Visualising and representing

  • 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?

  • Surprising Transformations
    problem

    Surprising transformations

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

    I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

  • Summing squares
    problem

    Summing squares

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
  • Mystic Rose
    problem

    Mystic rose

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

    Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

  • 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?

  • Which is bigger?
    problem

    Which is bigger?

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

    Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

  • 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?

  • Filling the gaps
    problem

    Filling the gaps

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

    Which numbers can we write as a sum of square numbers?

  • Attractive Tablecloths
    problem

    Attractive tablecloths

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

    Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

  • 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?