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What Is a Bar Model? How to Use This Maths Problem-Solving Method in Your Classroom

Written by B

Teaching mathematical problem-solving to your students is a crucial element of mathematical understanding. They must be able to decipher word problems and recognise the correct operation to use in order to solve the problem correctly (rather than freaking out as soon as they see a mathematical problem in words). But what is the best strategy for embedding this knowledge into your students? Enter the Bar Model Method , also known in education as a tape diagram, strip diagram, or tape model.

The model has gained traction in classrooms around the world, so you may be thinking it’s time to introduce it in your classroom. But what is the bar model all about, and what are the advantages of using this method with primary students? The maths teachers on the Teach Starter team are here with a quick primer to help you decide if this is the right path for your maths class!

Explore the latest maths teaching resources from Teach Starter!

What Is a Bar Model?

The Bar Model is a mathematical diagram that is used to represent and solve problems involving quantities and their relationships to one another.

It was developed in Singapore in the 1980s when data showed Singapore’s primary school students were lagging behind their peers in math. An analysis of testing data at the time showed less than half of Singapore’s students in years 2-4 could solve word problems that were presented without keywords such as ‘altogether’ or ‘left.’ Something had to be done, and that something was the introduction of the bar model, which has been widely credited with rocketing the kids of Singapore to the top of maths scores for kids all around the globe.

At its core, the bar model is an explicit teaching and learning strategy for problem-solving. The actual bar model consists of a set of bars or rectangles that represent the quantities in the problem, and the operations are represented by the lengths and arrangements of the bars. Among its strengths is the fact that it can be applied to all operations, including multiplication and division . They’re also useful when it comes to teaching students more advanced maths concepts, such as ratios and proportionality.

The Bar Model combines the concrete (drawings) and the abstract (algorithms or equations) to help the student solve the problem.

How to Use a Bar Model in Math

Whether you’re calling it a bar model, a strip diagram, or a tape diagram, the concept is the same – you have rectangular bars (or strips) that are laid out horizontally to represent quantities and the relationships between them.

• The bars themselves — horizontal rectangles—  represent the problem.
• The length of the bar(s) represents the quantity.
• The locations of the bars show the relationship between the quantities.

Visualising this relationship helps students decide which operation to use to solve the problem. The student then labels the known quantities with numbers and labels the unknown quantities with question marks.

The three basic structures are:

• Part-Part-Whole
• Equal Parts

Our printable  Bar Model Poster Pack is a perfect way to introduce your students to the basics of the Bar Model!

Many teachers (particularly in the primary years) will recognise elements of the Bar Model as being similar to the Part-Part-Whole method we’ve been teaching forever.

The Bar Model could be looked at as an extension of this concept. It can be used by students right through primary school (and beyond) not only to solve addition and subtraction problems but to tackle multiplication and division word-based problems as well.

Teaching with the Bar Model

The Bar Model can easily be incorporated into your primary maths instruction, from simple addition to more complex multiplication and division and so on. Here are just a few ideas from our teacher team:

• Use part–whole bar models to show word problems with a missing number element to teach addition or subtraction.
• Incorporate into your  CUBES strategy  — The E in CUBES stands for Evaluate and Draw. As a Bar Model is a drawing, this is the perfect place to use it.
• Use the bar model method to help students see how a bar must be cut into equal parts when multiplying and dividing.
• Help students visualise  fractions with the bar model — Use the rectangles to help students see how the fractions relate to whole numbers by showing the relationship between the numerator and denominator.

Explore our complete collection of curriculum-aligned resources for teaching about operations !

Banner image via Shutterstock/Komuso Colorsandia

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One of them was literally The Singapore Bar Model and I can’t remember the other. I’ve moved schools in between time and left the books at my previous school.?

Thanks for your comment Karen. We hope this blog was helpful.

I'm so pleased to see this on Teach Starter. I have been 'fiddling' around with this strategy for a couple of years now. We have recently bought some books to help us finally do this a bit better.

Hi, Karen! Thanks for your positive comment. It's a really interesting strategy and it's just starting to pick up popularity. I'd love to hear which books you've bought!

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What are bar models and how to use them to solve problems

What are bar models where did they come from.

Bar models have been part of the Singapore Ministry of Education’s mathematics’ concrete, pictorial, abstract process since the late 1980s.

