Maths
At Haberdashers' Crayford Primary, mathematics is understood to be an essential life skill which enables children to understand and access the world around them. We want our students to leave our school as confident mathematicians who value the subject and understand its importance in their school life and beyond.
We foster a love of maths through embedding a mastery approach, where mathematical content is taught in depth through creative means, allowing children to flourish as confident mathematicians. We use a systematic approach which includes the use of manipulatives and representations, to engage our pupils and allow them to visualise mathematical structures.
‘Mastery of mathematics is not a fixed state but a continuum. At each stage of learning, pupils should acquire and demonstrate sufficient grasp of the mathematics relevant to their year group, so that their learning is sustainable over time and can be built upon in subsequent years. This requires development of depth through looking at concepts in detail using a variety of representations and contexts and committing key facts, such as number bonds and times tables, to memory.’  NCETM
Our mastery approach[i] ensures that every child can succeed in maths. Maths teaching for mastery ‘rejects the idea that a large proportion of people ‘just can’t do maths’ NCTEM. We recognise that mathematical knowledge needs to be taught as declarative, procedural, and conditional[1] to ensure it is committed to longterm memory. We focus on teaching core concepts in depth, particularly in EYFS and KS1, to ensure they are embedded into longterm memory before introducing new material. When introduced, new material is delivered in small steps and builds upon core concepts. This approach ensures less ‘reteaching’ as pupils progress through their schooling. All pupils are taught together, so nobody gets left behind.
‘A mathematical concept or skill has been mastered when, through exploration, clarification, practice and application over time, a person can represent it in multiple ways, has the mathematical language to be able to communicate related ideas, and can think mathematically with the concept so that they can independently apply it to a totally new problem in an unfamiliar situation.’ – Helen Drury 2014
We have adopted the ‘five big ideas for teaching mastery’ from the NCETM which have been drawn from research which underpins teaching for mastery:
Coherence
Lessons are broken down into small, connected steps that gradually unfold the concept, providing access for all children and leading to a generalisation of the concept and the ability to apply the concept to a range of contexts.
Representation and Structure
Representations used in lessons expose the mathematical structure being taught, the aim being that students can do the maths without recourse to the representation.
Mathematical Thinking
If taught ideas are to be understood deeply, they must not merely be passively received but must be worked on by the student, thought about, reasoned with, and discussed with others.
Fluency
Quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics.
Variation
Variation is twofold. It is firstly about how the teacher represents the concept being taught, often in more than one way, to draw attention to critical aspects, and to develop deep and holistic understanding. It is also about the sequencing of the episodes, activities and exercises used within a lesson and follow up practice, paying attention to what is kept the same and what changes, to connect the mathematics and draw attention to mathematical relationships and structure.
The Five Big Ideas were first published by the NCETM in 2017.
Early Maths
In Early Years, mathematics is taught and learnt through play and practical experiences. Teachers provide daily input through carpet sessions and focus groups, which are developed as the year progresses. Much of the teaching is based on the NCETM’s mastering number approach to secure knowledge of number before moving onto other concepts such as addition, subtraction, and shape. Through the provision, children can apply what they have learnt to real life experiences.
We begin using the concrete, pictorial, abstract approach in early maths to ensure children have a strong understanding and foundation of number and calculation methods. We understand that in order to master maths, children need to be confident using a resource before they can understand pictorial and abstract calculation strategies. We have chosen to focus on using a tailored group of resources to ensure children have the time to practise using these until they cannot get them wrong. Using multilink cubes, rekenreks, and numicon are a focus in our early maths. These concrete resources are used to support learners though the school and in interventions to support the progress of children who need more targeted support.
Mastering number
Mastering number aims to secure firm foundations in the development of good number sense for all children from Reception through to Year 1 and Year 2. The aim over time is that children will leave KS1 with fluency in calculation and a confidence and flexibility with number. Attention will be given to key knowledge and understanding needed in Reception classes, and progression through KS1 to support success in the future. – NCETM
