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Related topic
Mathematics / Year 8 / Number
Curriculum content descriptions
recognise irrational numbers in applied contexts, including square roots and \(π\) (AC9M8N01)
Elaborations
- 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, \(3.141 < π < 3.142\)
- 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 \(A4\)
- 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 drawing software
General capabilities
ScOT terms
Irrational numbers, pi, Square roots