Their origins date back further than the late 1980s, though. They were used as part of the American psychologist and educationalist, Jerome Bruner’s three-part lesson process in the late-1960s. (To learn more about three-part lessons, please read our blog that delves deeper into the concrete, pictorial, abstract approach to mathematics teaching and learning.)

Bar models have more recently become popularised in the UK and North America due to the push for better PISA rankings for mathematics by the governments of the UK, US and Canada, specifically by applying Singaporean teaching and learning strategies in their schools.

Different ways of using bar models

Bar models can be used by children (and grown-ups, too!) for a variety of uses: partitioning numbers in place value, all four operations individually (addition, subtraction, multiplication and division), multi-step and mixed operation questions, fractions, percentage increases and decreases, times tables, calculating missing angles and much, much more!

When it comes to progressing from using physical equipment (concrete), to pictorial (sketched) learning into abstract mathematics, bar models are one of the key structures that work as a bridge throughout the process. They can be used with concrete equipment, in a purely pictorial way, and as an aide-memoire when writing abstract number sentences.

Using the bar model flow chart to unpack RUCSAC

RUCSAC is an acronym that has been popular for teachers to help children unpick word problems.

Read the question carefully Underline keywords in the question Choose the required operation(s) Solve the problem Answer the problem Check your answer

Many teachers have fallen out of love with RUCSAC, particularly because underlining the keywords is quite a vague instruction. (Or, on some posters, even worse, understanding the question.)

The following flow chart helps to unpack and repurpose RUCSAC to the point of usefulness once more.

Using bar models in a concrete/pictorial way in KS1

Take the following word problem:

If Jamal has three apples and Ruth has two apples, how many apples do they have altogether?

To help children solve this problem, we could use a bar model and mathematical equipment. You could use either real apples, counters, cubes, or similar, as represented in the solution below. Shown in the Number Stacks video later in the blog is another handy resource: prepared bar model frames.

Using bar models in the “standard” pictorial way in KS1

We are presented with the same word problem, but this time, the bar model itself carries the pictorial nature of the solution.

Both parts hold numbers and the total bar holds also a number by itself, without the familiar unit of measurement (apples).

Using bar models in a pictorial/abstract way in KS1

Finally, with the same word problem in mind, we can see how using the bar model supports children in progressing to using abstract number sentences, with the + and = symbols employed in this scenario.

Using bar models in a concrete/pictorial way in KS2

If a picture is worth a thousand words, this wonderful video by Number Stacks is worth at least a million words in demonstrating best practices in using bar models in a concrete/pictorial manner in KS2. In this instance, focusing on fractions of amounts.

When it comes to bar models… plain paper is better than grid/squared paper!

Ultimately, bar models should lower the cognitive load of children. Using bar models should allow them to work through problems more quickly, not slow them down.

If a child is working out how many squares in their grid/square paper exercise book they need to use to draw the bar model, then this thinking is slowing them down.

The only time you want a series of bar models to have a difference in width between their total length is if children are using comparison bars or are working on a multi-step problem and have subtracted an amount in a previous step (or enlarged the total part if adding or multiplying later on in a multi-step problem).

Regardless, using plain paper allows children to create approximate equivalence and difference between bar models while maintaining a fluent, or near-fluent, pace in their working out.

Fixed policy vs. varied bar model presentation

Some schools and schemes will advocate for one type of bar model usage over another.

Some might exclusively use bar models like those shown on the left of the slide above, while others might favour bars curly brackets, and double arrow-headed lines, as on the right-hand side of the slide.

There is certainly strength in having a consistent and preferred set of representations for children to become confident with initially; however, ultimately, it serves children best to be aware of a range of representations, especially given the various familiar and less familiar ways bar models are presented in the end of key stage assessment papers.

Part-part-whole bars vs. comparison bar models

The use of part-part-whole bars versus bars with curly brackets is particularly apparent when performing subtraction calculations.

Here, the following word problem has been posed: “If Ahmed and Eve have 8 oranges in total and Ahmed has five oranges, how many oranges does Eve have?”

So, using our bar model flow chart, we can draw up a part-part-whole bar model.

Do you have the total? Yes. So, we put 8 in the total bar.

Do we have parts or are we missing a part? We are missing Eve’s part.

Are the parts equal or unequal? We do not know yet, but it is likely that they are unequal. So, we know to draw a bar model for subtraction, as shown above (on the left-hand side of the slide).

