A Square of Cubes in Year 4

It's a curious and wondrous fact that the sum of the first n cubes is the square of the nth triangular number.

For instance, with n=3, the first three cubes

 - here made in Cuisenaire rods - can be reassembled into a square:

The square is six units wide, six being the third triangle number.

The puzzle then, was to make the cubes and then make a square from them. The class managed that successfully and it might have finished there, but when the following day they were asked to create a growing pattern of their own in Cuisenaire rods

four of the girls chose to return to the square of cubes and make it bigger:

and bigger - swallowing up all the Cuisenaire rods in the school, until they had created a monster:

The next day, while the rest of the class explained their own patterns, the four girls enthused about their creation.

It was time to have a closer look at the patterns of numbers hidden inside this huge square:

square numbers

triangle numbers

And then, to round it all off, a display outside the class:

with the invitation to make the cubes and the squares from the same rods:

We rounded it all off by inviting the Year 2s and Year 3s to find out what it was all about.  The four girls explained their creation brilliantly!