X Tables
Problem Solving

Bar model problem solving

Use bars to represent parts, wholes and comparisons.

Quick answer

Bar model problem solving is a method that uses rectangles or bars to help you understand and solve maths problems by showing parts and wholes clearly.

Learning outcome

By the end of this page, you will be able to use bar models to solve addition, subtraction, multiplication, and division problems by drawing bars to show what you know and what you need to find out. Success signs:
  • You can draw a bar to show a whole amount
  • You can use bars to show parts that make up a whole
  • You can solve word problems by drawing bar models
  • You can compare amounts using bar models

Why this matters

Bar models help you understand what a maths problem is really asking. When you see a problem on paper, it can be hard to know what to do. Bar models make the problem visual and easier to solve. You can use them for problems about money, time, sharing, and even sports scores. This method helps you think about maths in a clearer way, whether you're at school or at home.

How it works

Bar models use rectangles to show amounts. Here are the simple steps:
  1. Read the problem carefully
  2. Identify what you know and what you need to find
  3. Draw a bar to show the whole amount
  4. Break the bar into parts if needed
  5. Use the bar to help you solve the problem

Examples you can see

Let's try some examples using bar models. Example 1: Addition Sarah has 8 apples. Her brother gives her 5 more apples. How many apples does Sarah have now? Draw a bar for 8 apples, then another bar for 5 apples. Put them together to show the total.
  1. Bar 1: 8 apples
  2. Bar 2: 5 apples
  3. Total: 8 + 5 = 13 apples
Example 2: Subtraction Tommy has 12 toy cars. He gives 4 to his friend. How many does he have left? Draw a bar for 12 cars. Then take away a part for 4 cars.
  1. Bar: 12 cars
  2. Take away: 4 cars
  3. Left: 12 - 4 = 8 cars
Example 3: Multiplication There are 6 boxes. Each box has 4 pencils. How many pencils are there altogether? Draw 6 bars, each showing 4 pencils.
  1. 6 boxes
  2. 4 pencils in each box
  3. Total: 6 × 4 = 24 pencils
Example 4: Division There are 15 cookies to share equally between 3 friends. How many cookies does each friend get? Draw a bar for 15 cookies. Split it into 3 equal parts.
  1. Bar: 15 cookies
  2. Split into 3 parts
  3. Each part: 15 ÷ 3 = 5 cookies

Try it as a mini adventure

The Treasure Hunt Challenge You and your friend are on a treasure hunt. You find a chest with 24 gold coins. You want to split them equally between you and your friend. Draw a bar model to show how many coins each person gets.
  1. Draw a bar to show 24 coins
  2. Split it into 2 equal parts
  3. Count how many coins are in each part
  4. Write your answer: 24 ÷ 2 = 12 coins each
You can also try this with different numbers:
  1. 24 coins split between 4 people
  2. 24 coins split between 6 people
  3. 24 coins split between 3 people

Common mistakes

  • Mistake: Drawing the wrong size bars for the amounts. Why it happens: Not reading the problem carefully. Fix: Read the problem again and check if the bars match the numbers.
  • Mistake: Forgetting to label the bars. Why it happens: Getting excited to draw and not thinking about what each bar shows. Fix: Always write what each bar represents, like "Apples", "Toys", or "Coins".
  • Mistake: Adding when you should subtract or vice versa. Why it happens: Not understanding what the problem is asking. Fix: Draw the bar model first, then decide if you need to add or subtract.
  • Mistake: Not using the bars to check your answer. Why it happens: Thinking the answer is done once you write the number. Fix: Use your bar model to double-check your calculation.

Parent and carer guide

Parents and carers can help by:
  • Encouraging children to read the problem twice before drawing
  • Letting children draw their own bars, even if they're not perfect
  • Asking questions like, "What do these bars show?" or "How can we use the bars to solve this?"
  • Practising with real-life examples, like sharing snacks or counting toys
  • Not worrying if the first bar models are messy – they get better with practice
If your child is struggling, try:
  • Using physical objects like counters or blocks to represent the bars
  • Starting with simple addition and subtraction problems
  • Reinforcing that bar models are a way to see the maths, not a test

Practice questions

  1. There are 9 red balloons and 7 blue balloons. How many balloons are there altogether?
  2. There are 14 stickers. You use 6. How many are left?
  3. There are 5 rows of chairs. Each row has 6 chairs. How many chairs are there?
  4. There are 20 sweets to share equally between 4 children. How many sweets does each child get?
  5. There are 12 pencils. 3 are broken. How many are not broken?
Answers:
  1. 9 + 7 = 16 balloons
  2. 14 - 6 = 8 stickers
  3. 5 × 6 = 30 chairs
  4. 20 ÷ 4 = 5 sweets
  5. 12 - 3 = 9 pencils

FAQ

What is a bar model?

A bar model is a way to show maths problems using rectangles or bars to represent amounts. It helps you see parts and wholes more clearly.

When should I use bar models?

You can use bar models for addition, subtraction, multiplication, and division problems. They are especially helpful for word problems where you need to understand what is happening.

Do I have to draw perfect bars?

No, your bars don't have to be perfect. They just need to show the right relationships between amounts. The idea is to help you think, not to make art.

Can I use bar models for fractions?

Yes! Bar models can also show fractions. For example, if you have a bar for 12 and you split it into 3 parts, each part shows 1/3 of 12.

Are bar models only for maths?

Bar models are mainly used in maths, but the idea of using pictures to understand problems can be helpful in other subjects too, like reading or science.