The Victorian

Curriculum

Subjects Mathematics

Levels Level 7, Level 8, Level 9, Level 10 and Level 10A

Curriculum Version Version dated

Date created 15 October 2023

Excepting logos, trademarks or other third-party content as indicated, the F–10 Victorian Curriculum content in this document is
licensed Creative Commons ‘Attribution-Non-Commercial-Share Alike’ (3.0 Australia).

The ® logo is a registered trade mark of the Victorian Curriculum and Assessment Authority.

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Table of Contents

Mathematics 3
Overview 4
About Mathematics 4
Mathematics 5
Overview 6
Rationale and Aims 6
Structure 7
Learning in Mathematics 8
Scope and Sequence 9
Curriculum F-10 9
Level 7 10
Level 8 17
Level 9 23
Level 10 28
Level 10A 34

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Mathematics

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 Mathematics

Overview

About Mathematics
The VCAA is developing the Victorian Curriculum F–10 Version 2.0, starting with the publication of the Mathematics Version 2.0
curriculum in Term 3 2023.

You can access both the current Mathematics curriculum and Mathematics Version 2.0 using the menu on this page.

Go to the VCAA website to find information about timelines for Mathematics Version 2.0 and the rest of the Victorian
Curriculum F–10 Version 2.0, to register for professional learning webinars and to find more supporting resources.

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Mathematics

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 Mathematics

Overview

Rationale and Aims

The VCAA is developing the Victorian Curriculum F–10 Version 2.0, starting with the publication of the Mathematics
Version 2.0 curriculum in Term 3 2023.

Go to the VCAA website to find information about timelines for Mathematics Version 2.0 and the rest of the Victorian
Curriculum F–10 Version 2.0, to register for professional learning webinars and to find more supporting resources.

Rationale
Mathematics provides students with access to important mathematical ideas, knowledge and skills that they will draw on in their
personal and work lives. The curriculum also provides students, as life-long learners, with the basis on which further study and
research in mathematics and applications in many other fields are built.

Mathematical ideas have evolved across societies and cultures over thousands of years, and are constantly developing. Digital
technologies are facilitating this expansion of ideas and provide new tools for mathematical exploration and invention. While the
usefulness of mathematics for modelling and problem solving is well known, mathematics also has a fundamental role in both
enabling and sustaining cultural, social, economic and technological advances and empowering individuals to become critical
citizens.

Number, measurement and geometry, statistics and probability are common aspects of most people’s mathematical experience
in everyday personal, study and work situations. Equally important are the essential roles that algebra, functions and relations,
logic, mathematical structure and working mathematically play in people’s understanding of the natural and human worlds, and
the interaction between them.

The Mathematics curriculum focuses on developing increasingly sophisticated and refined mathematical understanding, fluency,
reasoning, modelling and problem-solving. These capabilities enable students to respond to familiar and unfamiliar situations by
employing mathematics to make informed decisions and solve problems efficiently.

The curriculum ensures that the links between the various components of mathematics, as well as the relationship between
mathematics and other disciplines, are made clear. Mathematics is composed of multiple but interrelated and interdependent
concepts and structures which students apply beyond the mathematics classroom. For example, in Science, understanding
sources of error and their impact on the confidence of conclusions is vital; in Geography, interpretation of data underpins the
study of human populations and their physical environments; in History, students need to be able to imagine timelines and time
frames to reconcile related events; and in English, deriving quantitative, logical and spatial information is an important aspect of
making meaning of texts.

Aims
The Mathematics curriculum aims to ensure that students:

develop useful mathematical and numeracy skills for everyday life, work and as active and critical citizens in a
technological world
see connections and apply mathematical concepts, skills and processes to pose and solve problems in mathematics and
in other disciplines and contexts
acquire specialist knowledge and skills in mathematics that provide for further study in the discipline

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 Mathematics

appreciate mathematics as a discipline – its history, ideas, problems and applications, aesthetics and philosophy.

Structure
The curriculum is organised by the three strands of Number and Algebra, Measurement and Geometry, and Statistics and
Probability.

Each strand is organised by sub-­strands. Sub-strands group content descriptions under an appropriate concept, to provide both
a focus and a clear sequence for the development of related concepts and skills within strands and across levels.

Strands Number and Algebra Measurement and Statistics and Probability

Geometry
Sub- Number and place value Using units of measurement Chance
strands
Fractions and decimals Shape Data representation and
interpretation

Real numbers Geometric reasoning

Money and financial mathematics Location and transformation

Patterns and algebra Pythagoras and trigonometry

Linear and non­-linear

relationships

Number and Algebra

Number and Algebra are developed together, and each enriches the study of the other. Students apply number sense and
strategies for counting and representing numbers. They explore the magnitude and properties of numbers. They apply a range
of strategies for computation and understand the connections between operations. They recognise patterns and understand the
concepts of variable and function. They build on their understanding of the number system to describe relationships and
formulate generalisations. They recognise equivalence and solve equations and inequalities. They apply their number and
algebra skills to conduct investigations, solve problems and communicate their reasoning.

Measurement and Geometry

Measurement and Geometry are presented together to emphasise their relationship to each other, enhancing their practical
relevance. Students develop an increasingly sophisticated understanding of size, shape, relative position and movement of two-
dimensional figures in the plane and three-dimensional objects in space. They investigate properties and apply their
understanding of them to define, compare and construct figures and objects. They learn to develop geometric arguments. They
make meaningful measurements of quantities, choosing appropriate metric units of measurement. They build an understanding
of the connections between units and calculate derived measures such as area, speed and density.

Statistics and Probability

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 Mathematics

Statistics and Probability develops initially in parallel, with the curriculum progressively building links between them. Students
recognise and analyse data and draw inferences. They represent, summarise and interpret data and undertake purposeful
investigations involving the collection and interpretation of data. Students recognise variation, assess likelihood and assign
probabilities using experimental and theoretical approaches. They develop an increasingly sophisticated ability to critically
evaluate chance and data concepts and make reasoned judgments and decisions, as well as building skills to critically evaluate
statistical information and develop intuitions about data.

Achievement standards
In Mathematics, students progress along a curriculum continuum that provides the first achievement standard at Foundation and
then at Levels 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. Level 10 also has an optional Level 10A, which is intended for students requiring
further mathematical studies.

A 'Towards Foundation Levels A to D' curriculum is provided for students with disabilities or additional learning needs in this
curriculum area.

Learning in Mathematics
The proficiencies of Understanding, Fluency, Problem Solving and Reasoning are fundamental to learning mathematics and
working mathematically and are applied across all three strands Number and Algebra, Measurement and Geometry, and
Statistics and Probability.

Understanding refers to students building a robust knowledge of adaptable and transferable mathematical concepts and
structures. Students make connections between related concepts and progressively apply the familiar to develop new ideas.
They develop an understanding of the relationship between the ‘why’ and the ‘how’ of mathematics. Students build
understanding when they:

connect related ideas

represent concepts in different ways
identify commonalities and differences between aspects of content
describe their thinking mathematically
interpret mathematical information.

