## Farthings, ha’pennys and being tricked into teaching yourself

December 15th, 2010 | Categories: general math | Tags:

When I was 4 or 5 years old, my father taught me a lot of basic mathematics by exploiting my obsession with my grandmother’s collection of antiquated coins which I played with every chance I got.  I loved the weird and wonderful collection of shapes and denominations that made up old English money; thruppenny bits, florins, shillings, ha’pennys, crowns, guineas…..there seemed to be no end to the variety and I loved them all.  I was most definitely a noomtist which was the best rendition my  young self could give of the word ‘numismatist’.

A farthing is an old English coin that was worth a quarter of a penny and Gran had lots of them.  Dad would ask me things like “I’ve got a halfpenny and a farthing, if I changed the lot to farthings then how many would I have?” and “How many farthings are there in a sixpence”.  Initially I would answer these questions by physically counting the coins.  For example, I knew that there were 4 farthings in a penny so I would make 6 stacks of 4 and then count them, one by one, to get the answer: 1,2,3,4,5……21,22,23,24

This became laborious so at some point I’d answer similar questions by ‘counting in 4s’: 4,8,12…. and so on.  Eventually, I didn’t need to count – I just knew that 6 stacks of 4 was 24 and so I had been tricked into learning my 4 times table before I had even started school.  Dad, for his part, hadn’t delivered a single maths lesson – he just spent a few hours playing shopkeeper with his son.

Later, dad  told me that there was such a thing as a third-farthing (1/12 of a penny) but Gran didn’t have any.  If she did though, and he had 2 of them along with a farthing and a half-penny coin then how much money would he have?  Questions such as this taught me about the arithmetic of fractions with no mention of the words ‘common denominator’ in sight.  Good job too because, back then, I doubt I would have been able to pronounce ‘denominator’.

In fact it would be more accurate to say that I ‘discovered how to add fractions’ – my wily old dad didn’t teach me a thing – he just asked me questions about the fascinating little shiny things while we played games together.

1. I learned fractions baking with my mother as we increased or decreased the recipe. She did the same thing, if we making 2/3 of the recipe and the recipe calls for 2 cups of sugar, how much sugar do we need? Awesome way to learn this stuff!

–Loren

2. I still tell my class about how you use to trick me into “swapping” that small coin (1 pound) for this larger coin (10 pence or 50 pence).

Git.

3. @Matt C – hahaha….good times :)

4. Good way to learn/teach! I love all the old fractional coins; used to be half/third and quarter farthings as well as three farthing coins. Very collectable if not hugely valuable, they have a charm all their own.