How to use mathematical manipulative tools in the classroom

Mathematical manipulative tools are simply resources used by children to explore maths in a practical way. They are a key component of the Concrete-Pictorial-Abstract (CPA) approach used by Maths — No Problem!

Commonly used concrete maths resources include:

• Multilink cubes
• Numicon
• Counters
• Cuisenaire rods
• Bead strings
• Balance scales
• Dice
• Dominoes
• Clock faces
• Digit cards
• Hundred squares

You don’t need to limit yourself to purpose-made maths resources. If you’re working with a limited budget, consider creating your own quick and cheap manipulatives.

Many teachers create their own resources using everyday equipment. This is useful for grounding the lesson in a practical starting point. It offers the opportunity to surprise the children with a new way of seeing things.

Effective homemade and repurposed manipulative tools could involve:

• Toy money
• Jenga blocks
• Lego pieces
• Beads and buttons
• Dried pasta and beans
• Straws
• Paper plates

How do Manipulatives Help Students Learn Mathematics?

Working with manipulatives gives ownership back to the children. They can show you their solutions to a problem and try out your modelled examples themselves.

For children to understand a new concept, they need to:

• See different representations of it
• Use a range of manipulatives to explore ideas
• Build their mathematical vocabulary
• Develop ways to express their thinking process

How to Use Manipulatives in the Classroom

Every teacher finds their own way to make the most of mathematical manipulatives. Simple changes in the way you organise and use them in lessons can make a significant difference.

Consider:

1. How accessible are the resources?
2. Do you routinely use a range of manipulatives?
3. Do the children in your class know how they can use the resources in different ways?

1. Accessibility of Manipulatives

It is vital that concrete resources are used by all children. They are not just for struggling learners. Think about how you can make sure children access them independently when they need them.

Consider:

• Labelling trays so children can freely access them
• Displaying resources on top of a work surface
• Providing a box of manipulatives for each table to use when working in groups
• Labelling boxes that you can pull out during maths lessons and leave in a central location
• Praising children who use manipulatives to explain a concept to a partner or the class

Make sure you have adequate amounts of manipulatives. In larger schools, teachers might timetable lessons to share resources between classes. In smaller schools, year groups could buddy up to share in the same way.

2. Use a Range of Manipulatives

Every teacher has preferred ‘go-to’ resources, and it’s easy to become reliant on them. Aim to use a wider range to engage your class. Let them see the different possibilities manipulatives can offer. This will help to stop them compartmentalising and see links between ideas.

You could try:

• Using different manipulative tools to show the same concept
• Discussing which resources suit a problem and why
• Asking children to use different manipulatives to show the same answer
• Using the same manipulative to answer lots of different types of questions to show how flexible they can be

As children move on to abstract thinking, they can look back to their mathematical manipulative tools. This will help them to visualise solutions.

3: Teach Children How to Use Mathematical Manipulative Tools

Children need to become familiar with a resource before they can start to use it mathematically. Play before formal learning is essential. Allow children the chance to explore the manipulatives. Let them experiment, make mistakes and invent new ways to use them. They can talk about how effective and efficient these methods might be.

After this stage, modelling is essential. Verbalise your thought process as you use them to demonstrate problem-solving and calculations.

When working independently, encourage the children to choose what to use with ‘How could you show me...?’ questions. Ask them to explain their reasoning and demonstrate a concept to a partner or adult.

Enjoy Using Mathematical Manipulative Tools in your Classroom

Using concrete resources is an engaging way to bring maths to life. Starting with mathematical manipulatives allows children to visualise a concept. They can explore different ways to solve problems.

To effectively use these concrete resources, remember to have a wide range available. Allow your children time to become familiar with them. Ensuring that everyone has access will help promote them to all children. They will see them as a fantastic starting point in the journey to abstract thinking.