On 2005 Oct 10 , at 3:19 PM, Philip S Hall wrote:
How would you explain to your pupils the meaning of numbers like 0.2, 4.5, 2.342 etc
Remember you have to do with this without resorting to common fractions.
How would I explain decimal fractions without reference to common fractions?
Easy:
I would explain it just as I would explain the meaning of the digit "2" in the number "23". The two counts how many tens there are, where tens are groups of things when they are grouped in equal bundles of ten items each.
Going the other way, if the number was "2.3", the digit "3" tells how many tenths there are, where a tenth is one part when the whole is divided into ten equal pieces.
Yes, the concept of one-tenth is required but it does not need to be written as "1/10" and it does not need to be related to other non-decimal fractions like 1/3 or 1/12 or 17/32, etc. (And the parts do not even need to be named "tenths", if your really want to avoid even the appearance of using common fractions. You could call the parts "pieces of ten", or "parts", or "zippies", or "elephants" and get the same satisfactory result.)
Explaining that one whole may be divided into ten (equal) parts is no more difficult than explaining that numbers of wholes may be grouped into (equal) bundles of ten wholes. (And, explaining that hundredths are just tenths divided into ten parts is no more difficult than explaining that hundreds are just tens grouped into bundles of ten tens, etc.)
Regards,
Bill Hooper
Fernandina Beach, Florida, USA
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Make it simple; Make it Metric
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