# 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

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## Year 10A

### Year 10A Level Description

The 10A content descriptions are optional and are intended for students who require additional content to enrich and extend their mathematical study whilst completing the common Year 10 curriculum. It is not anticipated that all students will attempt the 10A content, but doing so would be advantageous for those intending to pursue Mathematical Methods (Course C) or Specialist Mathematics (Course D) in the senior secondary years. A selection of topics from the 10A curriculum can be completed according to the needs and interests of students.

### Year 10A Content Descriptions

#### Real numbers

Define rational and irrational numbers and perform operations with surds and fractional indices (ACMNA264 - Scootle )
Numeracy

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

Critical and Creative Thinking

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

• understanding that the real number system includes irrational 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
• Estimate and calculate

• extending the index laws to rational number indices
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

• performing the four operations with surds
Numeracy

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

Use the definition of a logarithm to establish and apply the laws of logarithms (ACMNA265 - Scootle )
Critical and Creative Thinking

Reflecting on thinking and processes
• Transfer knowledge into new contexts

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

Numeracy

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

• investigating the relationship between exponential and logarithmic expressions
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

• simplifying expressions using the logarithm laws
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

#### Patterns and algebra

Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (ACMNA266 - Scootle )
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

Reflecting on thinking and processes
• Transfer knowledge into new contexts

• investigating the relationship between algebraic long division and the factor and remainder theorems
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

#### Linear and non-linear relationships

Solve simple exponential equations (ACMNA270 - Scootle )
Critical and Creative Thinking

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

Numeracy

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

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

• investigating exponential equations derived from authentic mathematical models based on population growth
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

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

Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267 - Scootle )
Critical and Creative Thinking

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

Numeracy

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

• applying transformations, including translations, reflections in the axes and stretches to help graph parabolas, rectangular hyperbolas, circles and exponential functions
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
• Reflect on processes

Numeracy

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

Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (ACMNA268 - Scootle )
Numeracy

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

Critical and Creative Thinking

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

• investigating the features of graphs of polynomials including axes intercepts and the effect of repeated factors
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

Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts (ACMNA269 - Scootle )
Critical and Creative Thinking

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

Numeracy

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

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

• writing quadratic equations that represent practical problems
Numeracy

Estimating and calculating with whole numbers
• Estimate and calculate
• 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

#### Using units of measurement

Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (ACMMG271 - Scootle )
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

• using formulas to solve problems
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

Numeracy

Using measurement
• Estimate and measure with metric units

• using authentic situations to apply knowledge and understanding of surface area and volume
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

#### Geometric reasoning

Prove and apply angle and chord properties of circles (ACMMG272 - Scootle )
Numeracy

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

Critical and Creative Thinking

Reflecting on thinking and processes
• Transfer knowledge into new contexts

• performing a sequence of steps to determine an unknown angle or length in a diagram involving a circle, or circles, giving a justification in moving from one step to the next
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

Reflecting on thinking and processes
• Reflect on processes
• Transfer knowledge into new contexts

Numeracy

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

Literacy

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

• communicating a proof using a logical sequence of statements
Literacy

Word Knowledge
• Understand learning area vocabulary

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

Reflecting on thinking and processes
• Reflect on processes

• proving results involving chords of circles
Critical and Creative Thinking

Reflecting on thinking and processes
• Transfer knowledge into new contexts

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

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

Numeracy

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

#### Pythagoras and trigonometry

Establish the sine, cosine and area rules for any triangle and solve related problems (ACMMG273 - Scootle )
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

Reflecting on thinking and processes
• Reflect on processes

• applying knowledge of sine, cosine and area rules to authentic problems such as those involving surveying and design
Critical and Creative Thinking

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

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

Reflecting on thinking and processes
• Transfer knowledge into new contexts

Numeracy

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

Use the unit circle to define trigonometric functions, and graph them with and without the use of digital technologies (ACMMG274 - Scootle )
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

Critical and Creative Thinking

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

Numeracy

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

• establishing the symmetrical properties of trigonometric functions
Critical and Creative Thinking

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

Numeracy

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

• investigating angles of any magnitude
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

• understanding that trigonometric functions are periodic and that this can be used to describe motion
Numeracy

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

Critical and Creative Thinking

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

Solve simple trigonometric equations (ACMMG275 - Scootle )
Numeracy

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

Critical and Creative Thinking

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

• using periodicity and symmetry to solve equations
Numeracy

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

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
• Consider alternatives
• Seek solutions and put ideas into action

Apply Pythagoras’ Theorem and trigonometry to solving three-dimensional problems in right-angled triangles (ACMMG276 - Scootle )
Numeracy

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

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

• investigating the applications of Pythagoras' theorem in authentic problems
Critical and Creative Thinking

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

Numeracy

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

#### Chance

Investigate reports of studies in digital media and elsewhere for information on their planning and implementation (ACMSP277 - Scootle )
Information and Communication Technology (ICT) Capability

Investigating with ICT
• Locate, generate and access data and information
• Select and evaluate data and information

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

Numeracy

Interpreting statistical information
• Interpret data displays

Literacy

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

• evaluating the appropriateness of sampling methods in reports where statements about a population are based on a sample
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

Ethical Understanding

Reasoning in decision making and actions
• Reflect on ethical action

Understanding ethical concepts and issues
• Explore ethical concepts in context

Literacy

Word Knowledge
• Understand learning area vocabulary

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

Numeracy

Interpreting statistical information
• Interpret data displays

• evaluating whether graphs in a report could mislead, and whether graphs and numerical information support the claims
Ethical Understanding

Reasoning in decision making and actions
• Reflect on ethical action

Understanding ethical concepts and issues
• Explore ethical concepts in context

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

Personal and Social Capability

Self-awareness
• Understand themselves as learners
• Recognise personal qualities and achievements

Social awareness
• Appreciate diverse perspectives

Literacy

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

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

Word Knowledge
• Understand learning area vocabulary

Numeracy

Interpreting statistical information
• Interpret data displays

#### Data representation and interpretation

Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278 - Scootle )
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

• using the standard deviation to describe the spread of a set of data
Literacy

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

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

Word Knowledge
• Understand learning area vocabulary

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

• using the mean and standard deviation to compare numerical data sets
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

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

Numeracy

Interpreting statistical information
• Interpret data displays

Use information technologies to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation (ACMSP279 - Scootle )
Information and Communication Technology (ICT) Capability

Investigating with ICT
• Locate, generate and access data and information

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
• Organise and process information

Numeracy

Interpreting statistical information
• Interpret data displays

• investigating different techniques for finding a ‘line of best fit’
Critical and Creative Thinking

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

Numeracy

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

### Year 10A Achievement Standards

There are no achievement standards for Year 10A in the Australian Curriculum: Mathematics. Please refer to the Year 10 Achievement Standards.