Reasoning, convincing and proving

  • circles in quadrilaterals
    problem

    Circles in quadrilaterals

    Age
    14 to 16
    Challenge level
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    Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

  • Model solutions
    problem

    Model solutions

    Age
    16 to 18
    Challenge level
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    How do these modelling assumption affect the solutions?
  • Back fitter
    problem

    Back fitter

    Age
    14 to 18
    Challenge level
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    10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

  • Speeding boats
    problem

    Speeding boats

    Age
    14 to 16
    Challenge level
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    Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

  • Folding Fractions
    problem

    Folding fractions

    Age
    14 to 16
    Challenge level
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    What fractions can you divide the diagonal of a square into by simple folding?
  • Curvy areas
    problem

    Curvy areas

    Age
    14 to 16
    Challenge level
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    Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

  • problem

    Immersion

    Age
    14 to 16
    Challenge level
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    Various solids are lowered into a beaker of water. How does the water level rise in each case?

  • Multiples Sudoku
    problem

    Multiples Sudoku

    Age
    11 to 14
    Challenge level
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    Each clue in this Sudoku is the product of the two numbers in adjacent cells.

  • Dangerous driver?
    problem

    Dangerous driver?

    Age
    16 to 18
    Challenge level
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    Was it possible that this dangerous driving penalty was issued in error?

  • Prime sequences
    problem

    Prime sequences

    Age
    16 to 18
    Challenge level
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    This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?