Maths Intent, Implementation, and Impact ‘Growing Global Citizens’


At Broseley C of E Primary School, we intend to promote thinking, remembering and puzzling (problem solving). This will provide children with thinking models, recall strategies for strategic arithmetic and different types of problem solving from logic to patterns and rules. Fluency will be enriched through an algebraic approach, using generalities and principles of mathematics. This will support the management of cognitive load, requiring teaching sequences to focus on what must be remembered.
We intend to deliver a curriculum that allows pupils to be part of creative and engaging lessons allowing them to explore maths in depth, using mathematical vocabulary to reason and explain their workings. We encourage resilience, perseverance and an acceptance that struggle is often a necessary step in learning. We give each pupil a chance to believe in themselves as mathematicians.

  • Pupils make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems.
  • Pupils to justify and explain their work, using precise mathematical vocabulary, generalised statements and sentence stems to structure their ideas.
  • All pupils become fluent in the fundamentals so that they can more easily understand the underlying concepts; they can instantly recall knowledge accurately.
  • Pupils select from a range of strategies when calculating by noticing what is required of them and choosing the most efficient way to get there.
  • Pupils apply their knowledge and understanding to a variety of problems with increasing levels of difficulty and complexity, including those that have real-life applications. Fully develop independent learners with inquisitive minds who have secure mathematical foundations and an interest in self-improvement.
  • Pupils relate their mathematical knowledge to science and other subjects.

Our focus is getting children to have instant recall of their number facts and multiplication facts. Being fluent in calculation and knowing multiplication tables by heart are a maths essential. Knowing the multiplication tables (and their associated division facts) supports mathematical learning and understanding. Those children who have a strong grasp of them tend to be more self-assured when learning new concepts.

We aim to give all children in our school a secure and deep understanding of mathematical concepts through detailed and precise teaching in small, manageable steps – provided by NCETM and Whiterose. Stem sentences scaffold pupils learning from EYFS to year 6, ensuring all pupils know the detail and precise vocabulary throughout.
It is essential that we provide as many opportunities as possible for the children in our school to be successful through carefully planned lessons. This is provided through a range of representations: concrete, pictorial and abstract.


Our whole curriculum is shaped by our school vision, to ‘Grow Global Citizens’, which enables all children to thrive, regardless of their background, perceived ability or additional needs.
We teach the national curriculum, supported by the clear progression of skills and knowledge offered by the NCETM Spines. This, along with our bespoke long term plan and calculation policy ensures that skills and knowledge are built on year by year and sequenced to maximise learning for all children.
Maths lessons are planned using the teaching sequence detailed in the NCETM Spine documents: Spine 1 number, addition and subtraction; Spine 2 multiplication and division; Spine 3 fractions. They utilise the linked PowerPoint presentations to illustrate the key concepts and adapt these to further develop the children’s understanding.  When teaching Geometry, Measure and Statistics, this is supplemented by the Whiterose teaching blocks. Teachers read and use these documents to plan their teaching in small, detailed and precise steps. Based on this, teachers are then able to draw on a catalogue of resources available to them to provide a wide range of practise activities with increasing difficulty and complexity. The approach seeks to build flexible learners who can ‘think first’ with a depth of understanding that allows them to access a range of problems in a variety of formats. The variation of these is an essential part of the learning process and all teachers fully understand the difference between planned variation of concept and procedure.
Most lessons will follow a similar structure to the one identified below, however this is not something that we would expect in every lesson. Some maths lessons will be purely practical with no written work, others will be verbal and make use of informal recording using whiteboards and others will follow a more traditional ‘book-work’ format.
Almost all lessons will:

  • Begin with revision or recapping of previous learning through short quizzes, targeted questioning or a short written task.
  • Use appropriate concrete, pictorial and abstract models and images.
  • Follow a simple ‘I DO’, ‘WE DO’, ‘YOU DO’ approach where the work begins in a more scaffolded way, allowing early misconceptions to be identified and addressed. At each step, the children become more independent as their confidence grows.
  • Provide extension tasks to provide further challenge, including the ‘Dong Nao Jin’ questions from the NCETM Spines where appropriate or the use of open-ended ‘Now What?’ bubbles.

