AC9M8N01

recognise irrational numbers in applied contexts, including square roots and \(π\)

Elaborations

AC9M8N01_E1 - recognising that the real number system includes irrational numbers which can be approximately located on the real number line; for example, the value of \(π\) lies somewhere between \(3.141\) and \(3.142\) that is, \(3.141 < π < 3.142\)
AC9M8N01_E2 - using digital tools to systematically explore contexts or situations that use irrational numbers, such as finding the length of the hypotenuse in a right-angled triangle with the other \(2\) sides having lengths of one metre or \(2\) metres and one metre; or given the area of a square, finding the length of the side where the result is irrational; or finding ratios involved with the side lengths of paper sizes \(A0\), \(A1\), \(A2\), \(A3\) and \(A4\)
AC9M8N01_E3 - investigating the golden ratio in art and design, and historical approximations to \(π\) in different societies
AC9M8N01_E4 - connecting the ratio between the circumference and diameter of any circle to the irrational value of \(π\) using circular objects and string or dynamic drawing software

Achievement Standard Components

ASMAT801 - By the end of Year 8, students recognise irrational numbers and terminating or recurring decimals.