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The Ultimate Guide to Bar Modelling: How To Use and Apply the Bar Model In KS1 and KS2 Maths

Now that bar modelling is a staple of classrooms across the UK, we thought it was time to show you how we here at Third Space Learning use this pictorial representation within our 1-to-1 intervention lessons. The aim is to give you a few ideas of how you can use it too no matter what primary school year you teach maths to. Bar models for all we say! 

While maths used to be taught by working out page after page of calculations until the theory behind what you were doing got hammered into your brain through constant repetition.

The idea of using pictures as part of teaching maths was a rarity, but one idea that was introduced in the 1960s by Jerome Bruner – is now at the forefront of maths teaching – the concrete pictorial abstract approach (CPA), most frequently seen in our increasing use of the bar model!

If you think you need a quick revision on the bar model before you start, I recommend you have a read of this free resource – the Ultimate Guide to Bar Modelling – and take a look at the explainer videos on the bar model in our CPD video library.

The Ultimate Guide To Bar Modelling goes through in great detail:

  • What bar models are
  • The benefits of using them
  • How to introduce them into your school
  • Which types of maths problems they can help you to solve 
  • Much, much more!

What Is Bar Modelling?

The bar model method (sometimes known as the Singapore bar method) is a way of representing maths problems pictorially. Its use was popularised through the Singapore maths method, a maths mastery-focused teaching strategy from (unsurprisingly) Singapore that has been increasingly used in the UK. 

A bar model is, put simply, a diagram designed to aid with maths problem solving. Learners draw bars that are used to represent the known and unknown quantities in a problem, helping them visualise and contextualise all the relevant information in a question. This is especially important for complex word problems, where pupils might get confused by the ‘surface’ information. 

Bar modelling is one way of supporting children through the pictorial stage of the CPA approach to learning; bar models aren’t calculations themselves; they act as a visual comparison model that helps learners decide which operation to use to solve the problem. 

Bar models are often introduced with addition and subtraction problems, as these can be easily represented using bars of differing lengths. They can also be used with more complex topics however, such as statistics and data handling, percentages and so on.

While bar modelling is mainly used with Key Stage 2 pupils, it can be introduced in Key Stage 1 to great effect. It is usually too advanced for use with early years, however.

How We Use Bar Modelling

What I want to do in this post is outline how we use bar models here at Third Space Learning and how alongside our maths intervention the resources we have created could be effectively used to improve your teaching.

The core of the Third Space Learning offer is of course the pedagogy behind our online tuition for maths, because we are able to gauge immediately after every lesson, how successful it was and what we could do to improve it. In any week up to 6,000 pupils will be receiving one of our 270 lessons, and we record every lesson a child receives from their tutor so we can look back and review where and how progress was made or additional scaffolding was required. 

Since we started teaching 1-to-1 online in 2014 we’ve vastly increased the pictorial representations we use. Like many schools following a mastery approach to maths, we find that they just help children to develop deeper conceptual understanding. And far and away, the bar model is the best of the tools we use!

The Ultimate Guide to Bar Modelling

Get to grips with using the bar model method - from basic arithmetic to multi-step problems - ready to help your pupils use it in their lessons!

How We Use Bar Modelling In Our 1-to-1 Maths Intervention Lessons

Bar modelling is a mastery maths method that can be used to help teach many topics in maths, from place value and the four operations through to fractions to ratios. Their versatility is one of their strongest points in your classroom, and our online one too!

Find out more about teaching for mastery with our maths mastery toolkit.

Bar models are particularly useful if lessons where greater explanation is needed.  Here are the bar model methods we use across the maths curriculum to teach key topics.

Using bar modelling to teach fractions

From lessons on Simple equivalent fractions to Adding and Subtracting all kinds of fractions to Fraction problems, this topic is made more visual and easier to understand by simply inserting bar models into the lessons.

The nature of fractions makes the bar model the perfect way to teach them, and pupils often dividing a bar into the appropriate fraction very simple.

Our interactive learning platform means that no matter what question comes up, or what the conversation is that follows on from a question, both tutor and pupil are free to create their own bar model to help cement the point at hand.

Bar Modelling Lesson Slide

You may not have even known you were using a bar model when teaching fractions.

Hands up all those teachers who’ve used a fraction wall?

Fraction Wall Bar Model Lesson Slide

There you go, you’ve used a bar model!

To learn more about how the platform works, including about how we use the bar model, get in touch with the team today.

Using bar modelling to teach ratio and rates

Another pair of topics that lend themselves to the bar model well, ratio and rate based questions can be presented easily in a visual manner as a way to help pupils solve problems. As shown in the example below, by breaking the problem down in such a way, our tutors can explain the problem step-by-step to help ensure that the point has come across.

bar model ratio visualisation
A word problem from Third Space Learning’s online platform showing how to represent ratios.

Using bar modelling with word and number problems, estimating and decimals

Bar models are incredibly useful when working out KS2 SATs style Year 6 word problems or calculations involving number problems, estimation or decimals.

A bar model allows you to ‘unpack’ the question and set it out visually so that the child can see the difference in size of the bar models, depending on the size of the number, which can then help them to work out what the question is asking them to do.

In the example below, a tutor might first help a pupil use the bar model to estimate the value of the blue bar using the orange and purple bars, then help them attempt the inverse – using the estimated value of the blue bar to check that a subtraction yields a similar result.

Bar Modelling in a lesson about inverse calculations

Why we don’t use bar modelling for every topic

Crucially, we have only used bar models in a selection of lessons, as using them in every lesson would not only devalue their importance, but make pupils think that they are the only way to work out every problem.

While bar models can be used for most topics in maths, including multi-step word problems, they are only one weapon that a pupil should have in their arsenal.

How To Use Bar Modelling CPD Videos

If you explore the Third Space Learning Maths Hub, you will find that one of the topics is entitled Bar Models. Click on this and you will find over 30 videos on how to use bar models to teach a variety of subjects, from solving percentage problems to complex KS2 multiplicative problems, as well as videos explaining the basics of bar models and how to introduce them into Year 6.

Bar Model Videos On The Maths Hub

These videos are quick, usually being a few minutes long which means that they are great for teachers and children alike.

How you can use these bar modelling videos

As a teacher, you can use these videos whilst planning your lessons, to give you ideas about how to teach the topic or as a new way to approach the subject.

They can be used within lessons as starters, reminders or as part of a flipped learning platform, with pupils watching them at home, ready to use these skills to solve problems in class.

As mentioned, the collection of 34 videos we have on the Maths Hub on bar modelling covers a wide range of topics, and some of the subjects you will find covered include:

  • Bar Modelling: An Introduction
  • Bar Modelling: The Basics Explained
  • How To Use Bar Models To Help Solve A Multi Step Worded Fraction Problem
  • How To Use Bar Modelling For A Subtraction Problem
  • How To Get Pupils Solving Equations Using Bar Models
  • How To Solve A Complex Addition And Subtraction Word Problem Using Bar Modelling
  • How To Introduce Bar Modelling In Year 6
  • How To Use Bar Models To Solve A Simple Multiplication Problem
  • How To Use The Bar Model To Solve Multiplicative “Times Bigger” Problems
  • How To Use Bar Models To Solve Complex Problems Additive And Multiplicative Relationships
  • How To Use Bar Models To Solve A Simple Subtraction Problem
  • An Introduction To Bar Models For Comparison Problems
  • How To Use Bar Models To Help Solve A Multi Step Worded Multiplication Problem
  • How To Use Bar Models To Solve A Simple Fraction Problem
  • How To Use The Bar Model To Solve Percentage Problems

A peek behind the scenes of these premium bar modelling videos

Each of the videos discussed above are available to our premium Maths Hub subscribers, and the content within each of the videos has proven to be very popular. The videos are packed with useful tips and tricks about how to get the most from the bar model in your lessons. You won’t want to miss out on them so if you want to review them for use in your own school, please book a demo here.

Bar Model Lesson example Third Space

An example of a video explaining how bar modelling can help you with multi-step word problems.

bar model lesson example

Bar models being used to work out a ratio question.

