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Learning Areas#

See also: australian-curriculum, teaching

About this page

The base information on this page is generated automatically from machine-readable versions of version 9 of the Australian Curriculum using this project

In particular, it's an example of leveraging the reprogrammability of digital technologies to orchestrate (gather, weave and augment) a range of technologies (the Australian Curriculum, RDF, Python, Foam etc) for a very specific purpose. In this case specific to an individual teacher. Rather than make do with the generic Australian Curriculum site the same data as been woven into something more useful (for me).

Mathematics#

Mathematics#

Year 7#

Year level description

In Year 7, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to learning and doing mathematics that develop their understanding of and fluency with concepts, procedures and processes by making connections, reasoning, problem-solving and practice. Proficiency in mathematics enables students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently.

Students further develop proficiency and positive dispositions towards mathematics and its use as they:

  • extend their understanding of the integer and rational number systems, strengthen their fluency with mental calculation, written algorithms and digital tools; and routinely consider the reasonableness of results in context
  • use exponents and exponent notation to consolidate and formalise their understanding of representations of natural numbers, and use these to make conjectures involving natural numbers by experiment with the assistance of digital tools
  • recognise the use of algebraic expressions and formulas using conventions, notations, symbols and pronumerals. They interpret algebraic expressions and formulas, use substitution to evaluate and determine unknown terms where other values are given, and solve simple equations using a variety of methods
  • use mathematical modelling to solve practical problems involving rational numbers, ratios and percentages, formulating and making choices about representations, calculation strategies and communicating solutions within the context
  • use variables, constants, relations and functions to express relationships in real life data and interpret key features of their representation in rules, tables and graphs
  • extend their knowledge of angles to establish further relationships and apply these when solving measurement and spatial problems
  • create and use algorithms to classify shapes in the plane and use tools to construct shapes, including two-dimensional representations of prisms and other objects
  • use coordinates in the Cartesian plane to describe transformations
  • apply the statistical investigation process to obtain numerical data related to questions of interest, choose displays for the distributions of data and interpret summary statistics for determining the centre and spread of the data in context
  • conduct probability simulations and experiments involving chance events, construct corresponding sample spaces and observe related frequencies, comparing expected, simulated and experimental results.
Achievement Standard

By the end of Year 7, students represent natural numbers in expanded form and as products of prime factors, using exponent notation. They solve problems involving squares of numbers and square roots of perfect square numbers. Students solve problems involving addition and subtraction of integers. They use all 4 operations in calculations involving positive fractions and decimals, choosing efficient calculation strategies. Students choose between equivalent representations of rational numbers and percentages to assist in calculations. They use mathematical modelling to solve practical problems involving rational numbers, percentages and ratios in financial and other applied contexts, justifying choices of representation. Students use algebraic expressions to represent situations, describe the relationships between variables from authentic data and substitute values into formulas to determine unknown values. They solve linear equations with natural number solutions. Students create tables of values related to algebraic expressions and formulas, and describe the effect of variation.

They apply knowledge of angle relationships and the sum of angles in a triangle to solve problems, giving reasons. Students use formulas for the areas of triangles and parallelograms and the volumes of rectangular and triangular prisms to solve problems. They describe the relationships between the radius, diameter and circumference of a circle. Students classify polygons according to their features and create an algorithm designed to sort and classify shapes. They represent objects two-dimensionally in different ways, describing the usefulness of these representations. Students use coordinates to describe transformations of points in the plane.

They plan and conduct statistical investigations involving discrete and continuous numerical data, using appropriate displays. Students interpret data in terms of the shape of distribution and summary statistics, identifying possible outliers. They decide which measure of central tendency is most suitable and explain their reasoning. Students list sample spaces for single step experiments, assign probabilities to outcomes and predict relative frequencies for related events. They conduct repeated single-step chance experiments and run simulations using digital tools, giving reasons for differences between predicted and observed results.

