Visualising and representing

  • Is there a theorem?
    problem
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    Is There a Theorem?

    Age
    11 to 14
    Challenge level
    Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
  • One and three
    problem
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    One and Three

    Age
    14 to 16
    Challenge level
    Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400 metres from B. How long is the lake?
  • Hamiltonian Cube
    problem
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    Hamiltonian Cube

    Age
    11 to 16
    Challenge level
    Weekly Problem 36 - 2007
    Find the length along the shortest path passing through certain points on the cube.
  • John's train is on time
    problem
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    John's Train Is on Time

    Age
    11 to 14
    Challenge level
    A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
  • Cubes within Cubes revisited
    problem
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    Cubes Within Cubes Revisited

    Age
    11 to 14
    Challenge level
    Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
  • Seesaw Shenanigans
    problem
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    Seesaw Shenanigans

    Age
    3 to 7
    Challenge level

    A group of animals has made a seesaw in the woods. How can you make the seesaw balance?

  • Always, Sometimes or Never? KS1
    problem
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    Always, Sometimes or Never? KS1

    Age
    5 to 7
    Challenge level

    Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

  • Eightness of Eight
    problem
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    Eightness of Eight

    Age
    5 to 7
    Challenge level

    What do you see as you watch this video? Can you create a similar video for the number 12?

  • problem
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    Biscuit Decorations

    Age
    5 to 7
    Challenge level

    Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

  • Writing Digits
    problem
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    Writing Digits

    Age
    5 to 7
    Challenge level

    Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

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