The Square of Cubes... explained

There have already been three posts about this amazing Square of Cubes:

• Changing cubes to squares... BIG
• Sharing our feelings about the Square from Cubes
• Drawing square numbers, cube numbers and triangle numbers

But, now that we have a display about it outside the class:

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

it was time to invite the Year 2s and Year 3s to find out what it was all about. The four girls who created the giant square did a great presentation:

Square numbers, cube numbers, triangle numbers

Hidden in this amazing square

are some patterns of numbers. Today 4G drew some of them:

Here's three scanned and coloured images that we drew:

coloured by Maia

square numbers

triangle numbers

Can you see where these sets of numbers appear in our giant square?

Our feelings about the Square from Cubes

After the creation of this huge Cuisenaire rod square, there were lots of things to say. Mr Gregg said a little about triangle numbers:


Then the creators of the square made a video about everyone's reaction to it:



Now, there's a display up outside the classroom:

So, we'll need to do some explaining of the maths behind it for the younger children that go past, how we got these:

 and then how we made this:

And some of the things we notice about the square.

Cubes to squares... BIG

In our exploration of number patterns with Cuisenaire rods (see the previous post) Clara and Rozenn began to explore the cubes to squares puzzle we'd looked at together yesterday:

Using cubes of each rod in turn

 they built up the square from the centre.

Claudia was busy making cubes - so she joined in!

At this point Mr Gregg thought it would be wise to stop - it would be difficult to find 49 sevens. But the girls were determined to press on - and they did it:

"Probably best to stop now," Mr Gregg said. "You'll never find 64 eights."

But - and Alicia joined the team now - the girls were not going to stop.

 Nines involved going to all the teachers in the school, and working through playtime.

"Hooray!"

The nines complete

 For the tens, we couldn't find a hundred of them, so the girls used some of the base 10 equipment:

 And - drum roll! - here it is!

There's a strange pattern of the odd and even numbers - can you see it?

And the lengths of the squares follows a neat pattern too!

On Friday we'll have another look at the numbers involved.

This pattern is amazing and beautiful - well done to the four girls for pushing on with it!

UPDATE
Alicia has some Cuisenaire rods at home - and this morning she brought in ten tens. Now almost all the tens are orange like they should be!

Cubes to squares puzzle

Here's a little puzzle we tried in 4G. We made three cubes with Cuisenaire rods: a 1 x 1 x 1 cube, a 2 x 2 x 2 cube and a 3 x 3 x 3 cube.
Then, once we'd made them, we made a square with all the Cuisenaire rods that we'd used to make the cubes.

Here are some pictures:

the cubes

Then we made a 4 x 4 x 4 cube. After that, we added the fours we'd used into the square:

Then, some of us tried with five:

 Here's all the pictures: