Conjecturing and generalising

  • Filling the gaps
    problem

    Filling the gaps

    Age
    14 to 16
    Challenge level
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    Which numbers can we write as a sum of square numbers?
  • Can they be equal?
    problem

    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?

  • Generating Triples
    problem

    Generating triples

    Age
    14 to 16
    Challenge level
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    Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
  • Changing areas, changing perimeters
    problem

    Changing areas, changing perimeters

    Age
    11 to 14
    Challenge level
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    How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

  • 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?

  • 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...

  • Carroll Diagrams
    problem

    Carroll diagrams

    Age
    5 to 11
    Challenge level
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    Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

  • Seeing Squares
    problem

    Seeing squares

    Age
    5 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 square.

  • Dicey Addition
    problem

    Dicey addition

    Age
    5 to 11
    Challenge level
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    In these addition games, you'll need to think strategically to get closest to the target.

  • This Pied Piper of Hamelin
    problem

    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!