Cubes and cuboids

problem

Four Layers

Age

5 to 11

Challenge level

Can you create more models that follow these rules?
problem

Multilink Cubes

Age

7 to 11

Challenge level

If you had 36 cubes, what different cuboids could you make?
problem

Double Your Popcorn, Double Your Pleasure

Age

7 to 11

Challenge level

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.
problem

More Christmas Boxes

Age

7 to 11

Challenge level

What size square should you cut out of each corner of a 10 × 10 grid to make the box that would hold the greatest number of cubes?
problem

Dicey

Age

7 to 11

Challenge level

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
problem

Painted Faces

Age

7 to 11

Challenge level

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
problem

28 - Upward and Onward

Age

7 to 11

Challenge level

Can you find ways of joining cubes together so that 28 faces are visible?
problem

Little Boxes

Age

7 to 11

Challenge level

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
problem

Presents

Age

7 to 11

Challenge level

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
problem

Green Cube, Yellow Cube

Age

7 to 11

Challenge level

How can you paint the faces of these eight cubes so they can be put together to make a 2 × 2 × 2 cube that is green all over AND a 2 × 2 × 2 cube that is yellow all over?