Our aims for our Mathematics curriculum are to provide a foundation for understanding the world, the ability to reason mathematically, develop an appreciation of the power of Mathematics and a sense of enjoyment and curiosity about the subject. At William Harding we believe that Mathematics is a fundamental life skill, enabling thought, learning and expression and ensuring that our pupils can play a full and active part as individuals within society.  We aim to ensure that the children’s needs as learners and mathematicians are effectively met across the curriculum and that practice within the school is consistent and clear.

We aim for our pupils to;

  • become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

  • reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using concise mathematical language

  • solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

  • use discussion in order to learn; they should be able to elaborate and explain clearly their understanding and ideas, using concise Mathematical vocabulary

 At William Harding, Mathematics is taught through a mastery approach.  This means that lessons are carefully planned and taught progressively, developing pupils’ mathematical fluency, mathematical thinking and conceptual understanding.  Pupils’ ability to connect new ideas to concepts that have already been understood is at the heart of this approach. 


In the Foundation Stage, children are taught to count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number.

In Key Stage 1, the principal focus of mathematics teaching is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This involves working with numerals, words and the four operations.  By the end of year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value.

In Key Stage 2, the principal focus of Mathematics teaching is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This will ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers, to include larger numbers as the pupils progress. By the end of year 4, we aim for pupils to have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work.

Counting and Magic Maths

The National Curriculum states that the principal focus of mathematics teaching in Key Stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value.

In the Foundation Stage pupils are taught to count reliably from 1 to 20, placing them in order and saying which number is one more or one less than a given number.  They solve problems that involve combining groups of 2, 5 or 10.  The aim of Magic Maths is to embed these key skills. 

In Key Stage 1, the knowledge and skills developed in Magic Maths within the Foundation Stage are built upon and daily counting takes place in Year 2.

In Key Stage 2, there is an emphasis on daily counting to support pupils in becoming increasingly fluent in their development of number and secure in their understanding of the number system.  Magic Maths is applied as an intervention for specific pupils that may need further support and intervention. 


In the Foundation Stage pupils are taught to use quantities and objects, pupils learn to add and subtract two single-digit numbers and count on or back to find the answer. They learn to solve problems, including doubling, halving and sharing.

In Key Stage 1, pupils develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching also involves using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money. They are able to discuss and solve problems in familiar practical contexts, including using quantities.

 In Key Stage 2, pupils develop their ability to solve a range of problems, including those with simple fractions and decimal place value. Teaching ensures that pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It ensures that pupils can use measuring instruments with accuracy and make connections between measure and number. By the end of year 6, we aim for pupils to be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages.

Vocabulary development

Pupils’ acquisition and command of vocabulary are key to their learning and progress across the whole curriculum and vocabulary must be explicitly taught these skills. Teachers therefore develop vocabulary actively, building systematically on pupils’ current knowledge. They will increase pupils’ store of words in general and make links between known and new vocabulary. In this way, pupils expand the vocabulary choices that are available to them when they write. It is particularly important to introduce pupils to the language which defines each subject in its own right, such as accurate mathematical and scientific language.

William Harding School Mathematics Calculation Policy

William Harding School Mathematics Long-Term Overview