Bar model example being used in a Maths Hub video

A solution to a tricky fractions problem being worked through using the bar model. 

This vast collection of videos can be found alongside some amazing resources for KS2 on how to use bar models when teaching in the classroom.

If you would like to discover the videos and resources, they can be found on the Maths Hub.

How We Use Bar Modelling In Our Teacher Training

As part of their training to become tutors for Third Space Learning, our videos and lessons are used as materials to introduce them to the concept of bar models and how they can be effectively used to teach topics in maths.

As we at Third Space Learning consider bar modelling to be an important aid to excellent teaching, we created a tool that a tutor can use during a teaching session to create their own bar models.

Bar Modelling being used by maths tutors

The square button allows the tutor to quickly create bars to aid their teaching, which can be shaped to the size the tutor requires, whether it is being used for a part/whole or comparison bar model.

The button can even be used by the pupil with the instruction of the tutor, allowing them to try and create their own bar model to help them solve the problem they are attempting.

This continues into our post-session questions, where bar models are used as a pictorial guide to help pupils work out the problem they have been given.

Again, like with our lessons, bar models are used sparingly so that pupils can use a range of different methods. However, the lessons that use bar models will have post-session questions with bar models, so as to demonstrate their importance for that particular topic.

Bar Model Slide From Third Space Learning

Why We Use Bar Modelling In Our Lessons

At Third Space Learning, we support the focus on helping children master the topics they are taught in maths, and our adoption of bar models across our various resources demonstrates our desire to give children every tool they need to tackle the maths problems they face.

However, as stated earlier, bar models are just one way of teaching maths topics, not the only way, and it is not up to us to tell teachers what method they should use. Some teachers may already make great use of bar models in their teaching and our resources will be useful as a reminder or handy tool to use in a particular lesson they might have been struggling with.

New teachers, or teachers new to the idea of bar models, will find our resources will explain to them how important bar models can be and start to guide them into how and where they can be used.

How To Introduce Bar Modelling Into Your School
Another snippet from the Ultimate Guide To Bar Modelling

Our goal at Third Space Learning is to not only provide world class 1-to-1 tuition via our interventions, but to make pupils confident and well-rounded learners, utilising as many methods and ideas as possible to solve any problem they are given.

Bar models allow pupils to become more involved in their learning and as Benjamin Franklin said:

“Tell me and I forget. Teach me and I remember. Involve me and I learn.”

Things To Take-Away From This Blog

If you are in a rush, these five points summarise what we think about the bar model:

  • Bar models are an excellent way of visually portraying a problem, making it easier for pupils to understand what they are being asked to do.
  • Bar models should be used as one example of methods to solve problems, and are especially useful for certain topics, such as fractions, ratios or missing number problems.
  • Bar models can be used with children of any age group or ability, on a variety of mediums, from videos to whiteboards to multi-link cubes.
  • Bar models are especially useful when teaching pupils with learning difficulties or special needs, who might respond better to visual prompts.
  • Bar models form an important part of our 1-to-1 lessons as they give us a great chance to help pupils solve their problems in a visual manner. This can be replicated easily in the classroom too.

Read more

Do you have pupils who need extra support in maths?
Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons designed to plug gaps and boost progress.

Since 2013 we’ve helped over 60,000 primary school pupils become more confident, able mathematicians. You can learn more about the maths intervention or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Primary school tuition targeted to the needs of each child and closely following the National Curriculum.

Chris Xerri
Chris Xerri
E-learning Content Creator
Curriculum and content writer for Third Space Learning, Chris is responsible for creating, analysing and maintaining maths content, as well as contributing blogs and ideas for future development.
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Downloadable resource

The Ultimate Guide to Bar Modelling

Get to grips with using the bar model method - from basic arithmetic to multi-step problems - ready to help your pupils use it in their lessons!

Download Free Now!
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Downloadable resource

The Ultimate Guide to Bar Modelling

Get to grips with using the bar model method - from basic arithmetic to multi-step problems - ready to help your pupils use it in their lessons!

Download Free Now!