Exploring and noticing

  • Cosy corner
    problem

    Cosy corner

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

    Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

  • Two's company
    problem

    Two's company

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

    Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

  • Odds and Evens
    problem

    Odds and evens

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

    Are these games fair? How can you tell?

  • Flippin' discs
    problem

    Flippin' discs

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

    Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

  • Property chart
    problem

    Property chart

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

    A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

  • Complete the Square
    problem

    Complete the square

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

    Complete the squares - but be warned some are trickier than they look!

  • Chairs and Tables
    problem

    Chairs and tables

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

    Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

  • Board Block Challenge
    problem

    Board block challenge

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

    Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

  • Triangle Pin-Down
    problem

    Triangle pin-down

    Age
    7 to 11
    Challenge level
    filled star filled star filled star
    Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
  • Subtended angles
    problem

    Subtended angles

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

    What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?