Year 7 Maths (Stage 4)

What makes two fractions equal, how to build and simplify them, and using equivalence to compare.

Common denominators, benchmarking against a half, and putting fractions in order confidently.

The three ways of writing the same number, and moving between them in every direction.

Putting mixed forms in order by converting to a common form first.

Why some fractions stop and others repeat forever, dot notation, and predicting which is which.

Describing likelihood in words and numbers, and placing events on a 0-to-1 scale.

Listing every possible outcome, and when outcomes can be treated as equally likely.

Favourable outcomes over total outcomes, as a fraction, decimal and percentage.

Why probabilities sum to 1, and using "not happening" to solve problems faster.

Numerical (discrete or continuous) versus categorical (nominal or ordinal), and why the type decides the graph.

Organising raw data, grouping into intervals, and reading a frequency table.

Column graphs, dot plots, line graphs and stem-and-leaf — matching the display to the data.

Reading values, spotting trends, and recognising a misleading display.

The three measures of centre plus range: how to find each and which one to trust.

What negatives mean, where they sit, and reading them in real contexts.

Which is bigger, why −8 is less than −3, and ordering with confidence.

Axes, origin and four quadrants; plotting and naming points with coordinates.

Expressing a part of a whole in all three forms, and what "of" really means.

Why letters stand in for numbers, and reading algebraic notation correctly.

Turning words into expressions, and the conventions for writing them.

Replacing a pronumeral with a number and evaluating, including with negatives.

Commutative, associative and distributive laws, and why they hold for letters too.

Moving along the number line, and why subtracting a negative adds.

Common denominators, mixed numbers, and keeping the whole intact.

Lining up the decimal point, and checking answers by estimation.

Which terms can be added, which cannot, and simplifying expressions.

The sign rules, why two negatives make a positive, and applying them reliably.

Applying all four operations in the right order, brackets included.

Why multiplying can make a number smaller, cancelling first, and mixed numbers.

Reciprocals, why we flip and multiply, and what division by a fraction means.

Placing the decimal point, dividing by a decimal, and estimating to check.

What makes a number prime, why 1 is neither, and quick divisibility tests.

Factor trees, writing a number as a product of prime powers, and why it is unique.

Reading and writing powers, and what an index actually tells you to do.

Undoing a power, perfect squares and cubes, and estimating roots that are not exact.

Naming points, lines and angles; the marks that show equal sides, equal angles and parallels.

Naming by sides and by angles, and why every triangle has a name from both lists.

Why the three angles always total 180°, and using it to find a missing angle.

The six special quadrilaterals, their properties, and how the families overlap.

Finding unknown angles and sides by applying properties, with a reason for every step.

Rounding to a given accuracy, and estimating to check a measurement answer.

Distance around a shape, including composite figures and finding missing sides.

Where the formulas come from, and why a triangle is half a rectangle.

Cutting and rearranging into a rectangle, and finding the perpendicular height.

Three more formulas, where each comes from, and choosing the right one.

Why 1 m² is 10000 cm², and choosing a sensible unit for the job.

Comparing quantities by division, ratio notation, and the difference from a fraction.

Dividing by the highest common factor, and handling ratios with units or fractions.

Dividing a quantity in a given ratio, and working backwards from one part.

Naming prisms, and drawing the front, side and top views of a solid.

Cross-section times length: one formula for every prism.

Cubic units, the cm³/mL/L bridges, and converting sensibly.

Splitting a solid into prisms, and adding or subtracting the parts.

The difference between an expression and an equation, the balance-scale picture, and solving as peeling with inverses.

Undoing addition, subtraction, multiplication and division, and reading which move to make before calculating.

Undoing two operations in reverse order, and turning a word problem into an equation.