Over the last week, a certain ‘Helen’ and ‘Ivan’ had become overnight stars and ultimate meme material in Singapore. For what, exactly?
For measuring the weight of their coins, apparently.
The math problem that features Helen, Ivan, and their coins triggered a national outcry for its seeming difficulty, and has now gone viral and even been meme-ified by countless brands. Here is a selection for your viewing pleasure:
Sengkang Neighbourhood Police Centre:
Singapore General Hospital:
DBS:(All images taken from the respective brand’s Facebook pages.)
Jokes aside, many adults and parents reacted to the original PSLE question with a range of emotions, from being perplexed that they can’t solve the problem, to anger that 11-12 year-olds were expected to solve this question. While the milestone exam for primary 6 students in Singapore regularly receives a great deal of attention yearly, this year marks some significant differences.
Why parents are concerned: Rising awareness of mental health
Accounts by parents reported that some students were visibly frustrated during and after that fateful math paper. Some had been witnessed even bursting into tears and becoming nauseated. With the reveal of some of these difficult questions, some parents and other adults have taken to blaming the high standards of education for setting unrealistic expectations, contributing to the stress placed on children.
Do our exams really need to be so difficult? They ask. As we become more aware and sensitive towards issues of mental health, many naturally want to protect the mental health of their children. And they think that tough exams and the hyper-competitive environment it creates are detrimental to the mental health of our young.
As a result, many commented with wishes to reduce the difficulty of the exams for the sanity of our children.
Why parents are concerned: Uncertainties over new PSLE scoring system
It may also seem that parents this year are especially in a frenzy, due to the recent changes to the PSLE scoring system.
With T-scores now obsolete, PSLE takers will now be given scores according to Achievement Levels (ALs). The score for each subject ranges from AL 1 to 8, with AL 1 being the highest band (for students who score 90 marks or more on that subject). The overall PSLE score is the total sum of the scores on the 4 subjects.
This new system decreases the precision of the PSLE grade, resulting in more students who will receive the same PSLE score. Because of this, parents and students are worried that the difference of 1 AL can make a big difference to their eligibility for secondary schools. Reasonably, the reaction to this is then: added pressure to work hard to get a higher AL to increase one’s chances of getting into a good or desired secondary school.
Even before these changes, the PSLE has always been seen as a monumental and stress-inducing event for primary school students and their parents. With these added uncertainties, it is no wonder that one viral PSLE question can seem to be the last straw to many frazzled parents, reopening the floodgates to endless complaints, questions, and outcries.
Why tough questions are needed in the PSLE
However, some parents and educators took a different perspective. After all, what is the purpose of an examination? In particular, this is a national exam.
Apart from assessing what a child has learnt in school, a good examination should also be able to differentiate the various learning abilities and achievements of the students. For example, it will not be practical to have an exam that is too easy. If everyone gets an A, that will be a problem when it comes to schools selection, which is so grades-dependent.
That is why an exam that is set properly will have questions of varying difficulties. It will then naturally sort students out according to their abilities, and filter out the difference between those who are good and those who are exceptional.
Was the question really so tough?
While exams need to include some difficult questions, exam setters still have to ensure the question is within the syllabus, and solvable by their takers.
Even though the Coin problem looks tricky to solve (and it is), it is well within the syllabus of what primary school students learn. In fact, you don’t need any advanced mathematical knowledge (not even basic algebra) to solve it. So, in that sense, the question wasn’t of an unrealistic standard.
Now, for those still wondering how to solve Helen’s and Ivan’s headache-inducing coins problem, don’t worry – you’re not alone. The trick is really to get a little creative with the way you think, and work logically with what you know.
Here’s how we solved it:
First, use the information you have to draw models of Helen’s and Ivan’s number of coins.
- Since they have the same number of coins, both Helen’s and Ivan’s bar should be the same length.
- Mark out the number of 20-cent coins they each have – from here, you can also deduce that Ivan has 40 more 20-cent coins than Helen has. Logically, Helen will then have 40 more 50-cent coins than Ivan has.
(a) Who has more money in coins and by how much?
Our first instinct is to find out the total amount that each of them have, and find the difference. However, with the limited information, we cannot find out the total amount they have.
Yet, we can solve it just by focusing on the difference – after all, that is what the question wants.
From your models, you’ll notice that some of the amounts of coins overlap. Helen and Ivan’s 64 20-cent coins and their unknown number of 50-cent coins are the same. The only difference lies in the 40 50-cents that Helen has, compared to Ivan’s 40 20-cents.
Now, seems easy enough, right? All you need to do is calculate the difference:
(b) Given that each 50-cent coin is 2.7g heavier than a 20-cent coin, what is the mass of Ivan’s coins in kilograms?
What we know:
- Helen’s coins weigh 1.134kg
- Each 50-cent coin is 2.7g heavier than a 20-cent coin
- Since Helen has more 50-cent coins, her coins are heavier.
- The only difference in weight will be between the 40 50-cent coins that Helen has, and the 40 20-cent coins that Ivan has.
Do you see it now? We can easily use the weight of Helen’s coins and the difference of the 40 50-cent coins versus the 40 20-cent coins to get the weight of Ivan’s coins. (Remember to convert your units correctly!)
1134-(40×2.7)=1026g = 1.026kg
Several commenters have gone so far as to say that the coin problem is so tough that it is probably a Math Olympiad question, unsuitable for the average primary school math student. But educators in the know would say – there are plenty of tougher problems, be it in previous year’s PSLE papers, or in actual Math Olympiad competitions.
Here are some more mind-boggling questions to work your brain:
2021 PSLE: Perimeter question
Hint: Move the lines around to form simpler, more familiar shapes.
(a) 11 (b) 57cm2
2019 PSLE: Triangles question
Hint: This question is all about looking out for patterns. No one is expecting you to draw out Figure 250! Instead, use the first few figures and numbers to find out the pattern.
a) First row: 15; Second row: 10; Third row, from left to right: 1, 4, 9, 16, 25
b) 62,500 triangles
2017 PSLE: Ribbon question
Jess needs 200 pieces of ribbon, each of length 110cm, to decorate a room for a party. Ribbon is sold in rolls of 25m each.
What is the least number of rolls of ribbon that Jess needs to buy?
Hint: The question looks very simple, but there is a trick in there: you have to realise that a portion of each roll of ribbon will be left over after dividing the rest into lengths of 110cm.
At least 10 rolls of ribbon.
If you are absolutely bothered that you can’t find the solution to these problems, we invite you to get in touch with our primary school and Math Olympiad tutors! We can also prepare your child to tackle such challenging questions so that they can face the PSLE and other exams with confidence.
As some educators have rightly pointed out, students are not meant to be able to answer all the questions on the exam. Having difficult questions on an exam is normal and expected – that’s what exams are supposed to be like! Even as we enrol our kids in PSLE Math tuition class to prepare them better for challenging and novel questions, we should also teach our children not to beat themselves up for not being able to answer every question perfectly.
What may be more important is teaching our children to be resilient. Mistakes and failures are part of life, and what matters is that we have put in the effort to do our best. Practising this spirit of resilience doesn’t just apply to those who have taken the PSLE this year, but also to the P4 and 5s who will face it in the coming years, and even secondary school students who will face even tougher exams in the O Levels.