# Perimeter of a rectangle

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 Perimeter of a rectangle. Topic Visualisation Format / structure Embedded GeoGebra applet and guidance notes. Subject Age of students / grade 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. The following related applet by the same author is for use with secondary school students: Circumference of a Circle Files and resources to view and download GeoGebra file: Guidance notes: Acknowledgement Irina Boyadzhiev

## Guidance notes

I. Overview

The goal of this applet is to introduce a very young learner to the concept of a perimeter, and in particular, the perimeter of a rectangle. A rectangle can be brought to the number line and rolled there by dragging the slider. The opposite sides, pained in two different colors leave a trace on the number line as the rectangle comes in contact with it. The dimensions of the rectangle can be changed by dragging the upper corners in the direction of the arrows. The dimensions are restricted to whole numbers.

II. Suggested activities and learning outcomes

1. Construct several rectangles with different dimensions, roll them and measure their perimeters. The students should see a pattern using the different colors. With some repetitions they should be able to come up with a rule for finding the perimeter.

2. Make all sides the same length. Will the same rule work? Can we come up with a special rule in this case? Construct several squares and test the new rule.

3. Construct two different rectangles with the same perimeter, for example 10. Repeat this for other perimeters – 12 , 15 etc.

4. A challenge question – count the number of squares enclosed by the rectangles in the previous activity. Objective: Rectangle with equal perimeters don't necessarily have the same area.

5. A challenge question – if the width of the rectangle is 2 and the perimeter is 12,what is the length? The students can try several possible sides and check the perimeter before they come up with a rule for finding the side.

III. Learning objectives

• Introduce the concept of a perimeter of a rectangle and discover a rule for finding the perimeter (activity 1).
• General-to-special case (activity 2).
• Different rectangles can have the same perimeter (activity 3).

IV. Underlying pedagogical/teaching approach or rationale

This applet creates a well controlled environment for a young student to experiment and learn. The intention is to create a lasting understanding of what the perimeter of a rectangle is by allowing the student to construct and manipulate it. The perimeter is associated with a very concrete action, the use of different colors and a movement.