  • ASMAT701: By the end of Year 7, students represent natural numbers in expanded form and as products of prime factors, using exponent notation.
  • ASMAT702: They solve problems involving squares of numbers and square roots of perfect square numbers.
  • ASMAT703: Students solve problems involving addition and subtraction of integers.
  • ASMAT704: They use all 4 operations in calculations involving positive fractions and decimals, choosing efficient calculation strategies.
  • ASMAT705: Students choose between equivalent representations of rational numbers and percentages to assist in calculations.
  • ASMAT706: They use mathematical modelling to solve practical problems involving rational numbers, percentages and ratios, in financial and other applied contexts, justifying choices of representation.
  • ASMAT707: Students use algebraic expressions to represent situations, describe the relationships between variables from authentic data and substitute values into formulas to determine unknown values.
  • ASMAT708: They solve linear equations with natural number solutions.
  • ASMAT709: Students create tables of values related to algebraic expressions and formulas, and describe the effect of variation.
  • ASMAT710: They apply knowledge of angle relationships and the sum of angles in a triangle to solve problems, giving reasons.
  • ASMAT711: Students use formulas for the areas of triangles and parallelograms and the volumes of rectangular and triangular prisms to solve problems.
  • ASMAT712: They describe the relationships between the radius, diameter and circumference of a circle.
  • ASMAT713: Students classify polygons according to their features and create an algorithm designed to sort and classify shapes.
  • ASMAT714: They represent objects two-dimensionally in different ways, describing the usefulness of these representations.
  • ASMAT715: Students use coordinates to describe transformations of points in the plane.
  • ASMAT716: They plan and conduct statistical investigations involving discrete and continuous numerical data, using appropriate displays.
  • ASMAT717: Students interpret data in terms of the shape of distribution and summary statistics, identifying possible outliers.
  • ASMAT718: They decide which measure of central tendency is most suitable and explain their reasoning.
  • ASMAT719: Students list sample spaces for single step experiments, assign probabilities to outcomes and predict relative frequencies for related events.
  • ASMAT720: They conduct repeated single-step chance experiments and run simulations using digital tools, giving reasons for differences between predicted and observed results.
Number#
  • AC9M7N01

    describe the relationship between perfect square numbers and square roots, and use squares of numbers and square roots of perfect square numbers to solve problems

  • AC9M7N02

    represent natural numbers as products of powers of prime numbers using exponent notation

  • AC9M7N03

    represent natural numbers in expanded notation using place value and powers of 10

  • AC9M7N04

    find equivalent representations of rational numbers and represent rational numbers on a number line

  • AC9M7N05

    round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions

  • AC9M7N06

    use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies

  • AC9M7N07

    compare, order and solve problems involving addition and subtraction of integers

  • AC9M7N08

    recognise, represent and solve problems involving ratios

  • AC9M7N09

    use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation

Algebra#
  • AC9M7A01

    recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown

  • AC9M7A02

    formulate algebraic expressions using constants, variables, operations and brackets

  • AC9M7A03

    solve one-variable linear equations with natural number solutions; verify the solution by substitution

  • AC9M7A04

    describe relationships between variables represented in graphs of functions from authentic data

  • AC9M7A05

    generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane

  • AC9M7A06

    manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables

Measurement#
  • AC9M7M01

    solve problems involving the area of triangles and parallelograms using established formulas and appropriate units

  • AC9M7M02

    solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units

  • AC9M7M03

    describe the relationship between \(π\) and the features of circles including the circumference, radius and diameter

  • AC9M7M04

    identify corresponding, alternate and co-interior relationships between angles formed when parallel lines are crossed by a transversal; use them to solve problems and explain reasons

  • AC9M7M05

    demonstrate that the interior angle sum of a triangle in the plane is 180° and apply this to determine the interior angle sum of other shapes and the size of unknown angles

  • AC9M7M06

    use mathematical modelling to solve practical problems involving ratios; formulate problems, interpret and communicate solutions in terms of the situation, justifying choices made about the representation

Space#
  • AC9M7SP01

    represent objects in 2 dimensions; discuss and reason about the advantages and disadvantages of different representations

  • AC9M7SP02

    classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships

  • AC9M7SP03

    describe transformations of a set of points using coordinates in the Cartesian plane, translations and reflections on an axis, and rotations about a given point

  • AC9M7SP04

    design and create algorithms involving a sequence of steps and decisions that will sort and classify sets of shapes according to their attributes, and describe how the algorithms work

Statistics#
  • AC9M7ST01

    acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of data

  • AC9M7ST02

    create different types of numerical data displays including stem-and-leaf plots using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode

  • AC9M7ST03

    plan and conduct statistical investigations involving data for discrete and continuous numerical variables; analyse and interpret distributions of data and report findings in terms of shape and summary statistics

Probability#
  • AC9M7P01

    identify the sample space for single-stage events; assign probabilities to the outcomes of these events and predict relative frequencies for related events

  • AC9M7P02

    conduct repeated chance experiments and run simulations with a large number of trials using digital tools; compare predictions about outcomes with observed results, explaining the differences

Year 8#

Year level description

In Year 8, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to learning and doing mathematics that develop their understanding of and fluency with concepts, procedures and processes by making connections, reasoning, problem-solving and practice. Proficiency in mathematics enables students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently.

