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#
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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
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represent natural numbers as products of powers of prime numbers using exponent notation
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represent natural numbers in expanded notation using place value and powers of 10
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find equivalent representations of rational numbers and represent rational numbers on a number line
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round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions
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use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies
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compare, order and solve problems involving addition and subtraction of integers
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recognise, represent and solve problems involving ratios
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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#
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recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown
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formulate algebraic expressions using constants, variables, operations and brackets
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solve one-variable linear equations with natural number solutions; verify the solution by substitution
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describe relationships between variables represented in graphs of functions from authentic data
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generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane
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manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables
Measurement#
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solve problems involving the area of triangles and parallelograms using established formulas and appropriate units
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solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units
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describe the relationship between \(π\) and the features of circles including the circumference, radius and diameter
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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
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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
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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#
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represent objects in 2 dimensions; discuss and reason about the advantages and disadvantages of different representations
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classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships
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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
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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#
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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
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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
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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#
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identify the sample space for single-stage events; assign probabilities to the outcomes of these events and predict relative frequencies for related events
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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#
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recognise irrational numbers in applied contexts, including square roots and \(π\)
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establish and apply the exponent laws with positive integer exponents and the zero-exponent, using exponent notation with numbers
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recognise terminating and recurring decimals, using digital tools as appropriate
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use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate
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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#
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create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties
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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
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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
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experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns
Measurement#
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solve problems involving the area and perimeter of irregular and composite shapes using appropriate units
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solve problems involving the volume and capacity of right prisms using appropriate units
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solve problems involving the circumference and area of a circle using formulas and appropriate units
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solve problems involving duration, including using 12- and 24-hour time across multiple time zones
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recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure
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use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles
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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#
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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
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establish properties of quadrilaterals using congruent triangles and angle properties, and solve related problems explaining reasoning
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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
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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#
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investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques
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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
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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
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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#
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recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts
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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
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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#
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recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools
Algebra#
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apply the exponent laws to numerical expressions with integer exponents and extend to variables
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simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions
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find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane
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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
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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
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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#
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solve problems involving the volume and surface area of right prisms and cylinders using appropriate units
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solve problems involving very small and very large measurements, time scales and intervals expressed in scientific notation
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solve spatial problems, applying angle properties, scale, similarity, Pythagoras’ theorem and trigonometry in right-angled triangles
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calculate and interpret absolute, relative and percentage errors in measurements, recognising that all measurements are estimates
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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#
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recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity
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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
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design, test and refine algorithms involving a sequence of steps and decisions based on geometric constructions and theorems; discuss and evaluate refinements
Statistics#
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analyse reports of surveys in digital media and elsewhere for information on how data was obtained to estimate population means and medians
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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
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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
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choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context
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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#
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list all outcomes for compound events both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes
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calculate relative frequencies from given or collected data to estimate probabilities of events involving “and”, inclusive “or” and exclusive “or”
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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#
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recognise the effect of using approximations of real numbers in repeated calculations and compare the results when using exact representations
Algebra#
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expand, factorise and simplify expressions and solve equations algebraically, applying exponent laws involving products, quotients and powers of variables, and the distributive property
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solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation
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recognise the connection between algebraic and graphical representations of exponential relations and solve related exponential equations, using digital tools where appropriate
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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
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experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns
Measurement#
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solve problems involving the surface area and volume of composite objects using appropriate units
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interpret and use logarithmic scales in applied contexts involving small and large quantities and change
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solve practical problems applying Pythagoras’ theorem and trigonometry of right-angled triangles, including problems involving direction and angles of elevation and depression
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identify the impact of measurement errors on the accuracy of results in practical contexts
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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#
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apply deductive reasoning to proofs involving shapes in the plane and use theorems to solve spatial problems
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interpret networks and network diagrams used to represent relationships in practical situations and describe connectedness
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design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions
Statistics#
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analyse claims, inferences and conclusions of statistical reports in the media, including ethical considerations and identification of potential sources of bias
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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
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construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity
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construct two-way tables and discuss possible relationship between categorical variables
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plan and conduct statistical investigations of situations that involve bivariate data; evaluate and report findings with consideration of limitations of any inferences
Probability#
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#
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explain how hardware specifications affect performance and select appropriate hardware for particular tasks and workloads
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investigate how data is transmitted and secured in wired and wireless networks including the internet
Data representation#
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investigate how digital systems represent text, image and audio data using integers
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explain how and why digital systems represent integers in binary
Processes and production skills#
Acquiring, managing and analysing data#
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acquire, store and validate data from a range of sources using software, including spreadsheets and databases
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analyse and visualise data using a range of software, including spreadsheets and databases, to draw conclusions and make predictions by identifying trends
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model and query the attributes of objects and events using structured data
Investigating and defining#
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define and decompose real-world problems with design criteria and by creating user stories
Generating and designing#
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design algorithms involving nested control structures and represent them using flowcharts and pseudocode
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trace algorithms to predict output for a given input and to identify errors
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design the user experience of a digital system
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generate, modify, communicate and evaluate alternative designs
Producing and implementing#
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implement, modify and debug programs involving control structures and functions in a general-purpose programming language
Evaluating#
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evaluate existing and student solutions against the design criteria, user stories and possible future impact
Collaborating and managing#
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select and use a range of digital tools efficiently, including unfamiliar features, to create, locate and communicate content, consistently applying common conventions
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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#
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explain how multi-factor authentication protects an account when the password is compromised and identify phishing and other cyber security threats
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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#
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investigate how hardware and software manage, control and secure access to data in networked digital systems
Data representation#
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represent documents online as content (text), structure (markup) and presentation (styling) and explain why such representations are important
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investigate simple data compression techniques
Processes and production skills#
Acquiring, managing and analysing data#
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develop techniques to acquire, store and validate data from a range of sources using software, including spreadsheets and databases
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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
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model and query entities and their relationships using structured data
Investigating and defining#
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define and decompose real-world problems with design criteria and by interviewing stakeholders to create user stories
Generating and designing#
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design algorithms involving logical operators and represent them as flowcharts and pseudocode
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validate algorithms and programs by comparing their output against a range of test cases
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design and prototype the user experience of a digital system
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generate, modify, communicate and critically evaluate alternative designs
Producing and implementing#
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implement, modify and debug modular programs, applying selected algorithms and data structures, including in an object-oriented programming language
Evaluating#
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evaluate existing and student solutions against the design criteria, user stories, possible future impact and opportunities for enterprise
Collaborating and managing#
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select and use emerging digital tools and advanced features to create and communicate interactive content for a diverse audience
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use simple project management tools to plan and manage individual and collaborative agile projects, accounting for risks and responsibilities
Privacy and security#
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develop cyber security threat models, and explore a software, user or software supply chain vulnerability
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apply the Australian Privacy Principles to critique and manage the digital footprint that existing systems and student solutions collect