We have short daily sessions to embed the mastering number programme for EYFS and KS1. In EYFS, sessions may take longer to ensure the concept of number has been secured.
We also provide mastering number intervention sessions for selected pupils in KS2.
Structure and implementation
The curriculum prioritisation materials from the NCETM, as well as the White Rose Maths scheme, are used to support our intent for mathematics. The White Rose Maths scheme provides a ‘vast bank of clear, practical’ resources which can support children in securing mastery and beyond. Our teachers use the overviews to deliver the mathematics curriculum but are discouraged from rigidly following each lesson. This is to ensure the learning prioritised is based on the needs of the individuals.
‘In line with our mastery approach to the teaching and learning of mathematics, our schemes are split into blocks that allow plenty of time for thorough study of every topic. Teachers of course know their children and the experiences they have had best. We encourage teachers to use this knowledge to make the schemes work for them, adding extra time where necessary for topics that need most attention and adapting other learning accordingly.’ – White Rose Maths
This is then supported by regular, low stakes assessments, demonstrating a lowthreat, highchallenge model which builds children’s selfesteem. These can be seen at the beginning of each maths lesson for years 16 for example, where we use White Rose’s flashback four to recap key learning taught the previous day, week, term, and year.
Additionally, pupils complete daily arithmetic sessions (separate from their maths lesson) to develop their fluency.
All pupils complete the end of block assessments and teachers use these to inform future planning.
Planning
We use the S planning model to teach maths as a cohesive journey, rather than following a specific set of individual lessons produced by a scheme. The approach is flexible and allows teachers to consider: the teaching activities, representations, possible misconceptions, oracy, metacognition, feedback, and what might need to be in place, i.e., scaffolds for different groups of learners. This ensures that teachers are not influenced by the coverage, but by the depth at which pupils are learning. We focus on the needs of each individual student as opposed to where they should be at a particular point in the year.
Maths talk
Mathematical language and dialogue is a key aspect of our maths teaching and can be seen in lessons daily. Key vocabulary and question stems are visible in the classroom environment and give pupils the confidence to discuss their learning.
Stem sentences are available in each of the NCETM’s teacher guides. The stem sentences are repeated and used in different contexts to develop fluency.
Reasoning and Problem Solving
Research by Nunes (2009) identified the ability to reason mathematically as the most important factor in a pupil’s success in mathematics. It is therefore crucial that opportunities to develop mathematical reasoning skills are integrated fully into the curriculum. Such skills support deep and sustainable learning and enable pupils to make connections in mathematics. – NCETM
Through the supporting materials, teachers have access to a range of reasoning questions and to ensure our pupils can articulate their reasoning, we use the show it, draw it, explain it, prove it, justify it model alongside other depth questions and tasks. This allows pupils to think deeply about their responses and confidently articulate their reasoning.
Times Tables Rock Stars
Times Tables Rock Stars is a carefully sequenced programme of daily times tables practice.
Each week concentrates on a different times table, with a consolidation week for rehearsing the tables that have recently been practised every third week.
We celebrate participation in the programme weekly and expect pupils to complete a minimum of four sessions per week.
Footnotes
[i] The essential idea behind mastery is that all children need a deep understanding of the mathematics they are learning so that:
 future mathematical learning is built on solid foundations which do not need to be retaught;
 there is no need for separate catchup programmes due to some children falling behind;
 children who, under other teaching approaches, can often fall a long way behind, are better able to keep up with their peers, so that gaps in attainment are narrowed whilst the attainment of all is raised.
[1] Declarative knowledge can be prefaced with the sentence stem ‘I know that’ and consists of facts and concepts.
Procedural knowledge can be prefaced with the sentence stem ‘I know how’ and consists of a sequence of steps.
Conditional knowledge can be prefaced with ‘I know when’ and focuses on strategies to reason and problem solve.
Maths Overview
Reception
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Maths Progression Map
Progression in Addition and Subtraction


