# 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

#### Real numbers

Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208 - Scootle )
Literacy

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
• Navigate, read and view learning area texts
• Comprehend texts
• Interpret and analyse learning area texts

Word Knowledge
• Understand learning area vocabulary

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
• 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

• identifying direct proportion in real-life contexts
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

Apply index laws to numerical expressions with integer indices (ACMNA209 - Scootle )
Numeracy

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

• simplifying and evaluating numerical expressions, using involving both positive and negative integer indices
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

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

Numeracy

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

• representing extremely large and small numbers in scientific notation, and numbers expressed in scientific notation as whole numbers or decimals
Numeracy

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

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

#### Money and financial mathematics

Solve problems involving simple interest (ACMNA211 - 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
• Navigate, read and view learning area texts
• Comprehend texts
• Interpret and analyse learning area texts

Numeracy

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

Estimating and calculating with whole numbers
• Use money

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

• understanding that financial decisions can be assisted by mathematical calculations
Numeracy

Estimating and calculating with whole numbers
• Use money

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

Extend and apply the index laws to variables, using positive integer indices and the zero index (ACMNA212 - Scootle )
Numeracy

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

• understanding that index laws apply to variables as well as numbers
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

Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (ACMNA213 - Scootle )
Numeracy

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

• understanding that the distributive law can be applied to algebraic expressions as well as 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
• Estimate and calculate
• Understand and use numbers in context

• understanding the relationship between expansion and factorisation and identifying algebraic factors in algebraic expressions
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

#### Linear and non-linear relationships

Find the distance between two points located on the Cartesian plane using a range of strategies, including graphing software (ACMNA214 - Scootle )
Numeracy

Using spatial reasoning
• Interpret maps and diagrams

Information and Communication Technology (ICT) Capability

Managing and operating ICT
• Select and use hardware and software

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

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

• investigating graphical and algebraic techniques for finding distance between two points
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

• using Pythagoras' theorem to calculate distance between two points
Numeracy

Using spatial reasoning
• Interpret maps and diagrams

Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (ACMNA294 - Scootle )
Information and Communication Technology (ICT) Capability

Managing and operating ICT
• Select and use hardware and software

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

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

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

• investigating graphical and algebraic techniques for finding midpoint and gradient
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

• recognising that the gradient of a line is the same as the gradient of any line segment on that line
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
• Organise and process information
• Identify and clarify information and ideas

Sketch linear graphs using the coordinates of two points and solve linear equations (ACMNA215 - 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
• Seek solutions and put ideas into action
• Consider alternatives

Reflecting on thinking and processes
• Reflect on processes

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

• determining linear rules from suitable diagrams, tables of values and graphs and describing them using both words and algebra
Critical and Creative Thinking

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

Analysing, synthesising and evaluating reasoning and procedures
• Evaluate procedures and outcomes

Reflecting on thinking and processes
• Reflect on processes

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

Grammar knowledge
• Use knowledge of sentence structures

Word Knowledge
• Understand learning area vocabulary

Numeracy

Using spatial reasoning
• Interpret maps and diagrams

Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations (ACMNA296 - Scootle )
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

Using spatial reasoning
• Interpret maps and diagrams

Literacy

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

Word Knowledge
• Understand learning area vocabulary

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

Information and Communication Technology (ICT) Capability

Managing and operating ICT
• Select and use hardware and software

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

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

• graphing parabolas, and circles connecting x-intercepts of a graph to a related equation
Numeracy

Using spatial reasoning
• Interpret maps and diagrams

#### 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

#### Chance

List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events (ACMSP225 - Scootle )
Numeracy

Using spatial reasoning
• Interpret maps and diagrams

Interpreting statistical information
• Interpret chance events

• conducting two-step chance experiments
Critical and Creative Thinking

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

Numeracy

Interpreting statistical information
• Interpret chance events

• using systematic methods to list outcomes of experiments and to list outcomes favourable to an event
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 chance events

• comparing experiments which differ only by being undertaken with replacement or without replacement
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 chance events

Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or' (ACMSP226 - Scootle )
Numeracy

Interpreting statistical information
• Interpret chance events

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

• using Venn diagrams or two-way tables to calculate relative frequencies of events involving ‘and’, ‘or’ questions
Numeracy

Interpreting statistical information
• Interpret chance events

Using spatial reasoning
• Interpret maps and diagrams

• using relative frequencies to find an estimate of probabilities of ‘and’, ‘or’ events
Numeracy

Interpreting statistical information
• Interpret chance events

Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians (ACMSP227 - 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
• Reflect on processes

Literacy

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

Word Knowledge
• Understand learning area vocabulary

Numeracy

Interpreting statistical information
• Interpret data displays

Information and Communication Technology (ICT) Capability

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

Ethical Understanding

Reasoning in decision making and actions
• Consider consequences

Understanding ethical concepts and issues
• Explore ethical concepts in context

• investigating a range of data and its sources, for example the age of residents in Australia, Cambodia and Tonga; the number of subjects studied at school in a year by 14-year-old students in Australia, Japan and Timor-Leste
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

Intercultural Understanding

Interacting and empathising with others
• Consider and develop multiple perspectives

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
• Reflect on processes

Numeracy

Interpreting statistical information
• Interpret data displays

#### Data representation and interpretation

Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly and from secondary sources (ACMSP228 - Scootle )
Critical and Creative Thinking

Generating ideas, possibilities and actions
• Consider alternatives

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
• Comprehend texts
• Interpret and analyse learning area texts
• Navigate, read and view learning area texts

Word Knowledge
• Understand learning area vocabulary

Numeracy

Interpreting statistical information
• Interpret data displays

Ethical Understanding

Reasoning in decision making and actions
• Consider consequences

Understanding ethical concepts and issues
• Explore ethical concepts in context

• comparing the annual rainfall in various parts of Australia, Pakistan, New Guinea and Malaysia
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

Intercultural Understanding

Recognising culture and developing respect
• Explore and compare cultural knowledge, beliefs and practices

Critical and Creative Thinking

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

Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ (ACMSP282 - Scootle )
Numeracy

Interpreting statistical information
• Interpret data displays

• using stem-and-leaf plots to compare two like sets of data such as the heights of girls and the heights of boys in a class
Literacy

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

Interpreting statistical information
• Interpret data displays

Critical and Creative Thinking

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

• describing the shape of the distribution of data using terms such as ‘positive skew’, ‘negative skew’ and 'symmetric' and 'bi-modal'
Literacy

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

Word Knowledge
• Understand learning area vocabulary

Grammar knowledge
• Use knowledge of sentence structures

Numeracy

Interpreting statistical information
• Interpret data displays

Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (ACMSP283 - Scootle )
Literacy

Word Knowledge
• Understand learning area vocabulary

Visual Knowledge
• Understand how visual elements create meaning

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

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

Interpreting statistical information
• Interpret data displays

• comparing means, medians and ranges of two sets of numerical data which have been displayed using histograms, dot plots, or stem and leaf plots
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

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

### 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.