Mathematics Version 2.0 - Curriculum

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Foundation Level

Foundation Level Description

In Foundation, learning in Mathematics builds on each student’s prior learning and experiences, including the learning opportunities acquired through the implementation of the Victorian Early...

Foundation Level Content Descriptions

Number

name, represent and order numbers, including zero to at least 20, using physical and virtual materials and numerals (VC2MFN01)
recognise and name the number of objects within a collection up to 5 using subitising (VC2MFN02)
quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning (VC2MFN03)
partition and combine collections up to 10 using part-part-whole relationships and subitising to recognise and name the parts (VC2MFN04)
represent practical situations, including simple financial situations, involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies (VC2MFN05)
represent practical situations that involve equal sharing and grouping with physical and virtual materials and use counting or subitising strategies (VC2MFN06)

Algebra

follow a short sequence of instructions; recognise, copy, continue and create repeating patterns represented in different ways (VC2MFA01)

Measurement

identify and compare attributes of objects and events, including length, capacity, mass and duration, use direct comparisons and communicate reasoning (VC2MFM01)
sequence days of the week and times of the day, including morning, lunchtime, afternoon and night-time, and connect them to familiar events and actions (VC2MFM02)

Space

sort, name and create familiar shapes; recognise and describe familiar shapes within objects in the environment, giving reasons (VC2MFSP01)
describe the position and location of themselves and objects in relation to other people and objects within a familiar space (VC2MFSP02)

Statistics

collect, sort and compare data represented by objects and images in response to given investigative questions that have only 2 outcomes and relate to familiar situations (VC2MFST01)

Foundation Level Achievement Standard

By the end of Foundation, students make connections between number names, numerals and position in the sequence of numbers from zero to at least 20. They use subitising and counting strategies to quantify collections. Students compare the size of collections to at least 20. They partition and combine collections up to 10 in different ways, representing these with numbers. Students represent practical situations, including simple financial situations involving money, that involve quantifying, equal sharing, adding to and taking away from collections to at least 10.

Students represent, continue and create simple repeating patterns.

Students identify the attributes of mass, capacity, length and duration, and use direct comparison strategies to compare objects and events. They sequence and connect familiar events to the time of day.

Students name, create and sort familiar shapes and give their reasoning. They describe the position and the location of themselves and objects in relation to other objects and people within a familiar space.

Students collect, sort and compare data in response to questions in familiar contexts.

Level 1

Level 1 Description

In Level 1, learning in Mathematics builds on each student’s prior learning and experiences, including the learning opportunities acquired through the implementation of the Victorian...

In Level 1, learning in Mathematics builds on each student’s prior learning and experiences, including the learning opportunities acquired through the implementation of the Victorian Early Years Learning and Development Framework (VEYLDF). Students engage in a range of approaches to the learning and doing of 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:

use their curiosity and imagination to explore situations, recognise patterns in their environment and choose ways of representing their thinking when communicating with others
demonstrate that numbers can be represented, partitioned and composed in various ways; recognise patterns in numbers; and extend their knowledge of numbers beyond 2 digits
use physical or virtual materials and diagrams when modelling practical problems through active learning experiences, recognise existing patterns, employ different strategies and discuss the reasonableness of answers
explain ways of making direct and indirect comparisons and begin to use uniform, informal units to measure some attributes
reason spatially and use spatial features to classify shapes and objects; recognise these shapes and objects in their environment; and use simple transformations, directions and pathways to move the positions of shapes and objects within a space
use simple surveys to collect and sort data, based on a question of interest; recognise that data can be represented in different ways; and explain patterns that they see in the results
develop a sense of equivalence, fairness, repetition and variability when they engage in play-based and practical activities.

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Level 1 Content Descriptions

Number

recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts (VC2M1N01)
partition one- and two-digit numbers in different ways using physical and virtual materials, including partitioning two-digit numbers into tens and ones (VC2M1N02)
quantify sets of objects, to at least 120, by partitioning collections into equal groups using number knowledge and skip counting (VC2M1N03)
add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies (VC2M1N04)
use mathematical modelling to solve practical problems involving additive situations, including simple money transactions; represent the situations with diagrams, physical and virtual materials; use calculation strategies to solve the problem (VC2M1N05)
use mathematical modelling to solve practical problems involving equal sharing and grouping; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem (VC2M1N06)

Algebra

recognise, continue and create pattern sequences, with numbers, symbols, shapes and objects including Australian coins, formed by skip counting, initially by twos, fives and tens (VC2M1A01)
recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit and recognising the importance of repetition in solving problems (VC2M1A02 )

Measurement

compare directly and indirectly and order objects and events using attributes of length, mass, capacity and duration, communicating reasoning (VC2M1M01 )
measure the length of shapes and objects using informal units, recognising that units need to be uniform and used end-to-end (VC2M1M02)
describe the duration and sequence of events using years, months, weeks, days and hours (VC2M1M03)

Space

make, compare and classify familiar shapes; recognise familiar shapes and objects in the environment, identifying the similarities and differences between them (VC2M1SP01)
give and follow directions to move people and objects to different locations within a space (VC2M1SP02)

Statistics

acquire and record data for categorical variables in various ways including using digital tools, objects, images, drawings, lists, tally marks and symbols (VC2M1ST01)
represent collected data for a categorical variable using one-to-one displays and digital tools where appropriate; compare the data using frequencies and discuss the findings (VC2M1ST02)

Level 1 Achievement Standard

By the end of Level 1, students connect number names, numerals and quantities, and order numbers to at least 120. They demonstrate how one- and two-digit numbers can be partitioned in different ways and that two-digit numbers can be partitioned into tens and ones. Students partition collections into equal groups and skip count in twos, fives or tens to quantify collections to at least 120. They solve problems involving addition and subtraction of numbers to 20 and use mathematical modelling to solve practical problems involving addition, subtraction, equal sharing and grouping, using calculation strategies.

Students use numbers, symbols and objects, including Australian coins, to create skip counting and repeating patterns, identifying the repeating unit.

Students compare and order objects and events based on the attributes of length, mass, capacity and duration, communicating their reasoning. They measure the length of shapes and objects using uniform informal units.

