Cubes and cuboids

  • Small pepper seedlings in turquoise pots.
    problem

    Twelve Cubed

    Age
    14 to 16
    Challenge level

    A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?

  • Inside Out
    problem

    Inside Out

    Age
    14 to 16
    Challenge level

    There are 27 small cubes in a 3 × 3 × 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you can colour every face of all of the smaller cubes?

  • Small pepper seedlings in turquoise pots.
    problem

    Cubic Covering

    Age
    14 to 16
    Challenge level

    A blue cube has blue cubes glued on all of its faces. Yellow cubes are then glued onto all the visible blue facces. How many yellow cubes are needed?

  • Summing squares
    problem

    Summing Squares

    Age
    14 to 16
    Challenge level
    Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
  • Small pepper seedlings in turquoise pots.
    problem

    Cubic Vision

    Age
    14 to 16
    Challenge level

    How many cubes can you see?

  • Small pepper seedlings in turquoise pots.
    problem

    Painted Purple

    Age
    14 to 16
    Challenge level

    Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?

  • Making Maths: Link-a-Cube
    page

    Making Maths: Link-A-Cube

    Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.
  • Thinking 3D
    article

    Thinking 3D

    How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?

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