NUMBER BONDS 



Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 

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







MENTAL CALCULATION 



add and subtract onedigit and twodigit numbers to 20, including zero 
add and subtract numbers using concrete objects, pictorial representations, and mentally, including: * a twodigit number and ones * a twodigit number and tens * two twodigit numbers * adding three onedigit numbers 
add and subtract numbers mentally, including: * a threedigit number and ones * a threedigit number and tens * a threedigit 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 (appears also in Written Methods) 
show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot 



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



WRITTEN METHODS 


Year 1 

Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
read, write and interpret mathematical statements involving addition (+), subtraction () and equals (=) signs (appears also in Mental Calculation) 


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) 

Comparing addition and subtraction statements 







INVERSE OPERATIONS, ESTIMATING AND CHECKING ANSWERS 


Finding a part when using a part whole model 

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, levels of accuracy. 


PROBLEM SOLVING 



Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
solve onestep 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 twostep problems in contexts, deciding which operations and methods to use and why 
solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why 
solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why

solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change (copied from Measurement) 
Solve problems involving addition, subtraction, multiplication and division 
Progression in Multiplication and Division


MULTIPLICATION & DIVISION FACTS 



Year 1 
Year 2 
Year 3 
Year 4 
Year 5 

Year 6 
count in multiples of twos, fives and tens (copied from Number and Place Value) 
count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward (copied from Number and Place Value) 
count from 0 in multiples of 4, 8, 50 and 100 (copied from Number and Place Value)

count in multiples of 6, 7, 9, 25 and 1 000 (copied from Number and Place Value)

count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000 (copied from Number and Place Value) 



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 





MENTAL CALCULATION 





write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for twodigit numbers times onedigit numbers, using mental and progressing to formal written methods 
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 numbers mentally drawing upon known facts 
perform mental calculations, including with mixed operations and large numbers



(appears also in Written Methods) 





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

recognise and use factor pairs and commutativity in mental calculations (appears also in Properties of Numbers) 
multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 
associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. ^{3}/_{8}) (copied from Fractions) 


WRITTEN CALCULATION 

Year 1 
Year 2 

Year 3 
Year 4 
Year 5 
Year 6 


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 twodigit numbers times onedigit numbers, using mental and progressing to formal written methods (appears also in Mental Methods) 
multiply twodigit and threedigit numbers by a onedigit number using formal written layout

multiply numbers up to 4 digits by a one or twodigit number using a formal written method, including long multiplication for twodigit numbers 
multiply multidigit numbers up to 4 digits by a twodigit whole number using the formal written method of long multiplication







divide numbers up to 4 digits by a onedigit number using 
divide numbers up to 4digits by a twodigit whole number using the formal written 





the formal written method of short division and interpret remainders appropriately for the context 
method of short division where appropriate for the context divide numbers up to 4 digits by a twodigit 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 






use written division methods in cases where the answer has up to two decimal places (copied from Fractions (including decimals) 


PROPERTIES OF NUMBERS: MULTIPLES, FACTORS, PRIMES, SQUARE AND CUBE NUMBERS 

Year 1 

Year 2 
Year 3 
Year 4 
Year 5 
Year 6 





recognise and use factor pairs and commutativity in mental calculations (repeated) 
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
use common factors to simplify fractions; use common multiples to express fractions in the same denomination (copied from Fractions)


know and use the vocabulary of prime numbers, prime factors and composite (nonprime) 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}) 
calculate, estimate and compare volume of cubes and cuboids using standard units, including centimetre cubed (cm^{3}) and cubic metres (m^{3}), and extending to other units such as mm^{3 }and km^{3} (copied from Measures) 



ORDER OF OPERATIONS 

Year 1 
Year 2 

Year 3 
Year 4 
Year 5 
Year 6 







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



INVERSE OPERATIONS, ESTIMATING AND CHECKING ANSWERS 



estimate the answer estimate and use use estimation to to a calculation and inverse operations to check answers to use inverse check answers to a calculations and operations to check calculation determine, in the answers (copied from (copied from Addition context of a problem, Addition and and Subtraction) levels of accuracy Subtraction)




PROBLEM SOLVING 

Year 1 
Year 2 

Year 3 
Year 4 
Year 5 
Year 6 

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



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 
solve problems involving similar shapes where the scale factor is known or can be found (copied from Ratio and Proportion) 


Progression in Number and Place Value


COUNTING 


Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number 


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 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 
count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward

count from 0 in multiples of 4, 8, 50 and 100;

count in multiples of 6, 7, 9, 25 and 1 000

count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000 

given a number, identify one more and one less 

find 10 or 100 more or less than a given number 
find 1 000 more or less than a given number





COMPARING NUMBERS 


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 1 000

order and compare numbers beyond 1 000 
read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit (appears also in Reading and Writing Numbers) 
read, write, order and compare numbers up to 10 000000 and determine the value of each digit (appears also in Reading and Writing Numbers) 
compare numbers with the same number of decimal places up to two decimal places (copied from Fractions) 


IDENTIFYING, REPRESENTING AND ESTIMATING NUMBERS 

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 




READING AND WRITING NUMBERS (including Roman Numerals) 


Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
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 1 000 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 (appears also in Comparing Numbers) 
read, write, order and compare numbers up to 10 000 000 and determine the value of each digit (appears also in Understanding Place Value) 
tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12hour and 24hour clocks (copied from Measurement) 
read Roman numerals to 1 000 (M) and recognise years written in Roman numerals. 



