multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 × 1/2 = 1/8]
recall multiplication and division facts for multiplication tables up to 12 × 12
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
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, am/pm, morning, afternoon, noon and midnight
order and arrange combinations of mathematical objects in patterns and sequences
recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value
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
calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
add and subtract amounts of money to give change, using both £ and p in practical contexts
recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
recognise 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 fraction
calculate 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 shapes
estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]
draw given angles, and measure them in degrees (°)
identify: * angles at a point and 1 whole turn (total 360°) * angles at a point on a straight line and half a turn (total 180°) * other multiples of 90° * use the properties of rectangles to deduce related facts and find missing lengths and angles * distinguish between regular and irregular polygons […]
divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6 ]
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]
calculate and interpret the mean as an average
interpret and construct pie charts and line graphs and use these to solve problems
draw and translate simple shapes on the coordinate plane, and reflect them in the axes
describe positions on the full coordinate grid (all 4 quadrants)
recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles
illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
recognise, describe and build simple 3-D shapes, including making nets
draw 2-D shapes using given dimensions and angles
calculate the area of parallelograms and triangles
recognise when it is possible to use formulae for area and volume of shapes
recognise that shapes with the same areas can have different perimeters and vice versa
convert between miles and kilometres
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 3 decimal places
solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate
enumerate possibilities of combinations of 2 variables
find pairs of numbers that satisfy an equation with 2 unknowns
express missing number problems algebraically
generate and describe linear number sequences
use simple formulae
solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
solve problems involving similar shapes where the scale factor is known or can be found
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 the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts
recall and use equivalences between simple fractions, decimals and percentages, including in different contexts
solve problems which require answers to be rounded to specified degrees of accuracy
use written division methods in cases where the answer has up to 2 decimal places
identify 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 places
multiply one-digit numbers with up to 2 decimal places by whole numbers
associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8 ]
add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
compare and order fractions, including fractions >1
use common factors to simplify fractions; use common multiples to express fractions in the same denomination
use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
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
use their knowledge of the order of operations to carry out calculations involving the 4 operations
identify common factors, common multiples and prime numbers
perform mental calculations, including with mixed operations and large numbers
divide 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 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
multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
solve number and practical problems that involve all of the above
use negative numbers in context, and calculate intervals across 0
round any whole number to a required degree of accuracy
read, write, order and compare numbers up to 10,000,000 and determine the value of each digit
complete, read and interpret information in tables, including timetables
solve comparison, sum and difference problems using information presented in a line graph
know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
identify 3-D shapes, including cubes and other cuboids, from 2-D representations
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
use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling
solve problems involving converting between units of time
measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints
convert between different units of metric measure [for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre]
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 involving number up to 3 decimal places
read, write, order and compare numbers with up to 3 decimal places
round decimals with 2 decimal places to the nearest whole number and to 1 decimal place
recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
read and write decimal numbers as fractions [for example, 0.71 = 71/100 ]
multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
add and subtract fractions with the same denominator, and denominators that are multiples of the same number
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 ]
identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
compare and order fractions whose denominators are all multiples of the same number
solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
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
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
multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000
multiply and divide numbers mentally, drawing upon known facts
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
establish whether a number up to 100 is prime and recall prime numbers up to 19
know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers
solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
add and subtract numbers mentally with increasingly large numbers
add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
read Roman numerals to 1,000 (M) and recognise years written in Roman numerals
solve number problems and practical problems that involve all of the above
round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 0
count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000
read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit
solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs
interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs
plot specified points and draw sides to complete a given polygon
describe movements between positions as translations of a given unit to the left/right and up/down
describe positions on a 2-D grid as coordinates in the first quadrant
identify acute and obtuse angles and compare and order angles up to 2 right angles by size
complete a simple symmetric figure with respect to a specific line of symmetry
identify lines of symmetry in 2-D shapes presented in different orientations
compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
find the area of rectilinear shapes by counting squares
measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres
solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days
read, write and convert time between analogue and digital 12- and 24-hour clocks
convert between different units of measure [for example, kilometre to metre; hour to minute]
estimate, compare and calculate different measures, including money in pounds and pence
solve simple measure and money problems involving fractions and decimals to 2 decimal places
compare numbers with the same number of decimal places up to 2 decimal places
round decimals with 1 decimal place to the nearest whole number
find 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 hundredths
