Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations Use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations

Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs Use standard units of mass, length, time, money and other measures, including with decimal quantities Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams

Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs. Use a calculator and other technologies to calculate results accurately and then interpret them appropriately

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8) Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric Derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors Reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraicallyUse algebraic methods to solve linear equations in one variable (including all forms that require rearrangement) Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities. Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data