We teach a ‘mastery’ mathematics curriculum using the CPA (concrete, pictorial and abstract) approach, see explanation below. This develops a deep understanding of place value, the four operations, number patterns and the relationships between operations. The CPA approach and maths talk support children’s exploration of mathematical concepts which develops children’s ability to recall number facts. Quick mental recall of facts aids children’s fluency, reasoning and problem solving skills.
Talking about maths is about using the correct vocabulary and discussion of concepts, patterns and connections. The children are encouraged to use full sentences to talk through solutions and reason. Such as ‘I know this because 5 + 5 = 10 so 5 + 6 is one more 5 + 6 =11’ or ‘I noticed that the pattern of 1 2 3 4 5 is repeated in the ones column when we count in ones or the tens column when we count in tens. Stem sentences are used alongside representations to help reveal the structure eg One part is ____. The other part is ____. The whole is ____. or If I know____ then I know____ because____
Please use the link below to refer to the school’s Progression in Calculation Guide.
Lessons will be sequenced to move between all three stages varying the models and resources to help deepen understanding, prove or explain answers.
Concrete – Using physical objects to solve maths problems.
Pictorial– Using drawings or a visual representation of concrete objects. It helps build a visual image of an abstract problem. It also highlights the connections between concepts such as addition and subtraction.
Abstract – this is the symbolic stage where symbols and numerals are used.
This Maths No problems video explains it further. https://mathsnoproblem.com/en/approach/concrete-pictorial-abstract/
Representations and Models
Different representations and models are used to support deep understanding. Some are part- part whole, tens frames, Numicon, bar models, base ten – sticks and bricks, place value counters, place value grid. Many of these may be new to you please follow the link and choose the Place Value video which uses place value to explain some of the models. There is also a short video called ‘Has maths changed?’ which may be of interest.
Please click on the link below to see an example of how some National Curriculum learning objectives (LO) can be taught using CPA approach and how this approach can be used to make connections to deepen understanding.