# Mathematics

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### Rationale

Learning mathematics creates opportunities for and enriches the lives of all Australians. The Australian Curriculum: Mathematics provides students with essential mathematical skills and knowledge in number and algebra, measurement and geometry, and statistics and probability.

### Aims

The Australian Curriculum: Mathematics aims to ensure that students:

are confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives and as active citizens.

### Key ideas

In Mathematics, the key ideas are the proficiency strands of understanding, fluency, problem-solving and reasoning. The proficiency strands describe the actions in which students can engage when learning and using the content.

### Structure

The Australian Curriculum: Mathematics is organised around the interaction of three content strands and four proficiency strands.
The content strands are number and algebra, measurement and geometry, and statistics and probability. They describe what is to be taught and learnt.

### PDF documents

Resources and support materials for the Australian Curriculum: Mathematics are available as PDF documents.
Mathematics: Sequence of content
Mathematics: Sequence of achievement

## Year 6

### Year 6 Level Description

The proficiency strands understanding, fluency, problem-solving and reasoning are an integral part of mathematics content across the three content strands: number and algebra, measurement and geometry, and statistics and probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. The achievement standards reflect the content and encompass the proficiencies.

At this year level:

• understanding includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making reasonable estimations
• fluency includes representing integers on a number line, calculating simple percentages, using brackets appropriately, converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring using metric units and interpreting timetables
• problem-solving includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays and finding the size of unknown angles
• reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another and explaining why the actual results of chance experiments may differ from expected results.

### Year 6 Content Descriptions

#### Number and place value

Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122 - Scootle )
• understanding that some numbers have special properties and that these properties can be used to solve problems
• representing composite numbers as a product of their prime factors and using this form to simplify calculations by cancelling common primes
• understanding that if a number is divisible by a composite number then it is also divisible by the prime factors of that number (for example 216 is divisible by 8 because the number represented by the last three digits is divisible by 8, and hence 216 is also divisible by 2 and 4)
Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123 - Scootle )
• applying strategies already developed for solving problems involving small numbers to those involving large numbers
• applying a range of strategies to solve realistic problems and commenting on the efficiency of different strategies
Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124 - Scootle )
• understanding that integers are ...-3, -2, -1, 0, 1, 2, 3,.....
• solving everyday additive problems using a number line
• investigating everyday situations that use integers, such as temperatures
• using number lines to position and order integers around zero

#### Fractions and decimals

Compare fractions with related denominators and locate and represent them on a number line (ACMNA125 - Scootle )
• demonstrating equivalence between fractions using drawings and models
Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126 - Scootle )
• understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractions
• solving realistic additive (addition and subtraction) problems involving fractions to develop understanding of equivalent fractions and the use of fractions as operators
• modelling and solving additive problems involving fractions by using methods such as jumps on a number line, or by making diagrams of fractions as parts of shapes
Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127 - Scootle )
• recognising that finding one third of a quantity is the same as dividing by 3
Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128 - Scootle )
• extending whole-number strategies to explore and develop meaningful written strategies for addition and subtraction of decimal numbers to thousandths
• exploring and practising efficient methods for solving problems requiring operations on decimals, to gain fluency with calculating with decimals and with recognising appropriate operations
Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129 - Scootle )
• interpreting the results of calculations to provide an answer appropriate to the context
Multiply and divide decimals by powers of 10 (ACMNA130 - Scootle )
• multiplying and dividing decimals by multiples of powers of 10
Make connections between equivalent fractions, decimals and percentages (ACMNA131 - Scootle )
• connecting fractions, decimals and percentages as different representations of the same number, moving fluently between representations and choosing the appropriate one for the problem being solved

#### Money and financial mathematics

Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132 - Scootle )
• using authentic information to calculate prices on sale goods

#### Patterns and algebra

Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133 - Scootle )
• identifying and generalising number patterns
• investigating additive and multiplicative patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern looking for patterns in the way the numbers increase/decrease
Explore the use of brackets and order of operations to write number sentences (ACMNA134 - Scootle )
• appreciating the need for rules to complete multiple operations within the same number sentence

#### Using units of measurement

Connect decimal representations to the metric system (ACMMG135 - Scootle )
• recognising the equivalence of measurements such as 1.25 metres and 125 centimetres
Convert between common metric units of length, mass and capacity (ACMMG136 - Scootle )
• identifying and using the correct operations when converting units including millimetres, centimetres, metres, kilometres, milligrams, grams, kilograms, tonnes, millilitres, litres, kilolitres and megalitres
• recognising the significance of the prefixes in units of measurement
Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137 - Scootle )
• recognising and investigating familiar objects using concrete materials and digital technologies
Connect volume and capacity and their units of measurement (ACMMG138 - Scootle )
• recognising that 1ml is equivalent to 1cm3
Interpret and use timetables (ACMMG139 - Scootle )
• planning a trip involving one or more modes of public transport
• developing a timetable of daily activities

#### Shape

Construct simple prisms and pyramids (ACMMG140 - Scootle )
• considering the history and significance of pyramids from a range of cultural perspectives including those structures found in China, Korea and Indonesia
• constructing prisms and pyramids from nets, and skeletal models

#### Location and transformation

Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142 - Scootle )
• designing a school or brand logo using transformation of one or more shapes
• understanding that translations, rotations and reflections can change the position and orientation but not shape or size
Introduce the Cartesian coordinate system using all four quadrants (ACMMG143 - Scootle )
• understanding that the Cartesian plane provides a graphical or visual way of describing location

#### Geometric reasoning

Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (ACMMG141 - Scootle )
• identifying the size of a right angle as 90° and defining acute, obtuse, straight and reflex angles
• measuring, estimating and comparing angles in degrees and classifying angles according to their sizes
• investigating the use of rotation and symmetry in the diagrammatic representations of kinship relationships of Central and Western Desert people
• recognising and using the two alternate conventions for naming angles

#### Chance

Describe probabilities using fractions, decimals and percentages (ACMSP144 - Scootle )
• investigating games of chance popular in different cultures and evaluating the relative benefits to the organisers and participants (for example Pachinko)
Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145 - Scootle )
• conducting repeated trials of chance experiments, identifying the variation between trials and realising that the results tend to the prediction with larger numbers of trials
Compare observed frequencies across experiments with expected frequencies (ACMSP146 - Scootle )
• predicting likely outcomes from a run of chance events and distinguishing these from surprising results

#### Data representation and interpretation

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147 - Scootle )
• comparing different student-generated diagrams, tables and graphs, describing their similarities and differences and commenting on the usefulness of each representation for interpreting the data
• understanding that data can be represented in different ways, sometimes with one symbol representing more than one piece of data, and that it is important to read all information about a representation before making judgments
Interpret secondary data presented in digital media and elsewhere (ACMSP148 - Scootle )
• investigating data representations in the media and discussing what they illustrate and the messages the people who created them might want to convey
• identifying potentially misleading data representations in the media, such as graphs with broken axes or non-linear scales, graphics not drawn to scale, data not related to the population about which the claims are made, and pie charts in which the whole pie does not represent the entire population about which the claims are made

### Year 6 Achievement Standards

By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They interpret secondary data displayed in the media.

Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students describe probabilities using simple fractions, decimals and percentages.