Students make, compare and classify shapes and objects using identifiable features. They give and follow directions to move people and objects within a space.

Students collect and record categorical data, create one-to-one displays, and compare and discuss the data using frequencies.

Level 2

Level 2 Description

In Level 2, learning in Mathematics builds on each student’s prior learning and experiences, including the learning opportunities acquired through the implementation of the Victorian...

In Level 2, learning in Mathematics builds on each student’s prior learning and experiences, including the learning opportunities acquired through the implementation of the Victorian Early Years Learning and Development Framework (VEYLDF). Students engage in a range of approaches to the learning and doing of 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:

recognise that mathematics can be used to investigate things they are curious about, to solve practical problems and to model everyday situations, describing their thinking and reasoning using familiar mathematical language
partition and combine numbers flexibly, recognising and describing the relationship between addition and subtraction and employing part-part-whole reasoning and relational thinking to solve additive problems
use number sentences to formulate additive situations and represent simple multiplicative situations using equal groups and arrays
use mathematical modelling to solve practical problems involving authentic situations by representing problems with physical and virtual materials, and diagrams, and using different calculation strategies to find solutions
compare and contrast related operations and use known addition and subtraction facts to develop strategies for unfamiliar calculations
recognise types of patterns in different contexts
partition collections, shapes and objects into equal parts and build a sense of fractions as a measure, connecting this to measures of turn and representations of time
use uniform units to measure, compare and discuss the attributes of shapes and objects, and the duration of events
describe spatial relationships such as the relative position of objects represented within a two-dimensional space
build the foundations for statistical inquiry by choosing questions based on their interests as they collect, represent and interpret data, and recognise features of different representations
develop a sense of equivalence, chance and variability when they engage in play-based and practical activities.

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Level 2 Content Descriptions

Number

recognise, represent and order numbers to at least 1000 using physical and virtual materials, numerals and number lines (VC2M2N01)
partition, rearrange, regroup and rename two- and three-digit numbers using standard and non-standard groupings; recognise the role of a zero digit in place value notation (VC2M2N02)
recognise and describe one-half as one of 2 equal parts of a whole and connect halves, quarters and eighths through repeated halving (VC2M2N03)
add and subtract one- and two-digit numbers, represent problems using number sentences and solve using part-part-whole reasoning and a variety of calculation strategies (VC2M2N04)
multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays and partitioning to support a variety of calculation strategies (VC2M2N05)
use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the context (VC2M2N06)

Algebra

recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern (VC2M2A01)
recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts (VC2M2A02)
recall and demonstrate proficiency with multiplication facts for twos; extend and apply facts to develop the related division facts using doubling and halving (VC2M2A03)
apply repetition in arithmetic operations, including multiplication as repeated addition and division as repeated subtraction (VC2M2A04)

Measurement

measure and compare objects based on length, capacity and mass using appropriate uniform informal units and smaller units for accuracy when necessary (VC2M2M01)
identify common uses and represent halves, quarters and eighths in relation to shapes, objects and events (VC2M2M02)
identify the date and determine the number of days between events using calendars (VC2M2M03)
recognise and read the time represented on an analog clock to the hour, half-hour and quarter hour (VC2M2M04)
identify, describe and demonstrate quarter, half, three-quarter and full measures of turn in everyday situations (VC2M2M05)

Space

recognise, compare and classify shapes, referencing the number of sides and using spatial terms such as ‘opposite’, ‘parallel’, ‘curved’ and ‘straight’ (VC2M2SP01)
locate positions in two-dimensional representations of a familiar space; move positions by following directions and pathways (VC2M2SP02)

Statistics

acquire data for categorical variables through surveys, observation, experiment and using digital tools; sort data into relevant categories and display data using lists and tables (VC2M2ST01)
create different graphical representations of data using software where appropriate; compare the different representations, and identify and describe common and distinctive features in response to questions (VC2M2ST02)

Level 2 Achievement Standard

By the end of Level 2, students order and represent numbers to at least 1000; apply knowledge of place value to partition, rearrange and rename two- and three-digit numbers in terms of their parts; and regroup partitioned numbers to assist in calculations. They use mathematical modelling to solve practical additive and multiplicative problems, including money transactions, representing the situation and choosing calculation strategies. Students identify and represent part-whole relationships of halves, quarters and eighths in measurement contexts.

Students describe and continue patterns that increase and decrease additively by a constant amount and identify missing elements in the pattern. They recall and demonstrate proficiency with addition and subtraction facts within 20 and multiplication facts for twos.

Students use uniform informal units to measure and compare shapes and objects. They determine the number of days between events using a calendar and read time on an analog clock to the hour, half-hour and quarter hour. Students use quarter, half, three-quarter and full measures of turn in everyday situations.

Students compare and classify shapes, describing features using formal spatial terms. They locate and identify positions of features in two-dimensional representations and move position by following directions and pathways.

Students use a range of methods to collect, record, represent and interpret categorical data in response to questions.

Level 3

Level 3 Description

In Level 3, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that...

In Level 3, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of 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:

become increasingly aware of the usefulness of mathematics to model situations and solve practical problems
recognise that mathematics has conventions and language enabling the unambiguous communication of ideas and results
experience the power of being able to manipulate numbers using a range of strategies that are based on proficiency with single-digit addition facts and their understanding of place value in the base-10 number system, partitioning and regrouping
begin to apply their understanding of algorithms and technology to experiment with numbers and recognise patterns
develop, extend and apply their addition and multiplication facts and related facts for subtraction and division through recognising connections between operations, and develop automaticity for 3, 4, 5 and 10 multiplication facts through games and meaningful practice
learn to formulate, choose and use calculation strategies, communicating their solutions within a modelling context
use metric units to measure and compare objects and events
recognise the relationship between dollars and cents and learn to represent money values in different ways, including virtual money
determine key features of objects and spaces, and use these when they build models and spatial representations
undertake, with guidance, statistical investigations that are meaningful to them, making decisions about their use and representation of categorical and discrete numerical data, and reporting findings
develop a qualitative understanding of chance and use the language of chance to describe and compare the outcomes of familiar chance events
become increasingly able to understand that different outcomes can be the results of random processes.