Fluency describes students developing skills in choosing appropriate procedures, carrying out procedures flexibly, accurately,
efficiently and appropriately, and recalling factual knowledge and concepts readily. Students are fluent when they:

make reasonable estimates

calculate answers efficiently
recognise robust ways of answering questions
choose appropriate methods and approximations
recall definitions and regularly use facts,
can manipulate expressions and equations to find solutions.

Problem-solving is the ability of students to make choices, interpret, formulate, model and investigate problem situations, select
and use technological functions and communicate solutions effectively. Students pose and solve problems when they:

use mathematics to represent unfamiliar or meaningful situations

design investigations and plan their approaches

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 Mathematics

apply their existing strategies to seek solutions

verify that their answers are reasonable.

Reasoning refers to students developing an increasingly sophisticated capacity for logical, statistical and probabilistic thinking
and actions, such as conjecturing, hypothesising, analysing, proving, evaluating, explaining, inferring, justifying, refuting,
abstracting and generalising. Students are reasoning mathematically when they:

explain their thinking

deduce and justify strategies used and conclusions reached
adapt the known to the unknown
transfer learning from one context to another
prove that something is true or false
make inferences about data or the likelihood of events
compare and contrast related ideas and explain their choices.

Information Communication Technologies and Mathematics

Information Communication Technologies (ICT) are powerful tools that can support student learning. Students can develop and
demonstrate their understanding of concepts and content in Mathematics using a range of ICT tools. It is also important that
students know how to use these ICT efficiently and responsibly, as well as learning how to protect themselves and secure their
data.

Details of how ICT can support student learning in Mathematics is set out in the attached Information Communication
Technologies and Mathematics pdf.

Scope and Sequence

The curriculum sets out what students are expected to learn and is designed as a continuum of learning. The curriculum is
being presented in a scope and sequence chart to support teachers to easily see the progression and assist in planning
teaching and learning programs to meet the diverse needs of students.

These charts include the content descriptions and achievement standards. It is advised that these charts are read in conjunction
with the introductory materials and the level/band descriptions in the curriculum.

The number of levels represented in each chart varies. Read the naming convention in the links below to assist in selecting the
most appropriate chart.

These charts are designed to be printed in A3 format.

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 Mathematics

Level 7
In Level 7, students work with powers of whole numbers, use index notation, represent numbers as products of powers of
prime numbers, and investigate square roots of perfect squares. They use number properties to assist with calculation and
order, and to add and subtract integers. Students find equivalent fractions, represent positive and negative fractions and
mixed numbers on a number line and add, subtract, multiply and divide fractions and decimals with and without the use of
technology. They express one quantity as a fraction of another, round to a specified number of decimal places, and convert
between fractions, decimals and percentages. They find percentages of quantities and one quantity as a percentage of
another. They solve simple ratio problems and calculate best buys with and without the use of technology.

Students use variables to express relationships in real life data, and interpret and analyse corresponding graphs. They use
pro-numerals to construct simple algebraic expressions and substitute numerical values into these. They solve simple linear
equations and plot points on the Cartesian plane.

Students use formulas for calculating areas of triangles, rectangles and related shapes, and volumes of cubes and
rectangular prisms. They form two-dimensional representations of prisms, buildings and other structures. They use simple
combinations of transformations, with and without technology, to create geometric patterns and identify line and point
symmetry, apply parallel line and transversal angle properties, angles sums in triangles and quadrilaterals, classify triangles
and quadrilaterals, and construct them using compass and straight edge and dynamic geometry technology.

Students construct sample spaces for simple experiments involving chance, and assign probabilities to outcomes. They use
data from primary and secondary sources to investigate issues of interest, and employ data displays such as dot plots and
stem and leaf plots to compare data sets, and calculate measures of centre and simple measures of spread to analyse and
interpret the data.

Number and Algebra

Number and place value Elaborations

Investigate index notation and represent whole numbers as defining and comparing prime and composite numbers
products of powers of prime numbers (VCMNA238) and explaining the difference between them
applying knowledge of factors to strategies for
expressing whole numbers as products of powers of
prime factors, such as repeated division by prime
factors or creating factor trees
solving problems involving lowest common multiples
and greatest common divisors (highest common
factors) for pairs of whole numbers by comparing their
prime factorisation

Investigate and use square roots of perfect square investigating square numbers such as 25 and 36 and
numbers (VCMNA239) developing square-root notation
investigating between which two whole numbers a
square root lies

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 Mathematics

Apply the associative, commutative and distributive laws to simplifying calculations

aid mental and written computation and make estimates for forming simple estimates for calculations involving
these computations (VCMNA240) multiple and/or combined operations

Compare, order, add and subtract integers (VCMNA241) using a variety of models to represent, add and
subtract integers

Real numbers Elaborations

Compare fractions using equivalence. Locate and exploring equivalence among families of fractions by
represent positive and negative fractions and mixed using a fraction wall or a number line (for example by
using a fraction wall to show that 2/3 is the same as
numbers on a number line (VCMNA242)
4/6 and 6/9)

Solve problems involving addition and subtraction of exploring and developing efficient strategies to solve
fractions, including those with unrelated denominators additive problems involving fractions (for example by
using fraction walls or rectangular arrays with
(VCMNA243)
dimensions equal to the denominators)

Multiply and divide fractions and decimals using efficient investigating multiplication of fractions and decimals,
written strategies and digital technologies (VCMNA244) using strategies including patterning and multiplication
as repeated addition, with both concrete materials and
digital technologies, and identifying the processes for
division as the inverse of multiplication

Express one quantity as a fraction of another, with and using examples for the quantities to be expressed and
without the use of digital technologies (VCMNA245) understanding the reasons for the calculations

Round decimals to a specified number of decimal places using rounding to estimate the results of calculations
(VCMNA246) with whole numbers and decimals, and understanding
the conventions for rounding

Connect fractions, decimals and percentages and carry out justifying choices of written, mental or calculator
simple conversions (VCMNA247) strategies for solving specific problems including those
involving large numbers
understanding that quantities can be represented by
different number types and calculated using various
operations, and that choices need to be made about
each
calculating the percentage of the total local municipal
area set aside for parkland, manufacturing, retail and
residential dwellings to compare land use

Find percentages of quantities and express one quantity as using authentic problems to express quantities as
a percentage of another, with and without digital percentages of other amounts
technologies. (VCMNA248)

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 Mathematics

Recognise and solve problems involving simple ratios understanding that rate and ratio problems can be
(VCMNA249) solved using fractions or percentages and choosing
the most efficient form to solve a particular problem

Money and financial mathematics Elaborations

Investigate and calculate 'best buys', with and without applying the unitary method to identify ‘best buys’
digital technologies (VCMNA250) situations, such as comparing the cost per 100g

