# 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 7

### Year 7 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 patterns in uses of indices with whole numbers, recognising equivalences between fractions, decimals, percentages and ratios, plotting points on the Cartesian plane, identifying angles formed by a transversal crossing a pair of lines, and connecting the laws and properties of numbers to algebraic terms and expressions
• fluency includes calculating accurately with integers, representing fractions and decimals in various ways, investigating best buys, finding measures of central tendency and calculating areas of shapes and volumes of prisms
• problem-solving includes formulating and solving authentic problems using numbers and measurements, working with transformations and identifying symmetry, calculating angles and interpreting sets of data collected through chance experiments
• reasoning includes applying the number laws to calculations, applying known geometric facts to draw conclusions about shapes, applying an understanding of ratio and interpreting data displays.

### Year 7 Content Descriptions

#### Number and place value

Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate
• Understand and use numbers in context

• defining and comparing prime and composite numbers and explaining the difference between them
Literacy

Grammar knowledge
• Use knowledge of sentence structures

Composing texts through speaking, writing and creating
• Compose spoken, written, visual and multimodal learning area texts

Word Knowledge
• Understand learning area vocabulary

Comprehending texts through listening, reading and viewing
• Navigate, read and view learning area texts
• Interpret and analyse learning area texts

Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

• applying knowledge of factors to strategies for expressing whole numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate
• Understand and use numbers in context

• solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of whole numbers by comparing their prime factorisation
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

Reflecting on thinking and processes
• Reflect on processes

Generating ideas, possibilities and actions
• Seek solutions and put ideas into action
• Consider alternatives

Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context
• Estimate and calculate

Investigate and use square roots of perfect square numbers (ACMNA150 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context
• Estimate and calculate

• investigating square numbers such as 25 and 36 and developing square-root notation
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context

• investigating between which two whole numbers a square root lies
Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context
• Estimate and calculate

• understanding that arithmetic laws are powerful ways of describing and simplifying calculations
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context

Compare, order, add and subtract integers (ACMNA280 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate
• Understand and use numbers in context

#### Real numbers

Compare fractions using equivalence. Locate and represent positive and negative fractions and mixed numbers on a number line (ACMNA152 - Scootle )
Numeracy

Using fractions, decimals, percentages, ratios and rates
• Apply proportional reasoning
• Interpret proportional reasoning

Literacy

Comprehending texts through listening, reading and viewing
• Navigate, read and view learning area texts
• Interpret and analyse learning area texts
• Comprehend texts

Composing texts through speaking, writing and creating
• Compose spoken, written, visual and multimodal learning area texts
• Compose texts

Word Knowledge
• Understand learning area vocabulary

• exploring equivalence among families of fractions by using a fraction wall or a number line (for example by using a fraction wall to show that 2/3 is the same as 4/6 and 6/9)
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Numeracy

Using fractions, decimals, percentages, ratios and rates
• Apply proportional reasoning
• Interpret proportional reasoning

Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153 - Scootle )
Numeracy

Using fractions, decimals, percentages, ratios and rates
• Interpret proportional reasoning
• Apply proportional reasoning

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Generating ideas, possibilities and actions
• Consider alternatives
• Seek solutions and put ideas into action

Reflecting on thinking and processes
• Reflect on processes

Literacy

Comprehending texts through listening, reading and viewing
• Navigate, read and view learning area texts
• Comprehend texts
• Interpret and analyse learning area texts

Composing texts through speaking, writing and creating
• Compose texts
• Compose spoken, written, visual and multimodal learning area texts

Word Knowledge
• Understand learning area vocabulary

• exploring and developing efficient strategies to solve additive problems involving fractions (for example by using fraction walls or rectangular arrays with dimensions equal to the denominators)
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

Generating ideas, possibilities and actions
• Consider alternatives
• Seek solutions and put ideas into action

Reflecting on thinking and processes
• Reflect on processes

Numeracy

Using fractions, decimals, percentages, ratios and rates
• Interpret proportional reasoning
• Apply proportional reasoning

Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154 - Scootle )
Numeracy

Using fractions, decimals, percentages, ratios and rates
• Apply proportional reasoning
• Interpret proportional reasoning

Information and Communication Technology (ICT) Capability

Creating with ICT
• Generate solutions to challenges and learning area tasks

• investigating multiplication of fractions and decimals, using strategies including patterning and multiplication as repeated addition, with both concrete materials and digital technologies, and identifying the processes for division as the inverse of multiplication
Information and Communication Technology (ICT) Capability

Creating with ICT
• Generate solutions to challenges and learning area tasks

Numeracy

Using fractions, decimals, percentages, ratios and rates
• Apply proportional reasoning
• Interpret proportional reasoning

Recognising and using patterns and relationships
• Recognise and use patterns and relationships

