## Sending & Receiving Cards

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!!!!

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 Exploring Wild & Wonderful Number Patterns ).

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.

It would be useful before starting this activity to have done some work on

Digital Roots. Introduce the idea of digital roots, perhaps starting from what they notice about the answers to the 9 times table, before starting this challenge, as it adds a new dimension of things that can be studied and enjoyed in the exploration of this set of numbers.

Tell me how you are working these out.

A useful thing which may not have been experienced in number patterns before that works well in this investigation is to look at how the numbers that occur later on in the series can be made from the addition of previous numbers in the set. e.g. 110 = 20 + 90, all these three numbers being found in this number pattern from the sending of cards.

Use dolls/teddy bears etc. to represent the people sending cards and have something ready to represent the cards.