UNDERSTANDING PLACE VALUE 



recognise the place value of each digit in a twodigit number (tens, ones)

recognise the place value of each digit in a threedigit number (hundreds, tens, ones)

recognise the place value of each digit in a fourdigit number (thousands, hundreds, tens, and ones) 
read, write, order and compare numbers to at least 1 000 000 and 
read, write, order and compare numbers up to 10 000 000 and determine the value of 




determine the value of each digit (appears also in Reading and Writing Numbers) recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents (copied from Fractions) 
each digit (appears also in Reading and Writing Numbers) 
find the effect of dividing a one or twodigit number by 10 and 100, identifying the value of the digits in the answer as units, tenths and hundredths (copied from Fractions) 
identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1 000 where the answers are up to three decimal places (copied from Fractions) 


ROUNDING 


Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 



round any number to the nearest 10, 100 or 1 000

round any number up to 1 000 000 to the nearest 10, 100, 1 000, 10 000 and 100 000 
round any whole number to a required degree of accuracy




round decimals with one decimal place to the nearest whole number (copied from Fractions)

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


PROBLEM SOLVING 



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 
Progression in Measurement

COMPARING AND ESTIMATING 



Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
compare, describe and solve practical problems for: * lengths and heights [e.g. long/short, longer/shorter, tall/short, double/half] * mass/weight [e.g. heavy/light, heavier than, lighter than] * capacity and volume [e.g. full/empty, more than, less than, half, half full, quarter] * time [e.g. quicker, slower, earlier, later] 
compare and order lengths, mass, volume/capacity and record the results using >, < and =


estimate, compare and calculate different measures, including money in pounds and pence (also included in Measuring)

calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm^{2}) and square metres (m^{2}) and estimate the area of irregular shapes (also included in measuring) 
calculate, estimate and compare volume of cubes and cuboids using standard units, including centimetre cubed (cm^{3}) and cubic metres (m^{3}), and extending to other units such as mm^{3 }and km^{3}. 
estimate volume (e.g. using 1 cm^{3 }blocks to build cubes and cuboids) and capacity (e.g. using water)

sequence events in chronological order using language [e.g. before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening] 
compare and sequence intervals of time

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, hours and o’clock; use vocabulary such as a.m./p.m., morning, afternoon, noon and midnight (appears also in Telling the Time) 



MEASURING and CALCULATING 

Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
measure and begin to record the following: * lengths and heights * mass/weight * capacity and volume * time (hours, minutes, seconds)

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, 
measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)

estimate, compare and calculate different measures, including money in pounds and pence (appears also in Comparing)

use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation including scaling.

solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate (appears also in Converting)


using rulers, scales, thermometers and measuring vessels 






measure the perimeter of simple 2D 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 


MEASURING and CALCULATING 



Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
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




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 







find the area of rectilinear shapes by counting squares

calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm^{2}) and square metres (m^{2}) and estimate the area of irregular shapes
recognise and use square numbers and cube numbers, and the notation for squared (^{2}) and cubed (^{3}) (copied from Multiplication and Division) 
calculate the area of parallelograms and triangles 
calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm^{3}) and cubic metres (m^{3}), and extending to other units [e.g. mm^{3 }and km^{3}]. 