Students further develop proficiency and positive dispositions towards mathematics and its use as they:

  • extend computation with combinations of the 4 operations with integers and positive rational numbers, recognise the relationship between fractions and their terminating or infinite recurring decimal expansions; they convert between fraction and decimal forms of rational numbers and locate them on the real number line
  • extend the exponent laws to numerical calculations involving positive and zero exponents, and solve a broad range of practical problems, using mental methods, written algorithms and digital tools
  • use mathematical modelling to solve problems in a broad range of contexts that involve ratios with 2 or more terms, percentage increase and decrease, proportions with decimal values, and rates in measurement contexts, and apply proportional reasoning
  • manipulate linear and other algebraic expressions, recognise and model situations using linear relations and solve related equations using tables, graphs and algebra
  • interpret and explain demonstrations and proofs of Pythagoras’ theorem and investigate irrational numbers, their infinite non-recurring decimal expansion and their approximate location on the real number line
  • select metric measurement units fit for purpose, convert between units, recognising the effects of different levels of measurement accuracy on the results of computations, and relate these to interval estimates for measurements in various contexts
  • apply knowledge of the relationships between π and the features of circles to solve problems involving circumference and area and establish sets of congruency and similarity conditions for common shapes in the plane and create algorithms to test for these conditions, discuss examples and counterexamples
  • construct and locate objects with reference to three-dimensional coordinates using digital tools
  • consider a variety of situations involving complementary and mutually exclusive events, combinations of 2 events; represent these using tables and diagrams, conducting simulations and calculating corresponding probabilities
  • examine experimental and observational data and identify populations and samples with respect to context; investigate variation in summary statistics across samples of varying size and discuss their findings.
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.

  • ASMAT801: By the end of Year 8, students recognise irrational numbers and terminating or recurring decimals.
  • ASMAT802: They apply the exponent laws to calculations with numbers involving positive integer exponents.
  • ASMAT803: Students solve problems involving the 4 operations with integers and positive rational numbers.
  • ASMAT804: They use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts.
  • ASMAT805: Students apply algebraic properties to rearrange, expand and factorise linear expressions.
  • ASMAT806: They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically.
  • ASMAT807: Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context.
  • ASMAT808: They make and test conjectures involving linear relations using digital tools.
  • ASMAT809: Students use appropriate metric units when solving measurement problems involving the perimeter and area of composite shapes, and volume of right prisms.
  • ASMAT810: They use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angle triangles.
  • ASMAT811: Students use formulas to solve problems involving the area and circumference of circles.
  • ASMAT812: They solve problems of duration involving 12- and 24-hour cycles across multiple time zones.
  • ASMAT813: Students use 3 dimensions to locate and describe position.
  • ASMAT814: They identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity.
  • ASMAT815: Students apply the properties of quadrilaterals to solve problems.
  • ASMAT816: They conduct statistical investigations and explain the implications of obtaining data through sampling.
  • ASMAT817: Students analyse and describe the distribution of data.
  • ASMAT818: 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.
  • ASMAT819: Students represent the possible combinations of 2 events with tables and diagrams, and determine related probabilities to solve practical problems.
  • ASMAT820: They conduct experiments and simulations using digital tools to determine related probabilities of compound events.
Number#
  • 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 model

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 patterns

Measurement#
  • 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 model

Space#
  • 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 works

Statistics#
  • 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 uncertainty

Probability#
  • 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 results

Year 9#

Year level description

In Year 9, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to learning and doing mathematics that develop their understanding of and fluency with concepts, procedures and processes by making connections, reasoning, problem-solving and practice. Proficiency in mathematics enables students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently.

Students further develop proficiency and positive dispositions towards mathematics and its use as they:

  • apply scientific notation in measurement contexts, routinely consider accuracy in measurement and work with absolute, relative and percentage errors in a range of different measurement contexts
  • work with the real number line as a geometric model for real numbers that provides a continuous measurement scale; locate different fractions exactly on the common scale of the real number line using scale and similarity, and locate some irrational square roots of natural numbers using Pythagoras’ theorem
  • use linear and quadratic functions to model a broad range of phenomena and contexts, make predictions, and represent these using tables, graphs and algebra, including with the use of digital tools
  • manipulate algebraic expressions involving variables, exponents, and the expansion and factorisation of simple quadratic expressions using a variety of techniques including tables, diagrams, algorithms and digital tools
  • formulate and solve related linear and non-linear equations exactly or approximately using numerical, graphical and algebraic approaches
  • solve measurement problems about the surface area and volume of objects and apply formulas to solve problems, calculating these and related dimensions of objects as required
  • use similarity, scale, trigonometry, enlargement transformations, the triangle inequality and Pythagoras’ theorem to solve practical problems using given sets of information
  • investigate probabilities of compound events from two-step experiments and solve related problems; use a variety of representations such as Venn diagrams, tree diagrams, two-way tables and grids to assist in determining the probabilities for these events; design experiments to gather empirical data about relative frequencies and use these to check their reasoning
  • compare multiple numerical data subsets in context and analyse their distributions with consideration of symmetry and skew; justify their choice of data representation with respect to data types and context, and critically review the statistical presentation of data and related arguments of others.
Achievement Standard

By the end of Year 9, students recognise and use rational and irrational numbers to solve problems. They extend and apply the exponent laws with positive integers to variables. Students expand binomial products, and factorise monic quadratic expressions. They find the distance between 2 points on the Cartesian plane, and the gradient and midpoint of a line segment. Students use mathematical modelling to solve problems involving change in financial and other applied contexts, choosing to use linear and quadratic functions. They graph quadratic functions and solve monic quadratic equations with integer roots algebraically. Students describe the effects of variation of parameters on functions and relations, using digital tools, and make connections between their graphical and algebraic representations.

