UK maths curriculum: Years 1 to 11
Browse all 389 mathematics curriculum references for maintained schools in England: the 227 statutory Year 1-6 requirements, the 65 Key Stage 3 subject-content requirements (Years 7-9) and the 97 GCSE subject-content items (Years 10-11). Each reference shows the DfE wording and the ChalkBee worksheets and teaching units that can support it. A resource link means relevant support is available; it does not claim that one worksheet covers every clause in a requirement.
Looking for primary English?
Browse all 113 top-level statutory English requirements, including nested clauses and honestly matched worksheets and teaching units.
About the reference IDs
The DfE does not publish alphanumeric codes for the primary or Key Stage 3 statements. IDs such as uk-ks2-y3-ma-npv-01 and uk-ks3-ma-alg-04 are stable ChalkBee references, not official curriculum codes. GCSE items ARE numbered in the DfE subject content; codes like N4 or A22 follow the domain-letter convention the awarding bodies (AQA, Edexcel, OCR) use for those same item numbers.
Statutory wording: DfE programme of study. List structure cross-checked against the official primary mathematics PDF. Crown copyright information is reproduced under the Open Government Licence v3.0.
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Year 1
Key Stage 1 · 20 requirementsNumber - number and place value
count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given numberWorksheets + unitcount, read and write numbers to 100 in numerals; count in multiples of 2s, 5s and 10sWorksheets + unitgiven a number, identify 1 more and 1 lessWorksheets + unitidentify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, leastWorksheets + unitread and write numbers from 1 to 20 in numerals and wordsWorksheets + unit
Number - addition and subtraction
read, write and interpret mathematical statements involving addition (+), subtraction (−) and equals (=) signsWorksheets + unitrepresent and use number bonds and related subtraction facts within 20Worksheets + unitadd and subtract one-digit and two-digit numbers to 20, including 0Worksheets + unitsolve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ? − 9Worksheets + unit
Number - multiplication and division
Number - fractions
Measurement
compare, describe and solve practical problems for:Worksheets + unitmeasure and begin to record the following:Worksheets + unitrecognise and know the value of different denominations of coins and notesWorksheets + unitsequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening]Worksheets + unitrecognise and use language relating to dates, including days of the week, weeks, months and yearsWorksheets + unittell the time to the hour and half past the hour and draw the hands on a clock face to show these timesWorksheets + unit
Geometry - properties of shapes
Geometry - position and direction
Year 2
Key Stage 1 · 34 requirementsNumber - number and place value
count in steps of 2, 3, and 5 from 0, and in 10s from any number, forward and backwardWorksheets + unitrecognise the place value of each digit in a two-digit number (10s, 1s)Worksheets + unitidentify, represent and estimate numbers using different representations, including the number lineWorksheets + unitcompare and order numbers from 0 up to 100; use <, > and = signsWorksheets + unitread and write numbers to at least 100 in numerals and in wordsWorksheets + unituse place value and number facts to solve problemsWorksheets + unit
Number - addition and subtraction
solve problems with addition and subtraction:Worksheets + unitrecall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100Worksheets + unitadd and subtract numbers using concrete objects, pictorial representations, and mentally, including:Worksheets + unitshow that addition of 2 numbers can be done in any order (commutative) and subtraction of 1 number from another cannotWorksheets + unitrecognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problemsWorksheets + unit
Number - multiplication and division
recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbersWorksheets + unitcalculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signsWorksheets + unitshow that multiplication of 2 numbers can be done in any order (commutative) and division of 1 number by another cannotWorksheets + unitsolve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contextsWorksheets + unit
Number - fractions
Measurement
choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vesselsWorksheets + unitcompare and order lengths, mass, volume/capacity and record the results using >, < and =Worksheets + unitrecognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular valueWorksheets + unitfind different combinations of coins that equal the same amounts of moneyWorksheets + unitsolve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving changeWorksheets + unitcompare and sequence intervals of timeWorksheets + unittell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these timesWorksheets + unitknow the number of minutes in an hour and the number of hours in a dayWorksheets + unit
Geometry - properties of shapes
identify and describe the properties of 2-D shapes, including the number of sides, and line symmetry in a vertical lineWorksheets + unitidentify and describe the properties of 3-D shapes, including the number of edges, vertices and facesWorksheets + unitidentify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]Worksheets + unitcompare and sort common 2-D and 3-D shapes and everyday objectsWorksheets + unit
