Year 8 Mathematics Achievement Standard – Australian Curriculum v9
This Achievement Standard describes what students are expected to know and do in Year 8 Mathematics by the end of the year. Teachers can use it to guide assessment design, collect evidence of learning, and ensure planning stays aligned with the Australian Curriculum v9.
What Students Should Know
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.
Content Descriptors by Strand
This standard is supported by 27 Content Descriptors:
Algebra
AC9M8A01 create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties AC9M8A02 graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution AC9M8A03 use mathematical modelling to solve applied problems involving linear relations, including financial contexts; formulate problems with linear functions, choosing a representation; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model AC9M8A04 experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patternsMeasurement
AC9M8M01 solve problems involving the area and perimeter of irregular and composite shapes using appropriate units AC9M8M02 solve problems involving the volume and capacity of right prisms using appropriate units AC9M8M03 solve problems involving the circumference and area of a circle using formulas and appropriate units AC9M8M04 solve problems involving duration, including using 12- and 24-hour time across multiple time zones AC9M8M05 recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure AC9M8M06 use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles AC9M8M07 use mathematical modelling to solve practical problems involving ratios and rates, including financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the modelNumber
AC9M8N01 recognise irrational numbers in applied contexts, including square roots and \(π\) AC9M8N02 establish and apply the exponent laws with positive integer exponents and the zero-exponent, using exponent notation with numbers AC9M8N03 recognise terminating and recurring decimals, using digital tools as appropriate AC9M8N04 use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate AC9M8N05 use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the modelProbability
AC9M8P01 recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts AC9M8P02 determine all possible combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific outcomes in practical situations AC9M8P03 conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe resultsSpace
AC9M8SP01 identify the conditions for congruence and similarity of triangles and explain the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations AC9M8SP02 establish properties of quadrilaterals using congruent triangles and angle properties, and solve related problems explaining reasoning AC9M8SP03 describe the position and location of objects in 3 dimensions in different ways, including using a three-dimensional coordinate system with the use of dynamic geometric software and other digital tools AC9M8SP04 design, create and test algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describe how the algorithm worksStatistics
AC9M8ST01 investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques AC9M8ST02 analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques to select and study samples AC9M8ST03 compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation AC9M8ST04 plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertaintyAt a Glance
| Strand | Substrand | CDs | Elaborations |
|---|---|---|---|
| Algebra | — | 4 | 17 |
| Measurement | — | 7 | 29 |
| Number | — | 5 | 17 |
| Probability | — | 3 | 11 |
| Space | — | 4 | 18 |
| Statistics | — | 4 | 18 |
| Total | 27 | 110 | |