Build it up more

This task follows on from Build it Up and takes the ideas into three dimensions!
Age
7 to 11
Challenge level
filled star filled star empty star
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 is written as a follow-on from Build it Up.

You could extend what you did in Build it Up by thinking of it in 3D!

The circles would then be spheres.

Each numbered sphere would then sit on the three underneath and the whole thing would end up being a triangular based pyramid.

So there would be six numbers (in an equilateral triangle) at the bottom, as in this example:

Build it \Up more
Then the next layer up would be:

 
Build it \Up more
So the top layer would be:

 
Build it \Up more
 
You can explore finding a triangle of six numbers (we don't use zero!) and add them in threes to give a triangle of three numbers. As in Build it Up, we would then like those three numbers to add to 15 at the very top of the pyramid.

Here's a pdf version of this activity: BuildItUpMore.pdf