A clear and consistent approach to effective manipulative use

Extensive research evidence has shown that manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). (objects that children or practitioners can interact with and move to represent mathematical ideas) can be powerful tools for supporting pupils to engage with mathematical ideas as part of high-quality mathematical teaching.

But just like any other tool – it’s when, why and how they are used which is most important.

A CLEAR approach

At St Peter’s Primary School, we have taken deliberate steps to ensure a consistent, whole-school approach to the use of manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). in maths. Our rationale is rooted in the CPA approach (Concrete – Pictorial – Abstract), where manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). act as a bridge between abstract ideas and children’s understanding. We call this our CLEAR approach:

1. Consistent rationale and purpose: manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). are not an optional extra but a key part of every child’s maths journey.
   Link to learning: resources are chosen to align with the concept being taught, so they are purposeful rather than decorative.
   Explicit teaching: children are shown how to use each manipulative effectively.
   Act as a scaffold: resources are removed once independence and fluency have been achieved.
   Remain visible and accessible: manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). are available across all classrooms and year groups.

This means that manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). are not limited to a small group of children but are available for all learners, at all stages.

Planning, implementation, and monitoring

Our planning begins with deliberate choices about which manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). to prioritise in each year group. For example:

• Year 1 – Numicon to support early number facts.
• Year 2 – Dienes to develop an understanding of place value.
• Year 3 – Counters to understand and manipulate multiplicative relationships.

Teachers are supported to plan lessons where manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). are carefully matched to the intended learning outcome. Senior leaders monitor through lesson visits and pupil voice to ensure that manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). are being used with purpose and consistency.

Progression Across the School

Consistency also comes through our calculation policy, which outlines how manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). and representations are carefully sequenced across year groups. For example, in Key Stage 1 (Year 2), children use Dienes and place value grids to add a multiple of ten to two-digit numbers.

KS1: Year 2 example

In Key Stage 2 (Year 5), the same principles are built upon as children move to more abstract methods such as column addition, including larger numbers and decimals. Here, place value counters and grids continue to be used to represent exchanges and to maintain the link between manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). and formal written methods.

KS2: Year 5 example

We recognise that achieving consistency is a long-term process. Teachers need confidence, subject knowledge and shared understanding to use manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). effectively.

Professional development has been central:

• Whole staff CPD sessions focused on why and how to use manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods)..
• Collaborative planning sessions to trial and adapt consistent approaches.
• Ongoing coaching and reflection to refine practice.

We are honest that this is still a work in progress. Developing teacher subject knowledge and ensuring alignment across the school takes time, but by investing in professional learning we are strengthening both teaching and pupil outcomes.

Looking Ahead

At St Peter’s, our CLEAR approach ensures manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). are not an ​‘extra’ but an integral part of teaching and learning. By making consistent, deliberate choices, we aim to provide every child with the tools to access mathematical ideas, deepen their understanding, and move confidently from concrete to abstract thinking.

Questions for reflection

• What deliberate choices have you made to ensure a consistent approach to the use of manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). across school?
• Are you explicit in which manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). should be used and why across the school?
• How do you ensure that teachers are confident in using manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). effectively?