They apply formulas to solve problems involving the surface area and volume of right prisms and cylinders. Students solve problems involving ratio, similarity and scale in two-dimensional situations. They determine percentage errors in measurements. Students apply Pythagoras’ theorem and use trigonometric ratios to solve problems involving right-angled triangles. They use mathematical modelling to solve practical problems involving direct proportion, ratio and scale, evaluating the model and communicating their methods and findings. Students express small and large numbers in scientific notation. They apply the enlargement transformation to images of shapes and objects, and interpret results. Students design, use and test algorithms based on geometric constructions or theorems.

They compare and analyse the distributions of multiple numerical data sets, choose representations, describe features of these data sets using summary statistics and the shape of distributions, and consider the effect of outliers. Students explain how sampling techniques and representation can be used to support or question conclusions or to promote a point of view. They determine sets of outcomes for compound events and represent these in various ways. Students assign probabilities to the outcomes of compound events. They design and conduct experiments or simulations for combined events using digital tools.

  • ASMAT901: By the end of Year 9, students recognise and use rational and irrational numbers to solve problems.
  • ASMAT902: They extend and apply the exponent laws with positive integers to variables.
  • ASMAT903: Students expand binomial products, and factorise monic quadratic expressions.
  • ASMAT904: They find the distance between 2 points on the Cartesian plane, and the gradient and midpoint of a line segment.
  • ASMAT905: Students use mathematical modelling to solve problems involving change in financial and other applied contexts, choosing to use linear and quadratic functions.
  • ASMAT906: They graph quadratic functions and solve monic quadratic equations with integer roots algebraically.
  • ASMAT907: Students describe the effects of variation of parameters on functions and relations, using digital tools, and make connections between their graphical and algebraic representations.
  • ASMAT908: They apply formulas to solve problems involving the surface area and volume of right prisms and cylinders.
  • ASMAT909: Students solve problems involving ratio, similarity and scale in two-dimensional situations.
  • ASMAT910: They determine percentage errors in measurements.
  • ASMAT911: Students apply Pythagoras’ theorem and use trigonometric ratios to solve problems involving right-angled triangles.
  • ASMAT912: They use mathematical modelling to solve practical problems involving direct proportion, ratio and scale, evaluating the model and communicating their methods and findings.
  • ASMAT913: Students express small and large numbers in scientific notation.
  • ASMAT914: They apply the enlargement transformation to images of shapes and objects, and interpret results.
  • ASMAT915: Students design, use and test algorithms based on geometric constructions or theorems.
  • ASMAT916: They compare and analyse the distributions of multiple numerical data sets, choose representations, describe features of these data sets using summary statistics and the shape of distributions, and consider the effect of outliers.
  • ASMAT917: Students explain how sampling techniques and representation can be used to support or question conclusions or to promote a point of view.
  • ASMAT918: They determine sets of outcomes for compound events and represent these in various ways.
  • ASMAT919: Students assign probabilities to the outcomes of compound events.
  • ASMAT920: They design and conduct experiments or simulations for combined events using digital tools.
Number#
  • AC9M9N01

    recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools

Algebra#
  • AC9M9A01

    apply the exponent laws to numerical expressions with integer exponents and extend to variables

  • AC9M9A02

    simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions

  • AC9M9A03

    find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane

  • AC9M9A04

    identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate

  • AC9M9A05

    use mathematical modelling to solve applied problems involving change including financial contexts; formulate problems, choosing to use either linear or quadratic functions; interpret solutions in terms of the situation; evaluate the model and report methods and findings

  • AC9M9A06

    experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns

Measurement#
  • AC9M9M01

    solve problems involving the volume and surface area of right prisms and cylinders using appropriate units

  • AC9M9M02

    solve problems involving very small and very large measurements, time scales and intervals expressed in scientific notation

  • AC9M9M03

    solve spatial problems, applying angle properties, scale, similarity, Pythagoras’ theorem and trigonometry in right-angled triangles

  • AC9M9M04

    calculate and interpret absolute, relative and percentage errors in measurements, recognising that all measurements are estimates

  • AC9M9M05

    use mathematical modelling to solve practical problems involving direct proportion, rates, ratio and scale, including financial contexts; formulate the problems and interpret solutions in terms of the situation; evaluate the model and report methods and findings

