# 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

#### Chance

Construct sample spaces for single-step experiments with equally likely outcomes (ACMSP167 - Scootle )
Critical and Creative Thinking

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

Numeracy

Interpreting statistical information
• Interpret chance events

• discussing the meaning of probability terminology (for example probability, sample space, favourable outcomes, trial, events and experiments)
Numeracy

Interpreting statistical information
• Interpret chance events

Critical and Creative Thinking

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

Literacy

Word Knowledge
• Understand learning area vocabulary

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

• distinguishing between equally likely outcomes and outcomes that are not equally likely
Numeracy

Interpreting statistical information
• Interpret chance events

Critical and Creative Thinking

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

Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168 - Scootle )
Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

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

Numeracy

Interpreting statistical information
• Interpret chance events

• expressing probabilities as decimals, fractions and percentages

Numeracy

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

#### Data representation and interpretation

Identify and investigate issues involving numerical data collected from primary and secondary sources (ACMSP169 - Scootle )
Ethical Understanding

Understanding ethical concepts and issues
• Explore ethical concepts in context

Exploring values, rights and responsibilities
• Explore rights and responsibilities
• Examine values
• Consider points of view

Literacy

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

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

Intercultural Understanding

Interacting and empathising with others
• Consider and develop multiple perspectives

Numeracy

Interpreting statistical information
• Interpret data displays

• obtaining secondary data from newspapers, the Internet and the Australian Bureau of Statistics
Literacy

Word Knowledge
• Understand learning area vocabulary

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

Numeracy

Interpreting statistical information
• Interpret data displays

• investigating secondary data relating to the distribution and use of non-renewable resources around the world
Literacy

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

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

Ethical Understanding

Understanding ethical concepts and issues
• Explore ethical concepts in context

Construct and compare a range of data displays including stem-and-leaf plots and dot plots (ACMSP170 - Scootle )
Literacy

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

Word Knowledge
• Understand learning area vocabulary

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

Visual Knowledge
• Understand how visual elements create meaning

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

Numeracy

Interpreting statistical information
• Interpret data displays

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

Interpreting statistical information
• Interpret data displays

Literacy

Word Knowledge
• Understand learning area vocabulary

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

Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (ACMSP171 - Scootle )
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
• Comprehend texts

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

Visual Knowledge
• Understand how visual elements create meaning

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

Numeracy

Interpreting statistical information
• Interpret data displays

• understanding that summarising data by calculating measures of centre and spread can help make sense of the data
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

Describe and interpret data displays using median, mean and range (ACMSP172 - Scootle )
Literacy

Word Knowledge
• Understand learning area vocabulary

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 spoken, written, visual and multimodal learning area texts
• Compose texts

Grammar knowledge
• Use knowledge of sentence structures

Critical and Creative Thinking

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

Analysing, synthesising and evaluating reasoning and procedures
• Apply logic and reasoning

Reflecting on thinking and processes
• Reflect on processes

Numeracy

Interpreting statistical information
• Interpret data displays

• using mean and median to compare data sets and explaining how outliers may affect the comparison
Numeracy

Interpreting statistical information
• Interpret data displays

Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

• locating mean, median and range on graphs and connecting them to real life
Critical and Creative Thinking

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

Numeracy

Interpreting statistical information
• Interpret data displays

### 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.