# Mathematics (Version 8.4)

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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 9

### Year 9 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 the relationship between graphs and equations, simplifying a range of algebraic expressions and explaining the use of relative frequencies to estimate probabilities and of the trigonometric ratios for right-angle triangles
• fluency includes applying the index laws to expressions with integer indices, expressing numbers in scientific notation, listing outcomes for experiments, developing familiarity with calculations involving the Cartesian plane and calculating areas of shapes and surface areas of prisms
• problem-solving includes formulating and modelling practical situations involving surface areas and volumes of right prisms, applying ratio and scale factors to similar figures, solving problems involving right-angle trigonometry and collecting data from secondary sources to investigate an issue
• reasoning includes following mathematical arguments, evaluating media reports and using statistical knowledge to clarify situations, developing strategies in investigating similarity and sketching linear graphs.

### Year 9 Content Descriptions

#### Using units of measurement

Calculate areas of composite shapes (ACMMG216 - Scootle )
Numeracy

Using measurement
• Estimate and measure with metric units

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

• understanding that partitioning composite shapes into rectangles and triangles is a strategy for solving problems involving area
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

Calculate the surface area and volume of cylinders and solve related problems (ACMMG217 - Scootle )
Critical and Creative Thinking

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

Reflecting on thinking and processes
• Reflect on processes

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

Numeracy

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

Using measurement
• Estimate and measure with metric units

Literacy

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

• analysing nets of cylinders to establish formulas for surface area
Numeracy

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

Using measurement
• Estimate and measure with metric units

Critical and Creative Thinking

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

• connecting the volume and capacity of a cylinder to solve authentic problems
Critical and Creative Thinking

Reflecting on thinking and processes
• Reflect on processes

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

Numeracy

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

Using measurement
• Estimate and measure with metric units

Solve problems involving the surface area and volume of right prisms (ACMMG218 - Scootle )
Literacy

Word Knowledge
• Understand learning area vocabulary

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

Comprehending texts through listening, reading and viewing
• Comprehend texts
• 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
• 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

Numeracy

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

Using measurement
• Estimate and measure with metric units

• solving practical problems involving surface area and volume of right prisms
Numeracy

Using measurement
• Estimate and measure with metric units

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

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

Reflecting on thinking and processes
• Reflect on processes

Investigate very small and very large time scales and intervals (ACMMG219 - Scootle )
Numeracy

Using measurement
• Operate with clocks, calendars and timetables

• investigating the usefulness of scientific notation in representing very large and very small numbers
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

#### Geometric reasoning

Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (ACMMG220 - Scootle )
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 texts
• Compose spoken, written, visual and multimodal learning area texts

Numeracy

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

• establishing the conditions for similarity of two triangles and comparing this to the conditions for congruence
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
• Visualise 2D shapes and 3D objects

• using the properties of similarity and ratio, and correct mathematical notation and language, to solve problems involving enlargement (for example, scale diagrams)
Numeracy

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

• using the enlargement transformation to establish similarity, understanding that similarity and congruence help describe relationships between geometrical shapes and are important elements of reasoning and proof
Literacy

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

Word Knowledge
• Understand learning area vocabulary

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

Numeracy

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

Solve problems using ratio and scale factors in similar figures (ACMMG221 - Scootle )
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

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

Numeracy

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

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

Critical and Creative Thinking

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

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

• establishing the relationship between areas of similar figures and the ratio of corresponding sides (scale factor)
Critical and Creative Thinking

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

Numeracy

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

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

#### Pythagoras and trigonometry

Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (ACMMG222 - Scootle )
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 texts
• 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

• understanding that Pythagoras' Theorem is a useful tool in determining unknown lengths in right-angled triangles and has widespread applications
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

• recognising that right-angled triangle calculations may generate results that can be integers, fractions or irrational numbers
Numeracy

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

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

Critical and Creative Thinking

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

Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (ACMMG223 - Scootle )
Numeracy

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

• developing understanding of the relationship between the corresponding sides of similar right-angled triangles
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

Apply trigonometry to solve right-angled triangle problems (ACMMG224 - Scootle )
Literacy

Word Knowledge
• Understand learning area vocabulary

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

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

Numeracy

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

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

• understanding the terms 'adjacent' and 'opposite' sides in a right-angled triangle
Critical and Creative Thinking

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

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

• selecting and accurately using the correct trigonometric ratio to find unknown sides (adjacent, opposite and hypotenuse) and angles in right-angled triangles
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

### Year 9 Achievement Standards

By the end of Year 9, students solve problems involving simple interest. They interpret ratio and scale factors in similar figures. Students explain similarity of triangles. They recognise the connections between similarity and the trigonometric ratios. Students compare techniques for collecting data from primary and secondary sources. They make sense of the position of the mean and median in skewed, symmetric and bi-modal displays to describe and interpret data.

Students apply the index laws to numbers and express numbers in scientific notation. They expand binomial expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment. They sketch linear and non-linear relations. Students calculate areas of shapes and the volume and surface area of right prisms and cylinders. They use Pythagoras’ Theorem and trigonometry to find unknown sides of right-angled triangles. Students calculate relative frequencies to estimate probabilities, list outcomes for two-step experiments and assign probabilities for those outcomes. They construct histograms and back-to-back stem-and-leaf plots.