Perimeter and area

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Do two rectangles that have the same area also have the same perimeter?

Lesson idea. The lesson idea is about a mathematics investigation, where students explore whether two rectanges that have the same area also have the same perimeter. This is of course not the case, but nevertheless it can be a misconception. Students initially vote, then do an investigation, and finally vote again as well as present their conclusions. The investigation offers an opportunity for same-task group work.

Teaching approach. A problem to inspire higher order(ta) questioning(ta) especially in whole class(ta) dialogic teaching(ta) encouraging pupils to engage in mathematical thinking(ta) and language(ta). You could use Geogebra(tool) in this investigation, as an example of same-task group work(ta). (edit)

Resource details
Title Exploring properties of rectangles: Perimeter and area.
Topic Polygons,  Perimeter,  Area
Teaching approach


Subject
Age of students / grade
Additional Resources/material needed


Files and resources to view and download

Questions to investigate:

  • Do two rectangles that have the same area also have the same perimeter?
  • How many properties of a rectangle (eg height, width, area, perimeter) need to be fixed to fully determine its other properties?
  • What configuration maximises the perimeter of a rectangle?
  • What configuration maximises its area?
Acknowledgement

This resource was contributed by Bjoern Hassler.