Patterns and algebra Elaborations

Introduce the concept of variables as a way of representing understanding that arithmetic laws are powerful ways
numbers using letters (VCMNA251) of describing and simplifying calculations and that
using these laws leads to the generality of algebra

Create algebraic expressions and evaluate them by using authentic formulas to perform substitutions
substituting a given value for each variable (VCMNA252)

Extend and apply the laws and properties of arithmetic to identifying order of operations in contextualised
algebraic terms and expressions (VCMNA253) problems, preserving the order by inserting brackets in
numerical expressions, then recognising how order is
preserved by convention
moving fluently between algebraic and word
representations as descriptions of the same situation

Design and implement mathematical algorithms using a finding the sum of a set of consecutive numbers using
simple general purpose programming language a loop structure
(VCMNA254) constructing geometric patterns such as a
honeycomb, using dynamic geometry functionality

Linear and non-linear relationships Elaborations

Given coordinates, plot points on the Cartesian plane, and plotting points from a table of integer values and
find coordinates for a given point (VCMNA255) recognising simple patterns, such as points that lie on
a straight line

Solve simple linear equations (VCMNA256) solving equations using concrete materials, such as
the balance model, and explain the need to do the
same thing to each side of the equation using
substitution to check solutions
investigating a range of strategies to solve equations

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 Mathematics

Investigate, interpret and analyse graphs from real life using travel graphs to investigate and compare the
data, including consideration of domain and range distance travelled to and from school
(VCMNA257) interpreting features of travel graphs such as the slope
of lines and the meaning of horizontal lines
using graphs of evaporation rates to explore water
storage
describing and comparing temperature during a day at
different times of the year from the corresponding
graphs

Measurement and Geometry

Using units of measurement Elaborations

Establish the formulas for areas of rectangles, triangles building on the understanding of the area of rectangles
and parallelograms and use these in problem solving to develop formulas for the area of triangles
(VCMMG258) establishing that the area of a triangle is half the area
of an appropriate rectangle
using area formulas for rectangles and triangles to
solve problems involving areas of surfaces

Calculate volumes of rectangular prisms (VCMMG259) investigating volumes of cubes and rectangular prisms
and establishing and using the formula V = l × b × h
understanding and using cubic units when interpreting
and finding volumes of cubes and rectangular prisms

Shape Elaborations

Draw different views of prisms and solids formed from using aerial views of buildings and other 3-D
combinations of prisms (VCMMG260) structures to visualise the structure of the building or
prism

Location and transformation Elaborations

Describe translations, reflections in an axis, and rotations describing patterns and investigating different ways to
of multiples of 90° on the Cartesian plane using produce the same transformation such as using two
successive reflections to provide the same result as a
coordinates. Identify line and rotational symmetries
translation
(VCMMG261)
creating and re-creating patterns using combinations
of reflections and rotations, using digital technologies

Geometric reasoning Elaborations

Classify triangles according to their side and angle identifying side and angle properties of scalene,
properties and describe quadrilaterals (VCMMG262) isosceles, right-angled and obtuse-angled triangles
describing squares, rectangles, rhombuses,
parallelograms, kites and trapeziums

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 Mathematics

Demonstrate that the angle sum of a triangle is 180° and using concrete materials and digital technologies to
use this to find the angle sum of a quadrilateral investigate the angle sum of a triangle and
quadrilateral
(VCMMG263)

Identify corresponding, alternate and co-interior angles defining and classifying pairs of angles as
when two straight lines are crossed by a transversal complementary, supplementary, adjacent and
vertically opposite
(VCMMG264)

Investigate conditions for two lines to be parallel and solve constructing parallel and perpendicular lines using
simple numerical problems using reasoning (VCMMG265) their properties, a pair of compasses and a ruler, and
dynamic geometry software
defining and identifying the relationships between
alternate, corresponding and co-interior angles for a
pair of parallel lines cut by a transversal

Statistics and Probability

Chance Elaborations

Construct sample spaces for single-step experiments with discussing the meaning of probability terminology. For
equally likely outcomes (VCMSP266) example, probability, sample space, favourable
outcomes, trial, events and experiments
distinguishing between equally likely outcomes and
outcomes that are not equally likely

Assign probabilities to the outcomes of events and expressing probabilities as decimals, fractions and
determine probabilities for events (VCMSP267) percentages

Data representation and interpretation Elaborations

Identify and investigate issues involving numerical data obtaining secondary data from newspapers, the
collected from primary and secondary sources Internet and the Australian Bureau of Statistics
(VCMSP268) investigating secondary data relating to the distribution
and use of non-renewable resources around the world

Construct and compare a range of data displays including understanding that some data representations are
stem-and-leaf plots and dot plots (VCMSP269) more appropriate than others for particular data sets,
and answering questions about those data sets
using ordered stem-and-leaf plots to record and
display numerical data collected in a class
investigation, such as constructing a class plot of
height in centimetres on a shared stem-and-leaf plot
for which the stems 12, 13, 14, 15, 16 and 17 have
been produced

Calculate mean, median, mode and range for sets of data. understanding that summarising data by calculating
Interpret these statistics in the context of data measures of centre and spread can help make sense
of the data
(VCMSP270)

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 Mathematics

Describe and interpret data displays using median, mean using mean and median to compare data sets and
and range (VCMSP271) explaining how outliers may affect the comparison
locating mean, median and range on graphs and
connecting them to real life

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 Mathematics

Level 7 achievement standard

Number and Algebra

Students solve problems involving the order, addition and subtraction of integers. They make the connections between whole
numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving all
four operations with fractions, decimals, percentages and their equivalences, and express fractions in their simplest form.
Students compare the cost of items to make financial decisions, with and without the use of digital technology. They make
simple estimates to judge the reasonableness of results. Students use variables to represent arbitrary numbers and connect the
laws and properties of number to algebra and substitute numbers into algebraic expressions. They assign ordered pairs to given
points on the Cartesian plane and interpret and analyse graphs of relations from real data. Students develop simple linear
models for situations, make predictions based on these models, solve related equations and check their solutions.

Measurement and Geometry

Students use formulas for the area and perimeter of rectangles. They classify triangles and quadrilaterals and represent
transformations of these shapes on the Cartesian plane, with and without the use of digital technology. Students name the types
of angles formed by transversals crossing parallel lines and solve simple numerical problems involving these lines and angles.
They describe different views of three-dimensional objects, and use models, sketches and digital technology to represent these
views. Students calculate volumes of rectangular prisms.

Statistics and Probability

Students identify issues involving the collection of discrete and continuous data from primary and secondary sources. They
construct stem-and-leaf plots and dot-plots. Students identify or calculate mean, mode, median and range for data sets, using
digital technology for larger data sets. They describe the relationship between the median and mean in data displays. Students
determine the sample space for simple experiments with equally likely outcomes, and assign probabilities outcomes.

