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subtraction

Subtraction bar models

Represent difference and missing parts visually.

Quick answer

Subtraction bar models are visual tools that help you see subtraction problems clearly. They show the whole amount, the part you take away, and the remaining part. You can use them to find the difference between two numbers or to find a missing number in a subtraction problem.

Learning outcome

By the end of this page, you will be able to use bar models to solve subtraction problems and understand how subtraction works with whole and parts. Success signs:
  • You can draw a bar model to show a subtraction problem
  • You can find the missing part in a subtraction bar model
  • You can solve word problems using bar models
  • You can explain how bar models help you understand subtraction

Why this matters

Bar models are a helpful way to think about subtraction because they make it easier to see what is happening in a problem. Whether you are working out how many cookies are left after sharing or how much more money you need to buy something, bar models help you understand the maths behind it. This skill is important for solving bigger maths problems later, like word problems, fractions, and algebra.

How it works

Bar models use rectangles to show amounts. Here are the steps to use them for subtraction:
  1. Draw a long bar to show the whole amount
  2. Draw a smaller bar inside it to show what is taken away
  3. Leave the rest of the bar to show what is left
  4. Use the bar model to help you find the answer
You can also use bar models to find a missing part in a subtraction problem. For example, if you know the whole and one part, you can find the other part.

Examples you can see

Let's look at some examples to help you understand how bar models work. Example 1: Finding the difference Imagine you have 12 apples and your friend has 7 apples. How many more apples do you have?
  • Draw a long bar for 12 apples
  • Draw a shorter bar for 7 apples inside it
  • Count the part that is left over
The bar model shows that you have 5 more apples than your friend. Example 2: Finding a missing part You have 15 sweets. You eat some and now you have 8 sweets left. How many sweets did you eat?
  • Draw a bar for 15 sweets (the whole)
  • Draw a bar for 8 sweets (the part left)
  • Find the part that is missing (the part eaten)
The bar model shows that you ate 7 sweets. Example 3: Word problem A shop has 20 balloons. Some balloons are sold, and now there are 12 balloons left. How many balloons were sold?
  • Draw a bar for 20 balloons (the whole)
  • Draw a bar for 12 balloons (the part left)
  • Find the part that was sold
The bar model shows that 8 balloons were sold.

Try it as a mini adventure

The Treasure Hunt Challenge You are on a treasure hunt! You start with 24 gold coins in your bag. Along the way, you find a chest with 9 more coins. But then, you meet a friendly pirate who asks you to give him 5 coins to help his crew. Now, how many coins do you have left?
  • Start with 24 coins in your bag
  • Find the chest with 9 coins (add them to your bag)
  • Give 5 coins to the pirate
Draw a bar model to help you figure out how many coins you have now.
  1. First bar: 24 coins (your starting amount)
  2. Second bar: 9 coins (found in chest)
  3. Third bar: 5 coins (given to pirate)
What is the total amount you had before giving coins away? What is the amount you have left?

Common mistakes

  • Mistake: Drawing the wrong bars or mixing up the whole and parts.
    Why it happens: Not reading the problem carefully or not understanding what the bars should represent.
    Fix: Read the problem again and decide what the whole amount is and what part is taken away.
  • Mistake: Forgetting to subtract or adding instead of subtracting.
    Why it happens: Confusing the operation or not understanding that subtraction means taking away.
    Fix: Always ask yourself, "What am I taking away?" or "What is left?"
  • Mistake: Drawing the bars too small or too big.
    Why it happens: Not thinking about the size of the numbers.
    Fix: Make sure your bars are proportional to the numbers in the problem.

Parent and carer guide

Helping your child with subtraction bar models is a great way to support their learning. Here are a few tips:
  • Start with simple examples using small numbers
  • Use physical objects like counters or blocks to show the bars
  • Ask your child to explain what each part of the bar model means
  • Encourage drawing their own bar models for different problems
  • Make it fun with games or real-life examples
If your child is struggling, try using a number line or counting backwards to help them understand subtraction. Remember, it's okay to make mistakes – that's how we learn!

Practice questions

  1. There are 18 birds in a tree. 5 fly away. How many birds are left?
  2. Tom has 14 marbles. He gives 6 to his friend. How many does he have now?
  3. A book has 25 pages. Sarah reads 10 pages. How many pages are left?
  4. There are 20 balloons in a box. 7 are popped. How many are left?
  5. Emma has 16 stickers. She uses 9. How many does she have left?
Answers:
  1. 13 birds
  2. 8 marbles
  3. 15 pages
  4. 13 balloons
  5. 7 stickers

FAQ

What is a bar model in subtraction?

A bar model is a visual way to show subtraction problems using rectangles. The long bar shows the whole amount, and the shorter bar shows what is taken away. The remaining part shows what is left.

How do I use a bar model to solve a subtraction problem?

First, draw a long bar for the whole amount. Then, draw a shorter bar inside it for the part taken away. The space left over is the answer.

Can I use bar models for any subtraction problem?

Yes, bar models work for most subtraction problems, especially word problems. They help you see what is happening in the problem.

Are bar models only for subtraction?

No, bar models can also be used for addition, multiplication, and division problems. They are a helpful tool for understanding all kinds of maths.

How can I help my child practice bar models at home?

You can use everyday situations like sharing food, counting toys, or shopping to create bar model problems. Encourage your child to draw their own bar models and explain their thinking.