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

TELLING THE TIME 

Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
tell the time to the hour and half past the hour and draw the hands on a clock face to show these times. 
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. 
tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12hour and 24hour clocks 
read, write and convert time between analogue and digital 12 and 24hour clocks (appears also in Converting) 


recognise and use language relating to dates, including days of the week, 
know the number of minutes in an hour and the number of hours in a day. 
estimate and read time with increasing accuracy to the 



weeks, months and years 
(appears also in Converting)

nearest minute; record and compare time in terms of seconds, minutes, hours and o’clock; use vocabulary such as a.m./p.m., morning, afternoon, noon and midnight (appears also in Comparing and Estimating) 






solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days (appears also in Converting) 
solve problems involving converting between units of time




CONVERTING 



Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 

know the number of minutes in an hour and the number of hours in a day. (appears also in Telling the Time)

know the number of seconds in a minute and the number of days in each month, year and leap year

convert between different units of measure (e.g. kilometre to metre; hour to minute)

convert between different units of metric measure (e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram 
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 kilogram; litre and millilitre)

and vice versa, using decimal notation to up to three decimal places 



read, write and convert time between analogue and digital 12 and 24hour clocks (appears also in Converting)

solve problems involving converting between units of time

solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate (appears also in Measuring and Calculating) 



solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days (appears also in Telling the Time) 
understand and use equivalences between metric units and common imperial units such as inches, pounds and pints 
convert between miles and kilometres

Progression in Fractions (including decimals and percentages)


COUNTING IN FRACTIONAL STEPS 



Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 

Pupils should count in fractions up to 10, starting from any number and using the 1/2 and 2/4 equivalence on the number line (Non Statutory Guidance) 
count up and down in tenths 
count up and down in hundredths 




RECOGNISING FRACTIONS 



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}/ , ^{1}/ , ^{2}/ 3 4 4 and ^{3}/ of a length, 4 shape, set of objects or quantity

recognise, find and write fractions of a discrete set of objects: unit fractions and nonunit fractions with small denominators 
recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten

recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents (appears also in Equivalence)


recognise that tenths arise from dividing an object into 10 equal parts and in dividing one – digit numbers or quantities by 10. 

recognise, find and name a quarter as one of four equal parts of an object, shape or quantity 
recognise and use fractions as numbers: unit fractions and nonunit fractions with small denominators 



COMPARING FRACTIONS 





compare and order unit fractions, and fractions with the same denominators


compare and order fractions whose denominators are all multiples of the same number 
compare and order fractions, including fractions >1


COMPARING DECIMALS 


Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 



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 
identify the value of each digit in numbers given to three decimal places 

ROUNDING INCLUDING DECIMALS 





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 

EQUIVALENCE (INCLUDING FRACTIONS, DECIMALS AND PERCENTAGES) 



write simple fractions e.g. ^{1}/ of 6 2 = 3 and recognise the equivalence of 2 1 / and / . 4 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 (e.g. 0.71 = 71 / ) 100 
associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3 / ) 8 
recognise and use thousandths and relate them to tenths, hundredths and 




decimal equivalents 




recognise and write decimal equivalents to ^{1}/ ; ^{1}/ ; ^{3}/ 4 2 4

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 as a decimal fraction 
recall and use equivalences between simple fractions, decimals and percentages, including in different contexts. 
ADDITION AND SUBTRACTION OF FRACTIONS 

Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 


add and subtract fractions with the same denominator within one whole (e.g. ^{5}/ 7 + ^{1}/ = ^{6}/ ) 7 7

add and subtract fractions with the same denominator

add and subtract fractions with the same denominator and multiples of the same number 
add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number (e.g. 2 4 6 1 / + / = / = 1 / ) 5 5 5 5 

MULTIPLICATION AND DIVISION OF FRACTIONS 




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 (e.g. 1 1 1 / × / = / ) 4 2 8 
multiply onedigit numbers with up to two decimal places by whole numbers 






divide proper fractions by whole numbers (e.g. ^{1}/ ÷ 2 = 3 1 / ) 6

MULTIPLICATION AND DIVISION OF DECIMALS 

Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 





multiply onedigit numbers with up to two decimal places by whole numbers 



find the effect of dividing a one or twodigit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths 

multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places 





identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 





and 1000 where the answers are up to three decimal places 





associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. ^{3}/_{8}) 





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

PROBLEM SOLVING 

Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 


solve problems that involve all of the above

solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including nonunit fractions where the answer is a whole number 
solve problems involving numbers up to three decimal places





solve simple measure and money problems involving fractions and 
solve problems which require 




decimals to two decimal places.

knowing percentage and decimal equivalents of ^{1}/ , ^{1}/ , 2 4 1 2 4 / , / , / and those 5 5 5 with a denominator of a multiple of 10 or 25. 

