Maths Progression

Year 1Year 2Year 3
Counting•count to and across 100, forwards and backwards, beginning with
0 or 1, or from any given number
•count, read and write numbers to 100 in numerals; count in
multiples of twos, fives and tens
•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.
Place Value•recognise the place value of each digit in a two-digit number •compare and order numbers from 0 up to 100; use <, > and = signs•recognise the place value of each digit in a three-digit number
•compare and order numbers up to 1000
Representing number•identify and represent numbers using objects and pictorial
representations including the number line, & use language of:
equal to, more than, less than (fewer), most, least
•read and write numbers from 1 to 20 in numerals and words
•read, write and interpret mathematical statements involving
addition (+), subtraction (–) and equals (=) signs
•identify, represent and estimate numbers using different
representations, including the number line
•read and write numbers to at least 100 in numerals and in words
•identify, represent and estimate numbers using different
representations
•read and write numbers up to 1000 in numerals and in words
Number Facts (+/-)•given a number, identify one more and one less
•represent and use number bonds and related subtraction facts
within 20
•use place value and number facts to solve problems
recall and use addition and subtraction facts to 20 fluently, and
derive and use related facts up to 100
Mental +/-•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: TU+U, TU+T, TU+TU and
U+U+U
•show that addition of two numbers can be done in any order
(commutative) and subtraction of one number from another
cannot
•add and subtract numbers mentally, including: HTU+U, HTU+T
and HTU+H
Written +/-•add and subtract numbers with up to three digits, using formal
written methods of columnar addition and subtraction
Problems +/-•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,
pictorial and abstract representations
•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
•solve problems, including missing number problems, using
number facts, place value, and more complex addition and
subtraction
Number Facts (x/÷)•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
Mental (x/÷)•calculate mathematical statements for multiplication and division
within the multiplication tables and write them using the
multiplication (×), division (÷) and equals (=) signs
•show that multiplication of two numbers can be done in any
order (commutative) and division of one number by another
cannot
•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 methods
Written (x/÷)•Progress to formal written methods calculations as above
Problems (x/÷)•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.
Recognising
fractions
•recognise, find and name a half as one of two equal parts of an
object, shape or quantity
•recognise, find and name a quarter as one of four 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
Comparing
fractions
•compare and order unit fractions, and fractions with the same
denominators
•recognise and show, using diagrams, equivalent fractions with
small denominators
Finding
fractions of
quantities
•recognise, find and write fractions of a discrete set of objects:
unit fractions and non-unit fractions with small denominators
•recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators
Fraction
calculations
•add and subtract fractions with the same denominator within
one whole [for example, 5/7 + 1/7 = 6/7 ]
Decimals as
fractional
amounts
Ordering
decimals
Calculating with
decimals
Percentages
Fraction
problems
•solve problems using all fraction knowledge
Ratio &
Proportion
Algebra
Measures•compare, describe and solve practical problems for:
length/height, weight/mass, capacity/volume & time
•measure and begin to record length/height, weight/mass,
capacity/volume & time
•choose and use appropriate standard units to estimate and measure length/height (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels •compare and order lengths, mass, volume/capacity and record the results using >, < and =•measure, compare, add and subtract: lengths (m/cm/mm); mass
(kg/g); volume/capacity (l/ml)
Mensuration•measure the perimeter of simple 2-D shapes
Money•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
•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
•add and subtract amounts of money to give change, using both £
and p in practical contexts
Time•sequence events in chronological order using language
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
•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
•know the number of minutes in an hour and the number of hours
in a day
•tell and write the time from an analogue clock, including using
Roman numerals from I to XII, and 12-hour and 24-hour clocks
•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
•know the number of seconds in a minute and the number of days
in each month, year and leap year
compare durations of events
Shape
vocabulary
•recognise and name common 2-D shapes (e.g. Square, circle,
triangle)
•recognise and name common 3-D shapes (e.g. Cubes, cuboids,
pyramids & spheres)
(vertices, edges, faces, symmetry)•identify horizontal and vertical lines and pairs of perpendicular
and parallel lines
Properties of
2-d shape
•identify and describe the properties of 2-D shapes, including the
number of sides and line symmetry in a vertical line.
•compare and sort common 2-D and 3-D shapes and everyday
objects.
•draw 2-D shapes
Properties of
3-d shape
•identify and describe the properties of 3-D shapes, including the
number of edges, vertices and faces
•identify 2-D shapes on the surface of 3-D shapes.
compare and sort common 2-D and 3-D shapes and everyday
objects.
