Cube Nets
Years 2 - 10

There is a link in this activity to a different site where you will be able to play around with maths.

Preparation

  • Print this Investigation Guide.
  • You need scissors and a ruler.
  • You need a tiny amount of sticky tape or glue.
  • You need one (1) envelope.
  • Write the title of this challenge and today's date on a fresh page in your maths journal.

Getting Started

Cut the top strip off the Investigation Guide. Save the rest.

Polygons are closed shapes with straight sides.
In maths a Net is a collection of polygons joined along some of the sides.
To be a Net the collection must be able to fold up to make a 3D object.
One of these collections of six (6) squares makes a cube.
  • Cut out the one you think will work.
    Save the other two.
  • Carefully cut around the dark edge.
  • Fold along the join lines to check your hypothesis.
  • If it works, save it.
    If it doesn't try again until you find the one that does fold to make a cube.

Recording

The data in this activity is shapes. This is how you record the data you have so far.
  1. Find a way to stick your net flat on your journal page so that only one square is stuck down and so you can fold the net to make the cube.
  2. Cut out the other shapes and stick them in too. They can only go flat. Use arrows and words to explain why each one can't fold up.
This is only one net of a cube.
In this activity you will find more ways to make the net of a cube.
How many ways do you think there might be?
Record your guess.

Have fun exploring Cube Nets.

A Mathematics Playground

Parents & Teachers
The link in this section is safe. Mathigon is a UK not-for-profit company exploring and developing digital technology to support creative, student-driven mathematics learning. The simplicity and mathematical elegance of the playground space below speak to the depth and breadth of technical skill, and insight into education, that must dwell in the programming team. See further background information on site.
Click on this link to open PolyPad which is a mathematics playground.
https://mathigon.org/polypad
You will need to be able to switch between PolyPad and this Maths At Home page.

Your PolyPad screen is an infinite white 'field'.

  • There is a toolbox on the left.
  • The toolbox has drawers.
  • Click on the Polygons drawer.
The Polygons drawer opens.
There are lots of different polygons.
You are going to use the blue square.
  • Click and drag a blue square onto the field.
The square stays active inside its handlebox until you click away from it.
You need six squares.
  • Move your mouse back to the toolbox.
  • Click 5 times on the blue square.
Now you have enough squares to make the net of a cube.
  • You are going to make the net you made before.
  • Drag a square to join the start square.
  • Repeat until you make the net you know.
If you make too many squares it doesn't matter.
  • Drag your mouse around them.
  • Click the Delete button.
Can you see the Fold Net button?
  • Drag your mouse around the net.
  • Click the Fold Net button.
  • Watch your net fold up...
...but it doesn't look like a cube ... yet.
  • Click and hold on the folded net.
  • Move your hand around and watch the image appear to roll and move.
Of course it's not a cube.
The cube is in your journal.
But it is a cool way to represent a cube in
2 dimensions (2D).
  • Can you see how the app uses different colours to trick your eye into thinking it is 3D?
Did you see the new toolbar appear under the drawing?
Click unfold and watch what happens.

Now you know how to use PolyPad to find different nets of a cube.

Challenge 1

Find three (3) more cube nets.
  • Each time you find one draw it on your paper and cut it out.
  • Don't paste in your journal yet. Save it in an envelope instead.

Challenge 2

Think again about how many cubes nets there might be.
Go back and look at your guess.
You can change your guess if you want to.
Write a note about why you changed or why you didn't.
Find all the other cube nets.
  • Each time you find one draw it on your paper and cut it out.
  • Don't paste in your journal yet. Save it in an envelope instead.
This might take more than one day and you might have to print another sheet of paper.

Challenge 3

A mathematician's work begins with an interesting problem.
A problem is a problem because no one knows the answer ... no one!
So when a mathematician finds an answer they also have to be able to explain how they know it's the answer.
  • How do you know when you have found all the nets?

    Hint: Organise your data. It's in your envelope. Take out the nets you have made so far and try to organise them into groups.

Extra Challenges

  1. Think of another simple 3D object.
    For example a triangle pyramid or a square pyramid or a dog kennel.
    • Imagine unfolding it like PolyPad does.
    • In your journal sketch the net you imagine.
    • Use PolyPad to make the net and fold it up to test your hypothesis.
    • Record your experiment so someone else can understand what you imagined and what happened when you used PolyPad.

  2. Use the whatever you want from the PolyPad toolbox and do whatever you want with the shapes.
    Record your experiments - even if they don't work - and anything you discover.

Just Before You Finish

 

Answers & Discussion

These notes were originally written for teachers. We have included them to support parents to help their child learn from Cube Nets. They include photos of students working on the problem in a Year 7 classroom and slide shows of two learners folding up their different nets.

Send any comments or photos about this activity and we can start a gallery here.

 

Maths At Home is a division of Mathematics Centre