Content description VC2M8N01

Mathematics Version 2.0 / Level 8 / Number

Content description

recognise irrational numbers in applied contexts, including π and numbers that develop from the square root of positive real numbers that are not perfect squares, and recognise that irrational numbers cannot develop from the division of integer values by natural numbers

Elaborations

recognising that the real number system includes irrational numbers that 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
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 the paper sizes A0, A1, A2, A3 and A4
investigating the golden ratio in art and design, and historical approximations to π in different societies
connecting the ratio between the circumference and diameter of any circle to the irrational value of π using circular objects and string or dynamic geometry software

Code

VC2M8N01

Curriculum resources and support

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