•make 3-D shapes using modelling materials
recognise 3-D shapes in different orientations and describe them
Angles•recognise angles as a property of shape or a description of a turn
•identify right angles, recognise that two right angles make a halfturn, three make three quarters of a turn and four a complete turn
•identify whether angles are greater or less than right angle
Position &
Direction
•describe position, direction and movement, including whole, half,
quarter and three-quarter turns.
quarter and three-quarter turns.
•order and arrange combinations of mathematical objects in
patterns and sequences.
•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 ¾ turns
Interpreting
data
•interpret and construct simple pictograms, tally charts, block
diagrams and simple tables
•interpret and present data using bar charts, pictograms and
tables
Extract info
from data
•ask and answer simple questions by counting the number of
objects in each category and sorting the categories by quantity
•ask and answer questions about totalling and comparing
categorical data
•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

Year 4Year 5Year 6
Counting•count in multiples of 6, 7, 9, 25 and 1000
•find 1000 more or less than a given number
count backwards through zero to include negative numbers
•count forwards or backwards in steps of powers of 10 for any
given number up to 1 000 000
•interpret negative numbers in context, count forwards and
backwards with positive and negative whole numbers, including
through zero
•use negative numbers in context, and calculate intervals across
zero
Place Value•recognise the place value of each digit in a four-digit number
•order and compare numbers beyond 1000
•round any number to the nearest 10, 100 or 1000
•recognise the place value of each digit in a four-digit number
•order and compare numbers beyond 1000
•round any number to the nearest 10, 100 or 1000
•read, write, order and compare numbers up to 10 000 000 and
determine the value of each digit
•round any whole number to a required degree of accuracy
Representing number•identify, represent and estimate numbers using different
representations
•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 Roman numerals to 1000 (M) and recognise years written in
Roman numerals
•recognise and use square numbers and cube numbers, and the
notation for squared (²) and cubed (³)
Number Facts (+/-)
Mental +/-•add and subtract numbers mentally with increasingly large
numbers
•perform mental calculations, including with mixed operations
and large numbers
Written +/-•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
Problems +/- •estimate and use inverse operations to check answers to a
calculation
•solve addition and subtraction two-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
•solve addition and subtraction multi-step problems in contexts,
deciding which operations and methods to use and why
Number Facts (x/÷)•recall multiplication and division facts for multiplication tables up
to 12 × 12
•identify multiples and factors, including finding all factor pairs of
a number, and common factors of two 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
•identify common factors, common multiples and prime numbers
Mental (x/÷)•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
•recognise and use factor pairs and commutativity in mental
calculations
•multiply and divide numbers mentally drawing upon known facts
•multiply and divide whole numbers and those involving decimals
by 10, 100 and 1000
•perform mental calculations, including with mixed operations
and large numbers
Written (x/÷)•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
•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
•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 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
•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 context
Problems (x/÷)•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 multiplication and division including
using their knowledge of factors and multiples, squares and cubes
•solve problems involving addition, subtraction, multiplication and
division and a combination of these, including understanding the
meaning of the equals sign
•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
•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
•use estimation to check answers to calculations and determine,
in the context of a problem, an appropriate degree of accuracy
Recognising
fractions
•count up and down in hundredths;
•recognise that hundredths arise when dividing an object by one
hundred and dividing tenths by ten.
