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
Glossary
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
)
Express numbers in scientific notation
(ACMNA210 - Scootle
)
Patterns and algebra
Extend and apply the index laws to variables, using positive integer indices and the zero index
(ACMNA212 - Scootle
)
Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
(ACMNA213 - Scootle
)
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
)
Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software
(ACMNA294 - Scootle
)
Sketch linear graphs using the coordinates of two points and solve linear equations
(ACMNA215 - Scootle
)
Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations
(ACMNA296 - Scootle
)
Using units of measurement
Calculate areas of composite shapes
(ACMMG216 - Scootle
)
Investigate very small and very large time scales and intervals
(ACMMG219 - Scootle
)
Geometric reasoning
Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar
(ACMMG220 - Scootle
)
Solve problems using ratio and scale factors in similar figures
(ACMMG221 - Scootle
)
Pythagoras and trigonometry
Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles
(ACMMG222 - Scootle
)
Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles
(ACMMG223 - Scootle
)
Apply trigonometry to solve right-angled triangle problems
(ACMMG224 - Scootle
)
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
)
Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or'
(ACMSP226 - Scootle
)
Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians
(ACMSP227 - Scootle
)
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
)
Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’
(ACMSP282 - Scootle
)
Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
(ACMSP283 - Scootle
)