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Cashing Up

Age 5 to 11 Challenge Level:

What Money?


Maybe you have a shop at school, down the road or somewhere else nearby.
At the end of the day the shopkeeper has to look at the money in the till in order to count it up.

If it were in USA, the shopkeeper might find they have the following coins;
fourteen 1¢ coins
fifteen 5¢ coins
twenty eight 10¢ coins
fourteen 25¢ coins
twenty four $1 coins

... and also a large number of notes.

If it were in India the shopkeeper might find they have the following notes;
twelve ₹5 (rupees) notes
thirty two ₹10 notes
eighteen ₹20 notes
twenty seven ₹50 notes
four ₹100 notes

... and also some coins.

Which coin was the most common in the USA shop?
Which coin was the most common in the Indian shop?

The mathematical name for the most common item in a set of data is the 'mode'.

Can you think of a reason why the shopkeepers might be interested to know the modal number of coins?

You could search your room for collections of other things that can be sorted and then counted. You could then find the mode for them.

Photograph acknowledgements;

www.suppliesforless.com

Why do this problem?

This problem gives a simple context in which to look at averages, in particular the mode.

Possible approach

If you can get hold of a cash tray it would be good to actually be able to handle different coins/notes in your own currency.

The children can sit round such a tray and talk with you about what there are most/least of in the tray and how they would go about finding out. 

Once they have explored, you can introduce the mathematical vocabulary of 'mode', if appropriate.

Key questions

How did you find the mode?

Possible extension

Challenge children to change the mode of the set, for example, you could ask "what would have to happen for the  . . . . . .  to be the mode (choose another coin/note that does not represent the mode at the start)?" 

Possible support

Handling real money will help all children access this activity.