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'Four Layers' printed from http://nrich.maths.org/

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This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.)

It may be used to follow on from  Cubes Here and There.
 


 3 of Four
Looking at the three models here you may see that they have a lot in common although they are obviously different.
The things that are the same produce the rules.
So the rules are;
$1$/  Each colour stays at the same level in each model.
$2$/ Cubes of the same colour are not separated - they stay together.
$3$/ The numbers of cubes for each colour is fixed at $1, 2, 3$ and $4$.
$4$/ The cubes sit squarely face to face with no twists or slides.
 
Your challenge is to create more shapes that follow the four rules.
When you have done so, compare them and show similarities and differences.