Similarly, we can use a comparison bar model, as we are seeking to find the difference between the total amount of eight apples and Ahmed’s five apples. (Shown on the right-hand side of the slide.)

Either way, an adult modelling or children solving the word problem using either type of bar model should arrive at the correct answer. Eve has three apples.

Using bar models for subtraction in KS2

Bar models can be used for each of the four operations in KS2 (as well as multi-step, mixed operation problems, and more).

We have provided a similar subtraction word problem. Now the complexity has increased, as we are dealing with three-digit numbers and a unit of measurement, too.

Ahmed has to walk 453m to get to school. Eve has to walk 689m to get to school. What is the difference between the two friends’ walks to school?

Again, using our bar model flow chart, we can draw up a part-part-whole bar model.

Do you have the total? Yes. We know that Eve’s walk to school is the greatest distance. So, we will put 689m in the total bar.

Do we have parts or are we missing a part? We are missing the difference amount between the two friends’ walking distances to school. So, we will place Ahmed’s measurement of 453m in the known part bar.

Are the parts equal or unequal? Again, we do not know yet, but it is likely that they are unequal. So, we know to draw a bar model for subtraction, as shown above (on the left-hand side of the slide).

Much like the simpler subtraction word problem above, we can use a comparison bar model, as we are seeking to find the difference between Eve’s walk to school and Ahmed’s walk to school. Shown on the right-hand side of the slide is the comparison bar model.

Whether adults or children use the part-part-whole bar model or comparison bar model, assuming no transcription or calculation errors are made, the correct solution will be found: 236m.

Using bar models for addition

Bar models can be used to help solve addition calculations for all primary year groups.

Once more, we can use the bar model flow chart to help draw the bar model.

The word problem is: James has 237 tokens. Yasmin has 342 tokens. In total, how many tokens do the two friends have?

Do we know the total? No.

Are the parts equal? No, so we know it will be a bar model for addition.

Children should then draw two unequal parts, with 237 going into the smaller part and 342 going into the larger part.

Once they have completed the calculation, they will know that 579 is the sum (total). So, 579 goes into the whole bar.

Using bar models for multiplication

Bar models can be used for multiplication, from the 2 times table, all the way through to multi-digit by single-digit multiplication.

The word problem is: Farmer Sam has four cows. On average, each cow weighs 360 kg. How much do the cows weigh combined?

Here, we can use the bar model flow chart questions to help with demonstrating using bar models for multiplication.

Are the parts equal? Yes, so it is a multiplication calculation.

Next, do we know how many parts there are and how much each part is worth? Yes, four lots of 360kg.

So, using this information, children should be able to draw a bar model with four equal parts with 360kg in each part. Doing so should help them either mentally multiply or make jottings of repeated addition. The result, as shown, is 1,440kg.

Using bar models for division

Just as we have seen bar models used for addition, subtraction and multiplication, they work wonders for division, too!

The word problem is along a similar farmyard theme as the previous word problem: Farmer Sam has six rams that are all the same weight. In total, the six rams weigh 672 kg. How much does one ram weigh?

Do we know the total? Yes.

Are the parts going to be equal? Yes.

(And, into how many parts do we need to split the total? Six.)

So, in this case, children should then be able to start drawing their bar model with the total bar holding 672kg. They should then know to draw six equal part bars beneath the total bar.

If they are using mental strategies or a quick bus stop division calculation, children should then be able to write 112kg in each of the six parts, as well as after the equals symbol in a number sentence.

Using bar models for fractions of amounts

Bar models being used for fractions of amounts are covered in the Number Stacks video above, too.

When working with fractions of amounts, children will either be asked to find a unit fraction amount (one-third, one-fifth etc.) or a non-unit fraction amount (three-quarters, seven-tenths etc.). If it is a unit fraction of an amount problem, it requires the same as a division bar model solution, but when it is a non-unit fraction of an amount word problem, it requires a multi-step solution.

The word problem is: James had 355 marbles at the beginning of the year. By the end of the year, he has two-fifths of his marbles left. How many marbles has James lost? 

We can use the bar model flow chart questions to start helping us solve the problem.

Do we know the total? Yes. So, we can start by drawing a total bar with 355 written inside it.

Are there equal parts? Yes, we know we are going to be working with fifths, so there will be five equal parts.

