2D shapes and their properties

  • Shapely Tiling
    problem

    Shapely tiling

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?
  • Let Us Reflect
    problem

    Let us reflect

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

  • Semi-detached
    problem

    Semi-detached

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
  • Circumnavigation
    problem

    Circumnavigation

    Age
    14 to 16
    Challenge level
    filled star filled star filled star
    The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
  • Bow Tie
    problem

    Bow tie

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.
  • LOGO Challenge 8  - Rhombi
    problem

    LOGO challenge 8 - rhombi

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

    Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

  • LOGO Challenge 2 - Diamonds are forever
    problem

    LOGO challenge 2 - diamonds are forever

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

    The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.

  • LOGO Challenge 6 - Triangles and Stars
    problem

    LOGO challenge 6 - triangles and stars

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

    Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

  • LOGO Challenge 10 - Circles
    problem

    LOGO challenge 10 - circles

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

    In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.