Rectangular Relations TN

Teacher Notes

One of the challenges of mathematics is to provide opportunities for students to be creative with their mathematics, and to find activities that allow students of differing abilities to obtain satisfaction in this process. "Elegant solutions such as are found in most mathematics texts rarely spring fully formed from someone's brain . . .  but most beginner's do not realise this"1. The aim of this activity is to provide an opportunity for learners to experience the process by which mathematics is created.

Some students will remember the formula for trapeziums and parallelograms after seeing, or hearing it, just once. In my experience, a number of other students will continue to struggle to find the areas of these shapes right the way through to age 15+. When faced with a question concerning the area of a parallelogram or trapezium, they will panic. They have a faint recollection that they have done something like this before, but cannot remember, and consequently end up write nothing or multiply all, and any, measurements together. 

Through a concrete experience of using what they know to help shed some light on something they don't know, it is hoped that learner's will use the tools available to them, whatever they may be, to make progress, when next faced with uncertainty.


Displays take time, but they’re worth it! They provide a stimulating environment within which students are constantly reviewing previous knowledge and making new links and connections. I have often used these sort of displays:

(a) as a good, visual answer for students when they ask how to find the area of a trapezium or parallelogram.

(b) remind classes, during some practice exercises, why the formulae they are using for trapeziums and parallelograms works.

(c) provide an example of how human knowledge advances, solving the unfamiliar by applying the familiar in new, innovative ways: “don’t panic! Use what you know to help you make progress with what you don’t know!

Resources needed

  • Class set of scissors
  • Glue
  • Blu-Tak
  • Card or sugar paper to use as backing paper for mounting the display
  • Colouring crayons/felt tips (in case students don’t have their own)

Time needs

The activity does require a good 1h30 minutes if you want to allow time for students to finish the poster with parallelograms on one side and trapeziums on the other (if you're hanging them from the ceiling). I tend to use two 15 minute sections of each lesson to give follow up questions on parallelograms (the first lesson) and trapeziums (the second) and offer merits/rewards for anyone who comes back and completes their poster outside of class if they didn't manage to during the lesson.


Students can take photos of their pair/group's poster to keep on their phones, computers, use as a screensaver for a week before a test etc!




1 Mason, J., with Burton, L., and Stacey, K., 1985. Thinking Mathematically. Revised Edition. Pearson Education Ltd.

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