Exploring and noticing

  • Tiles on a Patio
    problem

    Tiles on a patio

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    How many ways can you find of tiling the square patio, using square tiles of different sizes?
  • A stack of open magazines on colourful pages.
    problem

    Magazines

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

    Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

  • Pebbles
    problem

    Pebbles

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

    Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

  • My New Patio
    problem

    My new patio

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
  • Roll these Dice
    problem
    Favourite

    Roll these dice

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

    Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

  • Presents
    problem

    Presents

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
  • Different coloured hula hoops.
    problem

    Bean bags for Bernard's bag

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

    How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

  • problem
    Favourite

    Round and round the circle

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

    What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

  • Domino Square
    problem
    Favourite

    Domino square

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

    Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

  • Prison Cells
    problem
    Favourite

    Prison cells

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?