Category: tasks

Thinking Upstream with a Quadratics Menu

Much of what appears in mathematics textbooks is what I like to call, downstream thinking. Downstream thinking usually involves two features that set the stage for learners. First, it provides a context (however doctored or engineered–often referred to as “pseudo-context”). Second, the problem provides a pre-packaged algebraic model that is assumed to have arisen from …

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 …

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 …

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 …

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: …

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 …

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). …