Initially, the total, 355, needs to be divided by 5, meaning each of the five parts is worth 71.

We then know that James has two-fifths of his marbles left, meaning he has lost three-fifths of his marbles.

So, the final step (shown above by a curly bracket, but could have been a second bar model), demonstrates three equal parts of 71.

3 × 71 = 213. Therefore, James lost 213 marbles.

Using bar models to calculate percentages

Calculating percentages with bar models is a derivative of the division bar model.

The word problem is:

At full price, a pair of shoes cost £60. The price is reduced by 20% in the summer sale. How much do the shoes cost in the summer sale?

Again, we can work through the bar model flow chart questions.

Do we know the total? Yes, £60. So, £60 goes into the total bar.

Is there equal or unequal parts? Using known facts, that 20% is equivalent to one fifth, children should then know to split the part bar into five equal parts.

Children can then use their times tables knowledge to divide 60 by 5, to state that 20% of the full price is £12.

Then, there is the option to either multiple £12 by 4, or subtract £12 from £60. Either way, the correct solution can be found: the shoes will cost £48 in the sale.

Using bar models for algebra

Bar models work wonderfully for algebra. They can be used for working with formulae, expressing rules, solving equations and much more!

Here, we look at using bar models to work out an unknown value.

We can answer the initial bar model flow chart question to start with…

Do we know the total? Yes. So, we can put 22 into the total bar.

Do we know any of the parts? Are any of them equal? Well, we know one of the parts is 4. We also know that there are two equal unknown parts, too.

So, we draw the topmost bar model on the right-hand side of the slide above to start.

We can then subtract the known part value, 4, from the total, 22, to get the difference, 18.

Then, we can draw a second bar model, as shown on the bottom right-hand side of the slide. Initially, as 18 in the total bar, and a ‘y’ in each of the two equal, unknown part bars.

Then, it’s a matter of dividing 18 by 2 to solve the equation and know that each ‘y’ is worth 9.

Using bar models to solve multi-step word problems

A bar model, or series of bar models, is a great structure for solving multi-step word problems.

A papaya weighs 700g. A watermelon weighs twice as much. a) What is the weight of the watermelon? b) What is the total weight of the papaya and watermelon combined?

Here, we can see the pupil is using free-form bar models and curly brackets, rather than the part-part-whole bar models we have seen in the majority of the blog.

The pupil has drawn what is known already: a bar representing the weight of a papaya, 700g.

He has then drawn two bars each roughly as wide as the papaya bar. He knows that the weight of the watermelon is double the weight of the papaya. So, he can calculate that 700g × 2 = 1,400g to find the weight of the watermelon.

Next, all he has to do is combine the two weights together to solve the second part of the word problem. Then, he is ready to show that the total weight of a papaya and a watermelon combined is 2,100g.

Using bar models to calculate missing angles

The strength of bar models is their versatility. It isn’t just when teaching addition, subtraction, multiplication and division that they are helpful! They can be used for many areas of the curriculum, including calculating missing angles.

Again, we can return to the bar model flow chart questions.

Do we know the total? Yes, it should be a known fact that a full turn is equal to 360 degrees. So, we can start by writing 360 degrees into the total bar.

Do we know any of the parts’ values? Are the parts equal? Yes, we do know some of the parts. No, they are not equal.

So, then we know to draw three unequal part bars. The largest part represents 227 degrees, the next largest is the right-angle value of 90 degrees, and the smallest part should be empty to start with…

Then, it is apparent from the bar model that 227 and 90 degrees need to be combined, then subtracted from 360 degrees. So, the missing angle is 43 degrees.

Further Festive Bar Model Practice

Subscribers and non-subscribers alike can download our Advent CalenBAR resources.

There are four daily challenges to encourage the use of bar models to solve problems. They come in PowerPoint and PDF format, with a handwriting and dyslexia-font, as well as providing question and answer pages!

BONUS: FREE Bar Model CPD Slides

Bonus: free bar model cpd webinar recording.

Problem Solved: Bar Model Math (Grade 3)

This companion website to Problem Solved: Bar Model Math features PDFs of all the word problems included in the book. Display these problems on your whiteboard during whole-class instruction to support your teaching or print them to hand out to students.

Select and click on any of the lessons below to get started.