Space#
  • AC9M9SP01

    recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity

  • AC9M9SP02

    apply the enlargement transformation to shapes and objects using dynamic geometry software as appropriate; identify and explain aspects that remain the same and those that change

  • AC9M9SP03

    design, test and refine algorithms involving a sequence of steps and decisions based on geometric constructions and theorems; discuss and evaluate refinements

Statistics#
  • AC9M9ST01

    analyse reports of surveys in digital media and elsewhere for information on how data was obtained to estimate population means and medians

  • AC9M9ST02

    analyse how different sampling methods can affect the results of surveys and how choice of representation can be used to support a particular point of view

  • AC9M9ST03

    represent the distribution of multiple data sets for numerical variables using comparative representations; compare data distributions with consideration of centre, spread and shape, and the effect of outliers on these measures

  • AC9M9ST04

    choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context

  • AC9M9ST05

    plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions

Probability#
  • AC9M9P01

    list all outcomes for compound events both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes

  • AC9M9P02

    calculate relative frequencies from given or collected data to estimate probabilities of events involving “and”, inclusive “or” and exclusive “or”

  • AC9M9P03

    design and conduct repeated chance experiments and simulations, using digital tools to compare probabilities of simple events to related compound events, and describe results

Year 10#

Year level description

In Year 10, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to learning and doing mathematics that develop their understanding of and fluency with concepts, procedures and processes by making connections, reasoning, problem-solving and practice. Proficiency in mathematics enables students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently.

Students further develop proficiency and positive dispositions towards mathematics and its use as they:

  • investigate the accuracy of decimal approximations to irrational real numbers; consider the accuracy of computation with real numbers in context and the use of logarithmic scales to deal with phenomena involving small and large quantities and change
  • apply numerical, graphical and algebraic approaches to analyse the behaviour of pairs of linear equations and linear inequalities in 2 variables
  • generalise and extend their repertoire of algebraic techniques involving quadratic and exponential algebraic expressions
  • use mathematical modelling to solve problems in applied situations exhibiting growth or decay using linear, quadratic and exponential functions; and solve related equations, numerically, graphically and algebraically, with the use of digital tools as applicable
  • solve measurement problems involving the surface area and volume of common objects, composite objects and irregular objects; use Pythagoras’ theorem and trigonometry of right-angled triangles to solve spatial problems in two- and three-dimensions, and manipulate images of their representations using digital tools
  • apply geometric theorems to deduce results and solve problems involving plane shapes, and interpret networks and network diagrams in authentic contexts
  • investigate conditional probability and its relation to dependent and independent events, including sampling with and without replacement; devise and use simulations to test intuitions involving chance events that may or may not be independent
  • compare different ways of representing the distribution of continuous data and interpret key features of the distribution; explore association between pairs of variables, decide the form of representation, interpret the data with respect to the context and discuss possible conclusions; use scatterplots to informally discuss and consider association between 2 numerical variables and informally consider lines of good fit by eye, interpolation, extrapolation and limitations.
Achievement Standard

By the end of Year 10, students recognise the effect of approximations of real numbers in repeated calculations. They use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying linear, quadratic and exponential functions as appropriate, and solve related equations, numerically and graphically. Students make and test conjectures involving functions and relations using digital tools. They solve problems involving simultaneous linear equations and linear inequalities in 2 variables graphically and justify solutions.

Students interpret and use logarithmic scales representing small or large quantities or change in applied contexts. They solve measurement problems involving surface area and volume of composite objects. Students apply Pythagoras’ theorem and trigonometry to solve practical problems involving right-angled triangles. They identify the impact of measurement errors on the accuracy of results. Students use mathematical modelling to solve practical problems involving proportion and scaling, evaluating and modifying models, and reporting assumptions, methods and findings. They use deductive reasoning, theorems and algorithms to solve spatial problems. Students interpret networks used to represent practical situations and describe connectedness.

They plan and conduct statistical investigations involving bivariate data. Students represent the distribution of data involving 2 variables, using tables and scatter plots, and comment on possible association. They analyse inferences and conclusions in the media, noting potential sources of bias. Students compare the distribution of continuous numerical data, using various displays, and discuss distributions in terms of centre, spread, shape and outliers. They apply conditional probability to solve problems involving compound events. Students design and conduct simulations involving conditional probability, using digital tools.

