Explaining, convincing and proving

  • Trapezium Four
    problem

    Trapezium four

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

    The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

  • Nicely Similar
    problem

    Nicely similar

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

    If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

  • Gutter
    problem

    Gutter

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

    Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

  • LCM Sudoku
    problem

    LCM Sudoku

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

    Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

  • For richer for poorer
    problem

    For richer for poorer

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

    Charlie has moved between countries and the average income of both has increased. How can this be so?

  • problem

    Immersion

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

    Various solids are lowered into a beaker of water. How does the water level rise in each case?

  • Folding Fractions
    problem

    Folding fractions

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    What fractions can you divide the diagonal of a square into by simple folding?
  • Speeding boats
    problem

    Speeding boats

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

    Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

  • Partly Painted Cube
    problem

    Partly painted cube

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

    Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

  • L-triominoes
    problem

    L-triominoes

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?