Visualising and representing

  • Gnomon dimensions
    problem

    Gnomon Dimensions

    Age
    14 to 16
    Challenge level
    These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.
  • Overlap
    problem

    Overlap

    Age
    14 to 16
    Challenge level

    A red square and a blue square overlap. Is the area of the overlap always the same?

  • A school corridor.
    problem

    Corridors

    Age
    14 to 16
    Challenge level

    A 10×10×10 cube is made from 27 2×2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.

  • Tetrahedra Tester
    problem

    Tetrahedra Tester

    Age
    14 to 16
    Challenge level

    An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

  • 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?

  • Triangles within Squares
    problem

    Triangles Within Squares

    Age
    14 to 16
    Challenge level

    Can you find a rule which relates triangular numbers to square numbers?

  • 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?

  • Making Tracks
    problem

    Making Tracks

    Age
    14 to 16
    Challenge level

    A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?

  • bio graphs
    problem

    Bio Graphs

    Age
    14 to 16
    Challenge level

    What biological growth processes can you fit to these graphs?

  • 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?
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