Working systematically

  • 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 cartoon worm.
    problem

    Worms

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

    Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

  • Newspapers
    problem

    Newspapers

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
  • 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.

  • 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?

  • Dice and Spinner Numbers
    problem

    Dice and Spinner Numbers

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

    If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

  • Room Doubling
    problem

    Room Doubling

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    Investigate the different ways you could split up these rooms so that you have double the number.
  • It Figures
    problem

    It Figures

    Age
    7 to 11
    Challenge level
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    Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
  • 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 bean bags 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?

  • Watch your Feet
    problem

    Watch Your Feet

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?