Geometry - position and direction
order and arrange combinations of mathematical objects in patterns and sequencesWorksheets + unituse mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise)Worksheets + unit
Statistics
interpret and construct simple pictograms, tally charts, block diagrams and tablesWorksheets + unitask and answer simple questions by counting the number of objects in each category and sorting the categories by quantityWorksheets + unitask-and-answer questions about totalling and comparing categorical dataWorksheets + unit
Year 3
Key Stage 2 · 33 requirementsNumber - number and place value
count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given numberWorksheets + unitrecognise the place value of each digit in a 3-digit number (100s, 10s, 1s)Worksheets + unitcompare and order numbers up to 1,000Worksheets + unitidentify, represent and estimate numbers using different representationsWorksheets + unitread and write numbers up to 1,000 in numerals and in wordsWorksheets + unitsolve number problems and practical problems involving these ideasWorksheets + unit
Number - addition and subtraction
add and subtract numbers mentally, including:Worksheets + unitadd and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtractionWorksheets + unitestimate the answer to a calculation and use inverse operations to check answersWorksheets + unitsolve problems, including missing number problems, using number facts, place value, and more complex addition and subtractionWorksheets + unit
Number - multiplication and division
recall and use multiplication and division facts for the 3, 4 and 8 multiplication tablesWorksheets + unitwrite and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methodsWorksheets + unitsolve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objectsWorksheets + unit
Number - fractions
count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10Worksheets + unitrecognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominatorsWorksheets + unitrecognise and use fractions as numbers: unit fractions and non-unit fractions with small denominatorsWorksheets + unitrecognise and show, using diagrams, equivalent fractions with small denominatorsWorksheets + unitadd and subtract fractions with the same denominator within one whole [for example, 5/7+1/7 = 6/7]Worksheets + unitcompare and order unit fractions, and fractions with the same denominatorsWorksheets + unitsolve problems that involve all of the aboveWorksheets + unit
Measurement
measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)Worksheets + unitmeasure the perimeter of simple 2-D shapesWorksheets + unitadd and subtract amounts of money to give change, using both £ and p in practical contextsWorksheets + unittell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocksWorksheets + unitestimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o’clock, am/pm, morning, afternoon, noon and midnightWorksheets + unitknow the number of seconds in a minute and the number of days in each month, year and leap yearWorksheets + unitcompare durations of events [for example, to calculate the time taken by particular events or tasks]Worksheets + unit
Geometry - properties of shapes
draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe themWorksheets + unitrecognise angles as a property of shape or a description of a turnWorksheets + unitidentify right angles, recognise that 2 right angles make a half-turn, 3 make three-quarters of a turn and 4 a complete turn; identify whether angles are greater than or less than a right angleWorksheets + unitidentify horizontal and vertical lines and pairs of perpendicular and parallel linesWorksheets + unit
Year 4
Key Stage 2 · 42 requirementsNumber - number and place value
count in multiples of 6, 7, 9, 25 and 1,000Worksheets + unitfind 1,000 more or less than a given numberWorksheets + unitcount backwards through 0 to include negative numbersWorksheets + unitrecognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s)Worksheets + unitorder and compare numbers beyond 1,000Worksheets + unitidentify, represent and estimate numbers using different representationsWorksheets + unitround any number to the nearest 10, 100 or 1,000Worksheets + unitsolve number and practical problems that involve all of the above and with increasingly large positive numbersWorksheets + unitread Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of 0 and place valueWorksheets + unit
Number - addition and subtraction
add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriateWorksheets + unitestimate and use inverse operations to check answers to a calculationWorksheets + unitsolve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and whyWorksheets + unit
Number - multiplication and division
recall multiplication and division facts for multiplication tables up to 12 × 12Worksheets + unituse place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbersWorksheets + unitrecognise and use factor pairs and commutativity in mental calculationsWorksheets + unitmultiply two-digit and three-digit numbers by a one-digit number using formal written layoutWorksheets + unitsolve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objectsWorksheets + unit
Number - fractions (including decimals)