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Express one quantity as a fraction of another, with and without the use of digital technologies (ACMNA155 - Scootle )
Numeracy

Using fractions, decimals, percentages, ratios and rates
• Interpret proportional reasoning
• Apply proportional reasoning

Information and Communication Technology (ICT) Capability

Creating with ICT
• Generate solutions to challenges and learning area tasks

• using authentic examples for the quantities to be expressed and understanding the reasons for the calculations
Numeracy

Using fractions, decimals, percentages, ratios and rates
• Interpret proportional reasoning
• Apply proportional reasoning

Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

Generating ideas, possibilities and actions
• Consider alternatives

Round decimals to a specified number of decimal places (ACMNA156 - Scootle )
Numeracy

Using fractions, decimals, percentages, ratios and rates
• Apply proportional reasoning
• Interpret proportional reasoning

• using rounding to estimate the results of calculations with whole numbers and decimals, and understanding the conventions for rounding
Numeracy

Using fractions, decimals, percentages, ratios and rates
• Interpret proportional reasoning
• Apply proportional reasoning

Estimating and calculating with whole numbers
• Estimate and calculate

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157 - Scootle )
Numeracy

Using fractions, decimals, percentages, ratios and rates
• Apply proportional reasoning
• Interpret proportional reasoning

• justifying choices of written, mental or calculator strategies for solving specific problems including those involving large numbers
Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas

Literacy

Comprehending texts through listening, reading and viewing
• Navigate, read and view learning area texts

Composing texts through speaking, writing and creating
• Compose spoken, written, visual and multimodal learning area texts

Word Knowledge
• Understand learning area vocabulary

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate
• Understand and use numbers in context

• understanding that quantities can be represented by different number types and calculated using various operations, and that choices need to be made about each
Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context
• Estimate and calculate

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

• calculating the percentage of the total local municipal area set aside for parkland, manufacturing, retail and residential dwellings to compare land use
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information

Numeracy

Using fractions, decimals, percentages, ratios and rates
• Interpret proportional reasoning
• Apply proportional reasoning

Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (ACMNA158 - Scootle )
Information and Communication Technology (ICT) Capability

Creating with ICT
• Generate solutions to challenges and learning area tasks

Numeracy

Using fractions, decimals, percentages, ratios and rates
• Interpret proportional reasoning
• Apply proportional reasoning

• using authentic problems to express quantities as percentages of other amounts
Numeracy

Using fractions, decimals, percentages, ratios and rates
• Apply proportional reasoning
• Interpret proportional reasoning

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Recognise and solve problems involving simple ratios (ACMNA173 - Scootle )
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Generating ideas, possibilities and actions
• Consider alternatives
• Seek solutions and put ideas into action

Reflecting on thinking and processes
• Reflect on processes

Literacy

Composing texts through speaking, writing and creating
• Compose texts
• Compose spoken, written, visual and multimodal learning area texts

Word Knowledge
• Understand learning area vocabulary

Comprehending texts through listening, reading and viewing
• Interpret and analyse learning area texts
• Comprehend texts
• Navigate, read and view learning area texts

Numeracy

Using fractions, decimals, percentages, ratios and rates
• Apply proportional reasoning
• Interpret proportional reasoning

• understanding that rate and ratio problems can be solved using fractions or percentages and choosing the most efficient form to solve a particular problem
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Numeracy

Using fractions, decimals, percentages, ratios and rates
• Interpret proportional reasoning

#### Money and financial mathematics

Investigate and calculate 'best buys', with and without digital technologies (ACMNA174 - Scootle )
Literacy

Comprehending texts through listening, reading and viewing
• Comprehend texts
• Interpret and analyse learning area texts
• Navigate, read and view learning area texts

Composing texts through speaking, writing and creating
• Compose spoken, written, visual and multimodal learning area texts
• Compose texts

Word Knowledge
• Understand learning area vocabulary

Numeracy

Estimating and calculating with whole numbers
• Use money

Information and Communication Technology (ICT) Capability

Creating with ICT
• Generate solutions to challenges and learning area tasks

Investigating with ICT
• Locate, generate and access data and information
• Define and plan information searches

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

• applying the unitary method to identify ‘best buys’ situations, such as comparing the cost per 100g
Literacy

Word Knowledge
• Understand learning area vocabulary

Comprehending texts through listening, reading and viewing
• Interpret and analyse learning area texts
• Navigate, read and view learning area texts

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Numeracy

Using measurement
• Estimate and measure with metric units

Estimating and calculating with whole numbers
• Use money

#### Patterns and algebra

Introduce the concept of variables as a way of representing numbers using letters (ACMNA175 - Scootle )
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

