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Maths Progression Map
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Declarative knowledge Procedural knowledgeConditional knowledge
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"I know that...""I know how...""I know when..."
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NurseryReceptionYear 1Year 2Year 3Year 4 Year 5Year 6KS3
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Conservation of number Link numerals and amounts: e.g. showing the right number of objects/ fingers to match the numeral, up to 5
Through play and exploration, beginning to learn that numbers are made up (composed) of smaller numbers
Spot smaller numbers ‘hiding’ inside
larger numbers
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Subtising Develop fast recognition of up to 3 objects, without having to count them individually (‘subitising’)Continue to develop subitising
skills for numbers within and beyond 5,
and increasingly connect quantities to
numerals
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Number and Place ValueKnow and recite number names, initially to five,
then ten in order.
Know that the last number reached when counting a small set of objects tells you how many there are in total (‘cardinal principle’).		Count from one to twenty, extending to larger numbers, including
crossing boundaries 19/20 and 29/30.
Count from one to ten forward and backward.
Count objects, actions and sounds up to 20.
Count to and across 100 from any number: Count in multiples of twos, fives and tensCount in steps of 2s, 3s and 5s from 0, and steps of ten from any numberCount in multiples of 4, 8, 50 and 100Count in multiples of 6, 7, 9, 25 and 1000; count backwards through zero to include negative numbersInterpret negative numbers in contextUse negative numbers to calculate intervals across zerounderstand and use place value for decimals, measures and integers of any size
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Compare numbers that are far apart, near to and next to each otherSort, order and compare objects and numbers from one to 10. Order numbers from one to 20.Compare numbers and sets of objectsCompare and order numbers up to 100 using the <, > and = symbolsCompare and order numbers up to 1,000Order and compare numbers beyond 1000Read, write, order and compare numbers to at least 1,000,000Read, write, order, compare and round numbers up to 10,000,000
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Knowing that the number does not change if things are rearranged (as long as none have been added or taken away)		Representing objects and one to one correspondence - knowing how to countCount, read and write numbers to 100 in numerals (up to 20 both in numerals and in words)Recognise place value in two-digit numbers Read write numbers to at least 100 in numerals and in words.Recognise the value of each digit in a three-digit number. Recognise the value of each digit in a four-digit number. Read Roman numerals to 1,000, including years
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Begin to generalise the one more than/one less than relationship between sequential numbers Say one more or one less for numbers up to 10
Say one more or one less for numbers up to 20		Identify one more and one lessRecognise their position (2-digit numbers) on a number lineRound any number to the nearest 10, 100 or 1,000Round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000Round any whole number to a required degree of accuracy
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Addition and SubtractionBegin to notice numerals (number symbols).
Experiment with their own symbols and marks as well as numerals.		Add two single-digit numbers
Subtract two single-digit numbers		Read, write and use the mathematical symbols +, – and =Recall and use number addition and subtraction facts to 20 and derive related factsAdd and subtract numbers mentally, including a three-digit number and ones, tens or hundreds interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning
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See' small numbers in a larger collection.
Partition a number of things into two groups and recognise that those two groups can be recombined to make the same total. 		Separate a group in different ways, beginning to recognise that the total is still the same.
Recognise that a whole can be divided into more than 2 parts.
Use number bonds and subtraction facts within 20Add and subtract one and two-digit numbers mentally and using objects Add and subtract numbers with up to three digits using standard column methodAdd and subtract numbers with four digits using the standard column methodAdd and subtract numbers with more than four digits, using formal column methodsSolve addition and subtraction multi-step problems in contexts, deciding which
operations and methods to use and why		use conventional notation for the priority of operations, including brackets recognise and use relationships between the operations +, –, ×, ÷, including inverse operations
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Compare quantities using language: ‘more than’, ‘fewer than’, 'same'. Automatically recall number bonds for numbers 0–5 and some to 10.Add and subtract one-digit and two-digit numbers to 20, including zeroUnderstand and use the inverse relationship between addition and subtraction to check calculations and to solve missing number problems.Understand addition can be done in any order(commutative)and subtraction of one number from another cannot.Estimate answers to calculations and use the inverse to check answersUse rounding to check answers and determine accuracyUse knowledge of the order of operations to carry out calculationsuse approximation, through rounding to the nearest whole number or to one decimal place, to estimate answers
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Multiplication and DivisionDouble and halve numbers up to tenUse concrete objects and pictorial representations to solve multiplication (doubling)Know and use the 2×, 5× and 10× tables, including recognising odd and even numbersTo recall and use multiplication and division facts for the 3, 4 and 8 multiplication tablesKnow multiplication and division facts for tables up to 12 × 12Recognise and use square and cube numbers, and know the notationUse square and cube numbersuse square, cube, square root and cube root
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In everyday situations, take or give two or three objects from a group.
