Year 8 Maths
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Skill navigator
Skills are grouped by curriculum strand. Exact Australian Curriculum wording remains available on every card.
Number
Some exact lengths and ratios cannot be written as fractions. Learn how square roots and π fit into the real number system, how to locate them approximately, and how…
ExampleAn irrational number has no exact value. It is exact; its decimal representation does not terminate/repeat
recognise irrational numbers in applied contexts, including square roots and π
Number
Build exponent laws from repeated multiplication, then apply product, quotient, power-of-a-power and zero-exponent rules only when their conditions are satisfied
ExampleWhich rule applies to aᵐ × aⁿ?
establish and apply the exponent laws with positive integer exponents and the zero-exponent, using exponent notation with numbers
Number
A rational number’s decimal terminates or eventually repeats. Simplify the fraction first, inspect the denominator’s prime factors, and use digital tools to confirm…
ExampleTesting an unsimplified denominator. Simplify the fraction first
recognise terminating and recurring decimals, using digital tools as appropriate
Number
Use meaning and number structure—not isolated sign slogans—to calculate with integers, fractions and decimals efficiently. Track signs, choose exact representations…
ExampleWhat is −10 + (−10)?
use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate
Number
Formulate real situations with signed rational numbers and percentages, choose efficient strategies, interpret financial or environmental results, and review whether the…
ExampleTemperature changes from 12°C to −3°C. What is the change?
use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model
Algebra
Treat algebraic expressions as structures that can be rewritten without changing their value. Expand and factorise with distributivity, combine only like terms, and…
ExampleSimplify: 3(a − b)
create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties
Algebra
Connect tables, graphs and algebra as representations of the same linear relationship. Solve equations and inequalities by preserving equality or order, then verify…
ExampleWhich table shows a linear relation? x: 1, 2, 3, 4; y: 5, 7, 9, 11
graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution
Algebra
Build a linear model from a starting value and constant rate, choose a useful representation, interpret parameters in context and decide where the model stops being…
ExampleThe intercept is just a graph feature. In context it often represents a fixed or initial amount
use mathematical modelling to solve applied problems involving linear relations, including financial contexts; formulate problems with linear functions, choosing a representation; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model
Algebra
Run controlled mathematical experiments: vary one feature at a time, predict what will happen, use digital tables and graphs to test the conjecture, then state a…
ExampleIf the coefficient of x is negative, the line:
experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns
Measurement
Decide whether the problem is about boundary length, enclosed area or both. Decompose composite shapes without overlap, infer missing lengths from aligned edges, and use…
ExampleAdding internal partition lines to perimeter. Only trace the external boundary
solve problems involving the area and perimeter of irregular and composite shapes using appropriate units
Measurement
A right prism repeats one cross-section through a perpendicular length, so volume equals cross-sectional area × prism length. Connect cubic units to capacity units before…
ExampleHow many millilitres are in 250 cm³?
solve problems involving the volume and capacity of right prisms using appropriate units
Measurement
Use d=2r, C=2πr=πd and A=πr² with the correct measure and units. Estimate before calculating, keep π exact until rounding is required, and work backwards from…
ExampleFor a circle of radius 5 cm, which is a correct bound for its area?
solve problems involving the circumference and area of a circle using formulas and appropriate units
Measurement
Treat a clock reading and an elapsed duration as different quantities. Convert moments to one common time-zone reference before comparing them, and track date changes…
ExamplePerth is UTC+8 and the time is 3:00 pm. What is the time in Suva, UTC+12?
solve problems involving duration, including using 12- and 24-hour time across multiple time zones
Measurement
A rate compares quantities measured in different units. Convert to a common or unit rate before comparing, keep units attached through calculations, and interpret the…
ExampleA worker earns $28 per hour. What type of rate is this?
recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure
Measurement
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Identify the right angle and hypotenuse first, then use the…
ExampleChoosing any side as c. c must be opposite the right angle and longest
use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles
Measurement
Turn a practical situation into quantities, ratios or rates; choose a representation; solve; then interpret the result and review whether proportionality, constant speed…
ExampleA map uses scale 1:50,000. A road measures 12 cm on the map. What is the actual length?
use mathematical modelling to solve practical problems involving ratios and rates, including financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model
Space
Congruent shapes match exactly; similar shapes preserve corresponding angles and scale every corresponding length by one common factor. Use valid conditions…
ExampleSame angles means congruent. Equal angles establish shape, not size; AAA proves similarity only
identify the conditions for congruence and similarity of triangles and explain the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations
Space
Use diagonals, congruent triangles, parallel-line angles and symmetry to establish quadrilateral properties instead of memorising a list. Then apply those properties to…
ExampleThe sum of one exterior angle at each vertex of any polygon is:
establish properties of quadrilaterals using congruent triangles and angle properties, and solve related problems explaining reasoning
Space
A three-dimensional coordinate system needs three ordered coordinates referenced to a chosen origin and axes. Compare ordered triples, layers, plan/elevation views and…
ExampleA drone is recorded at 35°S, 149°E and 120 m above sea level. Why is this a three-dimensional location?
describe the position and location of objects in 3 dimensions in different ways, including using a three-dimensional coordinate system with the use of dynamic geometric software and other digital tools
Space
Turn geometric criteria into an ordered decision process, trace it with examples, deliberately test edge cases and debug any branch that misclassifies congruent or…
ExampleWhich is a valid triangle congruence test?
design, create and test algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describe how the algorithm works
Statistics
Choose a data-collection method by matching the question and population, then evaluate practicality, sampling bias, measurement precision, error and ethics
ExampleA census collects data from:
investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques
Statistics
Analyse distributions from primary and secondary sources, and connect the reliability of conclusions to how the sample was selected
ExampleRandom means haphazard. Random sampling uses a defined chance process
analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques to select and study samples
Statistics
Random samples from the same population do not give identical results. Compare repeated samples and recognise that larger random samples usually give more stable…
ExampleTwo random samples of 50 students show 28/50 and 33/50 support for a uniform change. Which statement is correct?
compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation
Statistics
Plan a statistical investigation from question to report: define the population, select a fair and ethical sample, analyse the data, make a cautious inference and…
ExampleElectricity use increased by 18% during a lockdown. Which inference is best supported?
plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertainty
Probability
An event and its complement divide the same sample space into “A” and “not A”. Because nothing is omitted or counted twice, their probabilities add to 1—even when…
ExampleIf the probability of winning a prize is 0.37, what is the probability of not winning?
recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts
Probability
Represent every possible combination of two events systematically, then read “and”, inclusive/exclusive “or”, “at least” and mutually exclusive relationships without…
ExampleAt least one means:
determine all possible combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific outcomes in practical situations
Probability
Use repeated trials and well-designed digital simulations to estimate probabilities for compound events, compare relative frequency with theoretical probability, and…
Example1000 trials must give the exact theoretical probability. Random variation remains in finite samples
conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe results