my tires. For simplicity, let’s take the case of a smaller vehicle–a …

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Painting Tape

I came across the following situation while shopping for paint at a local home improvement store: Admittedly, the three varieties were not positioned like this, but this positioning does raise an interesting question. “We can see the packages are the same height, what is that height?” I see this question going one of two ways: The students realize that really any conceivable measurement is possible. (Barring, of course, zero and the negatives) One could make the argument that it also cannot be irrational, but this would be nit-picking. Can a roll of tape have a width of pi/6? Exactly? The …

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All Factors Considered

I have only been teaching for 2 years, but am already beginning to encounter the recursive nature of the profession. I have had several repeat classes in my 4 semesters of teaching, and they require the achievement of the same outcomes. This does not bother me, in general, because I am excited to see the improvement in my teaching. There is one unit, however, that has already frustrated me. Its ability to sabotage creative exploits is unrivaled throughout the mathematics curriculum; I am speaking of the unit on polynomial factoring. The topic was taught in isolation of numerical factors until this …

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Manipulative Revelation

I completed school before manipulatives were in vogue. I am still not sure that they are today (where I teach). I know that my department’s manipulatives are locked up in a cupboard. In this Potter-like clandestine state, I didn’t even learn of their existence until the end of the year. I was moving classrooms, and found a pile of algebra tiles that the previous teacher had left behind. I didn’t discover that I had manipulatives available to me until, ironically, I inquired where I could dispose of this rather large supply of algebra tiles. When I opened the doors of …

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Odd Factors

I am teaching 5 new classes next year. I am trying not to think of it that way; rather, I am taking it one step at a time. Unfortunately, most of these steps need to be taken during my summer vacation. This isn’t the end of the world; I am fairly stationary, and enjoy a mental workout as much as some enjoy time on the beach or in a foreign shopping mall. I began my massive preparation marathon with a unit for Grade 10 Precalculus on factoring. As I dove into the curriculum and textbooks, I found myself actually enjoying …

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Fractions From Digits

This week marked my baptism by fire into the twitter world. It was not long until I was neck deep in tweets, favorites, re-tweets, and followers. The eternal nerd awoke inside me when I was confronted with my first NCTM “Problem of the Day”. A simple, yet dangerously deep, question was posed. Wanting to cement my reputation as a responsible twit, I sat down and began to tinker with the theory. The question was as follows: How many different fractions can you write using only the digits 1,2,3 & 4? Be sure to include fractions greater than 1. Immediately, I …

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