Share amounts between groups		Calculate mathematical statements using the × and ÷ symbolsUse factor pairs and commutativity in mental calculationsIdentify multiples and factors, including finding factor pairs and common factors. Use the vocabulary of prime numbers, prime factors and composite numbers. Know prime numbers up to 19. Identify common factors, common multiples and prime numbersuse and interpret algebraic notation, including:
 ab in place of a × b
 3y in place of y + y + y and 3 × y
 a2 in place of a × a, a3 in place of a × a × a; a2
b in place of a × a × b
 b
a in place of a ÷ b
 coefficients written as fractions rather than as decimals
 brackets
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Multiplying two numbers can be done in any order(commutative)and division of one number by another cannotMultiply and divide numbers by 10, 100 or 1,000, including decimalsMultiply numbers with up to four digits by a two-digit number, using long multiplication
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Multiply two-digit and three-digit numbers by a one-digit number using formal written
layout		Use standard method for multiplication, including long multiplication for multiplying by two digitsMultiply a number with up to two decimal places by whole numbers
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Use concrete objects and pictorial representations to solve division problems (grouping, sharing)Divide three-digit numbers using deriving facts,
(for example 600 ÷ 3 = 200 can be derived from 2 x 3 = 6).		Divide numbers using standard written short divisionDivide numbers using short and long division, interpreting remainders as appropriate
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Shape, Space and MeasuresMake comparisons between objects relating to size, length, weight and capacity.Talk about and compare size, weight, length, capacity, position and distance -Measure and begin to record length, mass and volume Estimate and measure length, mass, temperature and capacity to the nearest appropriate unit and compare and order results using >,<and =.Measure, compare, add and subtract length, mass and volume using standard unitsConvert between different units of metric measurementUnderstand and use common approximate equivalences between metric and imperial units Convert measurements between smaller and larger units of measure, (including miles and km) including decimal notation of up to three decimal places.use standard units of mass, length, time, money and other measures, including with decimal quantities. Change freely between related standard units [for example time, length, area, volume/capacity, mass]
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Identify horizontal, vertical, parallel and perpendicular linesCompare and classify shapes, including quadrilaterals and trianglesMeasure and calculate the perimeter of composite rectilinear shapesCalculate the area of parallelograms and triangles
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Complete a simple symmetric figure with respect to a specific line of symmetryDistinguish between regular and irregular polygonsIllustrate and name the parts of a circle
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Find the area of rectilinear shapes by counting squaresCalculate the area of rectangles and estimate the area of irregular shapesCalculate and compare volume of cubes and cuboids
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Talk about and explore 2D e.g. circles, rectangles, triangles using informal and mathematical language: ‘sides’, ‘corners’; ‘straight’,

Identify and describe everyday 2D shapes. Compose and decompose shapes so that children recognise a shape can have other shapes within it, just as numbers can. Recognise and name common 2D shapesIdentify and describe properties of 2D shapes, including number of sides and symmetryMeasure the perimeter of simple 2D shapesUse the properties of rectangles to find missing lengths and angles
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Talk about and explore 3D shapes e.g. cuboids, using informal and mathematical language: ‘flat’, ‘round’

Identify and describe everyday 3D shapes. Find 2D shapes within 3D shapes. Select, rotate and manipulate shapes to develop spatial reasoning skills.Recognise and name common 3D shapesIdentify and describe properties of 3D shapes, including number of edges, vertices and facesIdentify 3D shapes from 2D representations
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Select shapes appropriately: flat surfaces for building, a triangular prism for a roof, etc.Combine shapes to make new ones – an arch, a bigger triangle, etc.Compare and sort common 2D and 3D shapes and everyday objects. Identify 2D shapes on the surface off 3D shapes
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Identify whether angles are greater than or less than a right angleKnow angles are measured in degrees and compare acute, obtuse and reflex anglesRecognise vertically opposite angles and find missing angles
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Draw and measure angles to the nearest degreeFind unknown angles in triangles, quadrilaterals and regular polygons
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Understand position through words alone – for example, “The bag is under the table,” – with no pointing. Explore how things look from different viewpoints including things that are near and far away. Order and arrange combinations of mathematical objects in patterns and sequences.Describe positions on a 2D grid using coordinates in the first quadrantIdentify angles at a point, in a turn and on a straight lineDescribe positions on the full coordinate grid
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Begins to describe a familiar routeDiscuss routes and locations, using words like ‘in front of’ and ‘behind’.Use mathematical vocabulary to describe position,direction and movement including movement in a straight line and distinguish between rotation as a turn and in terms of right angles for quarter,half, three quarters (clockwise and anti-clockwise.)Describe translations using a given unit to the left/right and up/downDescribe and represent the position of a shape following a reflection or translationTranslate shapes on a coordinate grid and reflect in the axes
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MoneyTalk about and compare amounts of moneyRecognise and know the value of all coins and notesCombine amounts of money to make a given value, including using £ and p symbols Find different combinations of coins that equal the same amount of money. Add and subtract money, including giving changeEstimate, compare and calculate money between pounds and pence
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TimeBegin to anticipate times of the day such as mealtimes or home timeTalk about time and order eventsTell the time to the hour and half past the hour, including drawing clocksCompare and sequence intervals of timeTell and write the time from an analogue clock, including using Roman numerals from
I to XII, and 12-hour and 24-hour clocks		Read, write and convert time between analogue and digital 12- and 24-hour clocksSolve problems involving converting between units of time
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Begin to describe a sequence of events in their immediate past/future. Begin to describe real or fictional events using words such as ‘first’, ‘then...Use language to sequence events in chronological orderTell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these timesEstimate 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, a.m./p.m., morning, afternoon, noon and midnight		Solve problems involving converting from hours to minutes; minutes to seconds;
years to months; weeks to days.
