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Making Maths

Cardboard Castles maths mission

A junior real-world challenge using cardboard castles to practise geometry without feeling like a worksheet.

Quick answer

By making cardboard castles, children can explore shapes, sizes, and measurements while learning about geometry in a fun, hands-on way.

Learning outcome

By the end of this page, you will be able to use everyday materials like cardboard to build a castle and identify the shapes, sizes, and measurements used in your creation. Success signs:
  • You can name 3 different 2D shapes used in your castle
  • You can measure the height of your castle using a ruler or tape measure
  • You can compare the sizes of different parts of your castle
  • You can explain how your castle uses different shapes to make it strong

Why this matters

Geometry is all around us, and building a cardboard castle helps you see it in action. When you design and build a castle, you're using shapes, measuring things, and thinking about how different parts fit together. This is exactly the kind of real-world maths that helps you understand how buildings, bridges, and even video games are made. Whether you're playing with LEGO, designing a Minecraft house, or drawing a castle, you're using the same ideas that grown-ups use when they build real things.

How it works

Making a cardboard castle is like solving a puzzle where you get to use your hands and your brain. First, you think about what shapes you want to use. Then you measure and cut them. Next, you put them together to build your castle. You might notice that some shapes work better than others, or that some parts need to be bigger or smaller. This is all geometry in action!

Examples you can see

Let's imagine you're building a castle with these materials:
  • Cardboard boxes for the walls
  • Triangular pieces for the roof
  • Rectangular pieces for the towers
  • Circular pieces for the windows
Example 1: Shape identification Your castle has a base made of square cardboard pieces. Each square is 10cm by 10cm. You use 4 squares to make one wall of your castle. This means you're using 4 equal squares to make a larger rectangle. Example 2: Measurement You measure the height of your castle and find it's 30cm tall. You notice that your tower is 15cm tall, and your main wall is 10cm tall. You can compare these sizes and see that the tower is taller than the wall. Example 3: Patterns You make a pattern with your castle windows. You put 3 circular windows in a row, then 2 more, then 3 again. This pattern of 3-2-3 helps you make your castle look neat and tidy.

Try it as a mini adventure

Adventure: The Cardboard Castle Challenge You're a young architect! Your mission is to build the most amazing cardboard castle using only cardboard, scissors, tape, and your imagination. Here's how to start:
  1. First time: Gather materials and plan your castle design
  2. Second time: Cut out 4 square pieces of cardboard (10cm by 10cm) for your base
  3. Third time: Cut 3 triangular pieces for your roof
  4. Fourth time: Measure and cut 2 rectangular pieces for your towers (15cm by 10cm)
  5. Fifth time: Measure the height of your castle and write it down
  6. Sixth time: Compare the sizes of your different castle parts
  7. Seventh time: Show your castle to a friend and explain the shapes you used

Common mistakes

  • Mistake: Using the wrong shapes for the job
    Why it happens: Children might try to use circles for walls, which don't stack well
    Fix: Use rectangles and squares for walls because they fit together better
  • Mistake: Not measuring before cutting
    Why it happens: Excitement makes children want to cut right away
    Fix: Always measure first, then cut, and double-check your measurements
  • Mistake: Thinking all shapes are the same size
    Why it happens: Children don't always notice that shapes can be different sizes
    Fix: Compare different shapes by measuring them or putting them side by side
  • Mistake: Not thinking about how shapes fit together
    Why it happens: Children focus on making one part, not how it connects to others
    Fix: Think about how shapes connect - like how a triangle fits on top of a rectangle

Parent and carer guide

This activity helps children understand that maths is all around them. You can help by:
  • Encouraging your child to talk about the shapes they're using
  • Asking questions like "What shape is this?" or "How tall is your tower?"
  • Letting them measure things themselves
  • Helping them compare sizes without being too directive
  • Showing how the shapes they're using relate to real buildings
What to say:
  • "I like how you're using rectangles for the walls"
  • "How did you measure your castle?"
  • "What shapes do you think are strongest for building?"
What not to worry about:
  • Whether the castle looks perfect - it's about the learning
  • If your child gets frustrated - that's normal
  • Whether they use exactly the right measurements - estimation is fine

Practice questions

  1. What shape is the base of your castle? (Answer: Square)
  2. If you use 4 rectangles that are 10cm by 5cm for your walls, what is the total area of the wall? (Answer: 200cm²)
  3. How many triangular pieces do you need for a roof with 3 sides? (Answer: 3)
  4. Which is taller - a 12cm tower or a 15cm wall? (Answer: The wall)
  5. What shape would be best for a castle window? (Answer: Circle or square)

FAQ

What shapes do I need for a cardboard castle?

For a cardboard castle, you'll need squares, rectangles, triangles, and circles. Squares and rectangles make good walls, triangles make good roofs, and circles work well for windows.

How can I measure my castle?

You can measure your castle with a ruler or tape measure. Measure the height, width, and depth of different parts. You can also measure how long each piece of cardboard is before cutting it.

Can I use this activity to learn about area?

Yes! When you put cardboard pieces together, you're learning about area. For example, if you have a rectangle that's 10cm by 5cm, its area is 50cm². You can add up all the pieces to find the total area of your castle.

What if I don't have cardboard?

You can use other materials like paper, blocks, or even food containers. The important part is thinking about shapes and measurements.

How does this connect to school maths?

This activity connects to school maths by teaching you about 2D and 3D shapes, measurement, and how different shapes fit together. These are all important skills you'll learn in class.