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	Comparison 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
Composition 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	Pattern 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	Measures 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
Assessment
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.
Presentation
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.

Impact 

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