recognise and show, using diagrams, families of common equivalent fractionsWorksheets + unitcount up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10Worksheets + unitsolve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole numberWorksheets + unitadd and subtract fractions with the same denominatorWorksheets + unitrecognise and write decimal equivalents of any number of tenths or hundredsWorksheets + unitrecognise and write decimal equivalents to 1/4, 1/2, 3/4Worksheets + unitfind the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredthsWorksheets + unitround decimals with 1 decimal place to the nearest whole numberWorksheets + unitcompare numbers with the same number of decimal places up to 2 decimal placesWorksheets + unitsolve simple measure and money problems involving fractions and decimals to 2 decimal placesWorksheets + unit
Measurement
convert between different units of measure [for example, kilometre to metre; hour to minute]Worksheets + unitmeasure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metresWorksheets + unitfind the area of rectilinear shapes by counting squaresWorksheets + unitestimate, compare and calculate different measures, including money in pounds and penceWorksheets + unitread, write and convert time between analogue and digital 12- and 24-hour clocksWorksheets + unitsolve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to daysWorksheets + unit
Geometry - properties of shapes
compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizesWorksheets + unitidentify acute and obtuse angles and compare and order angles up to 2 right angles by sizeWorksheets + unitidentify lines of symmetry in 2-D shapes presented in different orientationsWorksheets + unitcomplete a simple symmetric figure with respect to a specific line of symmetryWorksheets + unit
Geometry - position and direction
Year 5
Key Stage 2 · 49 requirementsNumber - number and place value
read, write, order and compare numbers to at least 1,000,000 and determine the value of each digitWorksheets + unitcount forwards or backwards in steps of powers of 10 for any given number up to 1,000,000Worksheets + unitinterpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 0Worksheets + unitround any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000Worksheets + unitsolve number problems and practical problems that involve all of the aboveWorksheets + unitread Roman numerals to 1,000 (M) and recognise years written in Roman numeralsWorksheets + unit
Number - addition and subtraction
add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)Worksheets + unitadd and subtract numbers mentally with increasingly large numbersWorksheets + unituse rounding to check answers to calculations and determine, in the context of a problem, levels of accuracyWorksheets + unitsolve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and whyWorksheets + unit
Number - multiplication and division
identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbersWorksheets + unitknow and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbersWorksheets + unitestablish whether a number up to 100 is prime and recall prime numbers up to 19Worksheets + unitmultiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbersWorksheets + unitmultiply and divide numbers mentally, drawing upon known factsWorksheets + unitdivide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the contextWorksheets + unitmultiply and divide whole numbers and those involving decimals by 10, 100 and 1,000Worksheets + unitrecognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)Worksheets + unitsolve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubesWorksheets + unitsolve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals signWorksheets + unitsolve problems involving multiplication and division, including scaling by simple fractions and problems involving simple ratesWorksheets + unit
Number - fractions (including decimals and percentages)
compare and order fractions whose denominators are all multiples of the same numberWorksheets + unitidentify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredthsWorksheets + unitrecognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5+4/5 = 6/5 = 1 1/5 ]Worksheets + unitadd and subtract fractions with the same denominator, and denominators that are multiples of the same numberWorksheets + unitmultiply proper fractions and mixed numbers by whole numbers, supported by materials and diagramsWorksheets + unitread and write decimal numbers as fractions [for example, 0.71 = 71/100 ]Worksheets + unitrecognise and use thousandths and relate them to tenths, hundredths and decimal equivalentsWorksheets + unitround decimals with 2 decimal places to the nearest whole number and to 1 decimal placeWorksheets + unitread, write, order and compare numbers with up to 3 decimal placesWorksheets + unitsolve problems involving number up to 3 decimal placesWorksheets + unitrecognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, and as a decimal fractionWorksheets + unitsolve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25Worksheets + unit
Measurement
convert between different units of metric measure [for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre]Worksheets + unitunderstand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pintsWorksheets + unitmeasure and calculate the perimeter of composite rectilinear shapes in centimetres and metresWorksheets + unitcalculate and compare the area of rectangles (including squares), including using standard units, square centimetres (cm²) and square metres (m²), and estimate the area of irregular shapesWorksheets + unitestimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]Worksheets + unitsolve problems involving converting between units of timeWorksheets + unituse all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scalingWorksheets + unit
