# 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

#### Using units of measurement

Establish the formulas for areas of rectangles, triangles and parallelograms, and use these in problem-solving (ACMMG159 - Scootle )
Numeracy

Using measurement
• Estimate and measure with metric units

• building on the understanding of the area of rectangles to develop formulas for the area of triangles
Numeracy

Using measurement
• Estimate and measure with metric units

Critical and Creative Thinking

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

• establishing that the area of a triangle is half the area of an appropriate rectangle
Numeracy

Using measurement
• Estimate and measure with metric units

Critical and Creative Thinking

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

• using area formulas for rectangles and triangles to solve problems involving areas of surfaces
Numeracy

Using measurement
• Estimate and measure with metric units

Calculate volumes of rectangular prisms (ACMMG160 - Scootle )
Numeracy

Using measurement
• Estimate and measure with metric units

• investigating volumes of cubes and rectangular prisms and establishing and using the formula V = l × b × h
Numeracy

Using measurement
• Estimate and measure with metric units

Critical and Creative Thinking

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

• understanding and using cubic units when interpreting and finding volumes of cubes and rectangular prisms
Numeracy

Using measurement
• Estimate and measure with metric units

Critical and Creative Thinking

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

#### Shape

Draw different views of prisms and solids formed from combinations of prisms (ACMMG161 - Scootle )
Numeracy

Using spatial reasoning
• Visualise 2D shapes and 3D objects

• using aerial views of buildings and other 3-D structures to visualise the structure of the building or prism
Numeracy

Using spatial reasoning
• Visualise 2D shapes and 3D objects

#### Location and transformation

Describe translations, reflections in an axis and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries (ACMMG181 - Scootle )
Literacy

Comprehending texts through listening, reading and viewing
• 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

Word Knowledge
• Understand learning area vocabulary

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

• describing patterns and investigating different ways to produce the same transformation such as using two successive reflections to provide the same result as a translation
Critical and Creative Thinking

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

Literacy

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

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

Word Knowledge
• Understand learning area vocabulary

Numeracy

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

• experimenting with, creating and re-creating patterns using combinations of reflections and rotations using digital technologies
Critical and Creative Thinking

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

Numeracy

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

Information and Communication Technology (ICT) Capability

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

#### Geometric reasoning

Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165 - Scootle )
Numeracy

Using spatial reasoning
• Visualise 2D shapes and 3D objects

Literacy

Word Knowledge
• Understand learning area vocabulary

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

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

• identifying side and angle properties of scalene, isosceles, right-angled and obtuse-angled triangles
Critical and Creative Thinking

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

Numeracy

Using spatial reasoning
• Visualise 2D shapes and 3D objects

• describing squares, rectangles, rhombuses, parallelograms, kites and trapeziums
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

Numeracy

Using spatial reasoning
• Visualise 2D shapes and 3D objects

Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (ACMMG166 - Scootle )
Numeracy

Using spatial reasoning
• Visualise 2D shapes and 3D objects

• using concrete materials and digital technologies to investigate the angle sum of a triangle and quadrilateral
Critical and Creative Thinking

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

Numeracy

Using spatial reasoning
• Visualise 2D shapes and 3D objects

Information and Communication Technology (ICT) Capability

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

Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (ACMMG163 - Scootle )
Numeracy

Using spatial reasoning
• Visualise 2D shapes and 3D objects

• defining and classifying pairs of angles as complementary, supplementary, adjacent and vertically opposite
Numeracy

Using spatial reasoning
• Visualise 2D shapes and 3D objects

Critical and Creative Thinking

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

Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (ACMMG164 - Scootle )
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
• Seek solutions and put ideas into action
• Consider alternatives

Reflecting on thinking and processes
• Reflect on processes

• constructing parallel and perpendicular lines using their properties, a pair of compasses and a ruler, and dynamic geometry software
Information and Communication Technology (ICT) Capability

Managing and operating ICT
• Select and use hardware and software

• defining and identifying the relationships between altenate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal
Critical and Creative Thinking

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

### 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.