This is what children aged 10 to 11 in year 7, should know for Maths, key stage 3.
Strand  Ref  Know how to 

NUMBER  7N1  Understand and use place value for decimals, measures and integers of any size 
7N2  Order positive and negative integers, decimals and fractions; 

7N3  Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor (HCF), lowest common multiple(LCM), prime factorisation, including using product notation and the unique factorisation property 

7N4  Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative 

7N5  Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals 

7N6  Recognise and use relationships between operations including inverse operations 

7N7  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 

7N8  Interpret and compare numbers in standard form A × 10^{n} 1 ≤ A < 10, where n is a positive or negative integer or zero 

7N9  Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and ⅜) 

7N10  Define percentage as 'number of parts per hundred', interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100% 

7N11  Interpret fractions and percentages as operators 

7N12  Use standard units of mass, length, time, money and other measures, including with decimal quantities 

7N13  Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures] 

7N14  Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b 

7N15  Use a calculator and other technologies to calculate results accurately and then interpret them appropriately 

7N16  appreciate the infinite nature of the sets of integers, real and rational numbers 

ALGEBRA  7A1  Use and interpret algebraic notation, including:

7A2  Substitute numerical values into formulae and expressions, including scientific formulae 

7A3  Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors 

7A4  Simplify and manipulate algebraic expressions to maintain equivalence by:


7A5  Understand and use standard mathematical formulae; rearrange formulae to change the subject 

7A6  Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs 

7A7  Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement) 

7A8  Work with coordinates in all four quadrants 

7A9  Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane 

7A10  Interpret mathematical relationships both algebraically and graphically 

7A11  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 algebraically 

7A12  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 

7A13  Find approximate solutions to contextual problems from given graphs of a variety of functions, including piecewise linear, exponential and reciprocal graphs 

7A14  Generate terms of a sequence from either a termtoterm or a positiontoterm rule 

7A15  Recognise arithmetic sequences and find the nth term 

7A16  Recognise geometric sequences and appreciate other sequences that arise. 

Ratio, proportion and rates of change  7R1  Change freely between related standard units [for example time, length, area, volume/capacity, mass] 
7R2  Use scale factors, scale diagrams and maps 

7R3  Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1 

7R4  Use ratio notation, including reduction to simplest form 

7R5  Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio 

7R6  Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction 

7R  Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions 

7R8  Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics 

7R9  Solve problems involving direct and inverse proportion, including graphical and algebraic representations 

7R10  use compound units such as speed, unit pricing and density to solve problems. 
Strand  Ref  Know how to 

Geometry and measures  7G1  Derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders) 
7G2  Calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes 

7G3  Draw and measure line segments and angles in geometric figures, including interpreting scale drawings 

7G4  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 

7G5  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 

7G6  Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles 

7G7  Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies 

7G8  Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures 

7G9  Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids 

7G10  Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles 

7G11  Understand and use the relationship between parallel lines and alternate and corresponding angles 

7G12  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 

7G13  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 

7G14  Use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving rightangled triangles 

7G15  Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D 

7G16  Interpret mathematical relationships both algebraically and geometrically. 

PROBABILITY  7P1  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 01 probability scale 
7P2  Understand that the probabilities of all possible outcomes sum to 1 

7P3  Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams 

7P4  Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities 

STATISTICS  7S1  Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers) 
7S2  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 

7S3  Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs 