Train maths quest: fractions

Quick answer

When you share food, maps, or treasure equally between friends on a train journey, you are using fractions – parts of a whole. You can split things into halves, thirds, quarters, and more equal pieces.

Learning outcome

By the end of this page, you will be able to split things into equal parts and understand what each part means using words like halves, thirds, quarters, and fifths.

• I can share 12 biscuits between 4 friends so each gets the same amount.
• I can draw a picture to show 1/3 of a pizza.
• I can use a real-life situation to explain what a fraction means.
• I can say which fraction is bigger when comparing 1/2 and 1/4.

Why this matters

Fractions help you understand how to share things fairly, like food or treasure. When you play games, go on train journeys, or even bake cookies, you use fractions. You might need to split a cake into 8 pieces or share a map between two people. Knowing fractions helps you be a fair friend and solve real problems!

How it works

Fractions are parts of a whole. The top number (numerator) tells how many parts you have. The bottom number (denominator) tells how many equal parts the whole is divided into.

1. Think of a whole object, like a pizza or a sandwich.
2. Divide it into equal parts – all the same size.
3. Count how many parts the whole is split into.
4. Count how many parts you have.
5. Write it as a fraction: parts you have over total parts.

Examples you can see

Imagine you have 12 sweets and want to share them equally with 3 friends. That means 12 sweets divided by 4 people (you and 3 friends).

This is the same as saying 12 ÷ 4 = 3, or 1/4 of the sweets for each person.

Now imagine you have a chocolate bar and break it into 6 equal pieces. If you eat 2 pieces, you have eaten 2/6 of the chocolate bar.

Let’s look at another example:

• You have a train journey that is 300 km long.
• You stop at 3 platforms.
• You want to split the journey equally between 3 stops.
• Each stop is 300 ÷ 3 = 100 km apart.
• So each part is 1/3 of the whole journey.

Try it as a mini adventure

Train Maths Quest: Fraction Adventure

You are on a train journey from London to Edinburgh. You have a treasure map, a sandwich, and 6 pieces of fruit. You must share them fairly with your 3 friends.

1. First, you split the treasure map into 4 equal parts. How much of the map does each friend get?
2. You have 12 pieces of fruit. How many pieces does each friend get?
3. You have a sandwich cut into 8 slices. You eat 3 slices. What fraction of the sandwich did you eat?
4. Your journey is 600 km. You stop at 4 platforms. How far apart are each of the platforms?
5. You have 10 cookies. You eat 2. What fraction of the cookies did you eat?

Common mistakes

• Mistake: Thinking 1/2 is smaller than 1/4 because 2 is bigger than 4.
• Why it happens: Children often think the bigger number in a fraction means the bigger part.
• Fix: Show that if you split a cake into 4 pieces, each piece is smaller than if you split it into 2 pieces.

• Mistake: Drawing a circle and shading 3 parts of 5, then calling it 3/5.
• Why it happens: Children may not understand that all parts must be equal.
• Fix: Use squares or rectangles and cut them into equal pieces before shading.

• Mistake: Saying 1/3 of 12 is 4, but not understanding that 1/3 means one part out of three equal parts.
• Why it happens: Children might know the calculation but not the meaning.
• Fix: Use physical sharing or drawing to show that 12 divided by 3 equals 4.

Parent and carer guide

Help your child understand fractions by using everyday sharing situations:

1. When sharing food, ask: “If we split this pizza into 4 pieces, what part is each of us?”
2. Use real objects like buttons, toys, or pasta to show equal sharing.
3. Play fraction games like “Split the sandwich” – each player gets a different fraction of a sandwich.
4. Encourage drawing pictures to represent fractions.
5. Don’t worry if they get confused at first – fractions take time to understand.

Practice questions

1. There are 12 apples. You eat 3. What fraction of the apples did you eat?
2. Split 15 biscuits between 5 friends. How many biscuits does each friend get?
3. You have a cake cut into 8 pieces. You eat 2 pieces. What fraction did you eat?
4. Split 20 sweets between 4 people. What fraction does each person get?
5. You have 10 cookies. You eat 5. What fraction did you eat?

Answers:

1. 3/12 = 1/4
2. 3 biscuits each
3. 2/8 = 1/4
4. 1/4
5. 5/10 = 1/2

FAQ

What is a fraction?

A fraction is a way to show part of a whole. For example, if you eat 2 slices of a pizza that has 8 slices, you ate 2/8 of the pizza.

Why do we need fractions?

Fractions help us share things fairly, measure parts of a whole, and solve problems in real life, like cooking, shopping, or splitting treasure!

How do I know if parts are equal?

Equal parts must be the same size. You can check by folding or cutting carefully. If you can’t tell, use a ruler or a measuring tool.

Can fractions be more than one?

Yes! If you eat 3 slices of a pizza that has 2 slices, you ate 3/2 or 1 and 1/2 pizzas.

What if I don’t understand fractions?

That’s okay! Start with simple sharing, use drawings, and practice with real objects. With time, it will make more sense!