4 LESSONS
Build confidence with numbers and algebra
Connect fractions, ratios, powers and equations through examples from everyday life.
Follow this series →MAKE SENSE OF NUMBERS
Free mathematics: understand numbers, patterns and data
Learn the reasoning behind the calculation. Work through fractions, equations, measurement and data with solved examples and practice you can check.
A guided place to begin
4 LESSONS
Understand graphs, measurement and data
Read relationships, measure space and reason about averages and chance.
Follow this series →Explore every topic
Mathematics
BeginnerFractions, decimals and percentages: one quantity, three forms
A half-filled bottle, 0.5 litre and 50% can describe related ideas, but only when the whole is clear.
Learning outcome: Convert among the three forms, combine fractional amounts, calculate a percentage change, and spot misleading comparisons that use different starting quantities.
Read the guide →Mathematics
BeginnerRatios, proportion and unit rates: compare fairly
A larger packet may cost more but offer a lower price per item.
Learning outcome: Interpret ratios, scale a mixture, compare unit prices and test whether a situation supports proportional reasoning.
Read the guide →Mathematics
BeginnerAlgebra: turn a situation into an expression and an equation
Algebra gives a name to an unknown quantity and expresses relationships that stay true.
Learning outcome: Build and simplify expressions, solve equations with one unknown, explain each operation and recognise impossible or unrestricted equations.
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IntermediateLinear equations and graphs: read a constant rate of change
A graph turns pairs of numbers into a visible relationship.
Learning outcome: Plot ordered pairs, calculate slope, recover a line's equation from two points and evaluate predictions against the assumptions of the model.
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BeginnerGeometry: measure boundaries, surfaces and space
Fencing a garden, covering a floor and filling a container ask three different measurement questions.
Learning outcome: Calculate rectangular, triangular and circular measures, split a compound shape into simpler pieces, and distinguish container capacity from the material needed to build it.
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BeginnerData: describe a typical value and the variation around it
An average can hide both an unusually large value and a wide gap between observations.
Learning outcome: Calculate and interpret mean, median, mode, range and interquartile range, compare data sets with the same mean, and avoid misleading averages of unequal groups.
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IntermediateProbability and risk: reason about uncertain outcomes
Uncertainty does not mean every outcome is equally likely.
Learning outcome: Construct a sample space, calculate complements and combined events, compare sampling with and without replacement, and interpret expected counts without treating them as promises.
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IntermediateExponents, roots and scientific notation: reason across scales
A tiny thickness and a huge count are easier to compare when powers of ten organise the numbers.
Learning outcome: Use exponent rules with their conditions, distinguish a square root from solutions of a squared equation, and calculate with large and small quantities in scientific notation.
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