AC9M8A04 Year 8 Mathematics

AC9M8A04 – Year 8 Mathematics: null

Strand

Algebra

Substrand

Algebra

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

experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

Elaborations

• using graphing software to investigate the effect of systematically varying parameters of linear functions on the corresponding graphs, making and testing conjectures; for example, making a conjecture that if the co-efficient of \(x\) is negative, then the line will slope down from left to right
• using graphing software to systematically contrast the graphs of \(y\;=\;2x\), -\(y\;=\;2x\), \(y\;=\;\)-\(2x\) and -\(y\;=\;\)-\(2x\) with those of \(y<2x\), \(-y<2x\), \(y<\)-\(2x\) and -\(y<\)-\(2x\) and those of \(y>2x\), -\(y>2x\), \(y>\)-\(2x\) and -\(y>\)-\(2x\), making and testing conjectures about sign and direction of the inequality
• using digital tools to investigate integer solutions to equations such as \(2x+3y\;=\;48\)
• exploring how linear functions are used in linear regression models as a statistical technique in machine learning of artificial intelligence agents; for example, linear functions are used to model the relationship between input variables and a target variable, to predict stock or house prices in the financial and real-estate sectors

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.