• Quick Order
  • Wishlists
  • 0
    £0.00 ex VAT
Back
Menu
Close
early years essentials
Shop everything you need for your early years setting with our handpicked collection of essentials.
Shop now
early years new in
Refresh your early years settings with 100s of new and exciting early years products to choose from.
Shop now
Little Learners banner
Subscribe to Little Learners, our free early years magazine packed full of ideas and inspiration to help your setting flourish.
Subscribe now
YPO range
Switch and save with our YPO range, with hundreds of products to choose from.
Shop now
YPO cosy collection
We're excited to be working in partnership with Cosy, a renowned supplier of high quality and imaginative products. Shop the full collection!
Shop now
  • Animated image for Facilities Management Facilities Management

    Essential services to help keep your school running smoothly.

  • Ingredients and cooking pans Food and Catering

    Everything you need for your school meals and catering requirements.

  • person working at a desk Furniture

    Helping you create inspiring spaces.

  • Computer screen and printer ICT

    Technology and communications to help you stay connected and current.

  • certificate and books Professional Services

    Supporting your people and professional services.

  • School bus Transport

    Help get your students from A to B.

  • light bulb Utilities

    Review your energy contracts to help save money.

school exercise books varied colours
Discover our complete range of exercise books.
Shop all
Blue school exercise book with ruled pages
Ruled paper exercise books for a range of subjects.
Shop ruled
Red school exercise book with squared paper
Squared paper exercise books, perfect for maths.
Shop squared
Always in stock essentials
Explore our large range of always available products and get what you need, when you need it.
Shop now
Making life easier for MATs
Explore the benefits YPO can provide to Academies and Multi Academy Trusts across the country.
Find out more
YPO range
Switch and save with our YPO range, with hundreds of products to choose from.
Shop now
YPO cosy collection
We're excited to be working in partnership with Cosy, a renowned supplier of high quality and imaginative products. Shop the full collection!
Shop now
  • Animated image for Facilities Management Facilities Management

    Essential services to help keep your school running smoothly.

  • Ingredients and cooking pans Food and Catering

    Everything you need for your school meals and catering requirements.

  • person working at a desk Furniture

    Helping you create inspiring spaces.

  • Computer screen and printer ICT

    Technology and communications to help you stay connected and current.

  • certificate and books Professional Services

    Supporting your people and professional services.

  • School bus Transport

    Help get your students from A to B.

  • light bulb Utilities

    Review your energy contracts to help save money.

school exercise books varied colours
Discover our complete range of exercise books.
Shop all
Blue school exercise book with ruled pages
Ruled paper exercise books for a range of subjects.
Shop ruled
Red school exercise book with squared paper
Squared paper exercise books, perfect for maths.
Shop squared
Always in stock essentials
Explore our large range of always available products and get what you need, when you need it.
Shop now
Making life easier for MATs
Explore the benefits YPO can provide to Academies and Multi Academy Trusts across the country.
Find out more
YPO range
Switch and save with our YPO range, with hundreds of products to choose from.
Shop now
  • Construction worker Buildings and Construction

    Our expert team can help with building, construction, repairs and alterations. Browse our frameworks.

  • Meeting Corporate and Financial Services

    Help to increase efficiencies and provide better support to your people.

  • Energy frameworks YPO Energy

    Find ways to reduce your energy consumption with our energy team.

  • Cleaning equipment Facilities and Waste Management

    Providing safe and cost effective working environments.

  • Fleet of white vans Fleet

    Whether you're looking for fleet hire or purchase, speak to our specialist team.

  • food and catering worker cooking Food and Catering

    Ordering food and catering couldn't be simpler with our UK Food Deal.

  • food and catering worker cooking Furniture

    Create environments that are tailored to your unique needs.

  • fleet and highways worker Highways

    Providing specialist industry knowledge to help meet your needs.

  • Corporate meeting HR and People

    Our team are here to help with all of your recruitment and training.

  • Woman using technology Technology and Communication

    We can help you source cost-effective solutions with a range of frameworks.

  • Construction worker Buildings and Construction

    Our expert team can help with building, construction, repairs and alterations. Browse our frameworks.

  • Meeting Corporate and Financial Services

    Help to increase efficiencies and provide better support to your people.