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 Mathematics

Level 8
In Level 8, students consolidate their proficiency with the four arithmetic operations, and combinations of these, for general
computation involving natural numbers, integers and rational numbers, with and without the use of technology. They
represent these numbers on the real number line. They extend the use of indices and develop the index laws using number
examples. Students investigate the relationship between decimal and fraction representations of rational numbers
(terminating and recurring decimals) and work with some irrational real numbers such as square roots and multiples and
fractions of π (pi). They solve a range of problems involving ratios, proportions, percentages and rates, with and without the
use of digital technologies.

Students generalise from number to algebra, and expand, factorise, simplify and substitute into simple algebraic
expressions. They plot linear relations on the Cartesian plane, with and without the use of digital technology, solve linear
equations and apply linear models.

Students convert between units for area and for volume, and solve problems involving duration using 12-hour and 24-hour
time, within a given time zone. They develop and use formulas for calculating perimeters and areas of quadrilaterals and
circles, and volumes of prisms, and solve related measurement problems.

Students use congruence and transformations to establish properties of plane shapes related to sides, angles and
symmetry, and solve related problems.

Students use the logical connectives ‘not’, ‘and’, ‘or’ and ‘either … or’ to relate events to probabilities, and use Venn
diagrams and two-way tables to calculate probabilities. They develop an understanding that probabilities range from 0 to 1
and that the sum of probabilities for events in a sample space is 1.

Students investigate and use various techniques for collecting data, including random sampling. They use digital technology
to explore the variability of proportions and means in random samples drawn from a given population, and investigate the
effect of individual data values, including outliers, on the measure of centre (average).

Number and Algebra

Number and place value Elaborations

Use index notation with numbers to establish the index evaluating numbers expressed as powers of positive
laws with positive integral indices and the zero index integers
(VCMNA272)

Carry out the four operations with rational numbers and using patterns to assist in finding rules for the
integers, using efficient mental and written strategies and multiplication and division of integers
appropriate digital technologies and make estimates for using the number line to develop strategies for adding
and subtracting rational numbers
these computations (VCMNA273)
making an estimate for the total of a family weekly
grocery bill with consideration of accuracy of the
estimate, or for problems involving the circumference
and area of a circle

Real numbers Elaborations

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 Mathematics

Investigate terminating and recurring decimals recognising terminating, recurring and non-terminating
(VCMNA274) decimals and choosing their appropriate
representations

Investigate the concept of irrational numbers, including π understanding that the real number system includes
(VCMNA275) irrational numbers

Solve problems involving the use of percentages, including using percentages to solve problems, including those
percentage increases and decreases and percentage involving mark-ups, discounts, and GST
error, with and without digital technologies (VCMNA276) using percentages to calculate population increases
and decreases
using percentage error to compare relative size of
error in calculations involving a given or actual value,
and an estimated or measured value

Solve a range of problems involving rates and ratios, understanding that rate and ratio problems can be
including distance-time problems for travel at a constant solved using fractions or percentages and choosing
the most efficient form to solve a particular problem
speed, with and without digital technologies (VCMNA277)
calculating population growth rates in Australia and
Asia and explaining their difference
finding one of distance travelled, time taken or
average speed given the other two quantities

Money and financial mathematics Elaborations

Solve problems involving profit and loss, with and without expressing profit and loss as a percentage of cost or
digital technologies (VCMNA278) selling price, comparing the difference
investigating the methods used in retail stores to
express discounts

Patterns and algebra Elaborations

Extend and apply the distributive law to the expansion of applying the distributive law to the expansion of
algebraic expressions (VCMNA279) algebraic expressions using strategies such as the
area model

Factorise algebraic expressions by identifying numerical recognising the relationship between factorising and
factors (VCMNA280) expanding
identifying the greatest common divisor (highest
common factor) of numeric and algebraic expressions
and using a range of strategies to factorise algebraic
expressions

Simplify algebraic expressions involving the four understanding that the laws used with numbers can
operations (VCMNA281) also be used with algebra

Use algorithms and related testing procedures to identify debugging search and sort programs
and correct errors (VCMNA282) testing a number for divisibility

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 Mathematics

Linear and non-linear relationships Elaborations

Plot linear relationships on the Cartesian plane with and completing a table of values, plotting the resulting
without the use of digital technologies (VCMNA283) points and determining whether the relationship is
linear
finding the rule for a linear relationship

Solve linear equations using algebraic and graphical solving real life problems by using variables to
techniques. Verify solutions by substitution (VCMNA284) represent unknowns

Plot graphs of non-linear real life data with and without the investigating different combinations of length and
use of digital technologies, and interpret and analyse these width of a rectangle for a fixed area, and drawing the
corresponding graph
graphs (VCMNA285)
using graphs to analysing change in the value of a
currency against another currency over a specified
period

Measurement and Geometry

Using units of measurement Elaborations

Choose appropriate units of measurement for area and choosing units for area including mm 2, cm 2, m 2,
volume and convert from one unit to another (VCMMG286) hectares, km 2, and units for volume including mm 3,
cm 3, m 3
recognising that the conversion factors for area units
are the squares of those for the corresponding linear
units
recognising that the conversion factors for volume
units are the cubes of those for the corresponding
linear units

Find perimeters and areas of parallelograms, trapeziums, establishing and using formulas for areas such as
rhombuses and kites (VCMMG287) trapeziums, rhombuses and kites

Investigate the relationship between features of circles investigating the circumference and area of circles
such as circumference, area, radius and diameter. Use with materials or by measuring, to establish an
understanding of formulas
formulas to solve problems involving determining radius,
investigating the area of circles using a square grid or
diameter, circumference and area from each other
by rearranging a circle divided into sectors
(VCMMG288)
solving problems given one of radius, diameter,
circumference or area of a circle, then the other
quantities are determined from this

Develop the formulas for volumes of rectangular and investigating the relationship between volumes of
triangular prisms and prisms in general. Use formulas to rectangular and triangular prisms
solve problems involving volume (VCMMG289)

Solve problems involving duration, including using 12- and identifying regions in Australia and countries in Asia
24-hour time within a single time zone (VCMMG290) that are in the same time zone

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 Mathematics

Geometric reasoning Elaborations

Define congruence of plane shapes using transformations understanding the properties that determine
and use transformations of congruent shapes to produce congruence of triangles and recognising which
transformations create congruent figures
regular patterns in the plane including tessellations with
establishing that two figures are congruent if one
and without the use of digital technology (VCMMG291)
shape lies exactly on top of the other after one or
more transformations (translation, reflection, rotation),
and recognising that the matching sides and the
matching angles are equal
exploring tiling patterns in art and design

Develop the conditions for congruence of triangles investigating the minimal conditions needed for the
(VCMMG292) unique construction of triangles, leading to the
establishment of the conditions for congruence (SSS,
SAS, ASA and RHS)
solving problems using the properties of congruent
figures
constructing triangles using the conditions for
congruence

Establish properties of quadrilaterals using congruent establishing the properties of squares, rectangles,
triangles and angle properties, and solve related numerical parallelograms, rhombuses, trapeziums and kites
problems using reasoning (VCMMG293) identifying properties related to side lengths, parallel
sides, angles, diagonals and symmetry

