‘Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.’ (National Curriculum, Mathematics Programme of Study, 2014)

Our Curriculum Intent for Mathematics 

Click here for our Mathematics Policy 2022

Click here for our Calculations Policy 2022

At Avening Primary School, we have adopted a Teaching for Mastery approach to mathematics to ensure that pupils have a deep and secure understanding of the concepts they are taught. Underlying this approach, is the belief that all children are able to succeed in becoming fluent mathematicians who are able to reason and solve a variety of problems by applying what they have learned in a range of contexts.

We aim for all pupils to become fluent in the fundamentals of the mathematics in line with the expectations of the National Curriculum, so that they develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. We aim for them to be able to solve problems and reason mathematically, as well as to have an appreciation of number and number operations which enables mental calculations and written procedures to be performed efficiently, fluently and accurately.

 To support the teaching and learning, throughout the school we use a ‘concrete, pictorial, abstract’ approach, where conceptual understanding is developed through concrete and visual representations, and where children are routinely asked to explain their reasoning as part of our daily maths lessons. This means that teachers use a range of resources when teaching and try, where possible, to introduce new topics with appropriate concrete and visual resources. These enable children to gain a deep understanding of the mathematical concept so that the learning is sustainable over time and the move to more abstract methods of calculating is supported. This allows children to build new learning upon prior knowledge. Challenge is provided though exposure to rich and sophisticated problems. The Knowledge Organisers below detail the different approaches we use to teach mathematical concepts. They also include examples of the concrete and visual representations that we use to support children's understanding of new learning. 

Year 1 Knowledge Organisers

Year 2 Knowledge Organisers

Year 3 Knowledge Organisers

Year 4 Knowledge Organisers

Year 5 Knowledge Organisers

Year 6 Knowledge Organisers


In addition to high levels of success, we aim for our pupils to have a positive attitude towards mathematics and to see mistakes or misconceptions as opportunities for learning. At the heart of all decisions relating to the teaching of mathematics, is the belief that all children can achieve with the right level of support and guidance.

 Curriculum Implementation

Despite being a school with mixed-age classes, teaching is delivered to year groups and planning is supported by ‘Can Do Maths’ (see year by year curriculum 'road' maps). Key concepts of number and place value, calculating, fractions, geometry, statistics and space are deliberately broken down into small steps to ensure all children are able to access the learning.

Please see the Knowledge Organisers below for progression from Year 1 to Year 6 in each strand of mathematics:

Place Value Progression

Addition Progression

Subtraction Progression

Multiplication Progression

Division Progression

Fractions Progression

Geometry Progression

Each class follows a similar structure to their daily lessons, with the main teaching planned and delivered using powerpoint slides.  A typical lesson design is as follows:



Do it – Can I do it?

Practise new skill

Twist it – Can I prove it?

 1 or 2 common misconceptions

Deepen it – Can I investigate?

Teach it/ practise it together – concrete and pictorial examples



Learn vocabulary

Learn what it is and what it is also (non-standard examples to ensure the children have grasped the new learning)

Have a go

Use apparatus

Practise it

Learn what it’s not

Answer true or false questions

Identify and correct mistakes

Find missing digits

Show me… show me another…

Explain and convince

Use problem solving skills and apply learning to different contexts

Here’s the answer, what’s the question?

What’s the same – what’s different?

Find missing digits

Always, sometimes or never

Support and challenge

Challenge 1:

Procedural fluency

Challenge 2:

Conceptual understanding

Challenge 3:

Mathematical thinking


 In addition to daily maths lessons, the children also have four ‘Maths Practice’ sessions each week. These sessions provide an opportunity for practising key number and arithmetic skills, as well as for rapid intervention should this be needed to address misconceptions or consolidate understanding from the main maths lesson. We use ArithmeKit to support our delivery of these fluency sessions.

 Fluency is further enhanced by our regular Rainbow Maths sessions, short low-stake tests to practise key number facts. In Years 1 and 2 the focus is mainly on number bonds. In Years 3 and 4, times table recall is our focus for these sessions; by the end of Year 4, all children are expected to be able to recall their tables up to 12 x 12.

 Times tables are reinforced at home, and sometimes at school, via the IT program Times Table Rock Stars which is used a part of our Share and Learn Home Learning from Key Stage 2.