  • Blue light Emergency Services

    A dedicated team set up to support you and offer tailored frameworks.

  • Energy frameworks YPO Energy

    Find ways to reduce your energy consumption with our energy team.

  • Cleaning equipment Facilities and Waste Management

    Providing safe and cost effective working environments.

  • Fleet of white vans Fleet

    Whether you're looking for fleet hire or purchase, speak to our specialist team.

  • food and catering worker cooking Food and Catering

    Ordering food and catering couldn't be simpler with our UK Food Deal.

  • food and catering worker cooking Furniture

    Create environments that are tailored to your unique needs.

  • health and social care workers Health and Social Care

    Help to support independent living by sourcing aids and equipment.

  • fleet and highways worker Highways

    Providing specialist industry knowledge to help meet your needs.

  • Corporate meeting HR and People

    Our team are here to help with all of your recruitment and training.

  • Woman using technology Technology and Communication

    We can help you source cost-effective solutions with a range of frameworks.

net zero 2023
To provide current perspective, expertise and guidance on the role of procurement in meeting net zero targets, public sector buying organisation YPO and local public sector innovation partnership iNetwork have come together again to host a series of free online webinars. Watch the series here.
Watch now
Energy hub
We know that securing energy contracts can be a complex and difficult process, but we are here to help you. Explore our Energy Hub to find help and guidance, latest updates and more.
Explore now
Price freeze
Discover prices frozen on 50 school essentials, with prices guaranteed until 2025. Get stocked up on your classroom essentials for less, and help support the NSPCC with every purchase!
Shop now
1000s of products dropped and locked until 2025
Discover 1000s of products dropped and locked until 2025! Shop now!
Shop now
New-In-Updated
Kit out your classroom and shop 100s of new products at great value prices.
Shop now
Clearance-Banner-Updated-2
Once they're gone... they're gone! Shop clearance here and save on a range of essentials.
Shop now
Banner
Make your budget go further with our collection of classpacks, and save on a range of classroom essentials.
Shop now
YPO range
Switch and save with our YPO range, with hundreds of products to choose from.
Shop now
Products
Close
Frameworks
Close
  • Construction worker Buildings and Construction

    Our expert team can help with building, construction, repairs and alterations. Browse our frameworks.

  • Meeting Corporate and Financial Services

    Help to increase efficiencies and provide better support to your people.

  • Blue light Emergency Services

    A dedicated team set up to support you and offer tailored frameworks.

  • Energy frameworks YPO Energy

    Find ways to reduce your energy consumption with our energy team.

  • Cleaning equipment Facilities and Waste Management

    Providing safe and cost effective working environments.

  • Fleet of white vans Fleet

    Whether you're looking for fleet hire or purchase, speak to our specialist team.

  • food and catering worker cooking Food and Catering

    Ordering food and catering couldn't be simpler with our UK Food Deal.

  • food and catering worker cooking Furniture

    Create environments that are tailored to your unique needs.

  • health and social care workers Health and Social Care

    Help to support independent living by sourcing aids and equipment.

  • fleet and highways worker Highways

    Providing specialist industry knowledge to help meet your needs.

  • Corporate meeting HR and People

    Our team are here to help with all of your recruitment and training.

  • Woman using technology Technology and Communication

    We can help you source cost-effective solutions with a range of frameworks.

What makes fractions difficult to understand?

‘Fractions’ is often a topic area that many adults (and children) find particularly challenging, leading to uncertainty and maths anxiety. For many of us, if we reflect on our childhood experience of learning about fractions, it was mostly abstract procedural-based learning of tips and tricks (with very little understanding, in many cases). Models, when used, were often a linear fraction wall, pizzas or other circular images - the relatable context was often linked to food. The relationships between these models were not always explored and therefore the connections and relationships were often missed or confused. 

Fractions, decimals, ratios and percentages are essentially different forms of notation for the same ‘rational numbers’ - we represent them symbolically in several different ways. Often these different forms are taught at different times or using different representations, resulting in children not making the connections. Not having a secure understanding of the relevant mathematical language can be a further hindrance for children in explaining their understanding. 

