Visualising and representing

  • 28 - upward and onward
    problem

    28 - upward and onward

    Age
    7 to 11
    Challenge level
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    Can you find ways of joining cubes together so that 28 faces are visible?
  • Painted Purple
    problem

    Painted purple

    Age
    14 to 16
    Challenge level
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    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?
  • Island Hopping
    problem

    Island hopping

    Age
    11 to 14
    Challenge level
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    What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?
  • Slick Summing
    problem

    Slick summing

    Age
    14 to 16
    Challenge level
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    Watch the video to see how Charlie works out the sum. Can you adapt his method?

  • Mystic Rose
    problem

    Mystic rose

    Age
    14 to 16
    Challenge level
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    Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

  • Diminishing Returns
    problem

    Diminishing returns

    Age
    11 to 14
    Challenge level
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    How much of the square is coloured blue? How will the pattern continue?

  • Tower of Hanoi
    problem

    Tower of Hanoi

    Age
    11 to 14
    Challenge level
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    The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

  • Christmas chocolates
    problem

    Christmas chocolates

    Age
    11 to 14
    Challenge level
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    How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

  • Polygon walk
    problem

    Polygon walk

    Age
    16 to 18
    Challenge level
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    Go on a vector walk and determine which points on the walk are closest to the origin.

  • Mach Attack
    problem

    Mach attack

    Age
    16 to 18
    Challenge level
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    Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.