Visualising and representing

  • Picture a Pyramid ...
    problem

    Picture a Pyramid

    Age
    7 to 11
    Challenge level

    Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

  • Flip
    problem

    Flip

    Age
    7 to 11
    Challenge level

    Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

  • Triangular Faces
    problem

    Triangular Faces

    Age
    7 to 11
    Challenge level
    This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
  • Display Boards
    problem

    Display Boards

    Age
    7 to 11
    Challenge level

    Design an arrangement of display boards in the school hall which fits the requirements of different people.

  • Painting Possibilities
    problem

    Painting Possibilities

    Age
    7 to 11
    Challenge level

    This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes and the small cubes that would fit inside each one.

  • Endless Noughts and Crosses
    game

    Endless Noughts and Crosses

    Age
    7 to 11
    Challenge level

    An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

  • A sheepdog herding a field of sheep.
    game

    Counter Roundup

    Age
    7 to 11
    Challenge level

    A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

  • Tetrahedron faces
    problem

    Tetrahedron Faces

    Age
    7 to 11
    Challenge level
    One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
  • Redblue
    problem

    Redblue

    Age
    7 to 11
    Challenge level
    Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
  • Shunting Puzzle
    problem

    Shunting Puzzle

    Age
    7 to 11
    Challenge level
    Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
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