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Level 3 Content Descriptions

Number

identify, explain and use the properties of odd and even numbers (VC2M3N01)
recognise, represent and order natural numbers using naming and writing conventions for numerals beyond 10 000 (VC2M3N02)
recognise and represent unit fractions including $\frac{1}{2}$ , $\frac{1}{3}$ , $\frac{1}{4}$ , $\frac{1}{5}$ and $\frac{1}{10}$ and their multiples in different ways; combine fractions with the same denominator to complete the whole (VC2M3N03)
add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator (VC2M3N04)
multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies (VC2M3N05)
estimate the quantity of objects in collections and make estimates when solving problems to determine the reasonableness of calculations (VC2M3N06)
recognise the relationships between dollars and cents and represent money values in different ways (VC2M3N07)
use mathematical modelling to solve practical problems involving additive and multiplicative situations, including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation (VC2M3N08)
follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns (VC2M3N09)

Algebra

recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences (VC2M3A01)
extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator (VC2M3A02)
recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts (VC2M3A03)

Measurement

identify which metric units are used to measure everyday items; use measurements of familiar items and known units to make estimates (VC2M3M01)
measure and compare objects using familiar metric units of length, mass and capacity, and instruments with labelled markings (VC2M3M02)
recognise and use the relationship between formal units of time, including days, hours, minutes and seconds, to estimate and compare the duration of events (VC2M3M03)
describe the relationship between the hours and minutes on analog and digital clocks, and read the time to the nearest minute (VC2M3M04)
identify angles as measures of turn and use right angles as a reference to compare angles in everyday situations (VC2M3M05)

Space

make, compare and classify objects, identifying key features and explaining why these features make them suited to their uses (VC2M3SP01)
interpret and create two-dimensional representations of familiar environments, locating key landmarks and objects relative to each other (VC2M3SP02)

Statistics

acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods, including frequency tables and spreadsheets (VC2M3ST01)
create and compare different graphical representations of data sets, including using software where appropriate; interpret the data in terms of the context (VC2M3ST02)
conduct guided statistical investigations involving the collection, representation and interpretation of data for categorical and discrete numerical variables with respect to questions of interest (VC2M3ST03)

Probability

identify practical activities and everyday events that involve chance, and describe possible outcomes and events as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’, explaining reasoning (VC2M3P01)
conduct repeated chance experiments; identify and describe possible outcomes, record the results, and recognise and discuss the variation (VC2M3P02)

Level 3 Achievement Standard

By the end of Level 3, students order and represent natural numbers beyond 10 000, classify numbers as either odd or even, and use the properties of odd and even numbers. They partition, rearrange and regroup two- and three-digit numbers in different ways to assist in calculations. Students extend and use single-digit addition and related subtraction facts and apply additive strategies to model and solve problems involving two- and three-digit numbers. They use a range of strategies to apply mathematical modelling to solve practical problems involving single-digit multiplication and division, recalling multiplication facts for twos, threes, fours, fives and tens. Students represent unit fractions and their multiples in different ways. They make estimates and determine the reasonableness...

Level 4

Level 4 Description

In Level 4, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that...

In Level 4, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of 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:

consolidate their knowledge and facility with arithmetic operations, and draw on their proficiency with number facts, fractions and decimals, to deepen their appreciation of how numbers work
develop and use strategies for multiplication that are based on their understanding of multiplication as an operation and their knowledge of laws for arithmetic operations
choose and use efficient mental and written strategies when modelling problems, communicating their solutions within the context of the situation
use algorithms to generate sets of numbers, recognising and describing any patterns that emerge
become aware of the importance of context and purpose when they make judgements and reflect on the reasonableness of measurements and the results of calculations, and how they choose to represent mathematics and mathematical information
measure and estimate common attributes of objects using conventional instruments and appropriate metric units
develop and use surveys to obtain data that is directly relevant to their statistical investigations
draw on their reasoning skills to analyse, categorise and order chance events and identify independent and dependent events
investigate variability by conducting repeated chance experiments and observing results.

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Level 4 Content Descriptions

Number

recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals (VC2M4N01)
investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9 (VC2M4N02)
find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation (VC2M4N03)
count by multiples of quarters, halves and thirds, including mixed numerals; locate and represent these fractions as numbers on number lines (VC2M4N04)
solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits (VC2M4N05)
develop efficient mental and written strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder (VC2M4N06)
choose and use estimation and rounding to check and explain the reasonableness of calculations, including the results of financial transactions (VC2M4N07)
solve problems involving purchases and the calculation of change to the nearest 5 cents with and without digital tools (VC2M4N08)
use mathematical modelling to solve practical problems that involve additive and multiplicative situations, including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation (VC2M4N09)
follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns (VC2M4N10)

Algebra

find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations (VC2M4A01)
recall and demonstrate proficiency with multiplication facts up to 10 × 10 and related division facts, and explain the patterns in these; extend and apply facts to develop efficient mental and written strategies for computation with larger numbers without a calculator (VC2M4A02)

Measurement

use scaled and digital instruments to interpret unmarked and partial units to measure and compare lengths, masses, capacities, durations and temperatures, using appropriate units (VC2M4M01)
recognise ways of measuring and approximating the perimeter and area of shapes and enclosed spaces, using appropriate formal and informal units (VC2M4M02)
solve problems involving the duration of time including situations involving ‘am’ and ‘pm’ and conversions between units of time (VC2M4M03)
estimate and compare angles using angle names including acute, obtuse, straight angle, reflex and revolution, and recognise their relationship to a right angle (VC2M4M04)

Space

explain and compare the geometric properties of two-dimensional shapes and three-dimensional objects (VC2M4SP01)
represent and approximate composite shapes and objects in the environment, using combinations of familiar shapes and objects (VC2M4SP02)
create and interpret grid reference systems using grid references and directions to locate and describe positions and pathways (VC2M4SP03)
recognise line and rotational symmetry of shapes and create symmetrical patterns and pictures, using dynamic geometry software where appropriate (VC2M4SP04)

Statistics

acquire data for categorical and discrete numerical variables to address a question of interest or purpose using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created (VC2M4ST01)
analyse the effectiveness of different displays or visualisations in illustrating and comparing data distributions, then discuss the shape of distributions and the variation in the data (VC2M4ST02)
conduct statistical investigations, collecting data through survey responses and other methods; record and display data using digital tools; interpret the data and communicate the results (VC2M4ST03)

Probability

describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events (VC2M4P01)
conduct repeated chance experiments to observe relationships between outcomes in games and other chance situations, and identify and describe the variation in results (VC2M4P02)

Level 4 Achievement Standard

By the end of Level 4, students use their understanding of place value to represent tenths and hundredths in decimal form and to multiply natural numbers by multiples of 10. Students use mathematical modelling to solve financial and other practical problems, formulating the problem using number sentences, solving the problem choosing efficient strategies and interpreting the results in terms of the situation. They use their proficiency with addition, subtraction, multiplication facts for tens (× 10) and related division facts to perform arithmetic operations to add and subtract, and multiply and divide numbers efficiently. They choose rounding and estimation strategies to determine whether results of calculations are reasonable. They recognise common equivalent fractions in familiar...

Students find unknown values in numerical equations involving addition and subtraction. They follow and create algorithms that generate sets of numbers and identify emerging patterns.

Students use appropriate scaled instruments and appropriate units to measure length, mass, capacity and temperature. They measure and approximate perimeters and areas for regular and irregular shapes. They convert between units of time when solving problems involving duration. Students compare angles relative to a right angle using angle names.

Students represent and approximate shapes and objects from their environment. Students create and interpret grid references. They identify line and rotational symmetry in plane shapes and create symmetrical patterns.

Students create many-to-one data displays, assess the suitability of displays for representing data and informally discuss the shape of distributions and variation in data. They use surveys and digital tools to generate categorical or discrete numerical data in statistical investigations and communicate their findings in context.

Students order events or the outcomes of chance experiments in terms of likelihood and identify whether events are independent or dependent. They conduct repeated chance experiments and describe the variation in results.

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Level 5

Level 5 Description

In Level 5, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that...

Level 5 Content Descriptions

Number

interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line (VC2M5N01)
express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another (VC2M5N02)
compare and order common unit fractions with the same and related denominators, including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line (VC2M5N03)
recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents (VC2M5N04)
solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies (VC2M5N05)
solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient mental and written calculation strategies and using digital tools where appropriate; check the reasonableness of answers (VC2M5N06)
solve problems involving division, choosing efficient mental and written strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction (VC2M5N07)
check and explain the reasonableness of solutions to problems, including financial contexts using estimation strategies appropriate to the context (VC2M5N08)
use mathematical modelling to solve practical problems involving additive and multiplicative situations, including simple financial planning contexts; formulate the problems, choosing operations and efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation (VC2M5N09)
follow a mathematical algorithm involving branching and repetition (iteration); create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples and divisibility; identify, interpret and describe emerging patterns (VC2M5N10)

Algebra

recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts (VC2M5A01)
find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations (VC2M5A02)

Measurement

choose appropriate metric units when measuring the length, mass and capacity of objects; use smaller units or a combination of units to obtain a more accurate measure (VC2M5M01)
solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units (VC2M5M02)
compare 12- and 24-hour time systems and solve practical problems involving the conversion between them (VC2M5M03)
estimate, construct and measure angles in degrees, using appropriate tools, including a protractor, and relate these measures to angle names (VC2M5M04)

Space

connect objects to their nets and build objects from their nets using spatial and geometric reasoning (VC2M5SP01)
construct a grid coordinate system that uses coordinates to locate positions within a space; use coordinates and directional language to describe position and movement (VC2M5SP02)
describe and perform translations, reflections and rotations of shapes, using dynamic geometry software where appropriate; recognise what changes and what remains the same, and identify any symmetries (VC2M5SP03)

Statistics

acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data (VC2M5ST01)
interpret line graphs representing change over time; discuss the relationships that are represented and conclusions that can be made (VC2M5ST02)
plan and conduct statistical investigations by posing questions or identifying a problem and collecting relevant data; choose appropriate displays and interpret the data; communicate findings within the context of the investigation (VC2M5ST03)

Probability

list the possible outcomes of chance experiments involving equally likely outcomes and compare to those that are not equally likely (VC2M5P01)
conduct repeated chance experiments, including those with and without equally likely outcomes, and observe and record the results; use frequency to compare outcomes and estimate their likelihoods (VC2M5P02)

Level 5 Achievement Standard

By the end of Level 5, students use place value to write and order decimals including decimals greater than one. They express natural numbers as products of factors and identify multiples and divisors. Students order and represent, add and subtract fractions with the same or related denominators. They represent common percentages and connect them to their fraction and decimal equivalents. Students use their proficiency with multiplication facts and efficient mental and written calculation strategies to multiply large numbers by one- and two-digit numbers and divide by one-digit numbers. They check the reasonableness of their calculations using estimation. Students use mathematical modelling to solve financial and other practical problems, formulating and solving problems, choosing arithmetic...

Students apply properties of numbers and operations to find unknown values in numerical equations involving multiplication and division. They design and use algorithms to identify and explain patterns in the factors and multiples of numbers.

Students choose and use appropriate metric units to measure the attributes of length, mass and capacity, and to solve problems involving perimeter and area. Students convert between 12- and 24-hour time. They estimate, construct and measure angles in degrees. Students use grid coordinates to locate and move positions.

Students connect objects to their two-dimensional nets. They perform and describe the results of transformations and identify any symmetries.

Students plan and conduct statistical investigations that collect nominal and ordinal categorical and discrete numerical data with and without digital tools. Students identify the mode and interpret the shape of distributions of data in context. They interpret and compare data represented in line graphs.

Students conduct repeated chance experiments, list the possible outcomes, estimate likelihoods and make comparisons between those with and without equally likely outcomes.

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Level 6

Level 6 Description

In Level 6, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that...

In Level 6, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of 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:

expand the repertoire of numbers they work with to include rational numbers and the use of integers in practical contexts, such as locating points in the 4 quadrants of a Cartesian plane
extend their knowledge of factors and multiples to understand the properties of prime, composite, triangular and square numbers
solve arithmetic problems involving all 4 operations with natural numbers of any size
use mathematical modelling to solve practical problems, choosing models, representations and calculation strategies, and justify solutions
apply computational thinking approaches to develop algorithms that use rules to generate numbers
develop a range of written and digital means for representing objects and three-dimensional spaces in 2 dimensions
apply their understanding of area and use multiplicative thinking to establish the formula for the area of a rectangle
begin to formally use deductive reasoning in spatial contexts involving lines and angles
describe and compare probabilities numerically
determine the mode and range and discuss the shape of distributions in their reports of findings from their statistical investigations
observe and compare long-run frequencies in repeated chance experiments and simulations.

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Level 6 Content Descriptions

Number

recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane (VC2M6N01)
identify and describe the properties of prime, composite, square and triangular numbers and use these properties to solve problems and simplify calculations (VC2M6N02)
apply knowledge of equivalence to compare, order and represent common fractions, including halves, thirds and quarters, on the same number line and justify their order (VC2M6N03)
apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers (VC2M6N04)
solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions (VC2M6N05)
multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts, using estimation and rounding to check the reasonableness of answers (VC2M6N06)
solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies with and without digital tools (VC2M6N07)
approximate numerical solutions to problems involving rational numbers and percentages, using appropriate estimation strategies (VC2M6N08)
use mathematical modelling to solve practical problems involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and using efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made (VC2M6N09)

Algebra

recognise and use rules that generate visually growing patterns and number patterns involving rational numbers (VC2M6A01)
find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations (VC2M6A02)
design and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns (VC2M6A03)

Measurement

convert between common metric units of length, mass and capacity; choose and use decimal representations of metric measurements relevant to the context of a problem (VC2M6M01)
establish the formula for the area of a rectangle and use it to solve practical problems (VC2M6M02)
measure, calculate and compare elapsed time; interpret and use timetables and itineraries to plan activities and determine the duration of events and journeys (VC2M6M03 )
identify the relationships between angles on a straight line, angles at a point and vertically opposite angles; use these to determine unknown angles, communicating reasoning (VC2M6M04)

Space

compare the parallel cross-sections of objects and recognise their relationships to right prisms (VC2M6SP01)
locate points in the 4 quadrants of the Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane (VC2M6SP02)
recognise and use combinations of transformations to create tessellations and other geometric patterns, using dynamic geometry software where appropriate (VC2M6SP03)

Statistics

interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using comparative displays or visualisations and digital tools; compare distributions in terms of mode, range and shape (VC2M6ST01)
identify statistically informed arguments presented in traditional and digital media; discuss and critique methods, data representations and conclusions (VC2M6ST02)
plan and conduct statistical investigations by posing and refining questions to collect categorical or numerical data by observation or survey, or identifying a problem and collecting relevant data; analyse and interpret the data and communicate findings within the context of the investigation (VC2M6ST03 )

Probability

describe probabilities using fractions, decimals and percentages; recognise that probabilities lie on numerical scales of 0–‍1 or 0%–100%; use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals (VC2M6P01 )
conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials (VC2M6P02)

Level 6 Achievement Standard

By the end of Level 6, students use integers to represent points on a number line and on the Cartesian plane. They solve problems using the properties of prime, composite, square and triangular numbers. Students order common fractions, giving reasons, and add and subtract fractions with related denominators. They use all 4 operations with decimals and connect decimal representations of measurements to the metric system. Students solve problems involving finding a fraction, decimal or percentage of a quantity and use estimation to find approximate solutions to problems involving rational numbers and percentages. They use mathematical modelling to solve financial and other practical problems involving percentages and rational numbers, formulating and solving the problem, and justifying choices.

Students find unknown values in numerical equations involving combinations of arithmetic operations. They identify and explain rules used to create growing patterns. They design and use algorithms to generate sets of numbers, using a rule.

Students interpret and use timetables, and measure, calculate and compare elapsed time. They convert between common units of length, mass and capacity. They use the formula for the area of a rectangle and angle properties to solve problems.

Students identify the parallel cross-section for right prisms. They create tessellating patterns using combinations of transformations. They locate an ordered pair in any one of the 4 quadrants on the Cartesian plane.

Students compare distributions of discrete and continuous numerical and ordinal categorical data sets as part of their statistical investigations, using digital tools. They critique arguments presented in the media based on statistics.

Students assign probabilities using common fractions, decimals and percentages. They conduct simulations using digital tools, to generate and record the outcomes from many trials of a chance experiment. They compare observed frequencies to the expected frequencies of the outcomes of chance experiments.

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Level 7

Level 7 Description

In Level 7, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that...

In Level 7, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of 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, develop and use algebraic expressions and formulas using conventions, notations, symbols and pronumerals; and 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 relating 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, and construct corresponding sample spaces and observe related frequencies, comparing expected, simulated and experimental results.

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Level 7 Content Descriptions

Number

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 (VC2M7N01)
represent natural numbers in expanded notation using powers of 10, and as products of powers of prime numbers using exponent notation (VC2M7N02)
find equivalent representations of rational numbers and represent positive and negative rational numbers and mixed numbers on a number line (VC2M7N03)
round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of computations (VC2M7N04)
multiply and divide fractions and decimals using efficient mental and written strategies, and digital tools (VC2M7N05)
use the 4 operations with positive rational numbers, including fractions and decimals, to solve problems using efficient mental and written calculation strategies (VC2M7N06)
find percentages of quantities and express one quantity as a percentage of another, with and without digital tools (VC2M7N07)
compare, order and solve problems involving addition and subtraction of integers (VC2M7N08)
recognise, represent and solve problems involving ratios (VC2M7N09)
use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts such as ‘best buys’; formulate problems, choosing representations and efficient calculation strategies, designing algorithms and using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation (VC2M7N10)

Algebra

recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown (VC2M7A01)
apply the associative, commutative and distributive laws to aid mental and written computation, and formulate algebraic expressions using constants, variables, operations and brackets (VC2M7A02)
solve one-variable linear equations of increasing complexity with natural number solutions; verify equation solutions by substitution (VC2M7A03)
investigate, interpret and describe relationships between variables represented in graphs of functions developed from authentic data (VC2M7A04)
generate tables of values from visually changing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane (VC2M7A05)
manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables (VC2M7A06)

