# Our Curriculum – Maths

This table details what will be taught and when, though since children develop at different speeds, some will be more proficient than others against these YEAR-END expectations for learning in Maths. Back to our Curriculum Wheel –>

Key stage |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Year 6 |

Number: Number and Place Value | read and write numbers from 1 to 20 in numerals and words. | read and write numbers to at least 100 in numerals and in words | read and write numbers up to 1000 in numerals and in words | read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value | read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit | read, write, order and compare numbers up to 10 000 000 and determine the value of each digit |

recognise the place value of each digit in a two-digit number (tens, ones) | recognise the place value of each digit in a three-digit number (hundreds, tens, ones) | recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones) | read Roman numerals to 1000 (M) and recognise years written in Roman numerals | |||

identify and represent numbers using objects and pictorial representations including the number line | identify, represent and estimate numbers using different representations, including the number line | identify, represent and estimate numbers using different representations | identify, represent and estimate numbers using different representations | |||

count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number | count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward | count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number | count in multiples of 6, 7, 9, 25 and 1000 | count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000 | use negative numbers in context, and calculate intervals across zero | |

count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens | ||||||

given a number, identify one more and one less | find 1000 more or less than a given numberr | |||||

count backwards through zero to include negative numbers | interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero | |||||

use the language of: equal to, more than, less than (fewer), most, least | compare and order numbers from 0 up to 100; use <, > and = signs | compare and order numbers up to 1000 | order and compare numbers beyond 1000 | round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000 | round any whole number to a required degree of accuracy | |

round any number to the nearest 10, 100 or 1000 | ||||||

use place value and number facts to solve problems | solve number problems and practical problems involving these ideas | solve number and practical problems that involve all of the above and with increasingly large positive numbers | solve number problems and practical problems that involve all of the above | solve number and practical problems that involve all of the above | ||

Number: Addition and Subtraction | Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Year 6 |

represent and use number bonds and related subtraction facts within 20 | recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 | |||||

add and subtract one-digit and two-digit numbers to 20, including zero | add and subtract numbers using concrete objects, pictorial representations, and mentally, including: – a two-digit number and ones – a two-digit number and tens – two two-digit numbers – adding three one-digit numbers | add and subtract numbers mentally, including: – a three-digit number and ones – a three-digit number and tens – a three-digit number and hundreds | add and subtract numbers mentally with increasingly large numbers | perform mental calculations, including with mixed operations and large numbers | ||

read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs | ||||||

show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot | 4 | |||||

add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction | add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate | add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) | ||||

solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ☐ – 9 | solve problems with addition and subtraction: – using concrete objects and pictorial representations, including those involving numbers, quantities and measures – applying their increasing knowledge of mental and written methods | solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction | solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why | solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why | solve problems involving addition, subtraction, multiplication and division | |

solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why | ||||||

recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. | estimate the answer to a calculation and use inverse operations to check answers | estimate and use inverse operations to check answers to a calculation | use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy | use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy | ||

Number: Multiplication and Division | Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Year 6 |

recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers | recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables | recall multiplication and division facts for multiplication tables up to 12 × 12 | multiply and divide numbers mentally drawing upon known facts | perform mental calculations, including with mixed operations and large numbers | ||

calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs | write 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 methods | |||||

show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot | ||||||

use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers | multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 | |||||

multiply two-digit and three-digit numbers by a one-digit number using formal written layout | multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers | multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication | ||||

divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context | divide 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 context | |||||

solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher | solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts | solve 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 objects | solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects | solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign | solve problems involving addition, subtraction, multiplication and division | |

solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes | ||||||

solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates | ||||||

use their knowledge of the order of operations to carry out calculations involving the four operations | ||||||

use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy | ||||||

recognise and use factor pairs and commutativity in mental calculations | identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers | identify common factors, common multiples and prime numbers | ||||

know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers | ||||||

establish whether a number up to 100 is prime and recall prime numbers up to 19 | ||||||

recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³) | ||||||

Fractions, Decimals and Percentages | Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Year 6 |

recognise, find and name a half as one of two equal parts of an object, shape or quantity | recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity | 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 10 | count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten | compare and order fractions whose denominators are all multiples of the same number | compare and order fractions, including fractions > 1 | |

recognise, find and name a quarter as one of four equal parts of an object, shape or quantity | write simple fractions for example, 1/2 of 6 = 3 | recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators | recognise 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 | |||

recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators | ||||||

compare and order unit fractions, and fractions with the same denominators | use common factors to simplify fractions; use common multiples to express fractions in the same denomination | |||||

add and subtract fractions with the same denominator within one whole [for example, 5/7 + 1/7 = 6/7] | add and subtract fractions with the same denominator | add and subtract fractions with the same denominator and denominators that are multiples of the same number | add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions | |||

solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number | ||||||

multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams | multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 × 1/2 = 1/8] | |||||

divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6] | ||||||

round decimals with one decimal place to the nearest whole number | round decimals with two decimal places to the nearest whole number and to one decimal place | solve problems which require answers to be rounded to specified degrees of accuracy | ||||

compare numbers with the same number of decimal places up to two decimal places | read, write, order and compare numbers with up to three decimal places | |||||

identifying the value of the digits in the answer as ones, tenths and hundredths | identify the value of each digit in numbers given to three decimal places | |||||

find the effect of dividing a one- or two-digit number by 10 and 100, | multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places | |||||

multiply one-digit numbers with up to two decimal places by whole numbers | ||||||

use written division methods in cases where the answer has up to two decimal places | ||||||

recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’ | ||||||

recognise the equivalence of 2/4 and 1/2 | recognise and show, using diagrams, equivalent fractions with small denominators | recognise and show, using diagrams, families of common equivalent fractions | identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths | use common factors to simplify fractions; use common multiples to express fractions in the same denomination | ||

recognise and write decimal equivalents of any number of tenths or hundredths | read and write decimal numbers as fractions [for example, 0.71 = 71/100] | associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8 ] | ||||

recognise and write decimal equivalents to 1/4,1/2, 3/4 | recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents | |||||

write percentages as a fraction with denominator 100, and as a decimal | recall and use equivalences between simple fractions, decimals and percentages, including in different contexts | |||||

solve 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 25. | ||||||

solve problems that involve all of the above | solve simple measure and money problems involving fractions and decimals to two decimal places | solve problems involving number up to three decimal places | ||||

Measurement | Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Year 6 |

sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening] | compare and sequence intervals of time | tell 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 clocks | |||

recognise and use language relating to dates, including days of the week, weeks, months and years | tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times | know the number of seconds in a minute and the number of days in each month, year and leap year | solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days | |||

tell the time to the hour and half past the hour and draw the hands on a clock face to show these times | know the number of minutes in an hour and the number of hours in a day. | compare durations of events [for example to calculate the time taken by particular events or tasks] | ||||

estimate 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 | ||||||

recognise and know the value of different denominations of coins and notes | recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value | add and subtract amounts of money to give change, using both £ and p in practical contexts | estimate, compare and calculate different measures, including money in pounds and pence | |||

find different combinations of coins that equal the same amounts of money | ||||||

solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change | ||||||

compare, describe and solve practical problems for: – lengths and heights [for example, long/short, longer/shorter, tall/short, double/half] – mass/weight [for example, heavy/light, heavier than, lighter than] – capacity and volume [for example, full/empty, more than, less than, half, half full, quarter] – time [for example, quicker, slower, earlier, later] | 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 vessels | measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml) | solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate | |||

measure and begin to record the following: – lengths and heights – mass/weight – capacity and volume – time (hours, minutes, seconds) | ||||||

Convert between different units of measure [for example, kilometre to metre; hour to minute] | convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre) | use, 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 three decimal places | ||||

understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints | convert between miles and kilometres | |||||

use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling | ||||||

measure the perimeter of simple 2-D shapes | measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres | measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres | recognise that shapes with the same areas can have different perimeters and vice versa | |||

find the area of rectilinear shapes by counting squares | calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm²) and square metres(m²) and estimate the area of irregular shapes | calculate the area of parallelograms and triangles | ||||

recognise when it is possible to use formulae for area and volume of shapes | ||||||

estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water] | calculate, 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] | |||||

solve problems involving converting between units of time | ||||||

use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling | ||||||

Geometry: Properties of Shapes | Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Year 6 |

recognise and name common 2-D and 3-D shapes, including: – 2-D shapes [for example, rectangles (including squares), circles and triangles] – 3-D shapes [for example, cuboids (including cubes), pyramids and spheres] | identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line | identify horizontal and vertical lines and pairs of perpendicular and parallel lines | identify lines of symmetry in 2-D shapes presented in different orientations | draw 2-D shapes using given dimensions and angles | ||

identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces | complete a simple symmetric figure with respect to a specific line of symmetry | illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius | ||||

identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid] | draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them | identify 3-D shapes, including cubes and other cuboids, from 2-D representations | recognise, describe and build simple 3-D shapes, including making nets | |||

compare and sort common 2-D and 3-D shapes and everyday objects | compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes | use the properties of rectangles to deduce related facts and find missing lengths and angles | compare and classify geometric shapes based on their properties and sizes | |||

distinguish between regular and irregular polygons based on reasoning about equal sides and angles. | … and find unknown angles in any triangles, quadrilaterals, and regular polygons | |||||

recognise angles as a property of shape or a description of a turn | identify acute and obtuse angles and compare and order angles up to two right angles by size | know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles | ||||

identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle | draw given angles, and measure them in degrees (o) | |||||

identify: – angles at a point and one whole turn (total 360°) – angles at a point on a straight line and 1/2 a turn (total 180°) – other multiples of 90° | recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles | |||||

Geometry: Position and Direction | Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Year 6 |

describe positions on a 2-D grid as coordinates in the first quadrant | describe positions on the full coordinate grid (all four quadrants) | |||||

plot specified points and draw sides to complete a given polygon | ||||||

describe position, direction and movement, including whole, half, quarter and three-quarter turns | use 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) | describe movements between positions as translations of a given unit to the left/right and up/down | identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed | draw and translate simple shapes on the coordinate plane, and reflect them in the axes | ||

Statistics | Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Year 6 |

ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity | solve one-step and two-step questions [for example, ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables | solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs | complete, read and interpret information in tables, including timetables | |||

ask and answer questions about totalling and comparing categorical data | ||||||

interpret and construct simple pictograms, tally charts, block diagrams and simple tables | interpret and present data using bar charts, pictograms and tables | interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs | solve comparison, sum and difference problems using information presented in a line graph | interpret and construct pie charts and line graphs and use these to solve problems | ||

calculate and interpret the mean as an average | ||||||

Algebra | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 |

Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same unit (Non-statutory guidance: Measurement) |
use simple formulae | |||||

recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³) Number: Multiplication and Division |
generate and describe linear number sequences | |||||

solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ☐ – 9 (Number: Addition & Subtraction) |
recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems (Number: Addition & Subtraction) |
solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction (Number: Addition & Subtraction) |
express missing number problems algebraically | |||

Solve 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 objects (Number: Multiplication & Division) |
||||||

recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 (Number: Addition & Subtraction) |
find pairs of numbers that satisfy an equation with two unknowns | |||||

represent and use number bonds and related subtraction facts within 20 (Number: Addition & Subtraction) |
enumerate possibilities of combinations of two variables | |||||

Ratio and Proportion | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 |

solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts | ||||||

solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison | ||||||

solve problems involving similar shapes where the scale factor is known or can be found | ||||||

solve problems involving unequal sharing and grouping using knowledge of fractions and multiples |

End.