At Emsworth Primary School, we value the importance of mathematics in everyday life. Our aim is to support children to develop the fundamental knowledge and fluency needed in order to solve problems, to reason and to work systematically and accurately. Through an engaging, challenging and exciting curriculum, we support children in embedding and mastering knowledge.
Concrete Pictorial and Abstract (CPA)
We follow a CPA approach. This approach creates strong foundations of knowledge in order for children to deepen their understanding or to move onto more challenging concepts. By following these steps we are providing children with a relational understanding. This means that they are able to answer problems and understand fully how and why it works. They are able to link their knowledge to other concepts.
The approach follows three key stages:
The first stage is the ‘concrete’ stage. Children use physical concrete resources and a hands-on approach to embed understanding of a concept or objective. For example, some resources which children may use include dienes, Numicon, place value counters and Tens grids.
Once children have mastered the concrete stage, they then move onto the ‘pictorial’ stage. At this point children are able to interpret and represent numbers and problems using images and diagrams. At this stage children may draw their own models and images to support their thinking.
Finally, children use their deep routed concrete and pictorial knowledge to move into the ‘abstract’ stage. Children solve problems which involve abstract representations. This may involve formal written methods. It is often beneficial for children to first use concrete or pictorial representations alongside an abstract representation, until their knowledge is secure.
This is an example of the concrete, pictorial and abstract approach within the Year 2 Multiplication topic.
3 x 4 =
We follow a maths mastery approach to learning at Emsworth Primary School. This means that children have the opportunity to master a concept before moving onto the next. We provide children with a variety of experiences and representations in order for them to successfully develop a depth of understanding. This may mean that once children have understood a concept in one context, they then apply this to other contexts and make links within the mathematics curriculum and to other subjects.
Fluency, problem solving and reasoning
Within our mathematics lessons we incorporate fluency, reasoning and problem solving opportunities. These 3 strands are needed in order for children to have a strongly embedded understanding. Becoming fluent within a concept means that children can confidently and successfully answer a problem. They can draw on mental maths methods or use the CPA approach. Problem solving often involves children applying their mathematical knowledge to open ended problems. Children develop curiosity, creativity and resilience skills when applying their knowledge to solve a problem. Reasoning tasks involve children using their dialogue and vocabulary to explain answers to problems.
These are examples of fluency, reasoning and problem solving tasks in the classroom.
*Images to follow*
- Links to prior knowledge, to different mathematics topics and across the curriculum
- Maths home learning set for children to consolidate understanding at home
- Maths working walls in every classroom to support children’s learning around current topic
- Interventions and small group teaching for those who have been identified as requiring extra support
- Pre-teaching concepts before lessons
- Cold and hot tasks to assess understanding before and after topics
- Flexible groupings with regular teacher assessment
- Catch up groups for those identified as being affected by remote learning
- Topic tracking made by maths leaders in order to identify gaps due to remote learning
- ‘Times table Rockstars’ from Years 2-6 in order for children to become fluent and can solve times tables with speed and precision.
The impact of the maths teaching at Emsworth Primary school enables children to be confident mathematicians and they enjoy talking about what they have learnt and are able to make links within Maths and to other subjects. Maths is engaging and children are appropriately challenged. Children make good progress and this is monitored and tracked regularly.
National Curriculum and EYFS
Please follow the link below to access the National Curriculum for Key Stage 1 and 2.
Please follow the link below to access the new EYFS Statutory Framework.
Whole School Long Term Map
The long term map is a working document and is subject to change depending on teacher assessment. For example, consolidation lessons may be added where appropriate.
Useful links and Resources