recognise and write decimal equivalents to 1/4 , 1/2 , 3/4
recognise and write decimal equivalents of any number of tenths or hundreds
add and subtract fractions with the same denominator
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
count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10
recognise and show, using diagrams, families of common equivalent fractions
solve 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 objects
multiply two-digit and three-digit numbers by a one-digit number using formal written layout
recognise and use factor pairs and commutativity in mental calculations
use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbers
solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
estimate and use inverse operations to check answers to a calculation
add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of 0 and place value
solve number and practical problems that involve all of the above and with increasingly large positive numbers
round any number to the nearest 10, 100 or 1,000
identify, represent and estimate numbers using different representations
order and compare numbers beyond 1,000
recognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s)
count backwards through 0 to include negative numbers
find 1,000 more or less than a given number
count in multiples of 6, 7, 9, 25 and 1,000
interpret and present data using bar charts, pictograms and tables
identify horizontal and vertical lines and pairs of perpendicular and parallel lines
identify 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 angle
recognise angles as a property of shape or a description of a turn
draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them
compare durations of events [for example, to calculate the time taken by particular events or tasks]
know the number of seconds in a minute and the number of days in each month, year and leap year
tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks
measure the perimeter of simple 2-D shapes
measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
solve problems that involve all of the above [counting tenths; recognise, find and write fractions; recognise and use fractions as numbers; recognise and show equivalent fractions; add and subtract fractions; compare and order unit fractions]
compare and order unit fractions, and fractions with the same denominators
add and subtract fractions with the same denominator within one whole [for example, 5/7 + 1/7 = 6/7 ]
recognise and show, using diagrams, equivalent fractions with small denominators
recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators
recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
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
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
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
recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction
estimate the answer to a calculation and use inverse operations to check answers
add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction
add and subtract numbers mentally, including: * a three-digit number and 1s * a three-digit number and 10s * a three-digit number and 100s
recognise the place value of each digit in a 3-digit number (100s, 10s, 1s)
solve number problems and practical problems involving these ideas
read and write numbers up to 1,000 in numerals and in words
identify, represent and estimate numbers using different representations
compare and order numbers up to 1,000
count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number
interpret and construct simple pictograms, tally charts, block diagrams and tables
ask-and-answer questions about totalling and comparing categorical data
ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity
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)
compare and sort common 2-D and 3-D shapes and everyday objects
identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]
identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
identify and describe the properties of 2-D shapes, including the number of sides, and line symmetry in a vertical line
know the number of minutes in an hour and the number of hours in a day
compare and sequence intervals of time
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
solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change
find different combinations of coins that equal the same amounts of money
compare and order lengths, mass, volume/capacity and record the results using >, < and =
write simple fractions, for example 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2
recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity
solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts
show that multiplication of 2 numbers can be done in any order (commutative) and division of 1 number by another cannot
recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems
show that addition of 2 numbers can be done in any order (commutative) and subtraction of 1 number from another cannot
add and subtract numbers using concrete objects, pictorial representations, and mentally, including: * a two-digit number and 1s * a two-digit number and 10s * 2 two-digit numbers * adding 3 one-digit numbers
recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
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
use place value and number facts to solve problems
read and write numbers to at least 100 in numerals and in words
recognise the place value of each digit in a two-digit number (10s, 1s)
identify, represent and estimate numbers using different representations, including the number line
compare and order numbers from 0 up to 100; use and = signs
count in steps of 2, 3, and 5 from 0, and in 10s from any number, forward and backward
explore characteristics of everyday objects and shapes and use mathematical language to describe them
use everyday language to talk about … time and money to compare quantities and objects and to solve problems
use everyday language to talk about size, weight, capacity, position, distance, … to compare quantities and objects and to solve problems
recognise, create and describe patterns
solve problems, including doubling, halving and sharing
count on or back to find the answer to addition and subtraction questions
place Numbers from 1 to 20 in order and say which number is one more or one less than a given number
using quantities and objects, add and subtract two single-digit numbers
count reliably with numbers from 1 to 20
describe position, direction and movement, including whole, half, quarter and three-quarter turns
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]
recognise and use language relating to dates, including days of the week, weeks, months and years
tell the time to the hour and half past the hour and draw the hands on a clock face to show these times
measure and begin to record the following: * lengths and heights * mass/weight * capacity and volume * time (hours, minutes, seconds) * recognise and know the value of different denominations of coins and notes * sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon […]
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]
recognise, find and name a quarter as 1 of 4 equal parts of an object, shape or quantity
recognise, find and name a half as 1 of 2 equal parts of an object, shape or quantity
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 one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ?- 9
add and subtract one-digit and two-digit numbers to 20, including 0
represent and use number bonds and related subtraction facts within 20
read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs
read and write numbers from 1 to 20 in numerals and words
identify 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, least
given a number, identify 1 more and 1 less
count, read and write numbers to 100 in numerals; count in multiples of 2s, 5s and 10s
count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number
