Reasoning, convincing and proving

  • Curve fitter
    problem

    Curve fitter

    Age
    14 to 18
    Challenge level
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    This problem challenges you to find cubic equations which satisfy different conditions.

  • Guess What?
    problem

    Guess what?

    Age
    7 to 11
    Challenge level
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    Can you find out which 3D shape your partner has chosen before they work out your shape?
  • Compare the Calculations
    problem

    Compare the calculations

    Age
    7 to 11
    Challenge level
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    Can you put these four calculations into order of difficulty? How did you decide?

  • Fruity Pairs
    problem

    Fruity pairs

    Age
    5 to 7
    Challenge level
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    Which two items of fruit could Kate and Sam choose? Can you order the prices from lowest to highest?

  • Triangle in a Trapezium
    problem

    Triangle in a trapezium

    Age
    11 to 16
    Challenge level
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    Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

  • The Farmers' Field Boundary
    problem

    The farmers' field boundary

    Age
    11 to 14
    Challenge level
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    The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

  • The square under the hypotenuse
    problem

    The square under the hypotenuse

    Age
    14 to 16
    Challenge level
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    Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

  • Less is More
    problem

    Less is more

    Age
    7 to 11
    Challenge level
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    Use your knowledge of place value to try to win this game. How will you maximise your score?
  • Neighbourly Addition
    problem

    Neighbourly addition

    Age
    7 to 14
    Challenge level
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    I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?