Reasoning, convincing and proving

  • 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?

  • Order, Order!
    problem

    Order, order!

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

    Can you place these quantities in order from smallest to largest?

  • Discuss and Choose
    problem

    Discuss and choose

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

    This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

  • Dicey Addition
    problem

    Dicey addition

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

    In these addition games, you'll need to think strategically to get closest to the target.

  • Place your orders
    problem

    Place your orders

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
  • Finding factors
    problem

    Finding factors

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

    Can you find the hidden factors which multiply together to produce each quadratic expression?

  • Largest Even
    problem

    Largest even

    Age
    5 to 11
    Challenge level
    filled star empty star empty star
    How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
  • Fill Me Up
    problem

    Fill me up

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

    Can you sketch graphs to show how the height of water changes in different containers as they are filled?

  • What numbers can we make?
    problem

    What numbers can we make?

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

    Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

  • More Dicey Decisions
    problem

    More dicey decisions

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?