Statistics and Probability

Chance Elaborations

Identify complementary events and use the sum of identifying the complement of familiar events
probabilities to solve problems (VCMSP294) understanding that probabilities range between 0 to 1
and that calculating the probability of an event allows
the probability of its complement to be found

Describe events using language of 'at least', exclusive 'or' posing 'and', 'or' and 'not' probability questions about
(A or B but not both), inclusive 'or' (A or B or both) and objects or people
'and' (VCMSP295)

Represent events in two-way tables and Venn diagrams using Venn diagrams and two-way tables to calculate
and solve related problems (VCMSP296) probabilities for events, satisfying 'and', 'or' and 'not'
conditions
understanding that representing data in Venn
diagrams or two-way tables facilitates the calculation
of probabilities
collecting data to answer the questions using Venn
diagrams or two-way tables

Data representation and interpretation Elaborations

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 Mathematics

Distinguish between a population and a sample and identifying situations where data can be collected by
investigate techniques for collecting data, including census and those where a sample is appropriate
census, sampling and observation (VCMSP297) investigating the differences between convenience,
judgemental and simple random sampling from a
population

Explore the practicalities and implications of obtaining data investigating the uses of random sampling to collect
through sampling using a variety of investigative processes data
(VCMSP298)

Explore the variation of means and proportions of random using sample properties to predict characteristics of
samples drawn from the same population (VCMSP299) the population

Investigate the effect of individual data values including using displays of data to explore and investigate
outliers, on the range, mean and median (VCMSP300) effects
exploring the effect of outliers on the range for
different sets of data by comparing its value with and
without outliers included

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 Mathematics

Level 8 achievement standard

Number and Algebra

Students use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply
the index laws to whole numbers. They identify and describe rational and irrational numbers in context. Students estimate
answers and solve everyday problems involving profit and loss rates, ratios and percentages, with and without the use of digital
technology. They simplify a variety of algebraic expressions and connect expansion and factorisation of linear expressions.
Students solve linear equations and graph linear relationships on the Cartesian plane.

Measurement and Geometry

Students convert between units of measurement for area and for volume. They find the perimeter and area of parallelograms,
rhombuses and kites. Students name the features of circles, calculate circumference and area, and solve problems relating to
the volume of prisms. They make sense of time duration in real applications, including the use of 24-hour time. Students identify
conditions for the congruence of triangles and deduce the properties of quadrilaterals. They use tools, including digital
technology, to construct congruent shapes.

Statistics and Probability

Students explain issues related to the collection of sample data and discuss the effect of outliers on means and medians of the
data. They use various approaches, including the use of digital technology, to generate simple random samples from a
population. Students model situations with Venn diagrams and two-way tables and explain the use of 'not', 'and' and 'or'.
Students choose appropriate language to describe events and experiments. They determine complementary events and
calculate the sum of probabilities.

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 Mathematics

Level 9
In Level 9, students develop familiarity with a broader range of non-linear and linear functions and relations, and related
algebra and graphs.

Students apply index laws with integer indices to a range of numerical expressions and extend this to algebraic expressions
involving numbers and pro-numerals. They use indices to express very large and very small numbers in scientific notation,
and apply this in measurement contexts. Students solve problems involving direct proportion and rates, and simple interest.
They apply coordinate geometry to finding the distance between two points in the Cartesian plane, and the midpoint and
gradient of a line segment joining two points. Students graph linear relations and solve linear equations, using tables of
values, graphs and algebra. They graph simple non-linear relations such as parabolas, the reciprocal function, and circles at
the origin, and solve simple related equations with and without the use of digital technology.

Students find areas of composite shapes and the surface area and volumes of right prisms and cylinders. They solve
problems involving very small and very large time scales and intervals, and use scientific notation in this context. Students
use similarity, enlargement transformations and apply geometric reasoning to solve problems involving ratio and scale
factors. They use Pythagoras theorem and trigonometry ratios to solve problems in the plane involving right angles triangles,
and develop an understanding that these involve irrational real numbers, which are generally represented by rational
approximations specified to a given accuracy.

Students list outcomes for two-step experiments involving selections with and without replacement, using arrays and tree
diagrams, and determine related probabilities. They use Venn diagrams and two-way tables to calculate probabilities and
relative frequencies from collected or given data to estimate probabilities. They identify issues and questions involving
categorical and numerical data, use back-to-back stem-plots and histograms to describe and compare the distribution of
data in terms of location (centre), spread and symmetry or skew.

Number and Algebra

Real numbers Elaborations

Solve problems involving direct proportion. Explore the identifying direct proportion in real-life contexts
relationship between graphs and equations corresponding
to simple rate problems (VCMNA301)

Apply index laws to numerical expressions with integer simplifying and evaluating numerical expressions,
indices (VCMNA302) using involving both positive and negative integer
indices

Express numbers in scientific notation (VCMNA303) representing extremely large and small numbers in
scientific notation, and numbers expressed in scientific
notation as whole numbers or decimals

Money and financial mathematics Elaborations

Solve problems involving simple interest (VCMNA304) understanding that financial decisions can be assisted
by mathematical calculations

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 Mathematics

Patterns and algebra Elaborations

Extend and apply the index laws to variables, using understanding that index laws apply to variables as
positive integer indices and the zero index (VCMNA305) well as numbers

Apply the distributive law to the expansion of algebraic understanding that the distributive law can be applied
expressions, including binomials, and collect like terms to algebraic expressions as well as numbers
where appropriate (VCMNA306) understanding the relationship between expansion
and factorisation and identifying algebraic factors in
algebraic expressions

Apply set structures to solve real-world problems using a sort algorithm to determine the median of a set
(VCMNA307) of numbers
exploring variation in proportion and means of random
samples, drawn from a population

Linear and non-linear relationships Elaborations

Find the distance between two points located on a investigating graphical and algebraic techniques for
Cartesian plane using a range of strategies, including finding distance between two points
graphing software (VCMNA308) using Pythagoras' theorem to calculate distance
between two points

Find the midpoint and gradient of a line segment (interval) investigating graphical and algebraic techniques for
on the Cartesian plane using a range of strategies, finding midpoint and gradient
including graphing software (VCMNA309) recognising that the gradient of a line is the same as
the gradient of any line segment on that line

Sketch linear graphs using the coordinates of two points determining linear rules from suitable diagrams, tables
and solve linear equations (VCMNA310) of values and graphs and describing them using both
words and algebra

Graph simple non-linear relations with and without the use graphing parabolas, and circles connecting x-
of digital technologies and solve simple related equations intercepts of a graph to a related equation
(VCMNA311)

Measurement and Geometry

Using units of measurement Elaborations

Calculate the areas of composite shapes (VCMMG312) understanding that partitioning composite shapes into
rectangles and triangles is a strategy for solving
problems involving area

Calculate the surface area and volume of cylinders and analysing nets of cylinders to establish formulas for
solve related problems (VCMMG313) surface area
connecting the volume and capacity of a cylinder to
solve authentic problems

