Category: graphing

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 …

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 …

Connecting Quadratic Representations

I always introduce linear functions with the idea of a growing pattern. Students are asked to describe growth in patterns of coloured squares, predict the values of future stages, and design their own patterns that grow linearly. Fawn’s VisualPatterns is a perfect tool for this. While stumbling around Visual Patterns with my Grade 9s, we …

On Collective Consciousness and Individual Epiphanies

I would like to begin with a conjecture: The amount of collective action in a learning system is inversely related to the possible degree of curricular specificity.¬† The mathematical action of a group of learners centred on a particular task gives rise to a unique way of being with the problem, but also reinvents the …

YouTube Relations

My goal this semester was to continue to improve my use of formative assessment (largely through the use of whiteboarding) and expand the role of Project-Based Learning in my classroom. Up to this point, I have developed a wide-scale PBL framework for an applied stream of math we have in the province called Workplace and …

Using Real-Time Graphs

I have a class of grade nine students this semester that are part of a stretch program. This essentially means that they get 160 hours to complete a 120 hour course. The class is designed to accommodate the transition from elementary school (Grades 1-8) into high school (Grades 9-12) for those students who feel uncomfortable¬†with …

The Mathematics of Laundry Soap

The grocery store is a brain workout for the mathematically inclined. Not only do the varying metric and imperial conversions tease out the micro-savings of bulk, but neon yellow discount signs encourage percentages and good ole’ multiplication tables. Often you find adults transfixed in a complex division trying to figure out which ham will be …

The Linear Relations of Hamburgers

Maybe you have seen the Burger King Stacker commercial where “Meat Scientists” work on an interesting problem. Needless to say, it piqued my curiosity the second I saw it; it was not long until I was trying to suck every ounce of mathematical value from the video. I am sure that I did not accomplish …