Reasoning, convincing and proving

  • A Knight's Journey
    article

    A knight's journey

    This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
  • Geometry and Gravity 2
    article

    Geometry and gravity 2

    This is the second of two articles and discusses problems relating to the curvature of space, shortest distances on surfaces, triangulations of surfaces and representation by graphs.
  • Pythagorean Triples II
    article

    Pythagorean triples II

    This is the second article on right-angled triangles whose edge lengths are whole numbers.

  • Pythagorean Triples I
    article

    Pythagorean triples I

    The first of two articles on Pythagorean Triples which asks how many right angled triangles can you find with the lengths of each side exactly a whole number measurement. Try it!

  • 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
    filled star empty star empty star

    Can you end up with all the occurrences of the same letter in this two-player game?