Conjecturing and generalising

  • Fit These Shapes
    problem

    Fit these shapes

    Age
    5 to 11
    Challenge level
    filled star empty star empty star
    What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
  • A little light thinking
    problem

    A little light thinking

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

    Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

  • Four Coloured Lights
    problem

    Four coloured lights

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?
  • Shapely Lines
    problem

    Shapely lines

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

    This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

  • Our Numbers
    problem

    Our numbers

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

    These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

  • problem

    Counting cogs

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

    Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

  • I Like ...
    problem

    I like ...

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

    Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

  • Growing Rectangles
    problem

    Growing rectangles

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

    What happens to the area and volume of 2D and 3D shapes when you enlarge them?

  • Times Tables Shifts
    problem

    Times tables shifts

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

    In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

  • Three Dice
    problem

    Three dice

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

    Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?