Place value
Place value is the value a digit has because of its position in a number.
Open lessonMathematics
Start with the foundations, follow a pathway or choose an idea that catches your attention. Every published lesson includes worked examples and checked practice.
Pathway 01 · 8 available
Number foundations
Positive and negative numbers
Positive numbers are above zero; negative numbers are below zero. Zero is neither positive nor negative.
Open lessonOrder of operations
Order of operations is the shared set of rules for deciding which calculation to do first.
Open lessonFractions
A fraction describes equal parts of a whole. The denominator counts the equal parts; the numerator counts the parts selected.
Open lessonDecimals
A decimal represents whole numbers and parts of a whole using places based on powers of ten.
Open lessonPercentages
A percentage is a fraction out of one hundred. The symbol % means “per hundred”.
Open lessonRatios and proportions
A ratio compares quantities multiplicatively. A proportion states that two ratios are equal.
Open lessonEstimation and rounding
Rounding replaces a number with a nearby value at a chosen level of precision. Estimation finds an approximate answer useful for a purpose.
Open lessonPathway 02 · 1 available
Everyday calculations
Discounts
A discount reduces a price by a specified amount or a percentage of the original price.
Open lessonUpcoming topics: Money · GST and tax examples · Simple and compound interest · Rates · Unit pricing · Time calculations · Reading bills and statements. These topics do not yet have standalone lessons.
Pathway 03 · 4 available
Algebra
Variables and expressions
A variable is a symbol that stands for a number. An expression combines numbers, variables and operations without asserting an equality.
Open lessonSubstitution
Substitution means replacing a variable with a known value while preserving the operations around it.
Open lessonSolving linear equations
A linear equation has variables only to the first power. Solving it means finding values that make both sides equal.
Open lessonRearranging formulas
Rearranging a formula makes a different variable the subject while preserving the relationship.
Open lessonUpcoming topics: Simplifying expressions · Formulas · Inequalities · Sequences. These topics do not yet have standalone lessons.
Pathway 04 · 4 available
Measurement
Metric units and conversion
Metric prefixes describe powers of ten applied to a unit. Converting changes the numerical representation without changing the quantity.
Open lessonPerimeter
Perimeter is the total distance around the outside boundary of a flat shape.
Open lessonArea
Area measures the amount of surface inside a two-dimensional boundary, in square units.
Open lessonVolume
Volume is the amount of three-dimensional space an object or substance occupies, measured in cubic units.
Open lessonUpcoming topics: Surface area · Scale · Accuracy and significant figures. These topics do not yet have standalone lessons.
Pathway 05 · 1 available
Geometry
Pythagoras’ theorem
In a right-angled triangle, the square of the longest side equals the sum of the squares of the other two sides.
Open lessonUpcoming topics: Lines and angles · Triangles · Polygons · Circles · Similarity · Basic trigonometry. These topics do not yet have standalone lessons.
Pathway 06 · 1 available
Graphs and coordinates
Coordinates and gradient
Coordinates locate a point using an ordered pair (x, y). Gradient measures how much y changes per unit change in x.
Open lessonUpcoming topics: Distance-time graphs · Interpreting real-world graphs. These topics do not yet have standalone lessons.
Pathway 07 · 1 available
Statistics and probability
Mean, median and mode
The mean is the total divided by the number of values. The median is the middle of an ordered list. The mode is the most frequent value.
Open lessonUpcoming topics: Tables and charts · Range · Distributions · Misleading graphs · Basic probability · Combined events · Risk and expected outcomes. These topics do not yet have standalone lessons.
Pathway 08 · 0 available
Advanced foundations
Upcoming topics: Indices · Scientific notation · Expanding and factorising · Quadratic foundations · Functions · Exponential relationships. These topics do not yet have standalone lessons.