Copyright © University of Cambridge. All rights reserved.

Meg and Mo are playing Marbles together. After each game, they each put their marbles in a pouch and hang the pouches on a balance while they go off for a snack. You can use the interactivity to experiment to help you answer the questions below.

After their first game, they each have the same number of marbles. Meg puts hers in the pouch 50cm to the left of the centre, and Mo puts hers 50cm to the right of the centre. Using the interactivity, you can check that this balances.

Suppose that when they come back, Meg moves her pouch to be 80cm away. Find where Mo must put her pouch so that it still balances.

If Meg moves her pouch to be 25cm from the pivot, find where Mo must put her pouch.

Full Screen Version

_________________________________________________________________________________

Meg wins the next game, and since she and Mo are playing for keeps, she now has more marbles than her friend.

They discover (by experimenting) that if Meg puts her pouch 30cm from the centre and Mo puts hers 50cm from the centre then the pouches balance. Use the interactivity to explore this further.

Full Screen Version

Fill in the table below so that when the pouches are at the distances shown, they balance.

Meg | Mo |

30cm | 50cm |

60cm | |

45cm | |

25cm |

Without using the interactivity, can you work out the distances from the centre in the table below that Meg and Mo must put their pouches so that they balance?

Meg | Mo |

90cm | |

40cm | |

60cm | |

20cm | |

24cm |

Try to explain how you worked it out.

After the third game, Meg has 10 marbles and Mo has 6.

They each put their pouches in a fixed place, as shown.

They find some more marbles, and can add and remove these marbles to and from their pouches.

Use the interactivity to explore this further.

Fill in the table to show how many marbles are needed on each side to make it balance.

Meg | Mo |

10 marbles | 6 marbles |

20 marbles | |

5 marbles | |

9 marbles |

Now, without using the interactivity, can you complete the table below showing how many marbles are needed on each side to make it balance?

Meg | Mo |

18 marbles | |

12 marbles | |

7 marbles |

Try to explain how you worked it out.