Exploring and noticing

  • Of all the areas
    problem
    Favourite

    Of all the areas

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

  • Fair Shares?
    problem
    Favourite

    Fair shares?

    Age
    14 to 16
    Challenge level
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    A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

  • What's Possible?
    problem
    Favourite

    What's possible?

    Age
    14 to 16
    Challenge level
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    Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

  • Tree tops
    problem
    Favourite

    Tree tops

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Can you make sense of information about trees in order to maximise the profits of a forestry company?

  • Tiny Nines
    problem
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    Tiny nines

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    What do you notice about these families of recurring decimals?

  • Pick's Theorem
    problem
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    Pick's theorem

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    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.

  • The Spider and the Fly
    problem
    Favourite

    The spider and the fly

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

  • Where to Land
    problem
    Favourite

    Where to land

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

  • Triangle in a Triangle
    problem
    Favourite

    Triangle in a triangle

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Can you work out the fraction of the original triangle that is covered by the inner triangle?

  • Areas of parallelograms
    problem
    Favourite

    Areas of parallelograms

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Can you find the area of a parallelogram defined by two vectors?