• understanding that arithmetic laws are powerful ways of describing and simplifying calculations and that using these laws leads to the generality of algebra
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Create algebraic expressions and evaluate them by substituting a given value for each variable (ACMNA176 - Scootle )
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate
• Understand and use numbers in context

Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

• using authentic formulas to perform substitutions
Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context
• Estimate and calculate

Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177 - Scootle )
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Reflecting on thinking and processes
• Transfer knowledge into new contexts

Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context
• Estimate and calculate

Literacy

Word Knowledge
• Understand learning area vocabulary

Comprehending texts through listening, reading and viewing
• Navigate, read and view learning area texts
• Interpret and analyse learning area texts
• Comprehend texts

• identifying order of operations in contextualised problems, preserving the order by inserting brackets in numerical expressions, then recognising how order is preserved by convention
Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context
• Estimate and calculate

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

• moving fluently between algebraic and word representations as descriptions of the same situation
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

Reflecting on thinking and processes
• Transfer knowledge into new contexts

Numeracy

Estimating and calculating with whole numbers
• Understand and use numbers in context
• Estimate and calculate

Literacy

Word Knowledge
• Understand learning area vocabulary

#### Linear and non-linear relationships

Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178 - Scootle )
Numeracy

Using spatial reasoning
• Interpret maps and diagrams

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information

• plotting points from a table of integer values and recognising simple patterns, such as points that lie on a straight line
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

Recognising and using patterns and relationships
• Recognise and use patterns and relationships

Solve simple linear equations (ACMNA179 - Scootle )
Critical and Creative Thinking

Generating ideas, possibilities and actions
• Seek solutions and put ideas into action
• Consider alternatives

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

Reflecting on thinking and processes
• Reflect on processes

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• solving equations using concrete materials, such as the balance model, and explain the need to do the same thing to each side of the equation using substitution to check solutions
Literacy

Comprehending texts through listening, reading and viewing
• Navigate, read and view learning area texts
• Interpret and analyse learning area texts

Grammar knowledge
• Use knowledge of sentence structures

Composing texts through speaking, writing and creating
• Compose spoken, written, visual and multimodal learning area texts

Word Knowledge
• Understand learning area vocabulary

Critical and Creative Thinking

Generating ideas, possibilities and actions
• Seek solutions and put ideas into action
• Consider alternatives

Reflecting on thinking and processes
• Reflect on processes

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

• investigating a range of strategies to solve equations
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate

Investigate, interpret and analyse graphs from authentic data (ACMNA180 - Scootle )
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

Reflecting on thinking and processes
• Reflect on processes

Literacy

Comprehending texts through listening, reading and viewing
• Comprehend texts
• Navigate, read and view learning area texts
• Interpret and analyse learning area texts

Visual Knowledge
• Understand how visual elements create meaning

Word Knowledge
• Understand learning area vocabulary

Numeracy

Interpreting statistical information
• Interpret data displays

• using travel graphs to investigate and compare the distance travelled to and from school
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Numeracy

Interpreting statistical information
• Interpret data displays

Literacy

Word Knowledge
• Understand learning area vocabulary

• interpreting features of travel graphs such as the slope of lines and the meaning of horizontal lines
Literacy

Word Knowledge
• Understand learning area vocabulary

Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Organise and process information
• Identify and clarify information and ideas

Numeracy

Interpreting statistical information
• Interpret data displays

• using graphs of evaporation rates to explore water storage
Critical and Creative Thinking

Inquiring – identifying, exploring and organising information and ideas
• Identify and clarify information and ideas
• Organise and process information

Numeracy

Interpreting statistical information
• Interpret data displays

Literacy

Word Knowledge
• Understand learning area vocabulary

### Year 7 Achievement Standards

By the end of Year 7, students solve problems involving the comparison, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving percentages and all four operations with fractions and decimals. They compare the cost of items to make financial decisions. Students represent numbers using variables. They connect the laws and properties for numbers to algebra. They interpret simple linear representations and model authentic information. Students describe different views of three-dimensional objects. They represent transformations in the Cartesian plane. They solve simple numerical problems involving angles formed by a transversal crossing two lines. Students identify issues involving the collection of continuous data. They describe the relationship between the median and mean in data displays.

Students use fractions, decimals and percentages, and their equivalences. They express one quantity as a fraction or percentage of another. Students solve simple linear equations and evaluate algebraic expressions after numerical substitution. They assign ordered pairs to given points on the Cartesian plane. Students use formulas for the area and perimeter of rectangles and calculate volumes of rectangular prisms. Students classify triangles and quadrilaterals. They name the types of angles formed by a transversal crossing parallel line. Students determine the sample space for simple experiments with equally likely outcomes and assign probabilities to those outcomes. They calculate mean, mode, median and range for data sets. They construct stem-and-leaf plots and dot-plots.