Year 9 Maths
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Skill navigator
Skills are grouped by curriculum strand. Exact Australian Curriculum wording remains available on every card.
Number
Rational and irrational numbers together form the real number system. Exact forms such as √2 and π preserve value, while decimals may be terminating, recurring or…
ExampleWhich number is irrational?
recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools
Algebra
Exponent laws describe repeated multiplication. Year 9 extends the laws to numerical expressions with integer exponents and to variables, including zero and negative…
Example0.475 written using powers of 10 is:
apply the exponent laws to numerical expressions with integer exponents and extend to variables
Algebra
Simplifying, expanding and factorising are connected ways of rewriting equivalent algebraic expressions. Year 9 extends these skills to binomial products and monic…
ExampleSimplify: 3x − 7x + 4
simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions
Algebra
Coordinates encode geometric information. From two points you can calculate gradient, midpoint and distance, then interpret each quantity in context
ExampleThe diagram shows line segment AB from A(2, 5) to B(6, 9). Use the scratchpad or notebook to find the gradient
find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane
Algebra
Quadratic rules, tables, parabolas, factors and roots are different representations of the same relationship. Year 9 connects graphical, numerical and algebraic solutions
ExampleA table has x-values 1, 2, 3, 4 and y-values 4, 7, 12, 19. What do the second differences show?
identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate
Algebra
Mathematical modelling turns a real situation into a linear or quadratic relationship, solves it, interprets the result and checks whether the model is reasonable
ExampleA roast cooks for 90 min and must rest for 20 min. What is the total time?
use mathematical modelling to solve applied problems involving change including financial contexts; formulate problems, choosing to use either linear or quadratic functions; interpret solutions in terms of the situation; evaluate the model and report methods and findings
Algebra
Changing parameters changes predictable graph features. Digital tools help test conjectures, but the goal is to connect graphical change to algebraic structure
ExampleChanging y = x to y = 2x does what?
experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns
Measurement
Surface area measures exposed covering; volume measures occupied space. Right prisms and cylinders require correct formulas, units and careful interpretation of which…
ExampleA rectangular prism net contains which faces?
solve problems involving the volume and surface area of right prisms and cylinders using appropriate units
Measurement
Scientific notation compresses extreme scales into a number between 1 and 10 multiplied by a power of 10, making comparison and calculation across large ranges more…
Example4.6 × 10⁹ years in decimal form is:
solve problems involving very small and very large measurements, time scales and intervals expressed in scientific notation
Measurement
Spatial problems often require choosing among angle facts, scale, similarity, Pythagoras and trigonometric ratios. The challenge is selecting the method that matches the…
ExampleA surveyor measures a horizontal distance of 30 m and a vertical rise of 16 m. What is the slope length?
solve spatial problems, applying angle properties, scale, similarity, Pythagoras’ theorem and trigonometry in right-angled triangles
Measurement
Every measured value is an estimate. Absolute error describes a difference in units; relative and percentage error scale that difference against the size of the quantity
ExampleActual attendance is 480 and estimated attendance is 500. What is the absolute error?
calculate and interpret absolute, relative and percentage errors in measurements, recognising that all measurements are estimates
Measurement
Ratio, rate, scale and direct proportion describe multiplicative relationships. Mathematical modelling uses them to formulate, solve, interpret and evaluate practical…
ExampleIf pay is $28 per hour, what is the pro-rata pay for 6 h?
use mathematical modelling to solve practical problems involving direct proportion, rates, ratio and scale, including financial contexts; formulate the problems and interpret solutions in terms of the situation; evaluate the model and report methods and findings
Space
Right triangles with the same acute angle are similar, so corresponding side ratios are constant. This similarity is the reason sine, cosine and tangent work
ExampleIn a right-angled triangle, the hypotenuse is:
recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity
Space
An enlargement multiplies every length from a centre by the same scale factor. Similarity preserves angle measures and shape while lengths, areas and other measures…
ExampleTwo similar triangles have side ratio 2:5. What can be said about their angle measures?
apply the enlargement transformation to shapes and objects using dynamic geometry software as appropriate; identify and explain aspects that remain the same and those that change
Space
A geometric algorithm is a precise sequence of construction steps and decisions. Good algorithms are tested on varied cases, refined for ambiguity and justified using…
ExampleWhich condition correctly tests whether three positive lengths a, b and c can form a non-degenerate triangle?
design, test and refine algorithms involving a sequence of steps and decisions based on geometric constructions and theorems; discuss and evaluate refinements
Statistics
Survey claims depend on how data were obtained. Year 9 students analyse reports containing numerical and categorical variables and judge whether sample summaries can…
ExampleA news article says 'Most Australians support banning single-use plastics' from a voluntary online survey of 1,200 readers. What is the strongest concern?
analyse reports of surveys in digital media and elsewhere for information on how data was obtained to estimate population means and medians
Statistics
Different sampling methods—and even different random samples using the same method—can produce different results. Representation choices can also amplify or hide…
ExampleA bar chart shows support for recycling: Group A is 62% and Group B is 65%, but the y-axis starts at 60%. What is the main issue?
analyse how different sampling methods can affect the results of surveys and how choice of representation can be used to support a particular point of view
Statistics
Distributions are compared using centre, spread and shape—not one summary number alone. Histograms and comparative displays reveal skew, symmetry, modes and outliers
ExampleIncomes are $40k, $42k, $45k, $48k, $50k, $52k and $200k. Which description best fits the distribution?
represent the distribution of multiple data sets for numerical variables using comparative representations; compare data distributions with consideration of centre, spread and shape, and the effect of outliers on these measures
Statistics
A good data display matches the variable type and the question. Choice of graph, scale, grouping and labels should make the intended comparison clear without distorting…
ExampleScores are 56,58,60,61,62,95. Which measure of centre is most affected by 95?
choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context
Statistics
A statistical investigation connects a clear question to appropriate data collection, analysis, representation and a conclusion whose strength matches the evidence
ExampleA secondary-data table shows median weekly income: Australia $1,300 and ACT $1,500. What is the difference?
plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions
Probability
Two-step chance experiments require a complete sample space. Replacement changes second-step probabilities; tree diagrams, tables and arrays help list outcomes without…
ExampleA coin is tossed twice. How many total outcomes are possible?
list all outcomes for compound events both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes
Probability
Relative frequency estimates probability from observed data. Combined events require precise language: AND means intersection, inclusive OR allows overlap, and exclusive…
ExampleA coin is tossed 500 times and lands Heads 260 times. What is the relative frequency of Heads?
calculate relative frequencies from given or collected data to estimate probabilities of events involving “and”, inclusive “or” and exclusive “or”
Probability
Simulation estimates probabilities that are difficult or impossible to determine exactly. A valid simulation must model the original chance process faithfully and use…
ExampleA simulation runs 10,000 coin tosses: Heads = 4,980. Estimated probability of Heads?
design and conduct repeated chance experiments and simulations, using digital tools to compare probabilities of simple events to related compound events, and describe results