Painted Faces

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



This activity is all about imagining, as you might do when you listen to a story or poem.


There is no need to write or draw anything


BUT


talking about it could be good
SO
find a friend to do this with!


Imagine a 3 by 3 by 3 cube made from 27 smaller cubes.

Perhaps it's here - but behind this cloud!

Image
Painted Faces
So, remove the cloud in your mind and there it is!


It's hanging in the air in front of you so you can just see one face of it and that face has been painted red

The right-hand side face has been painted yellow


The left-hand side face has been painted blue


The top face has been painted white


The underneath bottom face has been painted black


The back face has been painted green.


1. How many small cubes have just two of their faces painted?

2. Where are they?

3. What are the two colours on each of those small cubes that have two faces painted?

Now you could try the same things with a larger starting cube, that is 4 by 4 by 4, and answer the same three questions.

If you'd like to take these ideas a bit further, have a look at Painted Cube .