Visualising and representing

  • Same Face
    problem

    Same face

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    A cube is rolled on a plane, landing on the squares in the order shown. Which two positions had the same face of the cube touching the surface?
  • Travelator
    problem

    Travelator

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    When Andrew arrives at the end of the walkway, how far is he ahead of Bill?
  • Oldest and Youngest
    problem

    Oldest and youngest

    Age
    14 to 16
    Challenge level
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    Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?
  • Squares in a Square
    problem

    Squares in a square

    Age
    11 to 14
    Challenge level
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    In the diagram, the small squares are all the same size. What fraction of the large square is shaded?
  • Semicircular Design
    problem

    Semicircular design

    Age
    14 to 16
    Challenge level
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    Weekly Problem 9 - 2016
    The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?
  • Travelling by Train
    problem

    Travelling by train

    Age
    14 to 16
    Challenge level
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    Stephen stops at Darlington on his way to Durham. At what time does he arrive at Durham?
  • Doubly Symmetric
    problem

    Doubly symmetric

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    What is the smallest number of additional squares that must be shaded so that this figure has at least one line of symmetry and rotational symmetry of order 2?
  • Growing Surprises
    problem

    Growing surprises

    Age
    11 to 14
    Challenge level
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    Can you find the connections between linear and quadratic patterns?

  • Square Number Surprises
    problem

    Square number surprises

    Age
    14 to 16
    Challenge level
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    There are unexpected discoveries to be made about square numbers...

  • Multiple Surprises
    problem

    Multiple surprises

    Age
    11 to 16
    Challenge level
    filled star empty star empty star

    Sequences of multiples keep cropping up...