Visualising and representing

  • Triangles within Pentagons
    problem

    Triangles Within Pentagons

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

    Show that all pentagonal numbers are one third of a triangular number.

  • Packing 3D shapes
    problem

    Packing 3D Shapes

    Age
    14 to 16
    Challenge level
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    What 3D shapes occur in nature. How efficiently can you pack these shapes together?

  • Centre Square
    problem

    Centre Square

    Age
    14 to 16
    Challenge level
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    What does Pythagoras' Theorem tell you about the radius of these circles?

  • In or Out?
    problem

    In or Out?

    Age
    14 to 16
    Challenge level
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    Weekly Problem 52 - 2014
    Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?

  • Can you traverse it?
    problem

    Can You Traverse It?

    Age
    14 to 18
    Challenge level
    filled star empty star empty star

    How can you decide if a graph is traversable?

  • Data matching
    problem

    Data Matching

    Age
    14 to 18
    Challenge level
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    Use your skill and judgement to match the sets of random data.

  • Curve Hunter
    problem

    Curve Hunter

    Age
    14 to 18
    Challenge level
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    This problem challenges you to sketch curves with different properties.

  • 3D Treasure Hunt
    problem

    3D Treasure Hunt

    Age
    14 to 18
    Challenge level
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    Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

  • Calculating with cosines
    problem

    Calculating With Cosines

    Age
    14 to 18
    Challenge level
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    If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

  • Vanishing point
    problem

    Vanishing Point

    Age
    14 to 18
    Challenge level
    filled star filled star empty star
    How can visual patterns be used to prove sums of series?