Question
Give a fraction
with its value in between ^{2}/_{5} and ^{1}/_{2}.
(Note: the
denominator cannot be greater than 20)

Discussion
This is an openended question for primary (elementary) school, which ought to be easy because there are many possible answers and you just need to supply one that meets the requirements. However, most people are used to closedended questions, which have only one correct answer. This is what prompted a parent to pose this question on a parentsupport forum on Facebook.
Many people, including parents and even some private
tutors, began to supply their answers to this question. Much of the discussion clustered around the
idea of the midpoint or the average of the two given numbers, namely ^{1}/_{2}
(^{2}/_{5}
+ ^{1}/_{2}) or ^{9}/_{20},
and why that gives an answer.
Then Dr Kho Tek
Hong (retired curriculum specialist, the “father” of Singapore mathematics) chipped
in. He said that there are many possible
answers e.g. ^{3}/_{7},
^{4}/_{9}, ^{5}/_{11}, ^{5}/_{12},
^{6}/_{13}, etc. He
suggests that students be asked to justify their answers. [ By the way, here is an interesting method to compare fractions. ]
And I thought that was a stroke of educational brilliance
from The Guru! It shows the spirit of
the Singapore
mathematics curriculum – to get students to think, to be openminded, to use
logic and to be able to communicate mathematically. The Singapore curriculum is not meant
to torture students, nor to get them to toil around a tortuous path around a
high mountain seeking the elusive holy grail – although it often seems that way. Teachers, tutors and parents would do well to
help the learners it in the right spirit.
Mathematics is not always about calculations (although you need to do
some calculation). We also need to open our minds to multiple answers
as well as to embrace various methods and concepts.
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