AC9M8N01

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

Elaborations

AC9M8N01_E1recognising 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_E2using 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_E3investigating the golden ratio in art and design, and historical approximations to π in different societies
AC9M8N01_E4connecting 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