Problem Solved: Bar Model Math Grade 1

Problem Solved: Bar Model Math Grade 2

Problem Solved: Bar Model Math Grade 4

Problem Solved: Bar Model Math Grade 5

Problem Solved: Bar Model Math Grade 6

Mastery-Aligned Maths Tutoring

“The best thing has been the increase in confidence and tutors being there to deal with any misunderstandings straight away."

FREE daily maths challenges

A new KS2 maths challenge every day. Perfect as lesson starters - no prep required!

The Ultimate Guide To The Bar Model: How To Teach It And Use It In KS1 And KS2

Pete Richardson

Teaching the bar model in maths and different bar modelling techniques in KS2 and KS1 is essential if you want pupils to do well in their reasoning and problem solving. Here’s your step by step guide to how to teach the bar model as part of maths mastery lessons from early years through KS1 SATs right up to KS2 SATs type questions.

First we will look at the four operations and a progression of bar model representations that can be applied across school in Key Stage 1 and Key Stage 2.

Then we will look at more complex bar model examples for KS2 SATs, including how to apply bar models to other concepts such as fraction and equations.

Finally, look out at the end of the article for some further bar model worksheets and free resources to get you started.

What is bar modelling in maths?

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What is a bar model ? In maths a bar model is a pictorial representation of a problem or concept where bars or boxes are used to represent the known and unknown quantities. Bar models are most often used to solve number problems with the four operations – addition and subtraction , multiplication and division.

In word problems, bar models help children decide which operations to use or visualise problems.

The bar model is central to maths mastery, the pictorial stage in the concrete pictorial abstract (CPA) approach to learning. Bar models will not, however, do the calculations for the pupil; they simply make it easier for pupils to work out which calculation must be done to solve the problem.

Bar modelling is the term used when you are teaching, learning or applying your bar models, and drawing out each bar to represent the known and unknown quantities. Encouraging a child to ‘bar model’ a problem can help them to understand conceptually what maths operation is required from the problem, and how each part combines to make the whole.

Here bar modelling shows us that if 2 rectangles out of 3 rectangles are green, then two thirds of 12 must be 8. An understanding of bar models is essential for teaching how to solve all sorts of word problems especially those using four operations (addition, subtraction, multiplication, division), fractions and algebra.

Bar modelling is much used in Singapore and Asian Maths textbooks and is an essential part of the mastery maths approach used by schools at all stages of the national curriculum.

By using the bar method to visualise problems, pupils are able to tackle any kind of number problem or complex word problem.

Because bar models only require pencils and paper, they are highly versatile and can come in very useful for tests, especially SATs Reasoning Papers .

However the use of bar models can begin much earlier, from showing number bonds to ten or partitioning numbers as part of your place value work. 

Once a child is secure in their use of bar modelling for the four operations and can conceptualise its versatility, they can start to use it to visualise many other maths topics and problems, such as statistics and data handling .  

‘The Singapore Maths Model’ is another name for the bar model method. Despite this name however the Singapore bar model (like most of the maths mastery approach) is based heavily on the work of Bruner, Dienes and Bishop about the best way to help children learn : teaching for mastery. 

Bar models act as a ‘bridge’ between the concrete, pictorial and abstract (CPA in maths); once children are secure with using pictorial versions of their concrete materials, they can progress to using bars as visual representations.  

Bars are a more abstract way of representing amounts, making the transition to using wholly abstract numbers significantly less difficult. 

Also known as the ‘part part whole’ method or the comparison model, this kind of bar model uses rectangles to represent the known and unknown quantities as parts of a whole. This is an excellent method to help pupils represent the very common ‘missing number’ problems. 

This can be done in two ways: 

• As discrete parts to a whole – each unit in the problem has its own individual box, similar to using Numicon cubes. 
• As continuous parts to a whole – units are grouped into one box for each amount in the problem e.g. in 26 + 52, 26 would have one long bar, not 26 smaller rectangles joined together. 

When using the part-whole method, proportionality is key; all the bars must be roughly proportional to each other e.g. 6 should be about twice the length of 3. Often you’ll find this is referred to as the 

Part-whole models are generally used to visually represent the four operations, fractions, measure, algebra and ratio, but can be applied to many more topics (as long as they’re relevant!).

Read more: What Is The Part Whole Model ?

[FREE] Let's Practise Bar Model Word Problems KS2

25 scaffolded bar model word problems on the four operations. Questions suitable for Year 3 to Year 6.

