Exploring and noticing

  • Shady Symmetry
    problem

    Shady symmetry

    Age
    11 to 14
    Challenge level
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    How many different symmetrical shapes can you make by shading triangles or squares?

  • Pick's Theorem
    problem

    Pick's theorem

    Age
    14 to 16
    Challenge level
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    Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

  • Top-Heavy Pyramids
    problem

    Top-heavy pyramids

    Age
    11 to 14
    Challenge level
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    Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
  • Cinema Problem
    problem

    Cinema problem

    Age
    11 to 14
    Challenge level
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    A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?

  • Fitted
    problem

    Fitted

    Age
    7 to 11
    Challenge level
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    Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

  • Tiny Nines
    problem

    Tiny nines

    Age
    14 to 16
    Challenge level
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    What do you notice about these families of recurring decimals?

  • problem

    Ladybirds in the garden

    Age
    5 to 7
    Challenge level
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    In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

  • problem

    Clocks

    Age
    7 to 11
    Challenge level
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    These clocks have been reflected in a mirror. What times do they say?

  • Largest product
    problem

    Largest product

    Age
    11 to 14
    Challenge level
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    Which set of numbers that add to 100 have the largest product?