Year 10 Maths
Find the exact skill a learner needs, understand it clearly and open the right teaching or practice resource.
Skill navigator
Skills are grouped by curriculum strand. Exact Australian Curriculum wording remains available on every card.
Number
Small rounding choices can become meaningful after a value is reused many times. Learn when to keep fractions, π, roots or full calculator precision, how rounding differs…
ExampleWhich value is written in exact form?
recognise the effect of using approximations of real numbers in repeated calculations and compare the results when using exact representations
Algebra
Build the algebra fluency needed across Year 10: apply exponent laws correctly, move between expanded and factorised forms, simplify expressions without changing their…
ExampleSimplify x^5 × x^3
expand, factorise and simplify expressions and solve equations algebraically, applying exponent laws involving products, quotients and powers of variables, and the distributive property
Algebra
Solve situations with more than one condition. Learn when elimination, substitution or a graph is most efficient, how an intersection represents a common solution, and…
ExampleForgetting to reverse the sign: only reverse it when multiplying or dividing both sides by a negative
solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation
Algebra
Exponential change is about multiplication, not simply “a graph that curves”. Learn to recognise constant ratios, read the meaning of y = abˣ, connect tables, rules and…
Example“Any curved graph is exponential.” Quadratics and other functions also curve. Check the pattern or rule
recognise the connection between algebraic and graphical representations of exponential relations and solve related exponential equations, using digital tools where appropriate
Algebra
A model is more than a formula. Learn to formulate a real problem, choose between linear, quadratic and exponential models, calculate and interpret predictions, test…
Example“A curved graph means exponential.” Use differences, ratios and context to choose the family
use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings
Algebra
Use graphs, tables and digital tools systematically: make a conjecture, test it across cases and boundaries, refine it, and state what the evidence actually supports
ExampleTrusting one graph window without changing the scale
experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns
Measurement
Break complex objects into familiar prisms and cylinders, calculate only the surfaces or volumes that actually belong to the object, and keep units consistent throughout
ExampleAdding areas when the question asks for volume, or vice versa
solve problems involving the surface area and volume of composite objects using appropriate units
Measurement
On a logarithmic scale, equal visual steps represent equal multiplication factors rather than equal additions, allowing very large ranges to fit on one axis
ExampleTreating equal log-scale gaps as equal additive changes
interpret and use logarithmic scales in applied contexts involving small and large quantities and change
Measurement
Draw and label the right triangle first, then choose Pythagoras or the trigonometric ratio that links the known and unknown quantities
ExampleUsing Pythagoras on a triangle that is not right-angled
solve practical problems applying Pythagoras’ theorem and trigonometry of right-angled triangles, including problems involving direction and angles of elevation and depression
Measurement
Measurements are never infinitely precise. Instrument resolution, method, calibration and repeated approximation can change conclusions, especially when errors are…
ExampleUsing “accuracy” and “precision” as synonyms
identify the impact of measurement errors on the accuracy of results in practical contexts
Measurement
Scale models preserve corresponding ratios. Good modelling also checks units, physical constraints, standards and whether the chosen scale makes the design useful
ExampleA Year 10 student is solving a problem involving analyse and applying scale and ratios in situations such as production prototypes and 3d printing. Which option is mathematically valid?
use mathematical modelling to solve practical problems involving proportion and scaling of objects; formulate problems and interpret solutions in terms of the situation; evaluate and modify models as necessary, and report assumptions, methods and findings
Space
A proof is a chain of justified statements from accepted facts to a conclusion that must follow; a diagram or measurement alone is evidence, not proof
ExampleAssuming a diagram is drawn to scale
apply deductive reasoning to proofs involving shapes in the plane and use theorems to solve spatial problems
Space
Networks simplify real relationships into vertices and edges so routes, connections and structural properties can be analysed without unnecessary physical detail
ExampleNot defining what vertices/edges represent
interpret networks and network diagrams used to represent relationships in practical situations and describe connectedness
Space
Define the spatial problem, decompose it into manageable parts, create an algorithm or model, test against cases and constraints, then refine and justify the solution
ExampleWriting vague steps that another person could not execute
design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions
Statistics
A statistical claim is only as strong as its data, sample, representation, method and inference. Ethical reporting also considers whose data is used, how it is framed and…
ExampleAssuming a large sample is automatically representative
analyse claims, inferences and conclusions of statistical reports in the media, including ethical considerations and identification of potential sources of bias
Statistics
Compare distributions by centre, spread, shape and unusual values, and choose a display that answers the statistical question rather than one that merely looks familiar
ExampleComparing only medians and ignoring spread
compare data distributions for continuous numerical variables using appropriate data displays including boxplots; discuss the shapes of these distributions in terms of centre, spread, shape and outliers in the context of the data
Statistics
Describe association using direction, strength and form, then interpret it cautiously: a scatterplot can reveal a pattern but cannot by itself prove causation
ExampleSaying correlation proves causation
construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity
Statistics
Two-way tables cross-classify two categorical variables. Compare conditional percentages within groups, not just raw counts, before claiming an association
ExampleComparing raw counts when group sizes differ
construct two-way tables and discuss possible relationship between categorical variables
Statistics
A good bivariate investigation asks a focused question, measures two variables consistently, uses an appropriate display and limits conclusions to what the design and…
ExampleAsking a vague question with undefined variables
plan and conduct statistical investigations of situations that involve bivariate data; evaluate and report findings with consideration of limitations of any inferences
Probability
Words such as “given” or “knowing that” restrict the sample space. The denominator must match the condition before a conditional probability can be interpreted correctly
ExampleSwapping P(A|B) and P(B|A)
use the language of “if ... then”, “given”, “of”, “knowing that” to describe and interpret situations involving conditional probability
Probability
Design a simulation that matches the real dependency and replacement rules, repeat it enough times to stabilise frequencies, then interpret variation and limitations…
ExampleUsing equal random outcomes for unequal real probabilities
design and conduct repeated chance experiments and simulations using digital tools to model conditional probability and interpret results