Measurement

establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem-solving (VC2M7M01)
solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units (VC2M7M02)
describe the relationship between $π$ and the circumference, radius and diameter of a circle (VC2M7M03)
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 (VC2M7M04)
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 (VC2M7M05)
use mathematical modelling to solve practical problems involving ratios of lengths, areas and volumes; formulate problems, interpret and communicate solutions in terms of the situation, justifying choices made about the representation (VC2M7M06)

Space

represent three-dimensional objects in 2 dimensions; discuss and reason about the advantages and disadvantages of different representations (VC2M7SP01)
classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships (VC2M7SP02)
describe the effect of transformations of a set of points using coordinates in the Cartesian plane, including translations, reflections in an axis, and rotations about the origin (VC2M7SP03)
design 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 (VC2M7SP04)

Statistics

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 (VC2M7ST01)
create different types of displays of numerical data, including dot plots and 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 (VC2M7ST02)
plan and conduct statistical investigations for issues involving discrete and continuous numerical data, and data collected from primary and secondary sources; analyse and interpret distributions of data and report findings in terms of shape and summary statistics (VC2M7ST03)

Probability

identify the sample space for single-stage experiments; assign probabilities to the possible outcomes and predict relative frequencies for related experiments. (VC2M7P01)
conduct repeated chance experiments and run simulations with a large number of trials using digital tools; compare predicted with observed results, explaining the differences and the effect of sample size on the outcomes (VC2M7P02)

Level 7 Achievement Standard

By the end of Level 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 mental and written calculation strategies. Students choose between equivalent representations of rational numbers and percentages to assist in calculations and make simple estimates to judge the reasonableness of results. They use mathematical modelling to solve practical problems involving rational numbers, percentages and ratios in spatial, financial and other applied contexts, justifying...

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 and verify their solutions through substitution. Students create tables of values relating to algebraic expressions and formulas, and describe how the values change.

Students apply knowledge of angle relationships and the sum of angles in a triangle to solve problems, giving reasons. They establish and 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 design an algorithm to sort and classify shapes. They represent objects two-dimensionally in different ways, describing the usefulness of these representations. They use coordinates to describe transformations of points in the plane.

Students plan and conduct statistical investigations involving discrete and continuous numerical data, using appropriate displays. They 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 of events 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.

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Level 8

Level 8 Description

In Level 8, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that...

In Level 8, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of 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 recurring decimal representations; 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 representation and their approximate location on the real number line
select metric measurement units fit for purpose and 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, establish sets of congruency and similarity conditions for common shapes in the plane and create algorithms to test for these conditions, and 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, and combinations of 2 events; and 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.

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Level 8 Content Descriptions

Number

recognise irrational numbers in applied contexts, including $π$ and numbers that develop from the square root of positive real numbers that are not perfect squares, and recognise that irrational numbers cannot develop from the division of integer values by natural numbers (VC2M8N01)
establish and apply the exponent laws with positive integer exponents and the zero exponent, using exponent notation with numbers (VC2M8N02)
convert between fractions and terminating or recurring decimals, using digital tools as appropriate (VC2M8N03)
use the 4 operations with integers and with rational numbers, choosing and using efficient mental and written strategies, and digital tools where appropriate, and making estimates for these computations (VC2M8N04)
solve problems involving the use of percentages, including percentage increases and decreases and percentage error, with and without digital tools (VC2M8N05)
use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts involving profit and loss; formulate problems, choosing efficient mental and written calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the context, reviewing the appropriateness of the model (VC2M8N06)

Algebra

create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties (VC2M8A01)
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 (VC2M8A02)
use mathematical modelling to solve applied problems involving linear relations, including financial contexts involving profit and loss; formulate problems with linear functions, and choose a representation; interpret and communicate solutions in terms of the context, and review the appropriateness of the model (VC2M8A03)
use algorithms and related testing procedures to identify and correct errors (VC2M8A04)
experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns (VC2M8A05)

Measurement

solve problems involving the area and perimeter of irregular and composite shapes using appropriate units (VC2M8M01)
solve problems involving the volume and capacity of right prisms using appropriate units (VC2M8M02)
solve problems involving the circumference and area of a circle using formulas and appropriate units (VC2M8M03)
solve problems involving time and duration, including using 12- and 24-hour time across multiple time zones (VC2M8M04)
recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure (VC2M8M05)
use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles (VC2M8M06)
use mathematical modelling to solve practical problems involving ratios and rates, including distance-time problems for travel at a constant speed and financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model (VC2M8M07)

Space

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 (VC2M8SP01)
establish properties of quadrilaterals using congruent triangles and angle properties, and solve related problems explaining reasoning (VC2M8SP02)
describe in different ways the position and location of three-dimensional objects in 3 dimensions, including using a three-dimensional Cartesian coordinate system with the use of dynamic geometry software or other digital tools (VC2M8SP03)
design and test algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describe how the algorithm works (VC2M8SP04)

Statistics

distinguish between a population and a sample, and investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques (VC2M8ST01)
analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques (VC2M8ST02)
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 (VC2M8ST03)
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 (VC2M8ST04)

Probability

recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts (VC2M8P01)
determine all possible outcome combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific events in practical situations (VC2M8P02)
conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe results (VC2M8P03 )

Level 8 Achievement Standard

By the end of Level 8, students recognise irrational numbers as numbers that cannot develop from the division of integer values by natural 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 simplify, 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 plot linear and non-linear relations on the Cartesian plane, with and without the use of digital tools. 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 by developing algorithms and 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-angled 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 triangles and other common shapes, and design and test algorithms to test for congruency and similarity. Students apply the properties of quadrilaterals to solve problems.

Students 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 or simulations using digital tools to determine related probabilities of compound events.

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Level 9

Level 9 Description

In Level 9, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that develop...

In Level 9, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of 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 develop 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
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; and 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.