Geometry - properties of shapes
identify 3-D shapes, including cubes and other cuboids, from 2-D representationsWorksheets + unitknow angles are measured in degrees: estimate and compare acute, obtuse and reflex anglesWorksheets + unitdraw given angles, and measure them in degrees (°)Worksheets + unitidentify:Worksheets + unituse the properties of rectangles to deduce related facts and find missing lengths and anglesWorksheets + unitdistinguish between regular and irregular polygons based on reasoning about equal sides and anglesWorksheets + unit
Geometry - position and direction
Year 6
Key Stage 2 · 49 requirementsNumber - number and place value
read, write, order and compare numbers up to 10,000,000 and determine the value of each digitWorksheets + unitround any whole number to a required degree of accuracyWorksheets + unituse negative numbers in context, and calculate intervals across 0Worksheets + unitsolve number and practical problems that involve all of the aboveWorksheets + unit
Number - addition, subtraction, multiplication and division
multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplicationWorksheets + unitdivide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the contextWorksheets + unitdivide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the contextWorksheets + unitperform mental calculations, including with mixed operations and large numbersWorksheets + unitidentify common factors, common multiples and prime numbersWorksheets + unituse their knowledge of the order of operations to carry out calculations involving the 4 operationsWorksheets + unitsolve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and whyWorksheets + unitsolve problems involving addition, subtraction, multiplication and divisionWorksheets + unituse estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracyWorksheets + unit
Number - Fractions (including decimals and percentages)
use common factors to simplify fractions; use common multiples to express fractions in the same denominationWorksheets + unitcompare and order fractions, including fractions >1Worksheets + unitadd and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractionsWorksheets + unitmultiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 × 1/2 = 1/8]Worksheets + unitdivide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6]Worksheets + unitassociate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8]Worksheets + unitidentify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal placesWorksheets + unitmultiply one-digit numbers with up to 2 decimal places by whole numbersWorksheets + unituse written division methods in cases where the answer has up to 2 decimal placesWorksheets + unitsolve problems which require answers to be rounded to specified degrees of accuracyWorksheets + unitrecall and use equivalences between simple fractions, decimals and percentages, including in different contextsWorksheets + unit
Ratio and proportion
solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division factsWorksheets + unitsolve problems involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparisonWorksheets + unitsolve problems involving similar shapes where the scale factor is known or can be foundWorksheets + unitsolve problems involving unequal sharing and grouping using knowledge of fractions and multiplesWorksheets + unit
Algebra
use simple formulaeWorksheets + unitgenerate and describe linear number sequencesWorksheets + unitexpress missing number problems algebraicallyWorksheets + unitfind pairs of numbers that satisfy an equation with 2 unknownsWorksheets + unitenumerate possibilities of combinations of 2 variablesWorksheets + unit
Measurement
solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriateWorksheets + unituse, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to 3 decimal placesWorksheets + unitconvert between miles and kilometresWorksheets + unitrecognise that shapes with the same areas can have different perimeters and vice versaWorksheets + unitrecognise when it is possible to use formulae for area and volume of shapesWorksheets + unitcalculate the area of parallelograms and trianglesWorksheets + unitcalculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³]Worksheets + unit
Geometry - properties of shapes
draw 2-D shapes using given dimensions and anglesWorksheets + unitrecognise, describe and build simple 3-D shapes, including making netsWorksheets + unitcompare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygonsWorksheets + unitillustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radiusWorksheets + unitrecognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing anglesWorksheets + unit
Geometry - position and direction
Key Stage 3 (Years 7-9)
65 subject-content requirementsThe KS3 programme of study covers Years 7-9 as one key stage: the DfE does not allocate its bullets to individual years, so each reference here spans the whole key stage. The six subject-content areas below are the itemised statutory list; the programme's “Working mathematically” section (develop fluency, reason mathematically, solve problems) is cross-cutting process guidance applied through all of them rather than a separate list of codes.
