Exploring and noticing

  • Can you Make 100?
    problem
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    Can You Make 100?

    Age
    11 to 14
    Challenge level
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    How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?

  • Fractions Rectangle
    problem
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    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?

  • Number Families
    problem
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    Number Families

    Age
    11 to 14
    Challenge level
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    How many different number families can you find?

  • Odds, Evens and More Evens
    problem
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    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...

  • Sieve of Eratosthenes
    problem
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    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.

  • Two white rectangles on a wooden background, arranged like an equals sign.
    problem
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    Can They Be Equal?

    Age
    11 to 14
    Challenge level
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    Can you find rectangles where the value of the area is the same as the value of the perimeter?

  • Olympic Records
    problem
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    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
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    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?

  • Magic Letters
    problem
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    Magic Letters

    Age
    11 to 14
    Challenge level
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    Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

  • Fence it
    problem
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    Fence It

    Age
    11 to 14
    Challenge level
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    If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?