Education Technology

Rational Thinking

Activity Overview

Students explore the concept of the square root of a number through the side length of a square, dragging a point along a number line and numerical techniques. The activity focuses on continued improvement of the approximation and the concept of irrational through continuity.


ACMNA186 – Investigate the concept of irrational numbers, including π


  • Continuous
  • Rational
  • Irrational
  • Integer

About the Lesson

Students start with a square with integer side lengths and see that it is not possible to create a square with an area of 20 square cm. Spinners are attached to decimal places to progressively increase the accuracy, a better approximation results. A number line is used to improve accuracy with the ability to progressively zoom in for an even better approximation. The Babylonian technique is presented visually then numerically to find an even better approximation, leaving students to ponder “will we ever get there?”