Conjecturing and generalising

  • Same Number!
    problem

    Same number!

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

    If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

  • Last one standing
    problem

    Last one standing

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

    Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

  • 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.

  • problem

    How odd

    Age
    5 to 7
    Challenge level
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    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.

  • Light the Lights
    problem

    Light the lights

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

    Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

  • Light the Lights Again
    problem

    Light the lights again

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

    Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light?

  • Charlie's delightful machine
    problem

    Charlie's delightful machine

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

    Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?