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fractions

Bar models for fractions

Use bars to represent fraction word problems.

Quick answer

Bar models are a helpful way to draw fractions and solve fraction word problems. They use rectangles to show parts of a whole, making it easier to see how fractions work.

Learning outcome

By the end of this page, you will be able to use bar models to solve simple fraction word problems and understand how fractions show parts of a whole. Success signs:
  • You can draw a bar to show a fraction like 1/4 or 3/5
  • You can solve a word problem using a bar model
  • You can explain what the bars show about the fractions
  • You can use bar models to compare fractions

Why this matters

Bar models help you see fractions more clearly. When you solve problems about sharing, parts of a whole, or comparing amounts, bar models make it easier to understand what is happening. They are used in school, in real life, and even in games and puzzles. Knowing how to use them helps you think more clearly about fractions.

How it works

A bar model is a rectangle that shows a fraction. Here’s how to use it:
  1. Draw a rectangle to represent the whole
  2. Divide the rectangle into equal parts based on the denominator
  3. Shade or mark the parts that show the numerator
  4. Use the bar to solve the problem

Examples you can see

Let’s look at some examples using bar models to show fractions. Example 1: Showing 1/3 Imagine you have a pizza cut into 3 equal slices. If you eat 1 slice, you have eaten 1/3 of the pizza.
  • Draw a rectangle
  • Divide it into 3 equal parts
  • Shade 1 part
Example 2: Showing 2/5 You have 5 apples and you eat 2 of them. You have eaten 2/5 of the apples.
  • Draw a rectangle
  • Divide it into 5 equal parts
  • Shade 2 parts
Example 3: Solving a word problem Sarah has 12 sweets. She gives 1/4 of them to her friend. How many sweets does she give away?
  • Draw a bar for 12 sweets
  • Divide the bar into 4 equal parts
  • Each part is 3 sweets (because 12 ÷ 4 = 3)
  • 1/4 of 12 = 3 sweets

Try it as a mini adventure

Adventure: The Fraction Bakery You are the baker in a magical bakery where you make cookies shaped like fractions. Your boss asks you to make a special batch of 16 cookies.
  • 1/2 of the cookies must be chocolate chip
  • 1/4 of the cookies must be oatmeal raisin
  • 1/8 of the cookies must be sugar
  • The rest are gingerbread
Step-by-step challenge:
  1. Draw a bar to show 16 cookies
  2. Divide it into 8 equal parts (since 8 is the smallest number that fits 1/2, 1/4, and 1/8)
  3. Each part is 2 cookies (because 16 ÷ 8 = 2)
  4. 1/2 of 16 = 8 cookies (4 parts)
  5. 1/4 of 16 = 4 cookies (2 parts)
  6. 1/8 of 16 = 2 cookies (1 part)
  7. Remaining = 16 - 8 - 4 - 2 = 2 gingerbread cookies
Now, draw your bar and label each part to show how many of each cookie type you make.

Common mistakes

  • Mistake: Drawing the bar into unequal parts
    Why it happens: Not thinking carefully about equal sharing
    Fix: Use a ruler to make sure parts are the same size
  • Mistake: Forgetting to count how many parts make the whole
    Why it happens: Confusing numerator and denominator
    Fix: Always ask "How many equal parts are there in total?"
  • Mistake: Shading the wrong number of parts
    Why it happens: Not reading the problem carefully
    Fix: Read the fraction carefully and count the parts
  • Mistake: Thinking that 1/3 and 1/4 are the same size
    Why it happens: Not comparing the size of parts
    Fix: Use bar models to see that 1/3 is bigger than 1/4

Parent and carer guide

Parents and carers can help by:
  • Practising drawing bar models with your child
  • Using everyday situations like sharing food or dividing toys
  • Asking questions like "How many equal parts are there?" or "What does the shaded part show?"
  • Encouraging your child to explain their bar model
  • Not worrying if they make mistakes – it's part of learning!
What to say:
  • "Can you show me how you drew that bar?"
  • "What does one part represent?"
  • "How did you figure out how many cookies each part is?"
What not to do:
  • Don’t say "You're wrong" – instead, guide them to find the mistake
  • Don’t rush – let your child think through the steps
  • Don’t compare your child to others – focus on their progress

Practice questions

  1. Draw a bar to show 3/5 of 20
  2. If 1/4 of a class of 16 children are absent, how many children are absent?
  3. Draw a bar to show 2/3 of 12
  4. Tom has 24 stickers. He gives 1/6 of them to his friend. How many stickers does he give?
  5. Draw a bar to show 1/8 of 32
Answers:
  1. Bar divided into 5 parts, 3 shaded (3/5 of 20 = 12)
  2. 1/4 of 16 = 4 children
  3. Bar divided into 3 parts, 2 shaded (2/3 of 12 = 8)
  4. 1/6 of 24 = 4 stickers
  5. Bar divided into 8 parts, 1 shaded (1/8 of 32 = 4)

FAQ

What is a bar model?

A bar model is a rectangle that shows parts of a whole. It helps us understand fractions and solve problems.

How do I use bar models for fractions?

Draw a rectangle, divide it into equal parts, and shade the parts that show the fraction.

Can I use bar models for comparing fractions?

Yes! You can draw two bars to compare how big different fractions are.

Why do we use bar models?

Bar models make fractions easier to understand and solve problems more clearly.

Are bar models only for fractions?

No, they can also be used for addition, subtraction, multiplication, and division problems.