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Level 9 Content Descriptions

Number

recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers with and without using digital tools (VC2M9N01)

Algebra

apply the exponent laws to numerical expressions with integer exponents and the zero exponent, and extend to variables (VC2M9A01)
simplify algebraic expressions, apply the distributive law to expand algebraic expressions including binomial products, and factorise monic quadratic expressions (VC2M9A02)
sketch linear graphs of equations in various algebraic forms, using the coordinates of 2 points, and solve linear equations (VC2M9A03)
find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane (VC2M9A04)
identify and graph quadratic functions, solve quadratic equations graphically and numerically, and use null factor law to solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate (VC2M9A05)
use mathematical modelling to solve applied problems involving change, including financial contexts involving simple interest; formulate problems, choosing to use either linear or quadratic functions or other simple variations; interpret solutions in terms of the context; evaluate the model and report methods and findings (VC2M9A06)
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 (VC2M9A07)

Measurement

solve problems involving the volume and surface area of right prisms, cylinders and composite objects using appropriate units (VC2M9M01)
solve problems involving very small and very large measurements, timescales and intervals expressed in scientific notation (VC2M9M02)
solve spatial problems, applying angle properties, scale, similarity, ratio, Pythagoras’ theorem and trigonometry in right-angled triangles (VC2M9M03)
calculate and interpret absolute, relative and percentage errors in measurements (VC2M9M04)
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 (VC2M9M05)

Space

recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity (VC2M9SP01)
apply the enlargement transformation to shapes and objects using dynamic geometry software as appropriate; identify and explain, using language of similarity, ratio and scale, aspects that remain the same and those that change (VC2M9SP02)
design, test and refine algorithms involving a sequence of steps and decisions based on geometric constructions and theorems; discuss and evaluate refinements (VC2M9SP03 )

Statistics

analyse reports of surveys in digital media and elsewhere for information on how data was obtained around everyday questions and issues involving at least one numerical and at least one categorical variable, to estimate population means and medians (VC2M9ST01 )
analyse how different sampling methods, and different samples using the same method, can affect the results of surveys and how choice of representation can be used to support a particular point of view (VC2M9ST02)
represent the distribution of multiple data sets for numerical variables using comparative representations such as back-to-back stem-and-leaf plots and histograms; describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi-modal’; compare data distributions using mean, median and range to describe and interpret numerical data sets with consideration of centre, spread and shape, and the effect of outliers on these measures (VC2M9ST03 )
choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context (VC2M9ST04)
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 (VC2M9ST05 )

Probability

list all outcomes for two-step chance experiments both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes and events (VC2M9P01)
calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and’, inclusive ‘or’ and exclusive ‘or’ (VC2M9P02)
design and conduct repeated chance experiments and simulations using digital tools to estimate probabilities that cannot be determined exactly (VC2M9P03)

Level 9 Achievement Standard

By the end of Level 9, students recognise and use rational and irrational numbers to solve problems.

Students extend and apply the exponent laws with positive integers and the zero exponent to variables. They expand binomial products and factorise monic quadratic expressions. They find the distance between 2 points on the Cartesian plane, sketch linear graphs and find the gradient and midpoint of a line segment. Students use mathematical modelling to solve problems involving change, including simple interest in financial contexts and change in other applied contexts, choosing to use linear and quadratic functions. They graph quadratic functions and use null factor law to solve monic quadratic equations with integer roots algebraically. Students investigate and describe the effects of...

By the end of Level 9, students recognise and use rational and irrational numbers to solve problems.

Students apply formulas to solve problems involving the surface area and volume of right prisms, cylinders and composite shapes. They 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 and indirect proportion, ratio and scale, evaluating the model and communicating their methods and findings. Students express small and large numbers in scientific notation.

Students apply the enlargement transformation to images of shapes and objects, and interpret results. They design, use and test algorithms based on geometric constructions or theorems.

Students 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. They explain how sampling techniques and representation can be used to support or question conclusions or to promote a point of view.

Students determine sets of outcomes for two-step chance experiments and represent these in various ways. They assign probabilities to the outcomes of two-step chance experiments. They design and conduct experiments or simulations for combined events using digital tools.

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Level 10

Level 10 Description

In Level 10, learning in Mathematics builds on each student’s prior learning and experiences and provides the basis for a sound background in number, algebra, function, geometry...

In Level 10, learning in Mathematics builds on each student’s prior learning and experiences and provides the basis for a sound background in number, algebra, function, geometry and statistics. Students engage in a range of approaches to the learning and doing of 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; and 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 linear equations, pairs of linear equations and linear inequalities in 2 variables
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
solve related equations, linear inequalities and simultaneous linear equations, with and without the use of digital tools
explore the connection between tabular, graphical and algebraic representations of non-linear relations, including circles with centres at any location in the Cartesian plane
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; and 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.

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Level 10 Content Descriptions

Number

recognise the effect of using approximations of real numbers in repeated calculations and compare the results when using exact representations (VC2M10N01)

Algebra

factorise algebraic expressions by taking out a common algebraic factor (VC2M10A01)
simplify algebraic products and quotients using exponent laws (VC2M10A02)
apply the 4 operations to simple algebraic fractions with numerical or single variable denominators (VC2M10A03)
expand binomial products and factorise monic quadratic expressions using a variety of strategies (VC2M10A04)
substitute values into formulas to determine an unknown and rearrange formulas to solve for a particular term (VC2M10A05)
implement algorithms that use data structures using pseudocode or a general purpose programming language (VC2M10A06)
solve problems involving linear equations, including those derived from formulas (VC2M10A07)
solve linear inequalities and graph their solutions on a number line (VC2M10A08)
solve simultaneous linear equations, using algebraic and graphical techniques including using digital tools (VC2M10A09)
solve problems involving gradients of parallel and perpendicular lines (VC2M10A10)
explore the connection between algebraic and graphical representations of relations such as simple quadratic, reciprocal, circle and exponential, using digital tools as appropriate (VC2M10A11)
solve linear equations involving simple algebraic fractions (VC2M10A12)
solve simple quadratic equations using a range of strategies, including null factor law (VC2M10A13)
solve simple exponential equations (VC2M10A14)
use mathematical modelling to solve applied problems involving inverse proportion, growth and decay, including in financial contexts to establish the compound interest formula as repeated applications of simple interest; 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 (VC2M10A15)
solve equations graphically or using systematic numerical guess-check-and-refine with digital tools, with consideration of whether all solutions have been found (VC2M10A16)