Progression in Geometry: Properties of Shapes


IDENTIFYING SHAPES AND THIER PROPERTIES 


Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
recognise and name common 2D and 3D shapes, including: * 2D shapes [e.g. rectangles (including squares), circles and triangles] * 3D shapes [e.g. cuboids (including cubes), pyramids and spheres].

identify and describe the properties of 2D shapes, including the number of sides and line symmetry in a vertical line


identify lines of symmetry in 2D shapes presented in different orientations

identify 3D shapes, including cubes and other cuboids, from 2 D representations

recognise, describe and build simple 3D shapes, including making nets (appears also in Drawing and Constructing) 
identify and describe the properties of 3D shapes, including the number of edges, vertices and faces

illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius 

identify 2D shapes on the surface of 3D shapes, [for example, a circle on a cylinder and a triangle on a pyramid] 



DRAWING AND CONSTRUCTING 




draw 2D shapes and make 3D shapes using modelling materials; recognise 3D shapes in different orientations and describe them 
complete a simple symmetric figure with respect to a specific line of symmetry 
draw given angles, and measure them in degrees (^{o}) 
draw 2D shapes using given dimensions and angles 
recognise, describe and build simple 3D shapes, including making nets (appears also in Identifying Shapes and Their Properties) 
COMPARING AND CLASSIFYING 

Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 

compare and sort common 2D and 3D 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 and find unknown angles in any triangles, quadrilaterals, and regular polygons

distinguish between regular and irregular polygons based on reasoning about equal sides and angles 

ANGLES 



recognise angles as a property of shape or a description of a turn 

know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles 



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 
identify acute and obtuse angles and compare and order angles up to two right angles by size

identify: * angles at a point and one whole turn (total 360^{o}) * angles at a point on a straight line and ½ a turn (total 180^{o}) 
recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles 


than or less than a right angle 

* other multiples of 90^{o } 



identify horizontal and vertical lines and pairs of perpendicular and parallel lines 



Progression in Geometry: Position and Direction


POSITION, DIRECTION AND MOVEMENT 



Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
describe position, direction and movement, including half, quarter and threequarter 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 threequarter turns (clockwise and anticlockwise) 

describe positions on a 2D grid as coordinates in the first quadrant 
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)

describe movements between positions as translations of a given unit to the left/right and up/down 
draw and translate simple shapes on the coordinate plane, and reflect them in the axes. 




plot specified points and draw sides to complete a given polygon 




PATTERN 




order and arrange combinations of mathematical objects in patterns and sequences 




Progression in Algebra
EQUATIO 
NS 


Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
solve onestep problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = *  9 (copied from Addition and Subtraction) 
recognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems. (copied from Addition and Subtraction) 
solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction. (copied from Addition and Subtraction)


use the properties of rectangles to deduce related facts and find missing lengths and angles (copied from Geometry: Properties of Shapes) 
express missing number problems algebraically 
solve problems, including missing number problems, involving multiplication and division, including integer scaling (copied from Multiplication and Division) 


recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 (copied from Addition and Subtraction) 



find pairs of numbers that satisfy number sentences involving two unknowns 
represent and use number bonds and related subtraction facts within 20 (copied from Addition and Subtraction)





enumerate all possibilities of combinations of two variables 



FORMULAE 



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. (Copied from NSG measurement) 

use simple formulae 
recognise when it is possible to use formulae for area and volume of shapes (copied from Measurement) 




SEQUENCES 



sequence events in chronological order using language such as: before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening (copied from Measurement)

compare and sequence intervals of time (copied from Measurement) 




generate and describe linear number sequences 
order and arrange combinations of mathematical objects in patterns (copied from Geometry: position and direction) 







Progression in Statistics

INTERPRETING, CONSTRUCTING AND PRESENTING DATA 


Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 

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 
complete, read and interpret information in tables, including timetables 
interpret and construct pie charts and line graphs and use these to solve problems


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 





SOLVING PROBLEMS 




solve onestep and twostep questions [e.g. ‘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. 
solve comparison, sum and difference problems using information presented in a line graph

calculate and interpret the mean as an average 
Progression in Ratio and Proportion
Statements only appear in Year 6 but should be connected to previous learning, particularly fractions and multiplication and division 






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. 
Calculation policy