Variety of perimeters with fixed area

Interactive GeoGebra investigation that allows children (age 6-10) to explore an element of mathematics for themselves.

Lesson idea. Geogebra has been used to create a simple interactive applet. The applet and guidance notes on how to use it with students are included with the resource.

Resource details
Title	Variety of perimeter with fixed area
Topic
Teaching approach
Learning Objectives
Format / structure	Embedded GeoGebra applet and guidance notes.
Subject
Age of students / grade
Table of contents
Additional Resources/material needed
Useful information
Related ORBIT Wiki Resources	This activity is a result of the 2013 ORBIT/GeoGebra Competition that asked entrants to create an open-ended activity that supports interactive teaching and active learning for the 6-10 age range.
Other (e.g. time frame)
Files and resources to view and download	GeoGebra file: File:Variety of perimeters with fixed area.ggb Guidance notes: File:Variety of perimeters with fixed areas.doc
Acknowledgement	Anthony Or
License

Guidance notes

1) Overview

After learning the concepts of perimeter and area, it is easy for students to think that figures with larger perimeters would also have larger areas, and vice versa. This applet helps teachers to explore with students the variety of the perimeters of a figure formed by several congruent squares touching side by side. Together with the complementary applet Variety of areas with fixed perimeter, teachers can clarify with students that a figure with a larger area may have a smaller perimeter, and areas and perimeters are two different concepts.

2) Learning Objectives

• Recognise that figures with the same areas could have different perimeters.
• Recognise the strategy of minimizing the perimeters of figures with the same areas.

3) Teaching Approach

An enquiry teaching approach is expected. Students are asked to arrange 3 to 9 squares to form different figures and find their possible perimeters. Teacher then guide students to express their strategies of getting the largest and smallest perimeter with a certain number of squares.

4) Teacher’s Note

For each number of squares, ask students to record the possible perimeters in the table of the applet. Guide students to focus on the change of the perimeter when a square is dragged to a new position. Discuss with students the strategy of minimizing the perimeter, especially for 4 and 9 squares.