Explaining, convincing and proving

  • Product Sudoku
    problem
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    Product Sudoku

    Age
    11 to 16
    Challenge level
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    The clues for this Sudoku are the product of the numbers in adjacent squares.

  • Triangle in a Trapezium
    problem
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    Triangle in a Trapezium

    Age
    11 to 16
    Challenge level
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    Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

  • Pythagoras Proofs
    problem
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    Pythagoras Proofs

    Age
    11 to 16
    Challenge level
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    Can you make sense of these three proofs of Pythagoras' Theorem?

  • problem
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    Shopping Basket

    Age
    11 to 16
    Challenge level
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    The items in the shopping basket add and multiply to give the same amount. What could their prices be?

  • How old am I?
    problem
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    How Old Am I?

    Age
    14 to 16
    Challenge level
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    In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

  • Chances are
    problem
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    Chances Are

    Age
    14 to 16
    Challenge level
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    Which of these games would you play to give yourself the best possible chance of winning a prize?

  • problem
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    Salinon

    Age
    14 to 16
    Challenge level
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    This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

  • The Better Choice
    problem
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    The Better Choice

    Age
    14 to 16
    Challenge level
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    Here are two games you can play. Which offers the better chance of winning?

  • Where is the dot?
    problem
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    Where Is the Dot?

    Age
    14 to 16
    Challenge level
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    A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

  • Making sixty
    problem
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    Making Sixty

    Age
    14 to 16
    Challenge level
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    Why does this fold create an angle of sixty degrees?