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 Mathematics

Solve problems involving the surface area and volume of solving practical problems involving surface area and
right prisms (VCMMG314) volume of right prisms

Investigate very small and very large time scales and investigating the usefulness of scientific notation in
intervals (VCMMG315) representing very large and very small numbers

Geometric reasoning Elaborations

Use the enlargement transformation to explain similarity establishing the conditions for similarity of two
and develop the conditions for triangles to be similar triangles and comparing this to the conditions for
congruence
(VCMMG316)
using the properties of similarity and ratio, and correct
mathematical notation and language, to solve
problems involving enlargement. For example, scale
diagrams
using the enlargement transformation to establish
similarityunderstanding that similarity and congruence
help describe relationships between geometrical
shapes and are important elements of reasoning and
proof

Solve problems using ratio and scale factors in similar establishing the relationship between areas of similar
figures (VCMMG317) figures and the ratio of corresponding sides (scale
factor)

Pythagoras and trigonometry Elaborations

Investigate Pythagoras’ Theorem and its application to understanding that Pythagoras' Theorem is a useful
solving simple problems involving right angled triangles tool in determining unknown lengths in right-angled
triangles and has widespread applications
(VCMMG318)
recognising that right-angled triangle calculations may
generate results that can be integers, fractions or
irrational numbers

Use similarity to investigate the constancy of the sine, developing understanding of the relationship between
cosine and tangent ratios for a given angle in right-angled the corresponding sides of similar right-angled
triangles
triangles (VCMMG319)

Apply trigonometry to solve right-angled triangle problems understanding the terms 'adjacent' and 'opposite'
(VCMMG320) sides in a right-angled triangle
selecting and accurately using the correct
trigonometric ratio to find unknown sides (adjacent,
opposite and hypotenuse) and angles in right-angled
triangles

Statistics and Probability

Chance Elaborations

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 Mathematics

List all outcomes for two-step chance experiments, both conducting two-step chance experiments
with and without replacement using tree diagrams or using systematic methods to list outcomes of
arrays. Assign probabilities to outcomes and determine experiments and to list outcomes favourable to an
event
probabilities for events (VCMSP321)
comparing experiments which differ only by being
undertaken with replacement or without replacement

Calculate relative frequencies from given or collected data using Venn diagrams or two-way tables to calculate
to estimate probabilities of events involving 'and' or 'or' relative frequencies of events involving ‘and’, ‘or’
questions
(VCMSP322)
using relative frequencies to find an estimate of
probabilities of ‘and’, ‘or’ events

Investigate reports of surveys in digital media and investigating a range of data and its sources. For
elsewhere for information on how data were obtained to example, the age of residents in Australia, Cambodia
and Tonga, or the number of subjects studied at
estimate population means and medians (VCMSP323)
school by 14-year-old students in Australia, Japan and
Timor-Leste

Data representation and interpretation Elaborations

Identify everyday questions and issues involving at least comparing the annual rainfall in various parts of
one numerical and at least one categorical variable, and Australia, Pakistan, New Guinea and Malaysia
collect data directly from secondary sources (VCMSP324)

Construct back-to-back stem-and-leaf plots and histograms using stem-and-leaf plots to compare two like sets of
and describe data, using terms including ‘skewed’, data such as the heights of girls and the heights of
boys in a class
‘symmetric’ and ‘bi modal’ (VCMSP325)
describing the shape of the distribution of data using
terms such as ‘positive skew’, ‘negative skew’ and
'symmetric' and 'bi-modal'

Compare data displays using mean, median and range to comparing means, medians and ranges of two sets of
describe and interpret numerical data sets in terms of numerical data which have been displayed using
histograms, dot plots, or stem and leaf plots
location (centre) and spread (VCMSP326)

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 Mathematics

Level 9 achievement standard

Number and Algebra

Students apply the index laws using integer indices to variables and numbers, express numbers in scientific notation, solve
problems involving very small and very large numbers, and check the order of magnitude of calculations. They solve problems
involving simple interest. Students use the distributive law to expand algebraic expressions, including binomial expressions, and
simplify a range of algebraic expressions. They find the distance between two points on the Cartesian plane and the gradient
and midpoint of a line segment using a range of strategies including the use of digital technology. Students sketch and draw
linear and non-linear relations, solve simple related equations and explain the relationship between the graphical and symbolic
forms, with and without the use of digital technology.

Measurement and Geometry

Students solve measurement problems involving perimeter and area of composite shapes, surface area and volume of
rectangular prisms and cylinders, with and without the use of digital technology. They relate three-dimensional objects to two-
dimensional representations. Students explain similarity of triangles, interpret ratios and scale factors in similar figures, and
apply Pythagoras's theorem and trigonometry to solve problems involving angles and lengths in right-angled triangles.

Statistics and Probability

Students compare techniques for collecting data from primary and secondary sources, and identify questions and issues
involving different data types. They construct histograms and back-to-back stem-and-leaf plots with and without the use of
digital technology. Students identify mean and median in skewed, symmetric and bi-modal displays and use these to describe
and interpret the distribution of the data. They calculate relative frequencies to estimate probabilities. Students list outcomes for
two-step experiments and assign probabilities for those outcomes and related events.

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 Mathematics

Level 10
In Level 10, students extend their use of mathematical models to a wide range of familiar and unfamiliar contexts, involving
the use of all types of real numbers. They recognise the role of logical argument and proof in establishing mathematical
propositions. Students apply mental, written or technology-assisted forms of computation as appropriate, and routinely use
estimation to validate or provide bounds for their answers. They use exponential functions to model compound interest
problems.

Students expand, factorise, simplify and substitute into a wide range of algebraic expressions, including linear, quadratic,
and exponential terms and relations, as well as simple algebraic fractions with numerical denominators. They solve related
equations, linear inequalities and simultaneous linear equations, with and without the use of digital technology. They explore
the connection between tabular, graphical and algebraic representations of non-linear relations, including circles with
centres at any location in the Cartesian plane.

Students solve problems involving surface area and volume for a range of objects, and follow proofs of key geometric
results involving the application of congruence and similarity. They solve practical problems in two and three dimensions
involving right angles triangles, Pythagoras theorem and trigonometry.

Students extend their work in probability to combinations of up to three events, using lists, tables, Venn diagrams, tree
diagrams and grids as applicable to determine probabilities. They explore the concepts of conditional probability and
independence, and their application to solving problems involving chance events.

Students use quartiles and the interquartile range as a measure of spread, and construct and interpret boxplots to compare
data sets. They relate box plots to corresponding dot plots and histograms. Students explore the association between two
numerical variables using scatterplots, in particular with time as the independent variable. They discuss claims made using
statistics in various media articles and other reports, on issues of interest.