•recognise mixed numbers and improper fractions and convert
from one form to the other and write mathematical statements >
1 as a mixed number
Comparing
fractions
•recognise and show, using diagrams, families of common
equivalent fractions
•compare and order fractions whose denominators are all
multiples of the same number
•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
•compare and order fractions, including fractions > 1
Finding
fractions of
quantities
•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
Fraction
calculations
•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
•multiply proper fractions and mixed numbers by whole numbers,
supported by materials and diagrams
•add and subtract fractions with different denominators and
mixed numbers, using the concept of equivalent fractions
•multiply simple pairs of proper fractions, writing the answer in its
simplest form
•divide proper fractions by whole numbers
Decimals as
fractional
amounts
•recognise and write decimal equivalents of any number of tenths
or hundredths
•recognise and write decimal equivalents to ¼, ½ and ¾
•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
•read and write decimal numbers as fractions•associate a fraction with division and calculate decimal fraction
equivalents [for example, 0.375] for a simple fraction
•identify the value of each digit in numbers given to three decimal
places
Ordering
decimals
•round decimals with one decimal place to the nearest whole
number
•compare numbers with the same number of decimal places up to
two decimal places
•recognise and use thousandths and relate them to tenths,
hundredths and decimal equivalents
•round decimals with two decimal places to the nearest whole
number and to one decimal place
•read, write, order and compare numbers with up to three
decimal places
Calculating with
decimals
•multiply and divide numbers by 10, 100 and 1000 giving answers
up to three decimal places
•multiply one-digit number with up to two decimal places by
whole numbers
•use written division methods in cases where the answer has up to
two decimal places
Percentages•recognise the per cent symbol (%) and understand that per cent
relates to ‘number of parts per hundred’, and write percentages as
a fraction with denominator 100, and as a decimal
•solve problems involving the calculation of percentages [for
example, of measures, and such as 15% of 360] and the use of
percentages for comparison
Fraction
problems
•solve simple measure and money problems involving fractions
and decimals to two decimal places
•solve problems involving number up to three decimal places
•solve problems which require knowing percentage and decimal
equivalents of ½ , ¼ , 1/5 , 2/5 , 4/5 and those fractions with a
denominator of a multiple of 10 or 25
•solve problems which require answers to be rounded to specified
degrees of accuracy
•recall and use equivalences between simple fractions, decimals
and percentages, including in different contexts.
Ratio &
Proportion
•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 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.
Algebra•use simple formulae
•generate and describe linear number sequences
•express missing number problems algebraically
•find pairs of numbers that satisfy an equation with two unknowns
•enumerate possibilities of combinations of two variables.
Measures•Convert between different units of measure
estimate, compare and calculate different measures, including
money in pounds and pence
•convert between different units of metric measure
•understand and use approximate equivalences between metric
units and common imperial units such as inches, pounds and pints
•estimate volume and capacity
•solve problems involving the calculation and conversion of units
of measure, using decimal notation up to three decimal places
where appropriate
•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
convert between miles and kilometres
Mensuration•measure and calculate the perimeter of a rectilinear figure
(including squares) in centimetres and metres
find the area of rectilinear shapes by counting squares
•measure and calculate the perimeter of composite rectilinear
shapes in centimetres and metres
•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
•recognise that shapes with the same areas can have different
perimeters and vice versa
•recognise when it is possible to use formulae for area and volume
of shapes
•calculate the area of parallelograms and triangles
•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.
Money•use all four operations to solve problems involving measure [for
example, length, mass, volume, money] using decimal notation,
including scaling
Time•Convert between different units of measure (e.g. Hours to
minutes)
•read, write and convert time between analogue and digital 12-
and 24-hour clocks
•solve problems involving converting from hours to minutes;
minutes to seconds; years to months; weeks to days
•solve problems involving converting between units of time
Shape
vocabulary
•illustrate and name parts of circles, including radius, diameter
and circumference and know that the diameter is twice the radius
Properties of
2-d shape
•compare and classify geometric shapes, including quadrilaterals
and triangles, based on properties and sizes
•identify lines of symmetry in 2-D shapes presented in different
orientations
•complete a simple symmetric figure with respect to a specific line
of symmetry.
•use the properties of rectangles to deduce related facts and find
missing lengths and angles
•distinguish between regular and irregular polygons based on
reasoning about equal sides and angles.
•draw 2-D shapes using given dimensions and angles
compare and classify geometric shapes based on their properties
and sizes
Properties of
3-d shape
•identify 3-D shapes, including cubes and other cuboids, from 2-D
representations
•recognise, describe and build simple 3-D shapes, including
making nets
•find unknown angles in any triangles, quadrilaterals, and regular
polygons
Angles•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
•draw given angles, and measure them in degrees (°)
•identify angles at a point and one whole turn (total 360°); at a
point on a straight line and ½ a turn (total 180°)
•identify 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
Position &
Direction
•describe positions on a 2-D grid as coordinates in the first
quadrant
•describe movements between positions as translations of a given
unit to the left/right and up/down
•plot specified points and draw sides to complete a given polygon
•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
•describe positions on the full coordinate grid (all four quadrants)
•draw and translate simple shapes on the coordinate plane, and
reflect them in the axes.
Interpreting
data
•interpret and present discrete and continuous data using
appropriate graphical methods, including bar charts and time
graphs
•complete, read and interpret information in tables, including
timetables
•interpret and construct pie charts and line graphs
calculate and interpret the mean as an average
Extract info
from data
•solve comparison, sum and difference problems using
information presented in bar charts, pictograms, tables and other
graphs
•solve comparison, sum and difference problems using
information presented in a line graph
•use pie charts and line graphs to solve problems