‘Concrete-Pictorial-Abstract’ (CPA)

Children are taught Maths through the ‘Concrete-Pictorial-Abstract’ approach across all year groups. It focuses on laying strong foundations which can be built upon, through embedding models and images into the children’s long-term memories. This in turn reduces the cognitive load on the children’s working memories when approaching new concepts/tasks.

Concrete manipulatives are fundamental to the powerful Concrete-Pictorial-Abstract (CPA) approach and are a key resource in developing a deeper understanding of maths for pupils of all ages. Concrete resources can be used to develop children’s conceptual understanding of place value and the four operations.

Building on the concrete, we consider how we can make connections between concrete, pictorial and abstract ideas so children can truly master concepts, building on those strong foundations. Children will move on to using pictorial representations such as images, graphs or diagrams to solve problems. Once they have a good understanding of the topic, they should be able to take an abstract approach and solve maths problems using abstract concepts and symbols.

Written Calculations

Once children are familiar with a concept, they are encouraged to choose the most efficient method for calculating, be it mental calculation, jottings, or a formal written calculation appropriate to a given task. By the end of KS2, they will have been taught and be secure with using a compact standard method for each operation.

Children are encouraged to:

• Use models, images and manipulatives to aid conceptual understanding
• Establish mental methods, based on a good understanding of place value
• Use formal jottings to aid mental calculations
• Develop the use of empty number lines to help mental imagery and aid recording
• Use partitioning and recombining to aid informal methods
• Introduce expanded written methods
• Develop expanded methods into compact standard written form

Mental Calculations

Mental calculation is important to speed up children’s thinking and reasoning. As part of this, our children take part in the ‘100 club’, achieving badges as they work through their times tables and related division facts. This is an effective motivational tool, and the children look forward to achieving all 7 badges to reach their goal – a 100 Clubber! Further up the school, this is then extended to decimal and fraction tables so they can continue striving for excellence.

Problem solving and reasoning

Being able to reason and problem solve is also at the heart of our curriculum, so opportunities for these are integrated into each unit of work. Children can explore different types of problem-solving tasks both in class and through the use of the outdoor learning environment, which includes our Maths trail. Reasoning is encouraged throughout lessons, both in written form and verbally, to deepen the children’s mathematical understanding.

Maths Mechanics

Maths Mechanics sessions are provided in addition to the main teaching lesson. These are shorter sessions, that provide time for children to focus on key targets, to develop and embed foundation skills and to explore and address gaps in understanding or misconceptions.