Nobody much enjoys fractions, but one of Michael Rosen’s poems offers an unusual approach to some very profound ideas which we’d normally never consider tackling in primary school.
If you don’t put your shoes on
before I count fifteen
then we won’t go
to the woods to climb the chestnut
Every family knows this conversation, where a child is trying to complete a task to a time limit but the count is reaching the end and the task is still incomplete.
So Rosen’s count goes:
Fourteen and a half, of course,
Fourteen and three quarters,
Fourteen and seven eights,
Now isn’t this a wonderfully accessible approach to some very deep ideas?
*** Fractions are used to split up whole numbers into smaller bits.
*** Fractions are artificial and are invented to solve a problem (the 19th century mathematician Kronecker said “God made natural numbers; all else is the work of man”).
*** The numbers have a logical and predictable basis.
*** The series can go on as long as we want – even if we go as far as Fourteen and 1023/1024 someone’s sure to want to go on to Fourteen and 2047/2048, ….
*** So the series is in fact infinite.
*** Each term is getting closer and closer to 15.
*** The remaining gap gets smaller every time, but
*** The series never quite gets to 15.
*** The bigger the denominator the smaller the value of the unit fraction.
*** There are lots of number patterns to explore.
The last time I asked permission to use the poem Rosen’s agent demanded a vast fee, so you’ll have to track down the poem for yourself. I found it in Rosen’s collection “Quick, Let’s Get Out Of Here”, but you won’t have to try very hard before you locate a copy on the internet. I had a search recently and was interested to see someone else who uses it with children – but they were using it from a completely different starting point, exploring how children cope with stressful situations such as completing a task under pressure.