Properties of rectangles - perimeter and area

Well? Lesson ideas can be as long as one sentence wide.

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 this can be a misconception. Students initially vote, then do an investigation, and finally vote again as well as present. 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).

Resource details
Title	Do two rectangles that have the same area also have the same perimeter?
Topic	[[Topics/Area|Area]],  [[Topics/Perimeter|Perimeter]],  [[Topics/Polygons|Polygons]]
Teaching approach	[[Teaching Approaches/Higher order|Higher order]],  [[Teaching Approaches/Questioning|Questioning]],  [[Teaching Approaches/Whole class|Whole class]],  [[Teaching Approaches/Dialogic teaching|Dialogic teaching]],  [[Teaching Approaches/Mathematical thinking|Mathematical thinking]],  [[Teaching Approaches/Language|Language]],  [[Teaching Approaches/Group work|Group work]]
Subject	[[Resources/Maths|Maths]]
Age of students / grade	[[Resources/Secondary|Secondary]],  [[Resources/Primary|Primary]]
Additional Resources/material needed	Geogebra or another maths package could be used Example of a related Geogebra file
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.