The whole school teaching sequence for the year looks like this:


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Maths in EYFS

In EYFS children will get maths lessons most days, but maths will also be integrated into continuous provision and teachers will follow the children’s interests to apply mathematical skills throughout the day. This means that some children will access different skills in different circumstances depending on the child’s interests and will be through in the moment planning.
There are 6 main areas of learning in maths for EYFS. We have provided a suggested progression within each area.

Cardinality and Counting
Counting: saying number words in sequence
Counting: tagging each object with one number word
Counting: knowing the last number gives the total so far
Subitising: recognising small quantities without needing to count them all
Numeral meanings
Conservation: knowing that the number does not change if the things are rearranged

More than/less than
Identifying groups with the same number of things
Comparing number and reasoning
Knowing the ‘one more then/one less than’ relationship between counting numbers


Part-whole: identifying smaller numbers within a number
Inverse operations
A number can be partitioned into different pairs of numbers
A number can be partitioned into more than two numbers
Number bonds: knowing which pairs make up a given number

Continuing an AB pattern
Copying an AB pattern
make their own AB pattern
Spotting an error in an AB pattern
Identifying the unit of repeat
Continuing an ABC pattern
Continuing a pattern which ends mid-unit
Making their own ABB, ABBC patterns
Spotting an error in an ABB pattern
Symbolising the unit structure
Generalising structure to another context or mode
Making a pattern which repeat around a circle
Making a pattern around a boarder with a fixed number of spaces
Pattern-spotting around us

Shape and space
Developing spatial awareness: experiencing different viewpoints
Developing spatial vocabulary
representing spatial relationships
Shape awareness: developing shape awareness through construction
Identifying similarities between shapes
Showing awareness of properties of shape
Describing properties of shape
Developing an awareness of relationships between shapes

Recognising attributes
Comparing amounts of continuous quantities
Showing awareness of comparison in estimating and predicting
Comparing indirectly
Recognising the relationship between the size and number of units
Beginning to use units to compare things
Beginning to use time to sequence events
Beginning to experience specific time duration

In KS1
All KS1 children will receive a one-hour maths lesson every day. The National Curriculum states KS1 children need to develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words, and the four operations. Teaching should also involve using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money. To do this, children follow a programme of study where children gain exposure to a variety of conceptual variations, methods and structures to ensure full understanding before adding the use of operations.

There will also be a separate ‘Mastering Number’ session for 15minutes four days a week. These sessions focus on number sense, with the focus on children improving their mental strategies.

Children will also have maths morning work or short fluency sessions throughout the week to allow children to practise what they have learned after the lessons; these sessions will be as appropriate.

During Lower KS2

All Lower KS2 children will receive a one-hour maths lesson every day. The National Curriculum states that Lower KS2 children increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written methods, mental methods and perform calculations accurately with increasingly large whole numbers. There should be a development of the range of problems children attempt, including simple fractions and decimal place value. Children develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It should ensure that they could use measuring instruments with accuracy and make connections between measure and number. It is also expected that by the end of Year 4 children know all tables up to and including 12 times 12.

There will also be a separate multiplication session for 15minutes four days a week. These sessions focus on timetables recall and application using the ‘Counting Stick’ approach from NCETM, as well as supported through ‘See Why Multiplication’ Powerpoints and booklets.

There will also have maths morning work or short fluency sessions throughout the week to allow children to practise what they have learned after the lessons, these sessions will be as appropriate.

During Upper KS2
All upper Key Stage 2 children will receive one-hour of maths lesson a day. The National Curriculum states that the upper key stage 2 children can extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio. Pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems. Teaching in geometry and measures should consolidate and extend knowledge developed in number. Teaching should also ensure that pupils classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them.
There will also be a separate ‘Fluency’ session for 15minutes four days a week. These sessions will be targeted to ensure all children are proficient and fluent in arithmetic skills which is the foundation of maths learning.

There will also have maths morning work or short fluency sessions throughout the week to allow children to practise what they have learned after the lessons, these sessions will be as appropriate.