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Number
understand and use place value for decimals, measures and integers of any sizeUnit onlyorder positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥Worksheets + unituse the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation propertyWorksheets + unituse the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negativeWorksheets + unituse conventional notation for the priority of operations, including brackets, powers, roots and reciprocalsResource gaprecognise and use relationships between operations including inverse operationsResource gapuse 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 approximationsWorksheets + unitinterpret and compare numbers in standard form A × 10^n, 1 ≤ A < 10, where n is a positive or negative integer or 0Worksheets + unitwork interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)Worksheets + unitdefine percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%Worksheets + unitinterpret fractions and percentages as operatorsWorksheets + unituse standard units of mass, length, time, money and other measures, including with decimal quantitiesWorksheets + unitround numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]Worksheets + unituse approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ bWorksheets + unituse a calculator and other technologies to calculate results accurately and then interpret them appropriatelyResource gapappreciate the infinite nature of the sets of integers, real and rational numbersResource gap
Algebra
use and interpret algebraic notation, including:Worksheets + unitsubstitute numerical values into formulae and expressions, including scientific formulaeWorksheets + unitunderstand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factorsWorksheets + unitsimplify and manipulate algebraic expressions to maintain equivalence by:Worksheets + unitunderstand and use standard mathematical formulae; rearrange formulae to change the subjectWorksheets + unitmodel situations or procedures by translating them into algebraic expressions or formulae and by using graphsUnit onlyuse algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement)Worksheets + unitwork with coordinates in all 4 quadrantsWorksheets + unitrecognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian planeWorksheets + unitinterpret mathematical relationships both algebraically and graphicallyUnit onlyreduce a given linear equation in 2 variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraicallyWorksheets + unituse 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 equationsWorksheets + unitfind approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphsResource gapgenerate terms of a sequence from either a term-to-term or a position-to-term ruleWorksheets + unitrecognise arithmetic sequences and find the nth termWorksheets + unitrecognise geometric sequences and appreciate other sequences that ariseWorksheets + unit
Ratio, proportion and rates of change
change freely between related standard units [for example time, length, area, volume/capacity, mass]Worksheets + unituse scale factors, scale diagrams and mapsWorksheets + unitexpress 1 quantity as a fraction of another, where the fraction is less than 1 and greater than 1Worksheets + unituse ratio notation, including reduction to simplest formWorksheets + unitdivide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into 2 parts as a ratioWorksheets + unitunderstand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fractionWorksheets + unitrelate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functionsWorksheets + unitsolve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematicsWorksheets + unitsolve problems involving direct and inverse proportion, including graphical and algebraic representationsWorksheets + unituse compound units such as speed, unit pricing and density to solve problemsWorksheets + unit
Geometry and measures
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)Worksheets + unitcalculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapesWorksheets + unitdraw and measure line segments and angles in geometric figures, including interpreting scale drawingsWorksheets + unitderive 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 lineResource gapdescribe, 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 symmetricWorksheets + unituse the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of trianglesWorksheets + unitderive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologiesWorksheets + unitidentify properties of, and describe the results of, translations, rotations and reflections applied to given figuresWorksheets + unitidentify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate gridsWorksheets + unitapply the properties of angles at a point, angles at a point on a straight line, vertically opposite anglesWorksheets + unitunderstand and use the relationship between parallel lines and alternate and corresponding anglesWorksheets + unitderive 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 polygonsWorksheets + unitapply 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 proofsWorksheets + unituse Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled trianglesWorksheets + unituse the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-DWorksheets + unitinterpret mathematical relationships both algebraically and geometricallyResource gap
Probability
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 scaleWorksheets + unitunderstand that the probabilities of all possible outcomes sum to 1Worksheets + unitenumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagramsWorksheets + unitgenerate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilitiesWorksheets + unit
Statistics
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)Worksheets + unitconstruct 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 dataWorksheets + unitdescribe simple mathematical relationships between 2 variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphsWorksheets + unit
GCSE mathematics (Key Stage 4, Years 10-11)
97 subject-content itemsThe GCSE subject content (DfE, reference DFE-00233-2013) numbers its items within each domain; the codes below (N1-N16, A1-A25, R1-R16, G1-G25, P1-P9, S1-S6) are those DfE item numbers in the domain-letter form every awarding body uses. Foundation and Higher tier are distinguished by type:
- StandardStandard type: all students will develop confidence and competence with this content.
