Tips for teachers: 53. Using manipulatives and representations in maths

Oct 29, 2025 | Blogs

Tips for teachers: 53. Using manipulatives and representations in maths

Oct 29, 2025 | Blogs

‘Manipulatives play an important role in mathematics education. They bridge the gap between abstract concepts and tangible understanding, helping pupils grasp basic number sense. In fact, the National Curriculum emphasises their importance across all key stages, recognising that hands-on learning is vital for developing maths fluency, reasoning, and problem-solving skills.…manipulatives are simply hands-on tools that make abstract mathematical concepts concrete and visual. They’re the building blocks, quite literally in some cases, that help pupils wrap their heads around tricky number ideas through good old-fashioned play, exploration, and modelling.’ (Manipulatives in maths)

Using manipulatives in maths is crucial as they provide a tangible, hands-on approach to learning abstract concepts, enhancing student engagement, understanding, and problem-solving skills.

‘Using manipulatives and representations purposefully can support children to develop visual images. These are beneficial to all children but are paramount for learners with dyscalculia and struggling learners, helping them to ‘see’ the maths.’ (Manipulatives and representations)

Why should we use manipulatives and representations?

• Concrete Representation of Abstract Concepts: Manipulatives, like base-ten blocks or fraction circles, allow students to physically represent and manipulate mathematical ideas, making them easier to grasp and understand.

• Enhanced Engagement and Motivation: The hands-on nature of using manipulatives can make math lessons more engaging and enjoyable, leading to increased student motivation and interest in the subject.

• Improved Conceptual Understanding: By interacting with physical objects, students develop a deeper, more intuitive understanding of mathematical concepts, rather than just memorizing rules and procedures.

• Development of Problem-Solving Skills: Manipulatives provide opportunities for students to explore different strategies and approaches to solving problems, fostering critical thinking and problem-solving abilities.

• Bridging the Gap Between Concrete and Abstract: Manipulatives help students make connections between concrete, real-world representations of math concepts and their abstract, symbolic counterparts, facilitating a smoother transition to more advanced mathematical topics.

• Multisensory Learning: Manipulatives engage multiple senses (sight, touch, and sometimes even sound), which can lead to more effective learning and retention.

• Scaffolding Learning: Manipulatives can serve as a scaffold, providing support for students who are struggling with a particular concept, allowing them to build their understanding gradually.

• Increased Retention: When students actively engage with math concepts through manipulatives, they are more likely to retain that knowledge and apply it in different contexts.

• Promoting Mathematical Communication: Manipulatives can also be used to facilitate mathematical communication, as students can use them to explain their thinking and reasoning to others.

‘Manipulatives can be powerful tools for supporting pupils to engage with mathematical ideas. However, they are just tools and need to be used purposefully and appropriately in order to have an impact.’ (Making use of manipulatives)

This blog was written by Bretta Townend-Jowitt, Education Consultant and Trainer.

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