Reasoning, convincing and proving

  • Proof Sorter - The Square Root of 2 is Irrational
    interactivity

    Proof sorter - the square root of 2 is irrational

    Age
    16 to 18
    Challenge level
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    Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.
  • Proof Sorter - Geometric Sequence
    interactivity

    Proof sorter - geometric sequence

    Age
    16 to 18
    Challenge level
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    Can you correctly order the steps in the proof of the formula for the sum of the first n terms in a geometric sequence?
  • Proof Sorter - Quadratic Equation
    interactivity

    Proof sorter - quadratic equation

    Age
    14 to 18
    Challenge level
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    This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.
  • The Triangle Game
    game

    The triangle game

    Age
    11 to 16
    Challenge level
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    Can you discover whether this is a fair game?
  • Online
    game

    Online

    Age
    7 to 11
    Challenge level
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    Can you end up with all the occurrences of the same letter in this two-player game?

  • Yih or Luk tsut k'i or Three Men's Morris
    game

    Yih or Luk tsut k'i or Three Men's Morris

    Age
    11 to 18
    Challenge level
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    Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.

  • Anti-Magic Square
    problem

    Anti-magic square

    Age
    11 to 14
    Challenge level
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    You may have met Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different - can you still solve it?
  • Exponential intersection
    problem

    Exponential intersection

    Age
    16 to 18
    Challenge level
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    Can the pdfs and cdfs of an exponential distribution intersect?
  • Next-door Numbers
    problem

    Next-door numbers

    Age
    5 to 7
    Challenge level
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    Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
  • Angles inside
    problem

    Angles inside

    Age
    11 to 14
    Challenge level
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    Draw some angles inside a rectangle. What do you notice? Can you prove it?