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### Number and algebra

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# Sending Cards

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### Exploring Wild & Wonderful Number Patterns

### Pebbles

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Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 7 to 11

Challenge Level

There are many festivals and celebrations when we send cards to each other. Some schools organise a postal service within the school and some of the pupils get the job of being postmen/women.

Groups of children send cards to each other sometimes and that's really good for them all; it's a good feeling getting the cards.

Suppose there are three children, Georgie, Jo and Chris, and these three are really good friends. They decide to send cards to each other.

Georgie sends two cards, one to Jo and one to Chris.

Jo sends two cards, one to Georgie and one to Chris.

Chris sends two cards, one to Jo and one to Georgie.

So these three friends send six cards altogether. Also they get six cards altogether (two each)!!!!

What if in another class in that school there is a group of four children who are best friends and at this time of the year each sends the others a card.

Raj sends 3 cards, one to Bex, one to Jon and one to Loo.

Bex sends 3 cards, one to Raj, one to Jon and one to Loo.

Jon sends 3 cards....

Loo sends 3 cards....

So a lot more cards are sent by the four children altogether.

This season's challenge is to explore the number of cards that are sent altogether when there are 5 children, then 6, then 7, *etc.* , up to perhaps a class of 30 children who all send cards to each other and you work out how many cards are sent altogether.

Once you have this set of numbers it might be good to write them down underneath one another (a bit like you may have done when you did the investigation called EWWNP).

You could now, if you have not done it already, start looking at some of the things that pop up in this number pattern. I'm not sure what they all are of course, but I've seen a few patterns, so get searching for what YOU can find!

Then you'll be able to ask, "I wonder what would happen if I ...?'' about so many things.

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?