Once upon a time a shopkeeper sold a great many small items to lots of customers. Here I have chosen to tell the story ~ and show pictures ~ of just one of the many items sold ~ steel washers.

A steel washer ~ three more on the table

A pile of washers about to be counted

A handful of ten washers ~ a convenient number

A collection of counted washers ~

three piles of ten ~ four singles

If any shopkeeper spends too much time counting items for every customer ~ one ~ two ~ three ~ four ~ on ~ and on ~ then a queue will form.

Customers get grumpy if they have to wait in a queue. The shopkeeper decided to pack the washers into envelopes. Each envelope contains ten washers. Pictorially it looks like this ~

Counting ten washers

Put the washers into an envelope

Seal the envelope

Because of lots of things ~ the speedy service being one of them ~ the shopkeeper's trade flourished. People were buying a great many items at every visit.

If someone wanted forty-three washers the shopkeeper would hand over four envelopes and also three single washers ~ that was much quicker than counting up to forty-three.

43 washers ~ four envelopes of ten ~ and three singles

Everyone thought using envelopes was a good idea. Trade increased. The shopkeeper bundled ten envelopes into a package and tied it with string. Ten envelopes ~ each with ten washers ~ that means one hundred washers.

A bundle of ten envelopes ~

How many washers?

Two bundles ~ How many envelopes? ~

How many washers?

Here are three quick questions to check how things are going for you ~

How many envelopes? ~

How many washers?

How many envelopes? ~ and washers?

How many washers?

After some time the shopkeeper had to send someone to go to the stationery shop to buy more envelopes ~ stocks kept running low.

A box of envelopes ~ 1000 in a box ~

The '100 GSM' is a measure of quality ~ not quantity

Someone on the staff pointed out that the number of envelopes being used could be saved. The suggestion was made to put the washers straight into boxes ~ one hundred to a box. In that way there would also be a handy storage facility for the end-user.

Count 100 washers into a box

Prepare to close the lid

Shake the box to let the lid fit down

300 washers ready for collection ~ and three useful boxes ~ extra ~ free

Here is a short summary of the maths that was going on.

or 1 envelope = 10 washers

or 1 bundle = 10 envelopes ~

or 1 bundle = 100 washers

One box is equivalent to ten envelopes and contains 100 washers.

To return to our story ~ the shopkeeper had obviously had a good mathematical education. He chose to **work in tens** ~ ten washers ~ ten envelopes ~ maybe next year it will be **ten boxes** fit into one **carton**.

As a further update to the story ~ the shopkeeper is now a manufacturer of washers ~ with a huge factory ~ and living happily ever after.

Back to thinking about maths ~ hmmm ~ with ten boxes to one carton ~ how many washers in one carton?

Does a van take ten cartons?

Will ten vanloads fit into one container?

How many containers fit onto a train?

How many trainloads fit into a ship?

Finally ~ how many washers in a shipload?

The answer is ~ quite a lot!

Working in tens is what mathematicians do. Sometimes they are not very imaginative. Instead of parcelling things into envelopes ~ bundles ~ cartons ~ whatever ~ they use a different system.

They use **labels** ~ ones ~ tens ~ hundreds ~ thousands ~ tens-of-thousands ~ and so on. Some people call the 'ones' **units**. It means the same as **ones** or **singles**.

In shorthand ~ or in maths-code if you wish ~ we could have ~

or

C ~ B ~ E ~ S

or

thousands ~ hundreds ~ tens ~ units

or

T ~ H ~ T ~ U

or

thousands ~ hundreds ~ tens ~ ones

or

T ~ H ~ T ~ O

The important thing to note is that any one item is ten times greater than the one beside it on the right.

Not everyone works in tens when packaging ~ sometimes it is convenient to work in some other quantity [114067].

I have a note on

There is a commentary for staff ~ or parents ~ or carers ~ available for subscribers to BusyBusy [114043].

https://www.busybusy.co/page/11/40/43.htm

End of file