Conjecturing and generalising

  • Journeys in Numberland
    problem

    Journeys in Numberland

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

    Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

  • The add and take-away path
    problem

    The add and take-away path

    Age
    5 to 7
    Challenge level
    filled star empty star empty star
    Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
  • Area and perimeter
    problem

    Area and perimeter

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

    What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

  • Sitting round the party tables
    problem

    Sitting round the party tables

    Age
    5 to 11
    Challenge level
    filled star empty star empty star
    Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
  • Difference Dynamics
    problem

    Difference dynamics

    Age
    14 to 18
    Challenge level
    filled star empty star empty star
    Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
  • Your number was...
    problem

    Your number was...

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?
  • Sorting Logic Blocks
    problem

    Sorting logic blocks

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

    This activity focuses on similarities and differences between shapes.

  • How Odd
    problem

    How odd

    Age
    5 to 7
    Challenge level
    filled star filled star empty star
    This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
  • Ip Dip
    problem

    Ip dip

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

    "Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

  • Follow the numbers
    problem

    Follow the numbers

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

    What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.