- UnderlinedUnderlined type: all students will be assessed on this content; more highly attaining students will develop confidence and competence with all of it.
- Bold: Higher tierBold type: only the more highly attaining students (Higher tier) will be assessed on this content.
Standard plus underlined type is the full Foundation tier. ChalkBee GCSE resources are Foundation-first, so bold (Higher-only) items are mostly honest gaps for now. Source: GCSE mathematics subject content and assessment objectives, Crown copyright, reproduced under the Open Government Licence v3.0.
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GCSE items
Number
N1order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, >, ≤, ≥StandardWorksheets + unitN2apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative; understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals)StandardWorksheets + unitN3recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions); use conventional notation for priority of operations, including brackets, powers, roots and reciprocalsStandardResource gapN4use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theoremStandardWorksheets + unitN5apply systematic listing strategies including use of the product rule for countingStandardWorksheets + unitN6use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5; estimate powers and roots of any given positive numberStandardWorksheets + unitN7calculate with roots, and with integer and fractional indicesUnderlinedWorksheets + unitN8calculate exactly with fractions, surds and multiples of π; simplify surd expressions involving squares (e.g. √12 = √(4 × 3) = √4 × √3 = 2√3) and rationalise denominatorsStandardWorksheets + unitN9calculate with and interpret standard form A × 10^n, where 1 ≤ A < 10 and n is an integerStandardWorksheets + unitN10work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 or 3/8); change recurring decimals into their corresponding fractions and vice versaStandardWorksheets + unitN11identify and work with fractions in ratio problemsStandardWorksheets + unitN12interpret fractions and percentages as operatorsStandardWorksheets + unitN13use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriateStandardWorksheets + unitN14estimate answers; check calculations using approximation and estimation, including answers obtained using technologyStandardWorksheets + unitN15round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or roundingStandardWorksheets + unitN16apply and interpret limits of accuracy, including upper and lower boundsUnderlinedWorksheets + unitAlgebra
A1use and interpret algebraic notation, including:StandardWorksheets + unitA2substitute numerical values into formulae and expressions, including scientific formulaeStandardWorksheets + unitA3understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factorsStandardWorksheets + unitA4simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by:StandardWorksheets + unitA5understand and use standard mathematical formulae; rearrange formulae to change the subjectStandardWorksheets + unitA6know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofsUnderlinedResource gapA7where appropriate, interpret simple expressions as functions with inputs and outputs; interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’StandardUnit onlyA8work with coordinates in all four quadrantsStandardWorksheets + unitA9plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel and perpendicular lines; find the equation of the line through two given points, or through one point with a given gradientStandardWorksheets + unitA10identify and interpret gradients and intercepts of linear functions graphically and algebraicallyStandardWorksheets + unitA11identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the squareUnderlinedWorksheets + unitA12recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1/x with x ≠ 0, exponential functions y = k^x for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any sizeStandardWorksheets + unitA13sketch translations and reflections of a given functionBold: Higher tierResource gapA14plot and interpret graphs (including reciprocal graphs and exponential graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and accelerationStandardWorksheets + unitA15calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contextsBold: Higher tierResource gapA16recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given pointBold: Higher tierResource gapA17solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graphStandardWorksheets + unitA18solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula; find approximate solutions using a graphUnderlinedUnit onlyA19solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically; find approximate solutions using a graphUnderlinedWorksheets + unitA20find approximate solutions to equations numerically using iterationBold: Higher tierResource gapA21translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solutionUnderlinedUnit onlyA22solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable; represent the solution set on a number line, using set notation and on a graphUnderlinedWorksheets + unitA23generate terms of a sequence from either a term-to-term or a position-to-term ruleStandardWorksheets + unitA24recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (r^n where n is an integer, and r is a rational number > 0 or a surd) and other sequencesStandardWorksheets + unitA25deduce expressions to calculate the nth term of linear and quadratic sequencesStandardWorksheets + unitRatio, proportion and rates of change