There are a few steps involved in drawing a bar model and using it to solve a problem:

• Read the question carefully
• Circle the important information
• Determine the variables: who? what?
• Make a plan for solving the problem: what operation needs to be used?
• Draw the unit bars based on the information
• Re-read the problem to make sure that the bar models match the information given
• Complete the calculation using the determined operation.

Bar models KS1

Pupils in Reception and Year 1 will routinely come across calculations such as 4+3.

Often, these calculations will be presented as word problems: Aliya has 4 oranges. Alfie has 3 oranges. How many oranges are there altogether? With addition, subtraction and multiplication, to help children fully understand later stages of bar modelling, it is crucial they begin with concrete representations.

There are 2 models that can be used to represent addition:

Once they are used to the format and able to represent word problems with models in this way themselves (assigning ‘labels’ verbally), the next stage is to replace the ‘real’ objects with objects that represent what is being discussed (in this case, we replace the ‘real’ oranges with button counters):

The next stage is to move away from the concrete to the pictorial. As with all the stages, when pupils are ready for the next stage is a judgement call that is best decided upon within your school.

A general rule of thumb would be that towards the end of Year 1 or start of Year 2, pupils should be able to understand and represent simple addition (and subtraction) word problems pictorially and assign written labels in a bar model.

The penultimate stage is to represent each object as part of a bar, in preparation for the final stage:

The final stage stops the 1:1 representation. Each quantity is represented approximately as a rectangular bar:

As mentioned before, it is a judgement call for your school to make, but if you want pupils to use the bar model to support them in end of Key Stage 1 SATs tests, they are going to need to have had a fair amount of experience of this final stage.

The same concrete to pictorial stages can be applied to subtraction. However, whereas with addition it is really down to the pupil’s preference as to which of the 2 bar representations to use, with subtraction the teacher can nudge to pupils to one or other.

The reason? One represents a ‘part-part-whole’ model, the other a ‘find the difference’ model. Each will be more suited to different word problems and different pupils. Let’s examine those at the final stage of bar modelling:

Part-part-whole

Austin has 18 lego bricks. He used 15 pieces to build a small car. How many pieces does he have left?

Calculation: 18 – 15 =

Find the difference

Austin has 18 lego bricks. Lionel has 3 lego bricks. How many more lego bricks does Austin have than Lionel?

Calculation: 18 – 3 =

Bar model multiplication starts with the same ‘real’ and ‘representative counters’ stages as addition and subtraction. Then moves to its final stage, drawing rectangular bars to represent each group:

Each box contains 5 cookies. Lionel buys 4 boxes. How many cookies does Lionel have?

Due to the complexity of division, it is recommended to remain grouping and sharing until the final stage of bar modelling is understood. Then word problems such as the 2 below can be introduced:

Grace has 27 lollies. She wants to share them into 9 party bags for her friends. How many lollies will go into each party bag?

Grace has 27 lollies for her party friends. She wants each friend to have 3 lollies. How many friends can she invite to her party?

Now that we have established a structure across school that allows for children to use bar models for KS1 SATs, we are now ready to teach pupils how to use the bar model for a deeper understanding of complex problems during Key Stage 2 and particularly in preparation for KS2 SATs.

The key question at any stage, at any age is what do we know? By training pupils to ask this when presented with word problems themselves, they quickly become independent at drawing bar models.

For example, in the problem: Egg boxes can hold 6 eggs. We need to fill 7 boxes. How many eggs will we need?

We know that there will be 7 egg boxes, so we know we can draw 7 rectangular bars. We know that each box holds 6 eggs, so we can write ‘6 eggs’ or ‘6’ in each of those 7 rectangular bar. We know we need to find the amount of eggs we have altogether. We can see we will need to use repeated addition or multiplication to solve the problem.

Bar models KS2

Bar modelling can be used to solve Year 6 word problems . Let’s ramp up the difficulty a little. In a sample KS2 SATs, pupils are asked:

A bag of 5 lemons costs £1. A bag of 4 oranges costs £1.80. How much more does one orange cost than one lemon?

Pupils could represent this problem in the below bar model, simply by asking and answering ‘what do we know?’ This can

From here it should be straightforward for the pupils to ‘see’ or visualise their next step. Namely, dividing £1.80 by 4 and £1 by 5. Some pupils will not need the bar model to represent the next stage, but if they do, they would calculate and then allocate the cost onto the model:

Then those pupils that needed this stage, should be able to see that to answer the question, they need to calculate 45p – 20p. With the answer of 25p.

