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More Building with Cubes

Stage: 2 Challenge Level: Challenge Level:1

More Building with Cubes


Before you try this problem, you may like to have a go at Building with Cubes .

A. Imagine you have seven cubes. They are green, white, brown, pink, yellow, blue, and red:

seven cubes: green, white, brown, pink, yellow, blue, red


Now, try to picture making this building in your head:

Start with the blue and yellow cubes. Put them next to each other.
The blue cube is on the left. It is underneath a pink cube. Put the red cube just behind the yellow cube.
Put the green cube on top of the red cube.
Put the brown cube on the right of the yellow cube.
Put the white cube in front of the pink cube.

What does your building look like?
Try using cubes to check whether you had pictured it correctly.


B. Now imagine making a building with these eight cubes:

eight cubes: blue, yellow, orange, pink, brown, green, white, black



Start with three cubes in a row.
The centre cube is pink.
The blue cube is on the right of the pink cube.
The orange cube is on the left of the pink cube.
The blue cube is also underneath a yellow cube.
Put the black cube behind the orange cube.
Put the brown cube on top of the green cube and put them both behind the black cube.
Finally, put the white cube on top of the orange cube.

What does your building look like?
Try using cubes to check whether you had pictured it correctly.

C. Now try imagining a building with these ten cubes:

ten cubes: brown, pink, white, red, dark green, blue, orange, light green, white, black


Start with three cubes in a column.
The bottom cube is brown and the centre cube is blue.
The cube at the top is black.
Put the yellow cube underneath the red cube and put them both on the left hand side of the column of three cubes.
Rotate all five cubes a quarter turn anti-clockwise, keeping the columns pointing upwards.
Now put the dark green cube on the right of the yellow cube.
Put the white cube on the left of the brown cube and the pink cube on the left of the blue cube.
Put the light green cube on top of the black cube.
Rotate the whole building of nine cubes another quarter turn anti-clockwise (again keeping the columns vertical).
Finally, put the orange cube in front of the white cube.

What does your building look like?
Once again, try using cubes to check whether you had pictured it correctly.

We would love to receive pictures or photographs of your buildings.

Why do this problem?

This problem leads on from Building with Cubes by introducing larger numbers of cubes so that there is more information to be kept in your mind's 'eye' at one time. Being able to visualise is a useful skill which learners are often not used to drawing on. By explicitly talking about visualisation, and offering opportunities like this for your class to practise visualising, you will be encouraging them to use this skill in their independent problem solving.

This activity might also be a good context in which to introduce isometric paper to your class. Recording on this paper is a skill in itself, but it is extremely useful for drawing 3D images of cubes.

It would be a good idea for the class to try Building with Cubes before they tackle this problem, including having a go at the introductory activities described in that problem's notes.

Key questions

Can you see those two cubes in your head?
What about the third one?
If it is under/behind/ on the right of that one, where will it be?
As you picture each stage in your head, can you to draw it so that you can keep track of where the cubes are?
Tell me about the building in your head.

Possible extension

Learners could try, Green Cube, Yellow Cube.

Possible support

Suggest staying with Building with Cubes.