Visualising and representing

  • Troublesome Dice
    problem

    Troublesome dice

    Age
    11 to 14
    Challenge level
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    When dice land edge-up, we usually roll again. But what if we didn't...?
  • At least one...
    problem

    At least one...

    Age
    11 to 14
    Challenge level
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    Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?

  • What numbers can we make?
    problem

    What numbers can we make?

    Age
    11 to 14
    Challenge level
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    Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

  • Fractions Rectangle
    problem

    Fractions rectangle

    Age
    11 to 14
    Challenge level
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    The large rectangle is divided into quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

  • Odds, Evens and More Evens
    problem

    Odds, evens and more evens

    Age
    11 to 14
    Challenge level
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    Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

  • Number Pyramids
    problem

    Number pyramids

    Age
    11 to 14
    Challenge level
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    Try entering different sets of numbers in the number pyramids. How does the total at the top change?

  • Sieve of Eratosthenes
    problem

    Sieve of Eratosthenes

    Age
    11 to 14
    Challenge level
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    Follow this recipe for sieving numbers and see what interesting patterns emerge.

  • Olympic Records
    problem

    Olympic records

    Age
    11 to 14
    Challenge level
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    Can you deduce which Olympic athletics events are represented by the graphs?

  • Summing Consecutive Numbers
    problem

    Summing consecutive numbers

    Age
    11 to 14
    Challenge level
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    15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

  • Constructing Triangles
    problem

    Constructing triangles

    Age
    11 to 14
    Challenge level
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    Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?