Download more bar modelling questions: Let’s Practise Bar Models Four Operations

Here’s another example from the sample key stage 2 tests involving fractions and how it can be solved using a fraction bar model . On Saturday Lara read two fifths of her book. On Sunday, she read the other 90 pages to finish the book. How many pages are there in Lara’s book? If we create our bar model for what we know:

Pupils will then see that they can divide 90 by 3:

As fractions are ‘equal parts’ – a concept they should be familiar with from key stage 1 – they know that the other 2 fifths (Saturday’s reading) will be 30 pages each:

Then they can calculate 30 x 5 = 150

Download more bar modelling questions: Let’s Practise Bar Model Fractions 

There are lots of other areas bar models can assist pupil’s understanding such as ratio, percentages and equations. In this final example, we look at how an equation can be demystified using the comparison model:

2a + 7 = a + 11

Let’s draw what we know in a comparison model, as we know both sides of the equation will equal the same total:

The bars showing 7 and 11 could have been a lot smaller or larger as we don’t know their relative value to ‘a’ at this stage. However, it is crucial that the ‘a’ appearing first in both bars is understood to be equal (even if it is only approximately equal when drawn freehand in the bar). This allows the pupil to ‘see’ that to work out the second ‘a’ in the top bar, they can calculate 11-7.

So if that ‘a’ is 4, then both the other ‘a’s will also be 4. So each side of the equation will total 15. The below model shows all sections completed. This is not necessary for the pupils to do, the representation is merely useful until they can see the steps necessary to calculate whatever they are faced with:

At the SATs level most maths problems require multiple steps to solve, and incorporate numerous mathematical concepts e.g. money, fractions, four operations etc. 

While bar modelling can be used to represent all these steps at the same time, pupils may find it easier to identify each step and draw bars separately, forming the answer gradually. 

While there are some multi-step word problems that cannot be solved using this method, bar modelling does make a significant difference in pupil’s ability to work through the SATs. 

Where next?

Now you’re persuaded (we hope!) that bar modelling in maths is going to revolutionise problem solving across your school from early years onwards, here are some other bar modelling resources to help you out.

• FREE Ultimate Guide to Bar Modelling (including a bar modelling ppt) which will give a structure that can be put in place across the whole school to enable teachers to teach pupils the bar model consistently.
• FREE KS2 Bar Model Worksheet with blank bar models to support children who need a bit more help on using bar models for word problems
• Lots of Bar Modelling Worksheets on our Maths Hub , including those that look at the Bar Model for Multiplication, Bar Model for Division, Bar Model for Subtraction etc
• Bar Model Training through the Bar Model CPD videos on our Maths Hub specifically about teaching bar models – Year 1 through to Year 6.

What are you waiting for? Get a staff meeting booked, and encourage your staff to calculate difficult problems using bar models to support. They’ll be sold instantly and will be racing to go out and teach bar models to their own KS1 and KS2 pupils.

If you don’t believe me, use this problem to grab their attention:

Hussain wins first prize for his spectacular cake version of the Eiffel Tower. He generously gives three fifths of his winnings to his children and spends a third of what he had left. He has £80 left. How much money did he win?

With or without bar models? Which is easier? My guess is your staff will be hooked!

More on bar modelling and maths mastery techniques

• Third Space Sample Lessons on Bar Modelling KS1 and KS2
• Benefits of following a mastery in maths approach
• Bar modelling applied to improper fractions

If you’re looking for more  maths resources  that help develop  maths problem solving  techniques, all the  White Rose Maths  lesson slides contain a mix of fluency, reasoning and problem solving work as well as following a structured CPA approach; and on the  Third Space Maths Hub  you’ll find resources like Rapid Reasoning (daily word problems), and plenty of worked examples.

DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?

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FREE Guide to Maths Mastery

All you need to know to successfully implement a mastery approach to mathematics in your primary school, at whatever stage of your journey.

Ideal for running staff meetings on mastery or sense checking your own approach to mastery.

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Using bar models to represent addition and subtraction word problems

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Lesson details

Key learning points.

• In this lesson, we will use our knowledge of bar models to interpret if a word problem requires addition or subtraction.

