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A Message from fractions. They allow children to see that
one-half is the same size as two-quarters, or
MRS. DYER that three-quarters is more than one-half.

These hands-on experiences are vital in help-
ing pupils overcome confusion and develop
HEAD OF SCHOOL a solid mental model of fractions as parts of

a whole.
This stage is crucial across all areas of maths,
not just fractions. It moves learning beyond

ear Parents, memorisation and helps children make
I have had the pleasure this week of observing the Key Stage 1 children in sense of concepts through experience. As the Cambridge framework highlights, pupils
Dtheir Maths lessons. In Year 1 and 2 they are studying different aspects of should be active participants in their own learning—reasoning, problem solving, and

fractions. In year 1 they are looking at how a half can describe one of two equal parts justifying their thinking. Manipulatives encourage this kind of engagement and explora-
of a quantity. In Year 2 they are looking at how a half and a quarter can also be inter- tion, forming a bridge between the familiar world and new mathematical ideas.
preted as division.
Pictorial Representation: Bridging the Gap

Building Strong Mathematical Foundations: The Power of Concrete Once children are confident with concrete materials, we introduce visual representa-
Manipulatives in Primary Maths tions. This might include drawing bar models, pie charts, or number lines that reflect
Fractions can be one of the most challenging concepts in mathematics, not just for what they have done with the manipulatives. For fractions, this could mean shading
children but for adults too. Many of us remember struggling with the idea that one- parts of a shape, drawing a whole divided into equal parts, or using strip diagrams to

half is the same as two-quarters, or trying to understand how to add unlike fractions. compare sizes of different fractions. This pictorial stage reinforces understanding and
The difficulty often lies in the fact that fractions are taught too quickly in their abstract helps learners visualise the problem, particularly when solving more complex, mul-
form—using numbers and symbols—without first allowing learners to explore what ti-step tasks. It’s during this stage that children begin to
they truly represent. At Abuja Prep, we understand that to build confident and capable generalise and represent their thinking—a

mathematicians, children need time and support to develop a deep conceptual under- key element of Thinking and Working
standing, especially in topics like fractions. That’s why we follow a Concrete–Pictorial– Mathematically. They learn to communicate
Abstract (CPA) approach, fully aligned with the Cambridge Primary Maths Curriculum their reasoning more clearly and make con-
and its emphasis on Thinking and Working Mathematically.
nections between different areas of mathe-

matics. For example, understanding that 3/4
Concrete First: Building Real of 8 can be represented as a bar split into
Understanding four parts, with three shaded, helps bridge
Before children can understand the gap between conceptual understanding

numbers, patterns, or operations and calculation.
in abstract form, they need to
experience them in a tangible way. Abstract Thinking: Confident Mathematicians

Concrete manipulatives—such as Finally, pupils move towards abstract understanding, using symbols, equations, and
fraction circles, Cuisenaire rods, written methods. Because they have already explored the concept in concrete and pic-
Numicon, and paper folding—are torial forms, they approach this final stage with confidence and understanding. Rather
especially helpful when teaching

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