Simplify fractions by cancelling all common factors; identify equivalent fractions

Recognise the equivalence of percentages, fractions and decimals

Extend mental methods of calculation to include decimals, fractions and percentages

Multiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by single-digit whole numbers

Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations and methods

Check a result by considering whether it is of the right order of magnitude

Use letter symbols to represent unknown numbers or variables

Know and use the order of operations and understand that algebraic operations follow the same conventions and order as arithmetic operations

Plot the graphs of simple linear functions

Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle

Convert one metric unit to another (e.g. grams to kilograms); read and interpret scales on a range of measuring instruments

Compare two simple distributions using the range and one of the mode, median or mean

Understand and use the probability scale from 0 to 1; find and justify probabilities based on equally likely outcomes in simple contexts

Solve word problems and investigate in a range of contexts, explaining and justifying methods and conclusions

Add, subtract, multiply and divide integers

Use the equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and find the outcome of a given percentage increase or decrease

Divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion

Use standard column procedures for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations

Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket

Substitute integers into simple formulae

Plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of the form y = mx + c correspond to straight-line graphs

Identify alternate and corresponding angles; understand a proof that the sum of the angles of a triangle is 180° and of a quadrilateral is 360°

Enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor

Use straight edge and compasses to do standard constructions

Deduce and use formulae for the area of a triangle and parallelogram, and the volume of a cuboid; calculate volumes and surface areas of cuboids

Construct, on paper and using ICT, a range of graphs and charts; identify which are most useful in the context of a problem

Find and record all possible mutually exclusive outcomes for single events and two successive events in a systematic way

Identify the necessary information to solve a problem; represent problems and interpret solutions in algebraic, geometric or graphical form

Use logical argument to establish the truth of a statement

Add, subtract, multiply and divide fractions

Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole

Make and justify estimates and approximations of calculations

Construct and solve linear equations with integer coefficients, using an appropriate method

Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence, on paper and using ICT; write an expression to describe the nth term of an arithmetic sequence

Given values for m and c, find the gradient of lines given by equations of the form y = mx + c

Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations

Solve geometrical problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons

Know that translations, rotations and reflections preserve length and angle and map objects on to congruent images

Know and use the formulae for the circumference and area of a circle

Design a survey or experiment to capture the necessary data from one or more sources; determine the sample size and degree of accuracy needed; design, trial and if necessary refine data collection sheets

Communicate interpretations and results of a statistical enquiry using selected tables, graphs and diagrams in support

Know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems

Solve substantial problems by breaking them into simpler tasks, using a range of efficient techniques, methods and resources, including ICT; give solutions to an appropriate degree of accuracy

Present a concise, reasoned argument, using symbols, diagrams, graphs and related explanatory text.

Using and applying handling data

Specifying the problem and planning

Collecting data

Processing and representing data

Interpreting and discussing results

Using and applying number and algebra

Numbers and the number system

Calculations

Solving numerical problems

Equations, formulae and identities

Sequences, functions and graphs

Using and applying shape, space and measure

Geometrical reasoning

Transformations and coordinates

Measures and constructions