Swing Gate Infant School and Nursery


  • At Swing Gate we are passionate about the teaching of mathematics. We believe that every child can enjoy and succeed in mathematics.
  • Through our mathematics teaching we aim to:
  • Foster a positive learning attitude towards mathematics
  • Increase children’s confidence in mathematics so that they are able to express themselves and their ideas using the appropriate mathematical vocabulary
  • Develop children’s ability to work independently and in cooperation with others
  • Provide equal opportunities for all children to learn mathematics
  • Create a rich mathematical environment which supports children’s learning and use of mathematical equipment
  • Embody mathematics in a wide variety of situations so that children can realise its fascination and multiplicity of uses
  • Develop the children’s ability to solve problems, to reason, to think logically and to work systematically
  • Develop an understanding of mathematics through a process of enquiry and experiment
  • Inform and involve parents in the teaching of mathematics as their experiences and values have a major influence on their children
  • For every child to enjoy and succeed in mathematics, regardless of background.


How we teach mathematics

Our teaching focuses on building deep conceptual understanding and developing secure foundations that the children can use throughout their education. If children are able to recall key number facts, then they will be able to apply this to work with larger numbers and to reason and solve problems. Concepts are introduced using the Concrete Pictorial Abstract (CPA) approach. This involves introducing children to concepts using a wide range of concrete objects and pictorial representations before moving to abstract calculations and problems. Building or drawing a model makes it easier for children to visualise difficult abstract concepts. Children are challenged through problem solving activities which include missing number and word problems. Talk is an important part of our lessons and we like to challenge children to explain their thinking by asking them to ‘prove it’.


How we teach mathematics and how children learn has changed since many of us were at school.  We focus on building conceptual understanding, and spending time on deepening fundamental knowledge and skills.  If children have excellent understanding of basic number knowledge then they can use this to reason and solve problems.

Number sense 

For example - what is '7'?

How can I make it? 7 + 0 , 6 + 1, 5 + 2, 4 + 3

Is 4 + 3 the same as 3 + 4? So, do I know what 7 - 3 is? Or 7 - 4? (You get the idea!)

Can I recall those number bonds easily?

So if I'm adding 5 to 7 I know that 5 + 5 = 10 and then I need to add 2 more

Or if I have to take 7 away from 24, I could visualise 20 - 4 - 3 which helps me get to the answer more quickly.

What is double seven?  What is the relationship between doubling and halving?  And if I know that 7 + 7 = 14 then I know what 7 + 6 or 7 + 8 is because I recognise them as near doubles.

This is what we call number sense, and if children develop a real fluency with small numbers and understand them,  they can use this knowledge to work with larger numbers very easily.


Concrete - Pictorial - Abstract

Children need to manipulate concrete objects before they start calculating on paper.

After seeing a real example they are then encouraged to make a pictorial representation of it: this helps children visualise number and develop their mental capacity to do calculations.

Finally children will be encouraged to record calculations more formally as algorithms (sums).

 A child will be challenged by problem solving activities, and this does not always include larger numbers, but rather activities that develop thinking skills.  We often ask children to 'prove it' - in other words explain how they got to an answer and why other answers would be wrong.  Explaining your thinking is key to deepening your understanding.

We believe that children should discover that mathematics is fun and exciting and that it will provide them with a set of tools for everyday life.

In mathematics the children are introduced to a whole network of concepts and relationships which will provide them with a way of viewing and making sense of the world.  They will develop the knowledge to analyse and communicate information and ideas and to tackle a range of practical tasks and real life problems.  Good maths teaching is lively, engaging and challenges children to make connections in their learning.

How can you help?

  • Talk to your child about their learning- what are they learning in their maths lessons each day?
  • Talk about numbers all around you- door numbers, car registration numbers, bus numbers etc.
  • Help develop number fluency by playing counting games- playing cards, dice and board games are all fantastic opportunities to practise mental fluency.
  • Link maths to everyday activities- counting objects, paying with money in a shop, looking at patterns in nature, weighing ingredients, using mathematical language such as “more than” and “fewer than”.
  • Communicate positive messages about maths to your child- we want all children to believe that they can succeed at maths

Things to do at home

Websites which you can access and use at home include:

Swing Gate Lane, Berkhamsted, Hertfordshire HP4 2LJ

01442 863913