Exploring and noticing

  • Mirror, mirror...
    problem

    Mirror, mirror...

    Age
    11 to 14
    Challenge level
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    Explore the effect of reflecting in two parallel mirror lines.

  • Intersections
    problem

    Intersections

    Age
    14 to 18
    Challenge level
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    Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

  • Multiples Grid
    problem

    Multiples grid

    Age
    7 to 11
    Challenge level
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    What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

  • Tricky Triangles
    problem

    Tricky triangles

    Age
    5 to 7
    Challenge level
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    Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
  • There's always One isn't there
    problem

    There's always one isn't there

    Age
    14 to 16
    Challenge level
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    Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
  • Sort the Street
    problem

    Sort the street

    Age
    5 to 7
    Challenge level
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    Sort the houses in my street into different groups. Can you do it in any other ways?

  • Fraction Fascination
    problem

    Fraction fascination

    Age
    7 to 11
    Challenge level
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    This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

  • Sticks and Triangles
    problem

    Sticks and triangles

    Age
    7 to 11
    Challenge level
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    Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
  • Royal Arm Wrestling
    problem

    Royal arm wrestling

    Age
    11 to 14
    Challenge level
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    How many arm-wrestles will there be in the royal arm wrestling championship?
  • Wallpaper
    problem

    Wallpaper

    Age
    5 to 7
    Challenge level
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    These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?