  • ASMAT1001: By the end of Year 10, students recognise the effect of approximations of real  numbers in repeated calculations.
  • ASMAT1002: They use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying  linear,  quadratic and exponential functions as appropriate, and solve related equations, numerically and graphically.
  • ASMAT1003: Students make and test conjectures involving functions and relations using digital tools.
  • ASMAT1004: They solve problems involving simultaneous linear equations and linear inequalities in 2 variables graphically and justify solutions.
  • ASMAT1005: Students interpret and use logarithmic scales representing small or large quantities or change in applied contexts.
  • ASMAT1006: They solve measurement problems involving surface area and volume of composite objects.
  • ASMAT1007: Students apply Pythagoras’ theorem and trigonometry to solve practical problems involving right-angled triangles.
  • ASMAT1008: They identify the impact of measurement errors on the accuracy of results.
  • ASMAT1009: Students use mathematical modelling to solve practical problems involving  proportion and scaling, evaluating and modifying models, and reporting assumptions, methods and findings.
  • ASMAT1010: They use deductive reasoning, theorems and algorithms to solve  spatial problems.
  • ASMAT1011: Students interpret networks used to represent practical situations and describe connectedness
  • ASMAT1012: They plan and conduct statistical investigations involving bivariate data.
  • ASMAT1013: Students represent the distribution of data involving 2 variables, using tables and scatter plots, and comment on possible association.
  • ASMAT1014: They analyse inferences  and conclusions in the media, noting potential sources of bias.
  • ASMAT1015: Students compare the distribution of continuous numerical  data  using various displays, and discuss distributions in terms of centre, spread, shape and outliers.
  • ASMAT1016: They apply conditional probability  to solve problems involving compound events.
  • ASMAT1017: Students design and conduct simulations involving conditional probability, using digital tools.
Number#
  • AC9M10N01

    recognise the effect of using approximations of real numbers in repeated calculations and compare the results when using exact representations

Algebra#
  • AC9M10A01

    expand, factorise and simplify expressions and solve equations algebraically, applying exponent laws involving products, quotients and powers of variables, and the distributive property

  • AC9M10A02

    solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation

  • AC9M10A03

    recognise the connection between algebraic and graphical representations of exponential relations and solve related exponential equations, using digital tools where appropriate

  • AC9M10A04

    use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings

  • AC9M10A05

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

Measurement#
  • AC9M10M01

    solve problems involving the surface area and volume of composite objects using appropriate units

  • AC9M10M02

    interpret and use logarithmic scales  in applied contexts involving small and large quantities and change

  • AC9M10M03

    solve practical problems applying Pythagoras’ theorem and trigonometry of right-angled triangles, including problems involving direction and angles of elevation and depression

  • AC9M10M04

    identify the impact of measurement errors on the accuracy of results in practical contexts

  • AC9M10M05

    use mathematical modelling to solve practical problems involving proportion and scaling of objects; formulate problems and interpret solutions in terms of the situation; evaluate and modify models as necessary, and report assumptions, methods and findings

Space#
  • AC9M10SP01

    apply deductive reasoning to proofs involving shapes in the plane and use theorems to solve spatial problems

  • AC9M10SP02

    interpret networks and network diagrams used to represent relationships in practical situations and describe connectedness

  • AC9M10SP03

    design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions

Statistics#
  • AC9M10ST01

    analyse claims, inferences and conclusions of statistical reports in the media, including ethical considerations and identification of potential sources of bias

  • AC9M10ST02

    compare data distributions for continuous numerical variables using appropriate data displays including boxplots; discuss the shapes of these distributions in terms of centre, spread, shape and outliers in the context of the data

  • AC9M10ST03

    construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity

  • AC9M10ST04

    construct two-way tables and discuss possible relationship between categorical variables

  • AC9M10ST05

    plan and conduct statistical investigations of situations that involve bivariate data; evaluate and report findings with consideration of limitations of any inferences

Probability#
  • AC9M10P01

    use the language of “if .... then”, “given”, “of”, “knowing that” to describe and interpret situations involving conditional probability

  • AC9M10P02

    design and conduct repeated chance experiments and simulations using digital tools to model conditional probability and interpret results

Technologies#

Digital Technologies#

Years 7 and 8#

Year level description

By the end of Year 8 students should have had the opportunity to apply computational thinking by defining and decomposing real-world problems, creating user experiences, designing and modifying algorithms, and implementing them in a general-purpose programming language. This involves students practising problem decomposition, using approaches such as divide and conquer to more clearly understand a problem by describing its component parts. Students represent and communicate their algorithmic solutions using flowcharts and pseudocode. Students check their solutions meet the specifications by testing and debugging their algorithms before and during implementation. They develop a deeper understanding of abstraction by explaining how and why digital systems represent data as whole numbers, which are then represented in binary.

Students build on their skills from Mathematics (Statistics) in acquiring and interpreting data. In Digital Technologies, students continue to advance these skills and are also given opportunities to validate the data they acquire to ensure it is accurate and consistent. They collect and transform many types of data from a wide range of sources. Students model structured data in meaningful ways using spreadsheets and single-table databases, and analyse and visualise the data to extract meaning from it.

