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You are viewing the Victorian Curriculum F–10 Version 2.0.

Mathematics

INTRODUCTIONCURRICULUMSCOPE AND SEQUENCERESOURCESGLOSSARY

Curriculum

Levels

Foundation Level A

Foundation Level B

Foundation Level C

Foundation Level D

Foundation

Level 1

Level 2

Level 3

Level 4

Level 5

Level 6

Level 7

Level 8

Level 9

Level 10

Level 10A

In Foundation Level A, learning in Mathematics builds on each student’s daily experiences. Students engage in a range of approaches to the learning and doing of mathematics that encourage their awareness of mathematical concepts, skills, procedures and processes and that support the establishment of cause and effect and intentional responses. Through multiple exposures and repetition within their daily lives and routines, students become aware of the environment around them and respond to changes within that environment.

Students develop awareness of and positive dispositions towards mathematics and its use as they: 

  • experience number in their environment and experience physical and...

In Foundation Level B, learning in Mathematics builds on each student’s prior learning and experiences. Students begin to explore their world with increasing independence. They begin to develop their understanding of mathematical concepts, skills, procedures and processes through practical experiences. They participate in structured learning activities for short periods of time. Students begin to attend to learning activities, and to compare, match and sort objects.

Students begin to develop proficiency and establish positive dispositions towards mathematics and its use as they: 

  • rely on multisensory experiences, concrete materials, verbal prompts and gestures to support and facilitate their learning
  • look for and...

In Foundation Level C, learning in Mathematics builds on each student’s prior learning and experiences. Students demonstrate increased levels of independence, becoming more peer focused, intentionally participating in structured learning activities with others and communicating in a variety of ways. 

Students build their independence as they engage in a range of approaches to the learning and doing of mathematics. They develop their understanding of and fluency with concepts, skills, procedures and processes in practical situations and contexts for learning by making connections, reasoning, problem-solving and practice. Proficiency in mathematics enables students to respond to familiar and unfamiliar situations by employing mathematical strategies...

In Foundation Level D, learning in Mathematics extends to symbolic representation, building on each student’s prior learning and experiences. 

Students continue to build their independence as they engage in a range of approaches to the learning and doing of mathematics. They develop their understanding of and fluency with concepts, skills, 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 develop proficiency and positive dispositions towards mathematics and its use as they: 

  • start to connect number...

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 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, skills, 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...

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...

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...

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...

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...

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 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 their understanding of relationships to convert between forms of numbers, units and spatial...

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...

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...

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;...

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...

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...

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

Level 10A does not include an achievement standard and does not require reporting.

Students may extend their studies in the Number and Algebra strands to investigate the structure and properties of number systems, with further algebraic and graphical analysis of higher-order polynomials, and relations such as circles, hyperbolas and other inequalities. They could extend the study of trigonometry to include an introduction to simple equations and graphs of circular functions, and extend the study of exponents and exponential functions...

By the end of Foundation Level A, students participate in and respond to structured learning experiences, including counting, sharing, and adding and taking away from collections, in practical situations. 

Students respond to cause-and-effect experiences. 

Students participate in and respond to measurement activities through structured routine and non-routine activities and events during the school day.

Students observe and experience shapes and objects and respond to the sorting and naming of them. Students respond when the position of their body changes, and when they move to a different environment.

By the end of Foundation Level B, students identify ‘one’ object and ‘more’ objects, and recognise one or more number names. Students demonstrate an awareness of quantity and use direct comparison to determine ‘more’ and ‘different’ in practical situations, including partitioning and combining collections, sharing collections, and adding to and taking away from collections. 

Students initiate cause-and-effect experiences.

Students identify familiar objects as ‘big’ or ‘little’, using direct comparison in practical situations. They show anticipation in response to routine events when transitioning from one experience to another. 

Students investigate the attributes of shapes and objects. They use direct comparison to...

By the end of Foundation Level C, students recognise and name groups of at least 5. They use counting strategies to quantify collections to at least 5 and subitise to quantify collections to 3. They compare collections to identify ‘more’ and ‘less’. They communicate the number names from zero to at least 5 using stable number order. They partition and combine collections up to 5 in different ways. Students represent practical situations that involve quantifying and adding, taking away one from a collection up to 5 and equal sharing of a collection. 

Students copy simple repeating patterns. 

Students identify the...

By the end of Foundation Level D, students make connections between number names, numerals and position in the sequence of numbers from zero to at least 10. They use counting strategies to quantify collections to at least 10 and subitise to quantify collections to 4. Students compare the size of collections to at least 10. They partition and combine collections up to 10 in different ways. Students represent practical situations that involve quantifying, equal sharing between 2, and adding and taking away one from a collection up to 10. 

Students copy and continue simple repeating patterns. 

Students identify the attributes...

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...

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...

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...

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...

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...

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-...

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...

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...

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,...

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...

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...

There is no achievement standard for Level 10A.