R1change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contextsStandardWorksheets + unitR2use scale factors, scale diagrams and mapsStandardWorksheets + unitR3express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1StandardWorksheets + unitR4use ratio notation, including reduction to simplest formStandardWorksheets + unitR5divide 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; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)StandardWorksheets + unitR6express a multiplicative relationship between two quantities as a ratio or a fractionStandardWorksheets + unitR7understand and use proportion as equality of ratiosStandardWorksheets + unitR8relate ratios to fractions and to linear functionsStandardWorksheets + unitR9define percentage as ‘number of parts per hundred’; interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively; express one quantity as a percentage of another; compare two quantities using percentages; work with percentages greater than 100%; solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematicsStandardWorksheets + unitR10solve problems involving direct and inverse proportion, including graphical and algebraic representationsStandardWorksheets + unitR11use compound units such as speed, rates of pay, unit pricing, density and pressureStandardWorksheets + unitR12compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factorsStandardWorksheets + unitR13understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y; construct and interpret equations that describe direct and inverse proportionUnderlinedWorksheets + unitR14interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportionUnderlinedWorksheets + unitR15interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contextsBold: Higher tierResource gapR16set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processesUnderlinedWorksheets + unitGeometry and measures
G1use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries; use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written descriptionStandardWorksheets + unitG2use 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); use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the lineUnderlinedResource gapG3apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)StandardWorksheets + unitG4derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate languageStandardWorksheets + unitG5use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)UnderlinedWorksheets + unitG6apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofsUnderlinedWorksheets + unitG7identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors)StandardWorksheets + unitG8describe the changes and invariance achieved by combinations of rotations, reflections and translationsBold: Higher tierResource gapG9identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segmentStandardWorksheets + unitG10apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related resultsBold: Higher tierResource gapG11solve geometrical problems on coordinate axesStandardUnit onlyG12identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheresStandardWorksheets + unitG13construct and interpret plans and elevations of 3D shapesStandardWorksheets + unitG14use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)StandardWorksheets + unitG15measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearingsStandardWorksheets + unitG16know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders)StandardWorksheets + unitG17know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr²; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes; surface area and volume of spheres, pyramids, cones and composite solidsStandardWorksheets + unitG18calculate arc lengths, angles and areas of sectors of circlesUnderlinedWorksheets + unitG19apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figuresUnderlinedWorksheets + unitG20know the formulae for: Pythagoras’ theorem, a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figuresUnderlinedWorksheets + unitG21know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°UnderlinedWorksheets + unitG22know and apply the sine rule, a/sin A = b/sin B = c/sin C, and cosine rule, a² = b² + c² − 2bc cos A, to find unknown lengths and anglesBold: Higher tierResource gapG23know and apply Area = 1/2 ab sin C to calculate the area, sides or angles of any triangleBold: Higher tierResource gapG24describe translations as 2D vectorsStandardWorksheets + unitG25apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; use vectors to construct geometric arguments and proofsUnderlinedWorksheets + unitProbability
P1record describe and analyse the frequency of outcomes of probability experiments using tables and frequency treesStandardWorksheets + unitP2apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experimentsStandardResource gapP3relate relative expected frequencies to theoretical probability, using appropriate language and the 0 - 1 probability scaleStandardWorksheets + unitP4apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to oneStandardWorksheets + unitP5understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample sizeUnderlinedResource gapP6enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagramsStandardWorksheets + unitP7construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilitiesStandardWorksheets + unitP8calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptionsUnderlinedUnit onlyP9calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagramsBold: Higher tierResource gapStatistics
S1infer properties of populations or distributions from a sample, whilst knowing the limitations of samplingUnderlinedUnit onlyS2interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate useStandardWorksheets + unitS3construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate useBold: Higher tierResource gapS4interpret, analyse and compare the distributions of data sets from univariate empirical distributions through:StandardWorksheets + unitS5apply statistics to describe a populationStandardResource gapS6use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doingStandardWorksheets + unit