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Recognise and use language relating to datesKnow the number of minutes in an hour and the number of hours in a day.Know the number of seconds in a minute and the number of days in each month,
year and leap year
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Fractions and DecimalsRecognise, find and name a halfRecognise, find, name and write a third, a quarter, a half (two-quarters) and three-quarters of a shape, set of objects or quantityCount up and down in tenthsDivide one or two-digit numbers by 10 and 100, using tenths and hundredthsConvert between mixed numbers and improper fractionsUse common factors to simplify fractionsorder positive and negative integers, decimals and fractions
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Recognise, find and name a quarterWrite simple fraction facts, e.g. 1/2 of 6 = 3 and recognise equivalent fractions of 2/4 and 1/2Understand that tenths arise when objects or quantities are divided into ten equal partsRecognise and use tenths and hundredthsCompare and order fractions whose denominators are multiples of the same numberCompare and order fractions of any sizeuse the symbols =, ≠, <, >, ≤, ≥ to make order statements about positive and negative integers, decimals and fractions
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Compare and order unit fractions and fractions with the same denominatorRecognise and write decimal equivalents to a quarter, a half and three-quartersIdentify, name and write equivalent fractions including tenths and hundredthsAdd and subtract fractions with different denominators and mixed numbersuse the number line as a model for ordering integers, decimals and fractions
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Recognise and show equivalent fractionsRound decimals with one decimal place to the nearest whole numberAdd and subtract fractions with denominators that are multiples of the same numberMultiply simple pairs of proper fractionsround numbers and measures to different degrees of accuracy, for example to the nearest whole number or to one decimal place
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Find and write fractions of a set of objectsCompare numbers with up to two decimal placesMultiply proper fractions and mixed numbers by whole numbers, with practical or visual supportDivide proper fractions by whole numbersuse the four operations, including formal written methods, applied to integers and decimals; multiply proper and improper fractions, and mixed numbers, all both positive and negative
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Add and subtract fractions with common denominators (within one)Add and subtract fractions with the same denominator
Read and write decimal numbers as fractionsCalculate fractions of an amount Interpret fractions and percentages as operators
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Recognise and show, using diagrams, families of common equivalent fractionsRound decimals
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Solve problems to calculate quantities, and fractions to divide quantities, including non unit fractions where the answer is a whole numberAdd and subtract decimals
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Multiply and divide by 10, 100 and 1000
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Read, write, order and compare numbers with up to three decimal placesUse written division with answers of up to two decimal placesappreciate the infinite nature of the set of integers
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Recognise the % symbol and explain a percentage as a fraction with the denominator 100 (parts out of 100)Multiply a number with up to two decimal places by a whole numberwork interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)
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Order fractions, decimals and percentages
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Understand percentages and calculate percentages of an amount
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Recall and use equivalences between fractions, decimals and percentages
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StatisticsInterpret and construct simple tables, tally charts, block diagrams and pictogramsInterpret and present data using bar charts, pictograms and tablesInterpret and present discrete and continuous data on appropriate graphsComplete, read and interpret information in tables, including timetablesConstruct and interpret pie charts, bar charts and line graphsconstruct 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
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Ask and answer simple questions by counting the number of objects in each category sorting the categories by quantitySolve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs. Calculate and interpret the mean as an averagedescribe, 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)
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AlgebraTalk about and identify the patterns around them. e.g. stripes on clothes, designs on rugs and wallpaper. Use informal language like ‘pointy’, ‘spotty’, ‘blobs’, etc.Create repeating patterns of different structures e.g. ABAB, AAB, ABC etc.
Children begin to symbolise the unit structure e.g, a red dot = a red dinosaur.
Children apply a pattern to rule to a variety of resources. 		Generate and describe linear number sequencesdescribe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.
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Extend and copy ABAB patterns – stick, leaf, stick, leaf.
Create ABAB patterns. 		Use simple formulae
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Notice and correct an error in a repeating ABAB pattern.Spot an error in an ABAB and more complex pattern.
Identify the unit of repeat.
Continue and copy ABC, ABB, ABBC, AABB repeating patterns.

Express missing number problems algebraically
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Make a pattern around a circle.
Make a pattern around a border with a fixed number of spaces.
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Ratio and ProportionSolve problems involving ratio and proportion using multiplication and division facts
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Solve problems involving the calculation of percentagesdefine percentage as ‘number of parts per hundred’, and know their decimal and fraction equivalents
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Solve problems involving similar shapes where the scale factor is knownExtend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically
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