Parametric equations card sort

Recently I taught an observed lesson on the introduction of parametric equations (Core 4). One of the tasks which I used towards the end of the lesson was a self-designed card sort activity. This task requires students to match a set of parametric equations with their corresponding Cartesian relation and graph. Within one set of cards there are five groupings, with some of the Cartesian relation and graph cards remaining blank.


A key idea that one grouping in the card sort helps to address is how restrictions upon the parameterised equations may not result in the full Cartesian graph.

The parametric equations used in the task are x=\sin^2{t}, y=\cos^2{t}, which for all values of t only gives x and y values between -1 and 1. This results in the Cartesian graph of x+y=1, but only a small segment of it (see graph on the left).

When I implemented the task students got engaged with it quickly, some making matches and others getting stuck with manipulating equations to eliminate the parameter. There were certainly a number of challenges encountered, though I thought that the task itself really helped to test their understanding of what they had learnt during the lesson, and provided me with a better idea of who needed more support.parametriccardsort

Parametric and Cartesian equations cards

Graph cards

Solution sheet

Please feel free to provide me with any feedback on this task, I would be particularly interested in general thoughts or any suggestions on further developments that could be made to improve the task.

Please also let me know if you make use of this activity and if it is successful!