School

Read, write, compare, and order positive integers and decimals using place value.

Add and subtract positive integers and decimals accurately.

Multiply positive integers and decimals using written methods.

Divide positive integers and decimals using written methods.

Calculate with negative numbers using the four operations.

Apply the order of operations to calculations containing brackets and powers.

Identify factors, multiples, and prime numbers, and find the highest common factor and lowest common multiple of two numbers.

Round numbers to stated decimal places or significant figures and use rounding to estimate answers.

Generate equivalent fractions and simplify fractions to their lowest terms.

Convert between improper fractions and mixed numbers.

Compare and order fractions by using common denominators or decimal equivalents.

Add and subtract fractions and mixed numbers.

Multiply fractions and mixed numbers.

Divide fractions and mixed numbers.

Convert between fractions, terminating decimals, and percentages.

Calculate a given percentage of a quantity without and with a calculator.

Interpret ratio notation and simplify ratios, including ratios involving different units.

Divide a quantity into a given ratio.

Use the unitary method to solve direct-proportion problems.

Apply scale factors to recipes, maps, and scale drawings.

Calculate percentage increases and decreases.

Calculate percentage change between an original and a new value.

Compare prices by calculating unit rates and identify the best buy.

Solve problems involving rates such as speed and cost per unit.

Translate verbal descriptions into algebraic expressions.

Use index notation and evaluate positive integer powers and roots.

Substitute positive and negative values into algebraic expressions.

Collect like terms to simplify algebraic expressions.

Expand a single bracket by multiplication.

Factorise an expression by taking out a common factor.

Form and evaluate formulae that represent mathematical or real-world relationships.

Solve one-step linear equations using inverse operations.

Solve multi-step linear equations with the unknown on one side.

Solve linear equations with the unknown on both sides.

Solve linear equations containing a single expanded bracket.

Form and solve a linear equation from a word problem.

Solve a one-step linear inequality and represent its solutions on a number line.

Generate terms of a linear sequence from a term-to-term rule.

Find and use the nth-term rule of a linear sequence.

Plot and read coordinates in all four quadrants.

Complete a table of values for a linear equation.

Plot a straight-line graph from its equation.

Calculate the gradient of a straight line from two points.

Identify and interpret the gradient and intercept in an equation of the form y = mx + c.

Determine the equation of a straight line from its graph.

Interpret distance–time graphs, including stationary and constant-speed sections.

Use angle facts at a point, on a straight line, and for vertically opposite angles.

Find unknown angles formed by parallel lines and a transversal.

Use angle properties of triangles and quadrilaterals to find unknown angles.

Calculate interior and exterior angles of regular polygons.

Classify triangles and quadrilaterals from their side, angle, and symmetry properties.

Construct a triangle accurately using a ruler, compass, and protractor from given measurements.

Measure and draw three-figure bearings.

Describe and construct a locus satisfying a stated distance condition.

Convert between common metric units of length, area, volume, mass, and capacity.

Calculate the perimeter of compound two-dimensional shapes.

Calculate the area of triangles, parallelograms, trapezia, and compound shapes.

Calculate the circumference of a circle using its diameter or radius.

Calculate the area of a circle using its radius or diameter.

Calculate the volume of prisms, including cuboids and triangular prisms.

Calculate the surface area of cuboids and triangular prisms.

Use Pythagoras’ theorem to find a missing side in a right-angled triangle.

Reflect a shape in horizontal, vertical, and diagonal mirror lines on a coordinate grid.

Rotate a shape about a given centre through a stated angle and direction.

Translate a shape using a column vector.

Enlarge a shape from a centre of enlargement using a positive scale factor.

Describe a single transformation that maps one shape onto another.

Determine whether two shapes are congruent.

Use a linear scale factor to calculate missing lengths in similar shapes.

Use the midpoint formula to find the midpoint of a line segment on a coordinate grid.

Classify data as categorical, discrete, or continuous.

Organise raw data in a frequency table with suitable class intervals when needed.

Calculate the mean, median, mode, and range of an ungrouped data set.

Calculate the mean from a frequency table.

Construct and interpret bar charts and pie charts.

Construct and interpret stem-and-leaf diagrams.

Construct and interpret scatter graphs, including describing correlation.

Compare two data sets using appropriate averages and measures of spread.

Place probabilities on the probability scale from impossible to certain.

Calculate the probability of a single event from equally likely outcomes.

List all outcomes of two-stage experiments using a sample space diagram.

Use the fact that probabilities of mutually exclusive exhaustive outcomes sum to 1.

Estimate probability from experimental relative frequency.

Calculate probabilities of combined events using tables or tree diagrams.

Translate a multi-step mathematical word problem into an ordered sequence of calculations and check whether the result is reasonable.