Visualising and representing

  • problem
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    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?

  • problem
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    At Right Angles

    Age
    14 to 16
    Challenge level
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    Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

  • Speeding boats
    problem
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    Speeding Boats

    Age
    14 to 16
    Challenge level
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    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
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    Surprising Transformations

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

    Age
    14 to 16
    Challenge level
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    Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

  • Partly Painted Cube
    problem
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    Partly Painted Cube

    Age
    14 to 16
    Challenge level
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    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
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    Which Is Bigger?

    Age
    14 to 16
    Challenge level
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    Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

  • Fill Me Up Too
    problem
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    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
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    Filling the Gaps

    Age
    14 to 16
    Challenge level
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    Which numbers can we write as a sum of square numbers?