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Making Maths

Maths hiding in making things: cardboard castles

Use nets, cuboids and towers in a craft build.

Quick answer

Maths is all around us – even in the cardboard castles you build! When you make a castle, you're using shapes, measurements, counting, and even patterns. You're learning about cubes, cuboids, volume, and how to make things that stand up straight.

Learning outcome

By the end of this page, you will be able to build a cardboard castle and explain the maths you used, like how many rectangles or squares you needed, how tall your tower is, and how to make it stand up. Success signs:
  • You can identify shapes like rectangles and squares in your castle
  • You can count how many pieces you used
  • You can measure the height of your castle
  • You can explain how your castle stays up

Why this matters

Building with cardboard teaches you about shapes, space, and how things fit together. It helps you understand how maths is used in real life – like when you build a tower, measure how tall it is, or decide how many blocks you need. This is the start of learning about geometry and measurement, which you’ll use in school and in your future jobs.

How it works

When you build a cardboard castle, you’re using different shapes:
  1. First, you think about what your castle will look like
  2. Then, you choose shapes – like rectangles for walls or squares for towers
  3. You count how many of each shape you need
  4. You measure how tall or wide it should be
  5. You put it all together and see if it stands up

Examples you can see

Let’s imagine you’re building a castle with a square tower and rectangular walls. Example 1: The Square Tower A square tower has 4 sides that are all the same length. If each side is 10 cm, then you need 4 pieces of cardboard, each 10 cm long. That’s 40 cm of cardboard for the tower. Example 2: The Rectangular Walls If your castle has rectangular walls that are 15 cm wide and 10 cm tall, you need 4 walls. That’s 4 rectangles, and each rectangle has 2 sides that are 15 cm and 2 sides that are 10 cm. Example 3: The Roof A roof might be a triangle or a rectangle. If it’s a triangle, it has 3 sides. If it’s a rectangle, it has 4 sides. Example 4: The Whole Castle Let’s say your castle has:
  • 1 square tower (4 sides)
  • 4 rectangular walls (4 rectangles)
  • 1 triangular roof (3 sides)
That’s a total of 11 sides – and that’s how many pieces of cardboard you need!

Try it as a mini adventure

Adventure: Build a Cardboard Castle! You are a castle builder in a faraway land. You have 20 pieces of cardboard and must build the tallest castle possible. You can use:
  • Rectangles for walls
  • Squares for towers
  • Triangles for roofs
Your challenge is to:
  1. Decide how many of each shape you want
  2. Measure each piece
  3. Build your castle
  4. Count how many pieces you used
  5. Check if it stands up
Step 1: Choose your shapes. You might use 4 rectangles, 1 square, and 1 triangle. Step 2: Measure your cardboard. Each rectangle is 15 cm wide and 10 cm tall. Step 3: Build your castle. Place the square tower in the middle, then add the rectangles around it. Step 4: Count your pieces. 4 rectangles + 1 square + 1 triangle = 6 pieces. Step 5: Check if it stands. If it falls, try making the base wider. Step 6: Measure the height. Your castle is 30 cm tall.

Common mistakes

  • Mistake: Using the wrong shape for a part of the castle. For example, using a triangle for a wall instead of a rectangle.
    Why it happens: Not thinking about how shapes fit together.
    Fix: Think about how walls should be flat and tall, so rectangles work better than triangles.
  • Mistake: Forgetting to measure your pieces.
    Why it happens: Wanting to build quickly without planning.
    Fix: Take a few minutes to measure each piece before you cut it.
  • Mistake: Making the castle too tall and it falls over.
    Why it happens: Not thinking about balance and base size.
    Fix: Make a wide base and smaller top to keep it standing.

Parent and carer guide

You can help your child by:
  • Encouraging them to think about shapes before they start building
  • Letting them measure and cut cardboard themselves – it’s a great way to learn!
  • Asking questions like: “How many rectangles do you need?” or “How tall is your tower?”
  • Helping them count pieces and check if their castle stands up
  • Practising with simple maths like counting how many sides each shape has
What to say:
  • “What shapes are you using?”
  • “How many pieces do you think you’ll need?”
  • “Let’s measure your castle to see how tall it is.”
What not to worry about:
  • Not having perfect measurements – it’s okay to be a bit off
  • Not finishing the castle in one go – it’s a fun process
  • Not knowing all the maths – you’re learning together!

Practice questions

  1. How many rectangles do you need for 3 walls of a castle?
  2. If each rectangle is 10 cm wide, how wide is the total wall?
  3. How many sides does a square tower have?
  4. How many pieces of cardboard do you need for a castle with 2 square towers and 4 rectangular walls?
  5. If your castle is 25 cm tall and you add a 5 cm tower, how tall is it now?
Answers:
  1. 3 rectangles
  2. 30 cm
  3. 4 sides
  4. 6 pieces
  5. 30 cm

FAQ

What shapes are used in building a castle?

Castles use rectangles for walls, squares for towers, and triangles for roofs. These shapes help make the castle strong and look like a real castle.

Can I use any size cardboard?

Yes! You can use any size, but it’s easier if you use the same size for all pieces of the same shape.

How do I know if my castle will stand up?

Make a wide base and make sure the pieces are glued or taped well. A heavy base helps keep it upright.

Why is it helpful to measure my pieces?

Measuring helps you plan how much cardboard you need and makes sure your castle looks balanced and fits together well.

Can I build a castle with only triangles?

It’s hard to build a strong castle with only triangles because they don’t make flat walls. But you can use triangles for roofs or decorations.