Visualising and representing

  • Hollow Squares
    problem
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    Hollow Squares

    Age
    14 to 16
    Challenge level
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    Which armies can be arranged in hollow square fighting formations?

  • Quadratic Patterns
    problem
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    Quadratic Patterns

    Age
    14 to 16
    Challenge level
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    Surprising numerical patterns can be explained using algebra and diagrams...

  • Box plot match
    problem
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    Box Plot Match

    Age
    14 to 16
    Challenge level
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    Match the cumulative frequency curves with their corresponding box plots.

  • Isosceles Seven
    problem
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    Isosceles Seven

    Age
    14 to 16
    Challenge level
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    Is it possible to find the angles in this rather special isosceles triangle?

  • Picture Story
    problem
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    Picture Story

    Age
    14 to 16
    Challenge level
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    Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

  • Three cubes
    problem
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    Three Cubes

    Age
    14 to 16
    Challenge level
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    Can you work out the dimensions of the three cubes?

  • Triangle midpoints
    problem
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    Triangle Midpoints

    Age
    14 to 16
    Challenge level
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    You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

  • Five green equilateral triangles, arranged to almost make a complete pentagon.
    problem
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    Doesn't Add Up

    Age
    14 to 16
    Challenge level
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    In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

  • Plus Minus
    problem
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    Plus Minus

    Age
    14 to 16
    Challenge level
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    Can you explain the surprising results Jo found when she calculated the difference between square numbers?

  • Sitting Pretty
    problem
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    Sitting Pretty

    Age
    14 to 16
    Challenge level
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    A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?