Conjecturing and generalising

  • Counting Fish
    problem

    Counting fish

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

    I need a figure for the fish population in a lake. How does it help to catch and mark 40 fish?

  • problem

    Reaction timer

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

    This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

  • Interactive Spinners
    problem

    Interactive spinners

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

    This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

  • Logic Block Collections
    problem

    Logic block collections

    Age
    5 to 7
    Challenge level
    filled star empty star empty star
    What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?
  • problem

    In the bag

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

    Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

  • Least of All
    problem

    Least of all

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.
  • All tangled up
    problem

    All tangled up

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

    Can you tangle yourself up and reach any fraction?

  • Tug Harder!
    problem

    More Tug of war

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

    In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

  • Negative Power
    problem

    Negative powers

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

    What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?

  • Consecutive negative numbers
    problem

    Consecutive negative numbers

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

    Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?