Alexander First School

Acquire knowledge, prepare for the future, research in action


Maths at Alexander First School


At Alexander First School, we are determined to equip the pupils of AFS with a uniquely powerful set of tools to understand and change the world. These tools include using a well-sequenced concrete, pictorial and abstract (CPA) approach that ensures the children have a depth of understanding that promotes logical thinking, reasoning, problem solving and the ability to think in abstract ways. We recognise that mathematics is integral to all aspects of life and with this in mind; we endeavour to ensure that our children develop a positive and enthusiastic attitude towards mathematics that will stay with them.

At Alexander First School, we use the National Curriculum for Mathematics (2014) as the basis of our mathematics programme and teachers have access to many resources that facilitate effective teaching and learning. We are committed to ensuring that all pupils achieve mastery in the key concepts of mathematics, appropriate for their age group, in order that they make genuine progress and avoid gaps in their understanding that provide barriers to learning as they move through their education.

We have employed case-based research to study and unpick the particulars of what our pupils at Alexander First School need in order to achieve academic success. This is particularly pertinent for our Service pupils who experience disjointed educational provisions and so a firm understanding of the responses to teaching approaches and curriculum design is essential. This research has been coupled with an understanding of Policy Enactment theory which has enabled the school’s leadership to understand why certain aspects of our school policy is easier to implement than others and how staff can be supported in delivering a uniformed approach.


The Maths Subject Lead Team

The maths subject lead team believes that mathematics is an essential tool for everyday life and at Alexander First School we are committed to developing a positive attitude, competence and confidence in mathematical knowledge, concepts and skills. The children are expected to have an ability to solve problems, to reason, to think logically and to work systematically and where possible staff link learning to real life situations, giving the children a purpose and motivation to achieve.

We strongly advocate all children, of all abilities learning together, working together on the same mathematical theme with the same success criteria for the skill being explored. Differentiated activities ensure children have the practise and consolidation they require, whereas those children who need it can deepen their learning through using and applying, reasoning and fluency tasks.

Research around metacognition underpins our mathematical teaching in school. Teachers use precise questioning in class to test conceptual and procedural knowledge and effective modelling of concepts allows our children to view the workings and thinking of the master at work. Children are then given adequate time to practise concepts with scaffolds and supports being withdrawn to ensure the children have opportunity to grapple with new learning in order for it to be committed to long term memory eventually.


Moderation of the standards of children’s work and of the quality teaching in mathematics is our responsibility, alongside other members of the senior leadership team. Our work involves supporting colleagues in the teaching of mathematics, being informed about current developments in the subject, and providing a strategic lead and direction for the subject in the school.


Our Curriculum

A detailed, structured curriculum is mapped out across all phases, ensuring continuity and supporting transition. Effective mastery curricula in mathematics are designed in relatively small carefully sequenced steps, which must each be mastered before pupils move to the next stage. Fundamental skills and knowledge are secured first. This often entails focusing on curriculum content in considerable depth at early stages.


As a school, we are passionate about children acquiring the basic skills of mathematics that will be valuable to them as they move on to further education and beyond.

We hold the following skills in high regard and children are encouraged to:

  • have a well-developed sense of the size of a number and where it fits into the number system (place value)
  • know by heart number facts such as number bonds, multiplication tables, doubles and halves
  • use what they know by heart to figure out numbers mentally
  • calculate accurately and efficiently, both mentally and in writing
  • draw on a range of calculation strategies
  • make sense of number problems, including non-routine/’real’ problems and identify the operations needed to solve them
  • explain their methods and reasoning, using correct mathematical terms
  • judge whether their answers are reasonable and have strategies for checking them where necessary
  • suggest suitable units for measuring and make sensible estimates of measurements
  • explain and make predictions from the numbers in graphs, diagrams, charts and tables
  • develop spatial awareness and an understanding of the properties of 2D and 3D shapes


To provide adequate time for developing mathematics, maths is taught daily and discretely. However, application of skills is linked across the curriculum where appropriate and staff are keen to capitalise on opportunities in subjects such as STEM and geography, where learning becomes purposeful and encourages application.


Curriculum Design

Our mathematics curriculum has been designed with breadth and depth in mind. At Alexander First School, we do not want to merely cover curriculum content but for our children to have the skills and processes to apply their maths learning to a variety of contexts. Teaching staff designed the curriculum to ensure each National Curriculum objective is broken down with opportunities for fluency, reasoning and problem solving through a differentiated approach. Where possible, opportunities to provide real-life contexts for mathematical learning are sought. Teachers plan to teach essential maths skills that will support learning in science, history, geography and the other subjects. For example, teachers plan to cover data handling objectives in discrete maths lessons and then revisit and repeat the use of these skills during a science lesson where the children have been asked to plot the growth of a plant in different settings. Our priorities to provide children with essential lifelong skills are supported through our mathematics curriculum and we will continue to revisit our curriculum design each year to ensure that we offer our children the very best in an ever changing world and society.


Mastering the Curriculum

Mastery of maths means a deep, long-term, secure and adaptable understanding of the subject. Our teaching for mastery is based on ‘The Five Big Ideas’ (NCETM, 2017):

  • Coherence
  • Representation and Structure
  • Mathematical Thinking
  • Fluency
  • Variation

The Five Big Ideas (NCETM, 2017).


Teaching for mastery builds gradually as a child goes through school. It is a tool for life, and immeasurably more valuable than the short-term ability to answer questions in tests or exams. We are not in favour of labelling pupils as ‘high ability’ or ‘low ability’ and always put the ownership of learning on the children themselves. This approach is now the basis of each maths lesson and children are always given a choice of where they will begin their learning and are encouraged to take charge of the progress they make during the lesson by moving themselves on. Classes from Year 1 to Year 4 use graduated engagement activities which progress in challenge. This system enables the children to consolidate their understanding of concepts before moving on to apply their mathematical skills to reason and problem solve.


When walking into a typical maths lesson at Alexander First School, it is evident that there is a challenging, engaging ethos that promotes a positive and confident attitude to maths as an exciting, creative and relevant subject. We also want to ensure that all our children realise their potential, becoming confident and enthusiastic mathematicians. Our curriculum is designed to ensure that there is a focus on promoting core maths skills; such as multiplication tables, number bonds and place value; as well as practical maths and 'using and applying' skills which promote independent problem solving skills and mastery. 


Attached below are the various aspects of the maths curriculum that are covered by each year group in line with the National Curriculum expectations. These help teachers to ensure that all areas of the maths curriculum are covered for the relevant year group.

These plans are used as a guide for teachers to use in their maths planning. However, teachers are expected to use assessments and on-going daily marking to inform their planning and make changes to the length of time spent on units during the spring and summer term. Teachers track the objectives taught and analyse this data when planning their units.

Please find attached the calculation policy for addition, subtraction, multiplication and division also.


Times Tables

Times tables are taught throughout the school in a consistent manner which focuses on recall, fluency and eventually speed. An online programme is used to enable children to practise their times tables online, at home and at school. The children record and monitor their own progress and have a full awareness of the times tables they need to secure. Children are tested on a regular basis to ensure that they know all of their times tables by the expected stages in their education. Children are rewarded with stickers to mark their achievements. It is expected that children will know all of their times tables to 12 x 12 by the end of Year 4.


At Alexander First School we use an exciting, interactive maths programme to teach the children the essential skill of recalling their multiplication and division facts. The national expectation is that every child will be able to answer any times table question or division fact mentally within a five second period. Times Tables Rock Stars is an online programme which also requires the children to answer multiplication and division questions on paper at least three times per week, whist listening to rock music to motivate and engage them.


The online programme contains a competitive element where the children collect coins for every answer they input correctly. The more coins they earn, the more accessories they can buy for their avatar and the higher up the school leader board they will go. This resource is accessible and is a fun and engaging way to learn a vital mathematical skill.


Early Years Foundation Stage (EYFS)

Mathematics within the EYFS is developed through purposeful, play based experiences and will be represented throughout the indoor and outdoor provision. The learning will be based on pupils’ interests and schemas or current themes and will focus on the expectations from the Early Years Outcomes. As the pupils progress through, more focus is placed on representing their mathematical knowledge through more formal experiences. Pupils will be encouraged to record their mathematical thinking when ready and this will increase throughout the Foundation Stage. Assessment in the Foundation Stage is carried out through planned observations; incidental observation during child initiated activities and during teacher directed activities, which are informed through planning. All information obtained from these assessment strategies is transferred into the children’s individual profiles and recorded against the relevant Early Learning Goals. All assessment evidence is stored within the individual learning journeys. This includes online observations, photographs and a physical record of children’s work.


Maths Assessment

This section details the various assessment methods and practices used in Alexander First School through which we ensure that children are making appropriate progress and that the activities they take part in are suitably matched to their ability and level of development.


Formative Assessment (AfL) - (monitoring children’s learning)

Assessment is an integral and continuous part of the teaching and learning process at Alexander First School and much of it is done informally as part of each teacher’s day-to-day work. Teachers integrate the use of formative assessment strategies such as: effective questioning, clear learning objectives, the use of success criteria, effective feedback and response in their teaching and marking and observing children participating in activities. Findings from these types of assessment are used to inform future planning.


