Conjecturing and generalising

  • problem
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    Two Primes Make One Square

    Age
    7 to 11
    Challenge level
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    Can you make square numbers by adding two prime numbers together?

  • Four Go
    problem
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    Four Go

    Age
    7 to 11
    Challenge level
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    This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

  • Light the Lights Again
    problem
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    Light the Lights Again

    Age
    7 to 11
    Challenge level
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    Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light?

  • problem
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    This Pied Piper of Hamelin

    Age
    7 to 11
    Challenge level
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    Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

  • Six Ten Total
    problem
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    Six Ten Total

    Age
    7 to 11
    Challenge level
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    This challenge combines addition, multiplication, perseverance and even proof.

  • Seeing Rhombuses
    problem
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    Seeing Rhombuses

    Age
    7 to 11
    Challenge level
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    Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

  • Sticky Triangles
    problem
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    Sticky Triangles

    Age
    7 to 11
    Challenge level
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    Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
  • problem
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    Cut It Out

    Age
    7 to 11
    Challenge level
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    Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

  • Board Block Challenge
    problem
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    Board Block Challenge

    Age
    7 to 11
    Challenge level
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    Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

  • Finding 3D Stacks
    problem
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    Finding 3D Stacks

    Age
    7 to 11
    Challenge level
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    Can you find a way of counting the spheres in these arrangements?