Number and Algebra

Real numbers Elaborations

Solve simple problems involving inverse proportion identifying inverse proportion in real life contexts such
(VCMNA327) as exchange rates
modelling problems involving inverse proportion and
solving related equations

Money and financial mathematics Elaborations

Connect the compound interest formula to repeated working with authentic information, data and interest
applications of simple interest using appropriate digital rates to calculate compound interest and solve related
problems
technologies (VCMNA328)

Patterns and algebra Elaborations

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 Mathematics

Factorise algebraic expressions by taking out a common using the distributive law and the index laws to
algebraic factor (VCMNA329) factorise algebraic expressions
understanding the relationship between factorisation
and expansion

Simplify algebraic products and quotients using index laws applying knowledge of index laws to algebraic terms,
(VCMNA330) and simplifying algebraic expressions using both
positive and negative integral indices

Apply the four operations to simple algebraic fractions with expressing the sum and difference of algebraic
numerical denominators (VCMNA331) fractions with a common denominator
using the index laws to simplify products and quotients
of algebraic fractions

Expand binomial products and factorise monic quadratic exploring the method of completing the square to
expressions using a variety of strategies (VCMNA332) factorise quadratic expressions and solve quadratic
equations
identifying and using common factors, including
binomial expressions, to factorise algebraic
expressions using the technique of grouping in pairs
using the identities for perfect squares and the
difference of squares to factorise quadratic
expressions

Substitute values into formulas to determine an unknown solving simple equations arising from formulas
and re-arrange formulas to solve for a particular term re-arranging expressions to make a specified variable
(VCMNA333) the subject such as calculating the radius of a sphere
to produce a given volume

Implement algorithms using data structures in a general- using two-dimensional arrays such as matrices to
purpose programming language (VCMNA334) represent and implement sequences of
transformations of sets of points in the plane
using pointers in algorithms

Linear and non-linear relationships Elaborations

Solve problems involving linear equations, including those representing word problems with simple linear
derived from formulas (VCMNA335) equations and solving them to answer questions

Solve linear inequalities and graph their solutions on a representing word problems with simple linear
number line (VCMNA336) inequalities and solving them to answer questions

Solve simultaneous linear equations, using algebraic and associating the solution of simultaneous equations
graphical techniques including using digital technology with the coordinates of the intersection of their
corresponding graphs
(VCMNA337)

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 Mathematics

Solve problems involving gradients of parallel and solving problems using the fact that parallel lines have
perpendicular lines (VCMNA338) the same gradient and conversely that if two lines
have the same gradient then they are parallel
solving problems using the fact that the product of the
gradients of perpendicular lines is –1 and conversely
that if the product of the gradients of two lines is –1
then they are perpendicular

Explore the connection between algebraic and graphical sketching graphs of parabolas, and circles
representations of relations such as simple quadratic, applying translations, reflections and stretches to
reciprocal, circle and exponential, using digital technology parabolas and circles
as appropriate (VCMNA339) sketching the graphs of exponential functions using
transformations
plotting graphs of families of relations where the
product of two variable is equal to a fixed constant

Solve linear equations involving simple algebraic fractions solving a wide range of linear equations, including
(VCMNA340) those involving one or two simple algebraic fractions,
and checking solutions by substitution
representing word problems, including those involving
fractions, as equations and solving them to answer the
question

Solve simple quadratic equations using a range of using a variety of techniques to solve quadratic
strategies (VCMNA341) equations, including grouping, completing the square,
the quadratic formula, and choosing two integers with
the required product and sum

Solve equations using systematic guess-check-and-refine refining intervals on graphs and/or in tables of values
with digital technology (VCMNA342) to determine with increasing accuracy when the
values of two functions are approximately equal

Measurement and Geometry

Using units of measurement Elaborations

Solve problems involving surface area and volume for a investigating and determining the volumes and surface
range of prisms, cylinders and composite solids areas of composite solids by considering the individual
solids from which they are constructed
(VCMMG343)

Geometric reasoning Elaborations

Formulate proofs involving congruent triangles and angle applying an understanding of relationships to deduce
properties (VCMMG344) properties of geometric figures (for example the base
angles of an isosceles triangle are equal)

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 Mathematics

Apply logical reasoning, including the use of congruence distinguishing between a practical demonstration and
and similarity, to proofs and numerical exercises involving a proof (for example demonstrating triangles are
congruent by placing them on top of each other, as
plane shapes (VCMMG345)
compared to using congruence tests to establish that
triangles are congruent)
performing a sequence of steps to determine an
unknown angle giving a justification in moving from
one step to the next.
communicating a proof using a sequence of logically
connected statements

Pythagoras and trigonometry Elaborations

Solve right-angled triangle problems including those applying Pythagoras's Theorem and trigonometry to
involving direction and angles of elevation and depression problems in surveying and design
(VCMMG346)

Statistics and Probability

Chance Elaborations

Describe the results of two- and three-step chance recognising that an event can be dependent on
experiments, both with and without replacements, assign another event and that this will affect the way its
probability is calculated
probabilities to outcomes and determine probabilities of
events. Investigate the concept of independence
(VCMSP347)

Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ using two-way tables and Venn diagrams to
to investigate conditional statements and identify common understand conditional statements
mistakes in interpreting such language (VCMSP348) using arrays and tree diagrams to determine
probabilities

Data representation and interpretation Elaborations

Determine quartiles and interquartile range and investigate finding the five-number summary (minimum and
the effect of individual data values, including outliers on the maximum values, median and upper and lower
quartiles) and using its graphical representation, the
interquartile range (VCMSP349)
box plot, as tools for both numerically and visually
comparing the centre and spread of data sets
exploring the effect of varying data values, including
outliers, on the interquartile range for different sets of
data

Construct and interpret box plots and use them to compare understanding that box plots are an efficient and
data sets (VCMSP350) common way of representing and summarising data
and can facilitate comparisons between data sets
using parallel box plots to compare data about the age
distribution of Aboriginal and Torres Strait Islander
people with that of the Australian population as a
whole

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 Mathematics

Compare shapes of box plots to corresponding histograms investigating data in different ways to make
and dot plots and discuss the distribution of data comparisons and draw conclusions
(VCMSP351) using a dot plot, box-plot or histogram to construct a
cumulative frequency distribution for a set of data

Use scatter plots to investigate and comment on using authentic data to construct scatter plots, make
relationships between two numerical variables comparisons and draw conclusions
(VCMSP352)

Investigate and describe bivariate numerical data, investigating biodiversity changes in Australia since
including where the independent variable is time European occupation
(VCMSP353) constructing and interpreting data displays
representing bivariate data over time
constructing scatter-plots for two numerical variables
and investigate trends such as water storage levels
over time or weight and height distributions

Evaluate statistical reports in the media and other places investigating the use of statistics in reports regarding
by linking claims to displays, statistics and representative the growth of Australia's trade with other countries of
the Asia region
data (VCMSP354)
evaluating statistical reports comparing the life
expectancy of Aboriginal and Torres Strait Islander
people with that of the Australian population as a
whole

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 Mathematics

Level 10 achievement standard

Number and Algebra

Students recognise the connection between simple and compound interest. They solve problems involving linear equations and
inequalities, quadratic equations and pairs of simultaneous linear equations and related graphs, with and without the use of
digital technology. Students substitute into formulas, find unknown values, manipulate linear algebraic expressions, expand
binomial expressions and factorise monic and simple non-monic quadratic expressions, with and without the use of digital
technology. They represent linear, quadratic and exponential functions numerically, graphically and algebraically, and use them
to model situations and solve practical problems.

