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Could You solve this Qns?

To my students and strangers of the internet, this was a PSLE math question in 2019. It is one of the three questions that left our P6 students in tears. Can you solve it?

Typically, a primary school student is expected to do simple manipulations of shapes when it comes to geometry (study of shapes). This however, is not so simple a manipulation.

Take a minute or two before reading on to solve this question…

If you need some help, here is a clue:

If we were to shift one semicircle (shaded blue) as shown below, what will be the result length that it leaves behind? (blue line with qns mark)

Hopefully, you get the “eureka” moment, or maybe your genius mind already saw this at first glance. Now, the solution is near.

Find the distance of the red qns marks and solve this problem.

There is an alternative solution to this, but it involves algebra and simultaneous equation. I shan’t explain that here, but feel free to try it yourself. It always bugs me when primary students are shown model answers using simultaneous equation method, typically disguised as “units and parts” (ie. x and y are replaced by u and p). Especially since the algebra that they are exposed to is basic, they are not equipped to handle something like -x = 2x – 6, while students of all higher levels would chuckle at how trivial this equation is to solve (I hope…). Yet, we require them to use simultaneous equation method to solve their word problems? I hope that teachers do not just pull a fast one on their students and explain this as the model answer, without first letting them know that this is an advanced solving method. Worst, not even show the alternative method mentioned above, which leans closer towards geometry and gives a more intuitive feel of the solution.

I personally think that this was a challenging problem, and it needed a somewhat radical thinking (by the student) to solve it. No surprise here that many parents are complaining about the difficulty level. Of course, it is one thing to point fingers at the question, it is another whether the student doing it was properly trained. Do they even know that you can manipulate shapes around, and tried something? If not, then I say, the student was not properly trained in primary school geometry, rather probably just exposed to regurgitating specific solutions to specific problems. Then that’s the real shame.

But my rant ends here.

To you, my fellow stranger of the internet, if you have any challenging questions (regardless of pri/ sec/ JC), I welcome you to send it to me, and I may do a post on it.

I hope you/ your child managed to solve this problem with the clue, and gotten some thrill out of it. Or perhaps my rant gave you some insights about education in mathematics, then I am glad. In either case, I wish you a good day.

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