Reasoning, convincing and proving

  • problem

    The animals' sports day

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    One day, five small animals in my garden had a sports day. Who do you think won each race?

  • So it's times!
    problem

    So it's times!

    Age
    7 to 14
    Challenge level
    filled star filled star filled star

    How will you decide which way of flipping over and/or turning the grid will give you the highest total?

  • Calculating with cosines
    problem

    Calculating with cosines

    Age
    14 to 18
    Challenge level
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    If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?
  • problem

    The Domesday Project

    Age
    7 to 11
    Challenge level
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    Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

  • Dodgy proofs
    problem

    Dodgy proofs

    Age
    16 to 18
    Challenge level
    filled star filled star filled star
    These proofs are wrong. Can you see why?
  • All Change
    problem

    All change

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

  • Generating Triples
    problem

    Generating triples

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
  • Fill Me Up Too
    problem

    Fill me up too

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?