They apply design thinking by using divergent techniques, such as mind mapping, role-play and using graphic organisers, to generate design ideas for user experiences and solution designs. Students review these ideas against design criteria and created user stories throughout their implementation as general-purpose programming by assessing them against current and future needs. They extend the use of these design criteria and user stories to evaluate the future impact of existing solutions.

Students apply systems thinking by exploring the connections between hardware capabilities and tasks users want to perform. They investigate how data is transmitted via wired and wireless networks and explain the need for encryption to protect and secure data. Students use an increasing range of the features of digital tools to improve their efficiency and the consistency of the content they create, locate and communicate. They plan and manage projects individually and collaboratively, improving their control over the quality of their content. Students investigate personal security controls, including multi-factor authentication, to protect their data if passwords are compromised, and they understand the impact of phishing and other cyber security threats on people and data.

In Digital Technologies, students should have frequent opportunities for authentic learning by making key connections with other learning areas.

Achievement Standard

By the end of Year 8 students develop and modify creative digital solutions, decompose real-world problems, and evaluate alternative solutions against user stories and design criteria. Students acquire, interpret and model data with spreadsheets and represent data with integers and binary. They design and trace algorithms and implement them in a general-purpose programming language. Students select appropriate hardware for particular tasks, explain how data is transmitted and secured in networks, and identify cyber security threats. They select and use a range of digital tools efficiently and responsibly to create, locate and share content; and to plan, collaborate on and manage projects. Students manage their digital footprint.

  • ASTECTDI7801: By the end of Year 8 students develop and modify creative digital solutions, decompose real-world problems, and evaluate alternative solutions against user stories and design criteria.
  • ASTECTDI7802: Students acquire, interpret and model data with spreadsheets and represent data with integers and binary.
  • ASTECTDI7803: They design and trace algorithms and implement them in a general-purpose programming language.
  • ASTECTDI7804: Students select appropriate hardware for particular tasks, explain how data is transmitted and secured in networks, and identify cyber security threats.
  • ASTECTDI7805: They select and use a range of digital tools efficiently and responsibly to create, locate and share content; and to plan, collaborate on and manage projects.
  • ASTECTDI7806: Students manage their digital footprint.
Knowledge and understanding#
Digital systems#
  • AC9TDI8K01

    explain how hardware specifications affect performance and select appropriate hardware for particular tasks and workloads

  • AC9TDI8K02

    investigate how data is transmitted and secured in wired and wireless networks including the internet

Data representation#
  • AC9TDI8K03

    investigate how digital systems represent text, image and audio data using integers

  • AC9TDI8K04

    explain how and why digital systems represent integers in binary

Processes and production skills#
Acquiring, managing and analysing data#
  • AC9TDI8P01

    acquire, store and validate data from a range of sources using software, including spreadsheets and databases

  • AC9TDI8P02

    analyse and visualise data using a range of software, including spreadsheets and databases, to draw conclusions and make predictions by identifying trends

  • AC9TDI8P03

    model and query the attributes of objects and events using structured data

Investigating and defining#
  • AC9TDI8P04

    define and decompose real-world problems with design criteria and by creating user stories

Generating and designing#
  • AC9TDI8P05

    design algorithms involving nested control structures and represent them using flowcharts and pseudocode

  • AC9TDI8P06

    trace algorithms to predict output for a given input and to identify errors

  • AC9TDI8P07

    design the user experience of a digital system

  • AC9TDI8P08

    generate, modify, communicate and evaluate alternative designs

Producing and implementing#
  • AC9TDI8P09

    implement, modify and debug programs involving control structures and functions in a general-purpose programming language

Evaluating#
  • AC9TDI8P10

    evaluate existing and student solutions against the design criteria, user stories and possible future impact

Collaborating and managing#
  • AC9TDI8P11

    select and use a range of digital tools efficiently, including unfamiliar features, to create, locate and communicate content, consistently applying common conventions

  • AC9TDI8P12

    select and use a range of digital tools efficiently and responsibly to share content online, and plan and manage individual and collaborative agile projects

Privacy and security#
  • AC9TDI8P13

    explain how multi-factor authentication protects an account when the password is compromised and identify phishing and other cyber security threats

  • AC9TDI8P14

    investigate and manage the digital footprint existing systems and student solutions collect and assess if the data is essential to their purpose

Years 9 and 10#

Year level description

By the end of Year 10 students should have had the opportunity to apply computational thinking by defining and decomposing real-world problems, creating user experiences, designing and modifying algorithms, and implementing them, including in an object-oriented programming language. Students use techniques, including interviewing stakeholders to develop user stories, to increase the precision of their problem definitions and solution specifications. They verify their solutions solve the problem by validating their algorithms, represented as flowcharts and pseudocode, and using test cases to confirm the correctness of their solutions. Students develop their object-oriented programming skills, and apply them to develop, modify and debug programs. They explain the importance of abstraction by representing online documents in terms of content, structure and presentation, as well as exploring simple data compression techniques and comparing their effectiveness.