Prior to the start of each maths spine / Whiterose block
Each mathematical spine/block builds on one that has been previously taught (except for the very early Year 1 spines).  Each spine provides the teacher with a summary of the pre-requisite learning so that a brief revision or recap can take place prior to any new teaching. These sessions are vitally important if children are to see and understand the links between concepts.
Knowledge Organiser
There are four mathematical knowledge organisers – EYFS, KS1, LKS2 and UKS2. These have been created to give parents to give a clear understanding of what each child should be able to know and instantly recall by the end of each stage of their primary school experience.
Lesson overview
Knowing More and Remembering More
Lessons begin with a focus on ‘Knowing more and remembering more’ short session where pupils revisit the knowledge that has previously been taught to ensure that they have remembered this in order to build on it.
Vocabulary Focus

Lessons have a strong focus on vocabulary (Wow Words) and these are introduced throughout each lesson when appropriate. These words are displayed and modelled precisely and the children are expected to use them in their verbal explanations and written work where necessary.
In maths, there is also a reliance on the use of sentence stems. These provide a structured sentence for children to add specific details into. They provide a scaffold that allows children to better understand and articulate their findings. They are often displayed in the classroom and referred to and repeated during lessons.
The precise vocabulary is also modelled through the use of generalised statements. Most of these are happened upon by the children through the discovery of a generalisation and they are then presented in the most accurate and precise form. These are also displayed in class at the appropriate times. 

Progression in vocabulary examples from NCETM Spine 1-  

  • Reception: heavier, lighter, longer, shorter, more, fewer
  • Year 1: heavier, lighter, fewer, more, whole, part, addend, sum, ones
  • Year 2 – addend, sum, difference, more than, less than, subtract, ones, tens, minus, plus
  • Year 3- minus, increased, decreased, minuend, subtrahend, difference, hundreds
  • Year 4- thousand, ten thousand, hundred thousand, tenth, hundredth,
  • Year 5- negative, positive, additive, multiplicative, subtrahend, minuend, addend, sum, difference
  • Year 6- million, difference, minuend, subtrahend, difference, addend, sum, additive, multiplicative

Substantive and Disciplinary Knowledge
Pupils are taught substantive knowledge such key number facts, times tables and procedural algorithms throughout the curriculum. All of these facts are seen on the knowledge organisers but below is an example:
This starts with cardinality and bonds to five in EYFS. In KS1, this is built on by recalling bonds to 10 and 20 along with the start of tables, 2s, 5s, and 10s. In Lower KS2, this is built on by progressing to bonds within 1000 and expanding table knowledge to 12 times 12. In Upper KS2, this is furthered by looking at bonds to 100,00 and bonds to 1.

Disciplinary Knowledge/skills:
Pupils are taught disciplinary (second order) concepts in order to think, process and understand. This is shown though a variety of conceptual and procedural variation. Children first see a conceptual practically, before learning algorithms and strategies to attempt more complex questions.
Deeper thinking question
The majority of lessons are structured to include increasingly more challenging questions with reduced levels of scaffolding and structure. The questions often encourage children to think rather than repeat and always require children to ‘notice’ similarities and differences. In most cases, lessons will contain one or more open-ended question, investigation, justification and reason question or a ‘Dong Nao Jin’ (use your head) question which link new learning with existing learning or puts the content into a new context.
Support for Pupils with SEND
At the beginning of each unit of work, key pieces of knowledge for the unit are selected and work takes place to ensure that pupils with SEND are retaining and building on this. In addition, scaffolding ensures that pupils can meet the same learning objective as their peers. Adult support, more extensive access to manipulatives, pre-teaching of a concept or ‘work-shop’ style immediate interventions are regularly in place for children who need further support before moving on
At the beginning of each lesson, pupils either complete a ‘knowing more and remembering more’ task which assesses the knowledge they have retained from previous lessons and reactivates the knowledge that they will need to access the new teaching/learning. These can be simple directed questions, quizzes or activities.
Throughout lessons, teachers and TAs are constantly discussing, correcting and furthering children’s understanding through direct questioning and instant intervention. When whole class issues or misconceptions are discovered, teachers refocus the class and reteach or rephrase the learning.
At the end of each Spine, children are given a ‘Ready to Progress’ assessment to assess their knowledge and understanding of the content of that spine. At the end of each Whiterose block, there is an end of unit assessment to ensure the children have sufficient understanding. These assessments will inform interventions for children who have not fully grasped concepts.  Formative quizzes will take place weekly to ensure retention of number facts and timestables. This can be in the form of TT Rockstars, quizzes, interactive challenges, whiteboard work.
At the end of each term, children carry out NfER assessments to track their progress. This will be used as a diagnostic to inform future teaching.
Children in Year 2 complete their SATs during the Summer term, Year 4 sit the Multiplication Check during June and Year 6 sit their SATS tests in May.
At Broseley C of E, Maths is planned and delivered at a very high standard, and we set very high expectations for the students in the lesson. We expect the work in their books to be at the highest standard possible for each individual. We encourage writing to be done in pen and drawing to be done in pencil. Calculations are carried out on square paper and we do not encourage the use of erasers.


