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Positive and Negative Numbers
Addition & Subtraction
Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances
Properties of triangles and quadrilaterals
Geometry
Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths
Proportion Graphs
Ratio & Proportion
Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin when graphed
Proportional Reasoning Vocabulary
Ratio & Proportion
Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts
Ratio (age 11+)
Multiplication & Division
Use conventional notation for the priority of operations including brackets, powers, roots, and reciprocals; apply BIDMAS/BODMAS consistently to evaluate complex numerical expressions
Ratio Notation
Ratio & Proportion
Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations
Scale and similar shapes (age 11+)
Ratio & Proportion
Use scale factors to interpret and create scale diagrams and maps, calculating real-life distances from map measurements and vice versa
Sign Rules for Multiplication
Multiplication & Division
Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient
Solving Linear Equations
Algebra
Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients
Square and cube numbers
Number Representation & Place Value
Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations
Substituting into Formulae
Algebra
Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations
The Probability Scale
Probability
Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible
Types of angles (age 11+)
Geometry
Use conventional geometric terms and notation to describe, sketch, and draw points, lines, parallel and perpendicular lines, right angles, regular polygons, and reflectively/rotationally symmetric polygons
Understanding angles (age 11+)
Geometry
Apply the properties of angles at a point (360°), on a straight line (180°), and vertically opposite angles to find unknown angles in multi-step problems
Unit Conversions
Ratio & Proportion
Convert freely between related standard units of measurement (time, length, area, volume/capacity, mass) using decimal notation to up to three decimal places where appropriate
Using inverse operations
Multiplication & Division
Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations
Angles in triangles (age 12+)
Geometry
Know and use the criteria for triangle congruence (SSS, SAS, ASA, RHS), use standard labelling conventions for sides and angles of triangle ABC, and determine whether two triangles are congruent
Angles with parallel lines
Geometry
Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles
Circles: Circumference & Area
Geometry
Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts
Coordinates (age 12+)
Geometry
Understand similarity as a relationship where one shape is an enlargement of another; construct similar shapes by enlargement with a given scale factor and centre, with and without coordinate grids
Estimating by rounding
Number Representation & Place Value
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b; understand upper and lower bounds of rounded values
Factorising Expressions
Algebra
Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)
Linear Function Graphs
Algebra
Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context
Nth-Term Rules
Algebra
Find the nth-term expression for an arithmetic sequence by identifying the common difference and the zero-term, and use it to determine any term in the sequence or test whether a given number belongs to the sequence