Not too long ago, a mother posted the above grade three question on Facebook, and sought help from fellow parents: “Hi all, can anyone advise this P3 qn? Thanks!”
Before you read some of the replies or suggestions below, if you’re a parent or tutor, how would you solve this fraction question (with the mathematical knowledge of an average grade three student)?
A parent’s reply was: “This is a question that wants u to compare the fraction with half. Whichever fraction is smaller than half is the answer.
“To compare against half, take the denominator and divide by 2. If the numerator is less than the divided value, it is smaller than half.”
The mother replied, “蔡锦森 oh ic! Nv thought of that! Gosh, how to explain to a P3 ? 😝”
Another parent or tutor joined in: “So for such questions, there are 2 types. One type requires the student to compare against half. The other is to compare the difference with 1 whole. E.g. Which fraction is closest to 1? 7/8, 3/4, 6/7 etc”
Later, another member commented: “Normalize all the denominators and compare.”
Would you use any of the suggested strategies to solve the problem?
An Apt Question for Grade Three Students?
In the Singapore math curriculum, the guidelines for elementary school students (or primary school pupils) learning fractions at different grades are as follows:
Primary 2 (Grade 2): Add and subtract like fractions whose sum is less than 1.
Primary 3 (Grade 3): Learn equivalent fractions; add and subtract related fractions whose sum is less than 1.
Primary 4 (Grade 4): Along with improper and mixed numbers; add and subtract related fractions whose sum exceeds 1.
As I’ve zero idea about the source of this test question, I leave it to the reader to decide for themselves whether or not this grade three question is in line with the local syllabus. If not, why? Or do you think this question is somewhat ill-posed?
What If?
Imagine if the same question were to be assigned to a group of grade five students. How would they approach it?
Would most of them resort to a knee-jerk solution by finding the LCM of the four fractions, before comparing their numerators, rather than thinking whether a less-tedious or shorter method might do the job?
Or would they conveniently convert the fractions into decimals (with or without a calculator)?
The Art of Problem Posing
I wonder whether rephrasing the above question might make it mathematically (or fractionally?) more meaningful for students to apply their knowledge of comparing fractions. Say, what if we asked them to compare a set of fractions vis-à-vis a base fraction like 1/2?
Which of the following fractions is greater than 1/2?
A. 2/5 B. 3/7 C. 6/10 D. 4/9
Again, here too, the aim is to discourage students from religiously applying the fraction-decimal conversion, or from tediously converting these fractions to a common denominator.
At higher grades, we’d use larger fractions that would make finding equivalent fractions painfully tedious or time-consuming.
Meanwhile, may I encourage you to share how you’d tackle this fraction question without adding more pressure on students (who might already be suffering from some form of “fraction trauma” as a result of being subject to premature abstraction and procedural methods)?
Methodically & meaningfully yours.
© Yan Kow Cheong, June 29, 2023.