Maths lessons are engaging and well-resourced with the pupils acknowledging that the journey to finding an answer is the most important factor.

  • Pupils demonstrate a quick recall of facts and procedures. This includes the recollection of the times tables.
  • Pupils show confidence in believing that they will achieve and are keen to attempt a range of problems and demonstrating flexibility and fluidity to move between different contexts and representations of maths.
  • Pupils are developing skills in being articulate and can reason verbally (using precise vocabulary), pictorially and in written form.
  • Pupils are developing the ability to make connections between mathematical topics.
  • Pupils show a high level of pride in the presentation and understanding of the work. Children can independently apply their knowledge to a range of increasingly complex problems, with many opportunities to access greater depth.

Summative assessments are completed at the end of the academic year and reported to parents in the end of year report. National assessments are carried out at the end of KS1 and KS2, with a Multiplication Check at the end of year 4 and are reported to parents.
The maths leaders have a clear role and overall responsibility for the progress of all children in maths throughout school. Working with SLT, key data is analysed, and regular feedback is provided, to inform on progress and future actions.

Pupils leave our school with the knowledge and skills they need to succeed in secondary school and further education but also to function as a member of the local community and wider world.


 Whole school LTP – Maths






5 frame introduction
Introducing zero,1,2,3

Matching. Sorting & Comparing
Comparing amounts
Comparing size, mass & capacity Exploring pattern - making simple.
Spatial awareness
Simple 2D shape

Representing 4,5
Comparing 4,5
Composition of 4,5
Formation of 4,5
One more and less
Shapes with 4 sides.
Time- night and day
Circles and triangles
Positional language

Introductions of 10 frames
Comparing numbers to 5
Composition of 5
Comparing Mass
Comparing Capacity
Introducing Number 6, 7, 8,9 and exploring their composition.
Combining 2 groups


Use of 10 frames
Numbers 8,9,10
Making pairs.
Combining groups
Number bonds
3D shapes

Adding more
Taking away

Number 10 and beyond– subitising, counting, sorting, matching, comparing, ordering
Composition of numbers to 10 and beyond
Counting patterns to 10 and beyond

Sunflower Challenge

Sharing and grouping
Even and odd
Patterns and relationships

Spatial reasoning.
3D shape
Match, rotate, and manipulate
Pattern – AABB, BBA

Length, height.



Introduce part whole model to explore composition.