Measurement

solve problems involving the surface area and volume of composite objects using appropriate units (VC2M10M01)
interpret and use logarithmic scales in applied contexts involving small and large quantities and change (VC2M10M02 )
solve practical problems by applying Pythagoras’ theorem and trigonometry to right-angled triangles, including problems involving direction and angles of elevation and depression (VC2M10M03)
use mathematical modelling to solve practical problems involving direct and inverse proportion and scaling of objects; formulate problems and interpret solutions in terms of the situation, including the impact of measurement errors on the accuracy of results; evaluate and modify models as necessary, and report assumptions, methods and findings (VC2M10M04)

Space

apply deductive reasoning to formulate proofs involving shapes in the plane and use theorems to solve spatial problems (VC2M10SP01)
interpret networks and network diagrams used to represent relationships in practical situations and describe connectedness (VC2M10SP02)

Statistics

compare data distributions for continuous numerical variables using quartiles and interquartile range and appropriate data displays including boxplots, histograms and dot plots; discuss the shapes of these distributions in terms of centre, spread, shape and outliers in the context of the data (VC2M10ST01)
construct scatterplots and consider a line of good fit; comment on the association between the 2 numerical variables in terms of strength, direction and linearity (VC2M10ST02)
construct two-way tables and discuss possible relationship between categorical variables (VC2M10ST03)
analyse claims, inferences and conclusions of statistical reports in the media and other places, by linking claims to displays, statistics and representative data, including ethical considerations and identification of potential sources of bias (VC2M10ST04)
plan and conduct statistical investigations of situations that involve bivariate data, including where the independent variable is time; evaluate and report findings with consideration of limitations of any inferences (VC2M10ST05)

Probability

use the language of ‘if … then …’, ‘given’, ‘of’ and ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language, and describe and interpret situations involving conditional probability; design and conduct simulations using digital tools to model conditional probability and interpret results (VC2M10P01 )
describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events; investigate the concept of independence (VC2M10P02)

Level 10 Achievement Standard

By the end of Level 10, students recognise the effect of approximations of real numbers in repeated calculations.

Students 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. They make and test conjectures involving functions and relations using digital tools. Students substitute into formulas, find unknown values, manipulate linear and quadratic algebraic expressions, expand binomial expressions and factorise monic and simple non-monic quadratic expressions, with and without the use of digital tools. They solve problems involving linear equations and inequalities, quadratic equations and pairs of simultaneous linear equations and related graphs, algebraically and graphically, with and without the use of digital tools, and justify solutions. They represent linear, quadratic and exponential functions numerically, graphically and algebraically, and use them to model situations and solve practical problems. Students can design and implement simple algorithms using pseudocode or other general purpose programming language.

Students solve measurement problems involving surface area and volume of composite objects. They interpret and use logarithmic scales representing small or large quantities or change in applied contexts. 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 direct and inverse proportion and scaling, evaluating and modifying models, and reporting assumptions, methods and findings.

Students use deductive reasoning, theorems and algorithms to solve spatial problems. They interpret networks used to represent practical situations and describe connectedness.

Students compare univariate data sets by referring to summary statistics and the shape of their displays. They plan and conduct statistical investigations involving bivariate data, including where the independent variable is time. They represent the distribution of data involving 2 variables, using tables and scatterplots, 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.

Students apply conditional probability to solve problems involving compound events. They design and conduct simulations involving conditional probability, using digital tools.

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Level 10A

Level 10A Description

Level 10A provides optional, additional content to extend students in their mathematical studies in number, algebra, function, geometry, probability and statistics.

Level...

Level 10A Content Descriptions

Number

define rational and irrational numbers and perform operations with surds and fractional indices (VC2M10AN01)
perform operations on numbers involving fractional exponents and surds (VC2M10AN02)
use the definition of a logarithm to establish and apply the laws of logarithms and investigate logarithmic scales in measurement (VC2M10AN03)

Algebra

investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (VC2M10AA01)
devise and use algorithms and simulations to solve mathematical problems (VC2M10AA02)
simplify combinations of linear expressions with rational coefficients and the solution of related equations (VC2M10AA03)
explore the inverse relationship between exponential functions and logarithmic functions and the solution of related equations (VC2M10AA04)
describe, interpret, and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (VC2M10AA05)
apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (VC2M10AA06)
factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts (VC2M10AA07)
use function notation to describe the relationship between dependent and independent variables in modelling contexts (VC2M10AA08)
solve linear and non-linear simultaneous equations using graphing or systematic guess-check-and-refine with digital tools (VC2M10AA09)
experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns (VC2M10AA10)

Measurement

solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (VC2M10AM01)
explore the effect of increasingly small changes in the value of variables on the average rate of change and in relation to limiting values (VC2M10AM02)

Space

prove and apply relationships between angles and various lines associated with circles (radii, diameters, chords, tangents) (VC2M10ASP01)
establish the sine, cosine and area rules for any triangle and solve related problems (VC2M10ASP02)
use the unit circle to define the simple trigonometric functions of $y = \sin (x)$ , $y = \cos (x)$ and $y = \tan (x)$ as functions of a real variable, and graph them with and without the use of digital tools (VC2M10ASP03)
solve simple trigonometric equations (VC2M10ASP04)
apply Pythagoras’ theorem and trigonometry to solving three-dimensional problems in right-angled triangles (VC2M10ASP05)
design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions (VC2M10ASP06)

Statistics

calculate and interpret the mean and standard deviation of data and use these to compare data sets; investigate the effect of individual data values, including outliers, on the standard deviation (VC2M10AST01)
identify measures of spread, and understand their interpretation and usefulness with respect to different data distributions (VC2M10AST02)
use digital tools to investigate bivariate numerical data sets; where appropriate use a straight line to describe the relationship allowing for variation, make predictions based on this straight line and discuss limitations (VC2M10AST03)

Probability

explore counting principles, and factorial notation as a representation that provides efficient counting in multiplicative contexts, including calculations of probabilities (VC2M10AP01)
investigate reports of studies in digital media and elsewhere for information on their planning and implementation (VC2M10AP02)