Students consolidate their skills in data acquisition and interpretation, cleaning and validating data to ensure it is accurate, consistent and domain appropriate. They model multidimensional data in more complex spreadsheets and relational databases, filtering and querying it to give insights into its meaning, and to pose further questions or make conclusions. They visualise this data in customisable ways, allowing greater exploration of trends and outliers to support or challenge their analyses.

Students apply design thinking by using divergent techniques to generate design ideas for user experiences and solutions. They filter and prototype these ideas, developing user stories and applying design criteria based on current and future needs and enterprising opportunities, as well as their created user stories, and revise and further develop their preferred ideas based on their analysis. Students extend on these design criteria and user stories to evaluate the enterprise opportunities and future impact of existing solutions.

Students consolidate their systems thinking by exploring how the hardware and software components of digital systems interact to manage, control and secure access to data. They increasingly use advanced features of existing and emerging digital tools to create interactive content for a diverse audience. They explore simple tools that help plan tasks, timelines and responsibilities for individual and collaborative projects. Students extend their knowledge of the importance of security by developing cyber security threat models and exploring an example of a supply chain vulnerability. They critique the digital footprint created by existing systems and their own solutions by applying the Australian Privacy Principles.

In Digital Technologies, students should have frequent opportunities for authentic learning by making key connections to other learning areas.

Achievement Standard

By the end of Year 10 students develop and modify innovative digital solutions, decompose real-world problems, and critically evaluate alternative solutions against stakeholder elicited user stories. Students acquire, interpret and model complex data with databases and represent documents as content, structure and presentation. They design and validate algorithms and implement them, including in an object-oriented programming language. Students explain how digital systems manage, control and secure access to data; and model cyber security threats and explore a vulnerability. They use advanced features of digital tools to create interactive content, and to plan, collaborate on and manage agile projects. Students apply privacy principles to manage digital footprints.

  • ASTECTDI91001: By the end of Year 10 students develop and modify innovative digital solutions, decompose real-world problems, and critically evaluate alternative solutions against stakeholder elicited user stories.
  • ASTECTDI91002: Students acquire, interpret and model complex data with databases and represent documents as content, structure and presentation.
  • ASTECTDI91003: They design and validate algorithms and implement them, including in an object-oriented programming language.
  • ASTECTDI91004: Students explain how digital systems manage, control and secure access to data; and model cyber security threats and explore a vulnerability.
  • ASTECTDI91005: They use advanced features of digital tools to create interactive content, and to plan, collaborate on, and manage agile projects.
  • ASTECTDI91006: Students apply privacy principles to manage digital footprints.
Knowledge and understanding#
Digital systems#
  • AC9TDI10K01

    investigate how hardware and software manage, control and secure access to data in networked digital systems

Data representation#
  • AC9TDI10K02

    represent documents online as content (text), structure (markup) and presentation (styling) and explain why such representations are important

  • AC9TDI10K03

    investigate simple data compression techniques

Processes and production skills#
Acquiring, managing and analysing data#
  • AC9TDI10P01

    develop techniques to acquire, store and validate data from a range of sources using software, including spreadsheets and databases

  • AC9TDI10P02

    analyse and visualise data interactively using a range of software, including spreadsheets and databases, to draw conclusions and make predictions by identifying trends and outliers

  • AC9TDI10P03

    model and query entities and their relationships using structured data

Investigating and defining#
  • AC9TDI10P04

    define and decompose real-world problems with design criteria and by interviewing stakeholders to create user stories

Generating and designing#
  • AC9TDI10P05

    design algorithms involving logical operators and represent them as flowcharts and pseudocode

  • AC9TDI10P06

    validate algorithms and programs by comparing their output against a range of test cases

  • AC9TDI10P07

    design and prototype the user experience of a digital system

  • AC9TDI10P08

    generate, modify, communicate and critically evaluate alternative designs

Producing and implementing#
  • AC9TDI10P09

    implement, modify and debug modular programs, applying selected algorithms and data structures, including in an object-oriented programming language

Evaluating#
  • AC9TDI10P10

    evaluate existing and student solutions against the design criteria, user stories, possible future impact and opportunities for enterprise

Collaborating and managing#
  • AC9TDI10P11

    select and use emerging digital tools and advanced features to create and communicate interactive content for a diverse audience

  • AC9TDI10P12

    use simple project management tools to plan and manage individual and collaborative agile projects, accounting for risks and responsibilities

Privacy and security#
  • AC9TDI10P13

    develop cyber security threat models, and explore a software, user or software supply chain vulnerability

  • AC9TDI10P14

    apply the Australian Privacy Principles to critique and manage the digital footprint that existing systems and student solutions collect