Summative Assessment – (evaluating children’s learning)

More formal methods are used to determine the levels of achievement of children at various times during the school year: Termly assessments are used as a way of recording children’s progress in objectives covered across that specific term. This information is then updated on the online tracking tool available to teachers. These termly assessments are used throughout the year to aid planning.


Statutory End of Key Stage Assessment

The National Curriculum requires that each child is assessed at the end of KS1 and KS2. Statutory tests determine whether the children are working below, at or above the expected standard. In KS1, the assessments coupled with teacher assessment form the overall standard the children reach. To show that pupils have met the standard, teachers provide evidence that a pupil demonstrates consistent attainment of all the statements within the standard.


Assessment for Learning – Self and peer assessment

All children from Nursery to Year 4 are asked to make judgements about how they can improve their own work, through a range of self-assessment techniques (e.g. traffic lights, thumbs up – thumbs down etc.). Children are also given the opportunity to take part in peer-to-peer assessment where they support their peers in looking at how to improve their work. At the end of every lesson, each child reflects upon their learning to determine whether the anticipated outcome has been achieved. In response to this, after the teacher has marked the child’s work, they also identify the child’s level of achievement in relation to these aims/objectives. Discrepancies between child and teacher assessments are then addressed if necessary.


Maths and Spiritual, Moral, Social and Cultural Development


At Alexander First School, we use maths to support our children’s spiritual development by helping them to develop deep thinking and question the way in which the world works. We want them to feel delight when they have shown resilience and are able to solve questions they once found difficult to solve. Our children are inspired by our topic-linked curriculum and the links that maths have with other subjects (art, science, design and technology and computing to name a few). We strive to create opportunities that allow the children to use mathematical tools in all areas of learning. Mathematics helps children to make informed decisions in life, based on the skills and confidence gained from choosing the most appropriate method in solving problems. These skills are transferable to real-life situations and therefore help the children become more reflective, responsible and insightful individuals.



Moral development is supported through discussion about their mathematical understanding, challenging assumptions and supporting children to question information and data that they are presented with. We provide reasoning opportunities where the children are encouraged to prove their answer and give reasons for their thoughts. This allows them to evidence their views not just in maths but in the wider world. As a result, we support our children to understand how logical reasoning can be used to consider the consequences of particular decisions and choices and help them learn the value of mathematical truth.



At Alexander First School, self-esteem and building self-confidence is integral to social development and we use growth mind-set, metacognition and our differentiation model to support this. Collaborative learning is encouraged at AFS in the form of listening and learning from each other and paired discussion and working with partners. Our learning structures are based on our case-based research findings which have focused on what our pupil population and school community need in order to attain. 

This is supplemented with additional research works such as the active engagement and cooperation work by Dr Spencer Kagan. Working cooperatively enables the children to think for themselves and promotes the retention of new learning. The children are able to see the benefits of working together as a team and they understand that collaboration is the key to their success.



Maths supports pupil’s cultural development by developing an appreciation with the pupils that mathematics, its language and symbols have developed from many different cultures around the world. This is often learnt through the teaching of historical periods such as the Romans, the Greeks, the Mayans and many other cross-curricular topics. Our children are encouraged to appreciate the range of different cultures in school and further afield as an essential element of their preparation for life in modern Britain.


Cross-Curricular Mathematics

The National Curriculum statement for mathematics (DFE) refers to mathematical skills that ‘support learning across the curriculum’. At Alexander First School, we take advantage of opportunities that arise to link mathematical knowledge and skills across the curriculum. For example, children interpret pie charts to show the nutrients needed by a cat, human and a parrot in Year 3 and in Year 1 children sort and classify the features of seasonal changes. Other cross-curricular learning includes children in Year 1 and 2 ordering historical events on timelines, creating a pyramid structure using nets during the children’s Ancient Egypt topic in Year 4 and positional language is used regularly in fieldwork across the school. We recognise the importance of cross-curricula learning and how mathematics can be brought to life when it is linked to practical, real life examples.


Growth Mind Set

It is common to hear children say they are, ‘no good at maths’ or state that they, ‘can’t do maths!” At Alexander First School we aim to foster a ‘can do’ attitude towards maths. We encourage the children to change their mind set and think positively about their learning. The children have been taught to believe that they can ‘do maths.’ So instead of saying ‘I can’t do it!’ they children follow the sentence with YET! The children know that once they have learnt all the skills that they will eventually solve the problem. This growth mind-set approach towards maths helps us all to achieve more than we believe we can.


Pupil Voice

Our children have a love and enthusiasm for maths at Alexander First School and this is demonstrated in their values and attitudes.