Reflections

  • Reflecting Squarely
    problem

    Reflecting squarely

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

    In how many ways can you fit all three pieces together to make shapes with line symmetry?

  • Shady Symmetry
    problem

    Shady symmetry

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

    How many different symmetrical shapes can you make by shading triangles or squares?

  • Mirror, mirror...
    problem

    Mirror, mirror...

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

    Explore the effect of reflecting in two parallel mirror lines.

  • Reflecting Lines
    problem

    Reflecting lines

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

    Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

  • Transformation Game
    game
    Favourite

    Transformation game

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

    Why not challenge a friend to play this transformation game?

  • ...on the wall
    problem

    ...on the wall

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

    Explore the effect of reflecting in two intersecting mirror lines.

  • Surprising Transformations
    problem

    Surprising transformations

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

    I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

  • Attractive Tablecloths
    problem

    Attractive tablecloths

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

    Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

  • A Problem of time
    problem

    A problem of time

    Age
    14 to 16
    Challenge level
    filled star filled star filled star
    Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?
  • Flipping Twisty Matrices
    problem

    Flipping twisty matrices

    Age
    14 to 18
    Challenge level
    filled star empty star empty star

    Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.