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.
Why do this problem?
This activity challenges the most able pupils in their spatial awareness abilities. It also enables them to have something before them to explore and compare.
As this is intended for the most able I would suggest printing out the activity and discussing together first of all.
You could get started by asking the group to give you instructions to make the second or third model. Then let them produce their creations.
Tell me about your shapes.
So what have you found when comparing them?
What can you now explore about these?
Pose the question about balance, asking "Does it matter if the model is stable?".
You could encourage children to explore models containing an archway/bridge.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.