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

Starter quiz

4 questions.

8 Questions

2-Step Word Problems and Bar Models

These lessons, with videos, examples, solutions and worksheets, help students learn how to solve 2-step word problems using bar models in Singapore Math . Bar models are similar to tape diagrams used in Common Core Math.

Related Pages Comparison Word Problems 2-Step Word Problems More Word Problems & Singapore Math

The following diagrams show the Part-Part-Whole Models and Comparison Models. Scroll down the page for examples and solutions.

Weight Word Problems Liquid Volume Word Problems Measurement Word Problems

Words to Equations (Multiply/Divide) 2-Step Word Problems (Multiply/Divide) 2-Step Word Problems (Multiply/Divide/Add/Subtract)

Singapore Math: Grade 3a Unit 2 Some 2-step word problems.

• Jamie picked 17 flowers and Lindsey picked 12. They gave away 20 of the flowers. How many flowers were left?
• 125 children took part in a mathematics competition. 54 of them were girls. How many more boys than girls were there?
• Ali collected 137 stamps. He collected 27 stamps less than his sister. How many stamps did they collect altogether?

Singapore Math: Grade 3 How to solve a simple 2 step word problem using Bar Models?

Example: A washing machine costs $700, It costs $800 less than a refrigerator. Find the total cost of the two items?

Two-Step word problems

Example: 50 children attended the birthday party. 13 children left during the first hour. 9 children came in during the second hour. How many children were at the birthday party then?

Singapore Math: Grade 3 - 2 Step Basic Word Problems This presentation shows how bar models are used for simple word problems.

• 30 apples were harvested from a plantation. 5 were rotten. How many good apples were there?
• At a fruit store, there were 250 oranges. If 100 were small oranges, how many big oranges were there?
• Shop A sold 50 shirts in January. Shop B sold 25 more than shop A in the same month. How many shirts did they sell altogether?
• At Clara’s art exhibition, 120 visitors came on the first day. 20 fewer visitors came on the second day. How many visitors came to the exhibition on the two days?

4th Grade Word Problems and Bar Models

Example: Dad bought two hammers. One cost $18, the other cost $28 more. What was his total bill?

Example: Kim has 78 boxes of apples and 130 boxes of oranges. She sells some boxes of oranges. Now she has 159 boxes of apples and oranges left. a) How many boxes did she have at first? b) How many boxes of oranges did she sell?

Bar Models: Solving Word Problems (Singapore Math 5A)

Example: Rowan and Emma each had an equal number of popsicles. After Rowan ate 25 popsicles and Emma ate 31 popsicles, Rowan had twice as many as Emma. How many popsicles did they each have at first?

Example: In a basketball game, Marc, Jackson, and Cole scored 106 points altogether. Marc scored 15 more points than Jackson. Jackson scored 7 fewer than Cole. How many points did Cole score?

Example: Peter bought 32 chocolate bars at 4 for $3. He ate 2two of them and sold the rest at 3 for $4. How much money did he earn?

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Blank Bar Model Templates

Maths Resource Description

Blank Bar Model Templates are a set of educational resources designed to aid students in visualising mathematical concepts, particularly useful for Key Stage 2 learners. These templates serve as a visual strategy for solving word problems and understanding relationships between numbers. The bar models help children to break down complex problems into more manageable parts, making it easier to perform calculations and understand the structure of the problem. These templates are versatile tools that can be used across a range of mathematical topics, including addition, subtraction, multiplication, division, and fractions.

The collection includes a variety of blank templates, each one providing a clear and simple layout for students to fill in as they work through different mathematical challenges. By using these bar models, students can represent numbers and their components in a way that is both accessible and engaging. These templates are particularly valuable for visual learners and can be used in a classroom setting or at home for practice and reinforcement of mathematical concepts. The bar models aim to build a strong foundation in problem-solving skills, encouraging students to think critically and logically as they approach various mathematical tasks.

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Year 3 Singapore Bar Model Word Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

18 February 2016

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Theresa_Knott

A great start to bar modelling

Empty reply does not make any sense for the end user

brill! exactly what I was looking for

ybbil retsof

Keithellingham.

Love these, good examples to start to guide them. I will be using these for my lowest ability yr7s to build confidence and technique. Thank you.<br /> EBI had answer sheet to put on board for ease of marking.

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