Measurement and Geometry

Students solve and explain surface area and volume problems relating to composite solids. They use parallel and perpendicular
lines, angle and triangle properties, similarity, trigonometry and congruence to solve practical problems and develop proofs
involving lengths, angles and areas in plane shapes. They use digital technology to construct and manipulate geometric shapes
and objects, and explore symmetry and pattern in two dimensions.

Statistics and Probability

Students compare univariate data sets by referring to summary statistics and the shape of their displays. They describe
bivariate data where the independent variable is time and use scatter-plots generated by digital technology to investigate
relationships between two continuous variables. Students evaluate the use of statistics in the media. They list outcomes for
multi-step chance experiments involving independent and dependent events, and assign probabilities for these experiments.

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 Mathematics

Level 10A
Level 10A provides optional, additional content for students to be extended in their mathematical studies.

Students could extend work in number and algebra to investigate the structure and properties of number systems, with
further analysis of order relations and inequalities. They could extend the study of trigonometry to include an introduction to
circular functions and equations, or extend the study of indices and exponential functions to logarithms, including an
introduction to logarithmic functions.

Students could extend work in measurement and geometry to proving a broader range of geometric propositions solving
trigonometric problems in non-right angles triangles, or solving three dimensional problems involving surface area and
volume of cones and spheres and composite shapes.

Students could extend work in statistics and probability to explore the concepts of conditionality, dependence and
independence in depth, or consider how various measures of location and spread can be used to describe the distribution of
a data set, and investigate how robust these are with respect to variation in the data, in particular with respect to
measurement error.

Number and Algebra

Real numbers Elaborations

Define rational and irrational numbers and perform understanding that the real number system includes
operations with surds and fractional indices (VCMNA355) irrational numbers
extending the index laws to rational number indices
performing the four operations with surds

Use the definition of a logarithm to establish and apply the investigating the relationship between exponential and
laws of logarithms and investigate logarithmic scales in logarithmic expressions
measurement (VCMNA356) simplifying expressions using the logarithm laws
investigating the use of logarithmic scales to represent
very small and very large quantities

Patterns and algebra Elaborations

Investigate the concept of a polynomial and apply the investigating the relationship between algebraic long
factor and remainder theorems to solve problems division and the factor and remainder theorems
(VCMNA357)

Devise and use algorithms and simulations to solve applying a systematic guess-check-and-refine
mathematical problems (VCMNA358) algorithm to identify an approximate value for the root
of an equation in an interval
developing simulations for counter-intuitive problems
in probability such as the Monty Hall problem or
derangements

Linear and non-linear relationships Elaborations

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 Mathematics

Describe, interpret and sketch parabolas, hyperbolas, applying transformations, including translations,
circles and exponential functions and their transformations reflections in the axes and stretches to help graph
parabolas, rectangular hyperbolas, circles and
(VCMNA359)
exponential functions

Solve simple exponential equations (VCMNA360) investigating exponential equations derived from
authentic mathematical models based on population
growth

Apply understanding of polynomials to sketch a range of investigating the features of graphs of polynomials
curves and describe the features of these curves from their including axes intercepts and the effect of repeated
factors
equation (VCMNA361)

Factorise monic and non-monic quadratic expressions and writing quadratic equations that represent practical
solve a wide range of quadratic equations derived from a problems
variety of contexts (VCMNA362)

Use function notation to describe the relationship between identify independent and dependent variables in
dependent and independent variables in modelling modelling contexts and represent the relation between
them using tables, graphs and rules
contexts (VCMNA363)
using technology to draw graphs of functions defined
using function notation with consideration of domain
and range

Solve simultaneous equations using systematic guess- using graphs to determine a convergent set of
check-and-refine with digital technology (VCMNA364) intervals which contain a point of intersection of the
graphs of two functions
using cobweb diagram to solve simultaneous
equations numerically

Measurement and Geometry

Using units of measurement Elaborations

Solve problems involving surface area and volume of right using formulas to solve problems
pyramids, right cones, spheres and related composite using authentic situations to apply knowledge and
solids (VCMMG365) understanding of surface area and volume

Geometric reasoning Elaborations

Prove and apply angle and chord properties of circles performing a sequence of steps to determine an
(VCMMG366) unknown angle or length in a diagram involving a
circle, or circles, giving a justification in moving from
one step to the next
communicating a proof using a logical sequence of
statements
proving results involving chords of circles

Pythagoras and trigonometry Elaborations

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 Mathematics

Establish the sine, cosine and area rules for any triangle applying knowledge of sine, cosine and area rules to
and solve related problems (VCMMG367) authentic problems such as those involving surveying
and design

Use the unit circle to define trigonometric functions as establishing the symmetrical properties of
functions of a real variable, and graph them with and trigonometric functions
without the use of digital technologies (VCMMG368) investigating angles of any magnitude
understanding that trigonometric functions are periodic
and that this can be used to describe motion
identifying points on the unit circle via arc lengths in
radians, which correspond to specified values of the
circular functions sine, cosine and tangent

Solve simple trigonometric equations (VCMMG369) using periodicity and symmetry to solve equations

Apply Pythagoras’ theorem and trigonometry to solving investigating the applications of Pythagoras's theorem
three-dimensional problems in right-angled triangles in authentic problems
(VCMMG370)

Statistics and Probability

Chance Elaborations

Investigate reports of studies in digital media and evaluating the appropriateness of sampling methods
elsewhere for information on their planning and in reports where statements about a population are
based on a sample
implementation (VCMSP371)
evaluating whether graphs in a report could mislead,
and whether graphs and numerical information
support the claims

Data representation and interpretation Elaborations

Calculate and interpret the mean and standard deviation of using the standard deviation to describe the spread of
data and use these to compare data sets. Investigate the a set of data
effect of individual data values including outliers, on the using the mean and standard deviation to compare
numerical data sets
standard deviation (VCMSP372)
constructing distributions for the mean and standard
deviation of simple random samples from a population

Use digital technology to investigate bivariate numerical investigating different techniques for finding a ‘line of
data sets. Where appropriate use a straight line to describe best fit’
the relationship allowing for variation, make predictions using a fitted line to data to make predictions between
and beyond existing data value sand discuss
based on this straight line and discuss limitations
limitations of these predictions
(VCMSP373)

Victorian Curriculum | 25 February 2016 Page 36 of 37

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 Mathematics

Victorian Curriculum | 25 February 2016 Page 37 of 37

For more information see http://victoriancurriculum.vcaa.vic.edu.au/Copyright