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
    filled star filled star empty star

    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?

  • Which spinners?
    problem

    Which spinners?

    Age
    14 to 18
    Challenge level
    filled star empty star empty star

    Can you work out which spinners were used to generate the frequency charts?

  • problem

    The Domesday Project

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    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?

  • Which list is which?
    problem

    Which list is which?

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

    Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?

  • Statistical shorts
    problem

    Statistical shorts

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

    Can you decide whether these short statistical statements are always, sometimes or never true?

  • 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?
  • Transformations for 10
    problem

    Transformations for 10

    Age
    16 to 18
    Challenge level
    filled star filled star filled star

    Explore the properties of matrix transformations with these 10 questions.