AC9M8N01 Year 8 Mathematics

AC9M8N01 – Year 8 Mathematics: null

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Number

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Number

This Content Descriptor from Year 8 Mathematics provides the specific knowledge and skills students should learn. Use it to plan lessons, create learning sequences, and design assessments that align with the Australian Curriculum v9.

Content Descriptor

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

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

Achievement Standard This Supports

This Content Descriptor contributes to the following Achievement Standard:

Year 8 ASMATY8

Year 8 Mathematics Achievement Standard

By the end of Year 8, students recognise irrational numbers and terminating or recurring decimals. They apply the exponent laws to calculations with numbers involving positive integer exponents. Students solve problems involving the 4 operations with integers and positive rational numbers. They use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts. Students apply algebraic properties to rearrange, expand and factorise linear expressions. They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically. Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context. They make and test conjectures involving linear relations using digital tools. Students use appropriate metric units when solving measurement problems involving the perimeter and area of composite shapes, and volume of right prisms. They use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angle triangles. Students use formulas to solve problems involving the area and circumference of circles. They solve problems of duration involving 12- and 24-hour cycles across multiple time zones. Students use 3 dimensions to locate and describe position. They identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity. Students apply the properties of quadrilaterals to solve problems. They conduct statistical investigations and explain the implications of obtaining data through sampling. Students analyse and describe the distribution of data. They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range. Students represent the possible combinations of 2 events with tables and diagrams, and determine related probabilities to solve practical problems. They conduct experiments and simulations using digital tools to determine related probabilities of compound events.