Reasoning, convincing and proving

  • Placeholder: several colourful numbers
    problem

    Triangular intersection

    Age
    14 to 16
    Challenge level
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    What is the largest number of intersection points that a triangle and a quadrilateral can have?
  • Always, Sometimes or Never? KS1
    problem

    Always, sometimes or never? KS1

    Age
    5 to 7
    Challenge level
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    Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

  • Always, Sometimes or Never?
    problem

    Always, sometimes or never?

    Age
    5 to 11
    Challenge level
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    Are these statements relating to odd and even numbers always true, sometimes true or never true?

  • Open Squares
    problem

    Open squares

    Age
    7 to 11
    Challenge level
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    This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

  • Star Polygons
    problem

    Star polygons

    Age
    11 to 14
    Challenge level
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    Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

  • Same length
    problem

    Same length

    Age
    11 to 16
    Challenge level
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    Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

  • Subtraction Surprise
    problem

    Subtraction surprise

    Age
    7 to 14
    Challenge level
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    Try out these calculations. Are you surprised by the results?

  • Mega Quadratic Equations
    problem

    Mega quadratic equations

    Age
    14 to 18
    Challenge level
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    What do you get when you raise a quadratic to the power of a quadratic?