Added to all of this, we now have children in our primary schools who have had at least two years of disrupted teaching and who may have missed core conceptual understanding. Did you know that the Numicon approach develops key mathematical ideas and vocabulary, supporting children to develop a deep understanding? 

The Numicon learning theories and pedagogy

Many of us are familiar with Numicon Shapes, and often these are seen as an integral part to a developed mathematical understanding for the youngest children in school. The Numicon Shapes are one element of the Numicon approach; a way of teaching mathematics that grew out of a classroom-based research project conducted by Ruth Atkinson, Romey Tacon and Dr. Tony Wing.

There are two main learning theories that underpin the Numicon approach: Jerome Bruner’s enactive-iconic-symbolic representations, often referred to as concrete-pictorial-abstract (or the CPA approach) and Numicon’s own pedagogy.

In Numicon, we interpret Bruner’s representations as follows:

We do not see this as a progressively linear theory. Rather, we believe that by engaging in a concrete activity the children will also be developing their visualisation and describing their mathematical understanding. Sometimes the children might use a concrete resource to prove their thinking after they have worked using abstract notation. 

This theory links into the Numicon pedagogy wheel:

Numicon

All Numicon planning incorporates these learning theories, as exemplified below.

Adding fractions with Numicon

Let’s consider a Numicon activity taken from Book 3. In this activity children are writing adding sentences with fractions with the same denominator for the first time. If the Numicon planning is being followed in order, they will already have used resources to represent fractions and have met the language of numerator and denominator.

Start by asking the children to look at a six Shape. Ask, what is the relationship between one of the holes and the Numicon Shape? Agree one hole is one out of six or one-sixth. I would reinforce this understanding by counting the voids, one-sixth, two-sixths, three-sixths, four-sixths, five-sixths, six-sixths makes one whole. Next ask the children to cover their six Shape with two red, one green and three yellow pegs. Now ask them to discuss with their partner:

What fraction of the model is covered with red pegs, with green pegs, with yellow pegs?

numicon

There is no expectation that the children will discuss equivalent fractions for this model. However, if they do, you should discuss the relationships they can see.

Next ask the children to look closely at their model. Ask, what part of the fraction is represented by the Numicon pegs (The numerator) and what part is represented by the Numicon Shape? (The denominator). How does this help us to write the fraction two-sixths? (The two pegs sit on top of the Shape, i.e. the numerator sits on top of the denominator). Now ask the children to write an adding sentence to record the fraction of each colour in their model.

Numicon

Ask, what do you notice about the number sentence? Agree that in this example the denominator has remained consistent, but the numerator has been added together. Finally, ask the children to work with a partner to find different ways to fill the six-shape to see if they can form a generalisation for adding fractions with the same denominator. Agree that when we add fractions with the same denominator, what we actually add are the numerators. This will support the children to consider subtraction (and later multiplication) of a fraction by a whole number.

Final thoughts

How can we support children to secure a deeper understanding of fractions?

Finally, a further consideration is that Numicon has a core set of concrete resources which continue to be used as a child progresses through school. The resources are the same, but the mathematics we explore is different. Using the same resources supports the children’s confidence as they have already established the relationships and connections of the resources through play activities in the Early Years.

For example, here we have a baseboard being used to explore fractions, decimals and percentages:

Numicon

This is also a great activity to explore the equivalence between one-half and two-quarters.

Numicon 

A magnified one Shape becomes a decimal baseboard, here showing 0.1

Numicon 

Using the baseboard to explore percentages and connections between fractions, decimals and percentages e.g. 1/100 = 0.01 = 1% and 35/100 = 0.35 = 35%.

 

To learn how to get the most out of your school's Numicon resources with your Key Stage 2 pupils, you can sign up to the NCETM-accredited Professional Development course 'Progression with Numicon for ages 8-11 (KS2//P4-7). Click here to learn more.

 

Rebecca Holland is an independent Educational Consultant who has gained a wealth of experience as a primary teacher, subject leader, chair of governors, primary mathematics consultant and a school improvement consultant both in the UK and internationally. She is a lead maths consultant at Oxford University Press and is delighted to work on the authoring teams for Numicon and My Maths. 

No Image Available
Author

Rebecca Holland

Independent Educational Consultant