1.1 Comparison of quantities and measures
1.2 Part-part-whole

1.3 Composition of numbers 0-5 
1.4 Composition of numbers: 6 - 10

1.9 Composition of numbers: 20 – 100

1.10 Composition of numbers: 11-19

Geometry: Shape

1.5 Additive structures: introduction to aggregation and partitioning

1.6 Additive structures: introduction to augmentation and reduction

1.7 Addition and subtraction: strategies within 10

Measure: length and height

Measure: weight and volume

1.8 Composition of numbers: multiples of 10 up to 100

1.9 Composition of numbers: 20 – 100 (continued)

1.10 Composition of numbers: 11-19

2.1 Counting, unitising and coins

Measure: time

Geometry: position and direction


1.11 Addition and subtraction; bridging ten

1.12 Subtraction as difference

1.13 Addition and subtraction: two-digit numbers and single digit numbers

1.14 Addition and subtraction: two-digit numbers and multiples of ten

Measure: Time

2.2 Structures: multiplication representing equal groups

2.3 Times tables: groups of 2 and commutativity

2.4 Time tables: groups of 10 and 5, and factors of 0 and 1

Measure: capacity, volume and mass

2.5 Commutativity: doubling and halving

2.6 Structures: quotitive and partitive division

1.15 Addition: two-digit and two digit

1.16 Subtraction: two-digit and two-digit

Measure: Money

3.0 Fractions

Geometry: Shape

Geometry: Position and direction


1.17 – Composition and Calculation: 100 and bridging 100

1.18 – Composition and calculation: three-digit numbers

1.19 – Securing mental strategies: calculation up to 999

2.7 – Times Tables: 2, 4 and 8, and the relationship between them

1.20 – Algorithms: column addition

2.8 - Times Tables: 3, 6 and 9, and the relationship between them

1.21 – Algorithms: column subtraction

3.1 – Preparing for fractions: the part-whole relationship

3.2 – Unit fractions: identifying, representing and

3.3 – Non-unit fractions: identifying, representing and comparing

3.4 – Adding and subtracting within one whole

Measure: time

2.9 – Times tables: 7 and patterns within/across times tables

Geometry: properties of shape


1.22 – Composition and calculation: 1000 and four digit numbers

2.10 Connecting multiplication and division, and the distributive law

2.11 Times tables: 11 and 12

2.12 Division with remainders

2.13 Calculation: multiplying and dividing by 10 or 100

Geometry: properties of shape

1.23 – Composition and calculation: tenths

1.24 – Composition and calculation: hundredths and thousandths

1.25 – Addition and subtraction: money

2.14 Multiplication: partitioning leading to short multiplication

2.15 Division: partitioning leading to short division

2.16 Multiplicative contexts: area and perimeter (1

Geometry: position and direction

2.17 Structures: using measures and comparison to understand scaling

measure: time

3.5 Working across one whole: improper fractions and mixed numbers

3.6 Multiplying whole numbers and fractions


1.26 Composition and calculation: multiples of 1,000 up to 1,000,000

1.27 Negative numbers: counting, comparing and calculating

1.28 Common Structures

1.29 Using equivalence and the compensation property to calculate

Measure: area and perimeter

2.18 Using equivalence to calculate

2.19 Calculation: x/÷ decimal fractions by whole

2.20 Multiplication with three factors and volume

2.21 Factors, multiples, prime numbers and composite


2.22 Combining multiplication with addition and


Geometry: properties of shape

Geometry: position and direction

3.7 Finding equivalent fractions and simplifying fractions

3.8 Common denomination: more adding and subtracting

Measure: converting units

Measure Volume


1.30 – Composition and calculation: numbers up to 10, 000, 000

2.23 -  Multiplication strategies for larger numbers and long multiplication

2.24 -  Division: dividing by two-digit divisors

2.25 -  Using compensation to calculate

Geometry: position and direction

3.9 -  Multiplying fractions and dividing fractions by a whole number

3.10 -  Linking fractions, decimals and percentages

Measure: converting units

2.26 -  Mean average and equal shares

2.27 -  Scale factors, ratio and proportional

2.28 -  Combining division with addition and

2.29 -  Decimal place-value knowledge, multiplication and division

2.30 -  Multiplicative contexts: area and perimeter (2

1.31 -  Problems with two unknowns

Geometry; properties of shape

Geometry: position and direction


Useful links for parents:



Mastery of number EYFS and KS1
At Broseley C of E school we have implemented Mastering Number to support the 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.

Multiplication and Division – Counting Stick
At Broseley C of E school we have implemented the counting stick to support the learning of multiplication and division facts from years 2 to 6. The aim is for the children to have a faster recall and secure understanding of multiplication and division. We encourage our children to be flexible thinkers by providing children with a variety of methods to help them master their tables. Below are support materials to try at home:
NCETM – How to use a counting stick
Mrs Winfield times tables on a broomstick
MathsBot Counting Stick


EYFS Number FactsKS1 Number FactsKS2 Number FactsUKS2 Number Facts