Content descriptions – Foundation Level A

Students:

respond to number names and representations of number

VC2MFAN01

respond to changing collections of objects 

VC2MFAN02

respond to counting, comparing and labelling of collections

VC2MFAN03

respond to practical situations involving addition and subtraction of collections with physical and virtual materials

VC2MFAN04

respond to sharing objects or a collection equally, in practical situations

VC2MFAN05

Students:

respond to actions that have an effect

VC2MFAA01

Students:

respond to routine and non-routine events during the school day

VC2MFAM01

Students:

respond to shapes and objects in their environment

VC2MFASP01

respond to movement of objects, people or self within a familiar space

VC2MFASP02

Content descriptions – Foundation Level B

Students learn to:

identify number names and representations of number

VC2MFBN01

identify, name and represent ‘one’ and ‘more’ using physical and virtual materials

VC2MFBN02

compare the quantity of collections using direct comparison to identify which has more or if they are different

VC2MFBN03

partition and combine collections to make ‘more’ or ‘different’

VC2MFBN04

add or take away objects, using physical and virtual materials and matching to determine whether the changed total is more or different

VC2MFBN05

share physical objects and collections equally in practical situations

VC2MFBN06

Students learn to:

initiate and repeat actions that have an effect

VC2MFBA01

Students learn to:

identify whether 2 familiar objects are ‘big’ or ‘little’, using direct comparison

VC2MFBM01

recognise and participate in routine and non-routine daily events

VC2MFBM02

Students learn to:

match and sort objects and shapes that are ‘big’ or ‘little’, using direct comparison

VC2MFBSP01

indicate the location of known objects within a familiar environment

VC2MFBSP02

Content descriptions – Foundation Level C

Students learn to:

name and correctly sequence number names to at least 5

VC2MFCN01

recognise and name the number of objects within a collection up to 3 using subitising

VC2MFCN02

compare collections to at least 5 to identify if the collections are the same or which has ‘more’ and which has ‘less’

VC2MFCN03

partition and combine collections up to 5 to make ‘more’ and ‘less’

VC2MFCN04

represent practical situations involving addition, subtraction and quantification up to at least 5 with physical and virtual materials, and use matching or counting strategies

VC2MFCN05

represent practical sharing situations involving equal sharing between 2, using physical and virtual materials

VC2MFCN06

Students learn to:

copy repeating patterns represented in different ways

VC2MFCA01

Students learn to:

identify and compare attributes of 2 familiar objects, including length, capacity and mass, using direct comparison

VC2MFCM01

identify morning, afternoon and night-time, and connect routine and familiar events to these times

VC2MFCM02

Students learn to:

sort and name familiar shapes and objects

VC2MFCSP01

describe the location of objects or people within a familiar space, and follow simple instructions to move themselves or an object within a familiar environment

VC2MFCSP02

Students learn to:

compare data represented by objects in response to questions that have only 2 outcomes and relate to familiar situations

VC2MFCST01

Content descriptions – Foundation Level D

Students learn to:

name, represent and order numbers including zero to at least 10, using physical and virtual materials and numerals

VC2MFDN01

recognise and name the number of objects within a collection up to 4 using subitising

VC2MFDN02

quantify and compare collections to at least 10 using counting, and explain or demonstrate reasoning

VC2MFDN03

partition and combine collections up to 10 and find the changed value using counting strategies

VC2MFDN04

represent practical situations, including simple financial situations, involving addition, subtraction and quantification up to at least 10 with physical and virtual materials and use matching or counting strategies

VC2MFDN05

represent practical situations that involve equal sharing of a collection of up to 10 physical or virtual objects and use counting strategies

VC2MFDN06

Students learn to:

recognise, copy and continue repeating patterns represented in different ways

VC2MFDA01

Students learn to:

identify and compare attributes of objects and events, including length, capacity, mass and duration, using direct comparison

VC2MFDM01

sequence familiar routines and events using simple ordinal language and connect familiar events to times of the day, including morning, afternoon and night-time

VC2MFDM02

Students learn to:

sort and name familiar shapes and objects, and recognise and describe familiar shapes within objects in familiar environments

VC2MFDSP01

describe the position and location of objects or people in relation to themselves or known objects within a familiar space

VC2MFDSP02

Students learn to:

sort and compare data represented by objects and images in response to questions that have only 2 outcomes and relate to familiar situations

VC2MFDST01

Content descriptions – Foundation

Students learn to:

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

Students learn to:

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

VC2MFA01

Students learn to:

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

Students learn to:

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

Students learn to:

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

Content descriptions – Level 1

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Content descriptions – Level 2

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Content descriptions – Level 3

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Content descriptions – Level 4

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Content descriptions – Level 5

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Content descriptions – Level 6

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Content descriptions – Level 7

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Content descriptions – Level 8

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Content descriptions – Level 9

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Content descriptions – Level 10

Students learn to:

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

VC2M10N01

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Content descriptions – Level 10A

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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

Students learn to:

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