KS3 maths worksheets

Understand and use place value for decimals, measures and integers of any size.

Order integers, decimals and fractions; use =, ≠, <, >, ≤ and ≥.

Partial Finds the absolute value of an integer. Does not order integers, decimals and fractions.

Use primes, factors, multiples, HCF, LCM and prime factorisation.

Use the four operations with integers, decimals, fractions and mixed numbers, positive and negative.

Use the priority of operations, including brackets, powers, roots and reciprocals.

Recognise and use the relationships between operations, including inverses.

Use integer powers and real roots and distinguish exact roots from their decimals.

Interpret and compare numbers in standard form.

Work interchangeably with terminating decimals and their fractions.

Define and use percentage, percentage change and percentages over 100%.

Interpret fractions and percentages as operators.

Use standard units of mass, length, time, money and other measures.

Round numbers and measures to a given number of decimal places or significant figures.

Partial Rounds to two decimal places. Does not round to significant figures.

Use rounding to estimate answers and express the resulting error with inequalities.

Partial Chooses an accuracy to report to. Does not bound the error with an inequality.

Appreciate the infinite nature of the integers, reals and rationals.

Partial Sorts a number as rational or irrational. Does not ask about the infinitude of the sets.

Use algebraic notation: ab, 3y, a², a/b, coefficients and brackets.

Substitute numerical values into formulae and expressions.

Use the vocabulary of expressions, equations, inequalities, terms and factors.

Partial Evaluates the expression. Does not ask the child to name its parts.

Collect like terms, expand brackets, take out common factors and expand binomials.

Use standard formulae and rearrange a formula to change the subject.

Model situations by translating them into expressions, formulae and graphs.

Solve linear equations in one variable, including those needing rearrangement.

Work with coordinates in all four quadrants.

Recognise, sketch and produce graphs of linear and quadratic functions.

Interpret mathematical relationships both algebraically and graphically.

Reduce a linear equation to y = mx + c and interpret its gradient and intercept.

Use graphs to estimate values and find approximate solutions of simultaneous equations.

Partial Solves the system algebraically. Does not ask for the reading off a graph.

Find approximate solutions from graphs of piece-wise linear, exponential and reciprocal functions.

Partial Describes the shape of a graph. Does not read a solution off an exponential or reciprocal one.

Generate terms of a sequence from a term-to-term or position-to-term rule.

Recognise arithmetic sequences and find the nth term.

Recognise geometric sequences and other sequences that arise.

Change freely between related standard units of time, length, area, volume and mass.

Use scale factors, scale diagrams and maps.

Express one quantity as a fraction of another.

Use ratio notation, including reduction to simplest form.

Divide a quantity into two parts in a given part:part or part:whole ratio.

Partial Reads and simplifies the ratio. Does not divide an amount by it.

Understand a multiplicative relationship as either a ratio or a fraction.

Relate the language of ratio to fraction arithmetic and to linear functions.

Solve percentage change problems, including original value and simple interest.

Solve problems involving direct and inverse proportion.

Partial Solves direct proportion. Does not cover inverse proportion.

Use compound units such as speed, unit pricing and density.

Derive and apply formulae for the area of triangles, parallelograms and trapezia and the volume of prisms.

Calculate the perimeter and area of circles and composite shapes.

Draw and measure line segments and angles, including in scale drawings.

Partial Measures and draws angles with a protractor. Does not cover line segments or scale drawings.

Derive and use the standard ruler and compass constructions.

Describe and draw points, lines, parallel and perpendicular lines and polygons.

Use the conventions for labelling triangle ABC and the criteria for congruence.

Derive and illustrate the properties of triangles, quadrilaterals and circles.

Identify the properties and results of translations, rotations and reflections.

Construct congruent triangles and similar shapes by enlargement.

Apply the properties of angles at a point, on a straight line and vertically opposite.

Use the relationship between parallel lines and alternate and corresponding angles.

Derive the angle sum of a triangle and deduce the angle sum of any polygon.

Apply angle facts, congruence and similarity to derive results, including Pythagoras.

Use Pythagoras' theorem and trigonometric ratios in right-angled triangles.

Use the faces, edges and vertices of prisms, cylinders, pyramids, cones and spheres.

Interpret mathematical relationships both algebraically and geometrically.

Partial Uses the coordinate formulas. Does not ask for the algebra-geometry link to be stated.

Analyse the frequency of outcomes of simple experiments on the 0-1 probability scale.

Understand that the probabilities of all possible outcomes sum to 1.

Partial Finds the probability of one outcome. Does not ask for the outcomes together summing to 1.

Enumerate sets and their unions and intersections using tables, grids and Venn diagrams.

Generate theoretical sample spaces for single and combined events.

Describe a distribution by its graph, its mean, mode and median, and its spread.

Construct frequency tables, bar charts, pie charts and pictograms.

Describe relationships between two variables and illustrate with scatter graphs.