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Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Penta Post

Stage: 2 Challenge Level: Challenge Level:1

Penta Post

Here are the prices for 1st and 2nd class mail within the UK [in 2002].

Weight up to First Class Second Class
$60g$ $27p$ $19p$
$100g$ $41p$ $33p$
$150g$ $57p$ $44p$
$200g$ $72p$ $54p$
$250g$ $84p$ $66p$
$300g$ $96p$ $76p$
$350g$ $£1.09$ $87p$
$400g$ $£1.30$ $£1.05$
$450g$ $£1.48$ $£1.19$
$500g$ $£1.66$ $£1.35$
$600g$ $£2.00$ $£1.60$
$700g$ $£2.51$ $£1.83$
$750g$ $£2.69$ $£1.94$*
$800g$ $£2.91$  
$900g$ $£3.20$  
$1kg$ $£3.49$  

Costs for First Class items over $1kg$ are $£3.49$ and then $85p$ for each extra $250g$.
*Items over $750g$ cannot be sent second class.

You have an unlimited number of each of these stamps:

4p stamp 10p stamp 19p stamp 27p stamp 37p stamp £1.00 stamp

Reproduced by kind permission of Consignia plc. All rights reserved.

1/ Which stamps would you need to post a parcel weighing $825g$?

2/ I want to send a package 1st class which weighs $235g$. It is very small so I want to use as few stamps as possible. Which ones would I use?

3/ If I only had $3$ of each kind of stamp, which $2$nd class price could I not make?

4/ How many different combinations of stamps could be stuck on a letter weighing $140g$ if it goes 1st class?

5/ I use the following stamps to send two items, one 1st class and the other 2nd class:

E stamp 1st class stamp 2nd class stamp 10p stamp 10p stamp 4p stamp 4p stamp

What could their weights be?

Further extension to this activity can be carried out by considering the value of the stamps alone, as numbers $4$, $10$, $19$, $27$, $37$ & $100$. For example taking the $5$ lowest numbers [missing out the $100$] challenging the pupils to come up with the smallest number of ways you can get totals between $4$ and $50$. This could lead to questions about what totals can NOT be had, and checking to see if you've really got the smallest number of ways, each time.

All tables reproduced by kind permission of Consignia plc. All rights reserved.

UK folk need to be aware that all this has changed since 2009 ! (See Royal Mail)

Why do this problem?

This activity is a good everyday example of the use of addition and multiplication. It also helps pupils see the use of arithmetic in practical situations.

Possible approach

Start off a general discuss about posting to see what they know about posting letters and cards. When they are happy to talk about stamps present them with the challenge. You may prefer to update the charges and adapt the challenge to suit the current pricing system.

Key questions

Tell me how you have worked this out.

Possible extension

Pupils could invent their own question based upon the present-day costs of postage.