A Singapore Grade 4 Geometry Question

On Facebook, someone recently posted the above primary 4 (or grade 4) geometry question, asking for help from fellow parents. How would you do it (without calling on ChatGPT)?

If you’re a parent, homeschooler, or tutor, how would you explain it to an eight- or nine-year-old child, who’s struggling with non-drill-and-kill questions on area and perimeter?

Give It a Try First!

Try figuring out the answer on your own first before peeping at two parents’ quick-and-dirty solutions below. Better still, could you present an idiot-proof or peasant-friendly solution that even a smart dog or cat could understand?

 

Solution:

6 width and 6 long = 3units  of the rectangle.

1 rectangle -> 16cm.

3 rectangle 

16x3 = 48cm.

Stretch Your Mind!

Many moons ago, I was commissioned to write Mind Stretchers 2*, a grade 5 problem-solving math book, which was popular in a number of local schools and tuition centers—disturbingly, they’re guiltlessly or blatantly photostating entire chapter questions as part of their worksheets.

And I still recall that on the topic of Perimeter, I’d posed a number of routine and nonroutine questions. What surprised or tickled me then was when the Managing Editor asked me whether or not some of these questions are solvable, because at first glance, they look like there are missing information to solving them.

These geometry questions can give students (and probably their oft-math-anxious parents and teachers) some goose pimples out of fear or panic if they can’t figure out the answers offhand. 

Understandably, without a cool mind and some patience (or perseverance), even perimeter and area questions at the elementary (or olympiad) level can prove to be a challenge to math educators if they’re not trained to tackling them using the right approach.

Frustration and fear usually set in, especially for nonroutine questions that don’t normally appear in drill-and-kill school textbooks and workbooks.

Premature Testing

The danger of setting these types of brain-unfriendly questions too early, or having them prematurely in a class test, especially when most students have yet to fully grasp the concepts of area and perimeter, could be detrimental to the mental health of most average math students.

Parents who freeze at the sight of these questions would often exhibit a knee-jerk reaction, by getting a tutor for their child, if they’d afford it.

Tuition or No Tuition?

Most stressed parents often reason that if they couldn’t even solve these grade 4 questions, things would only get worse in later years, as the higher-grade topics get more complicated and the questions become more challenging. They just don’t want to see their child struggle in math, especially when they themselves had had a negative experience of the world’s most disliked school subject.

Even for math teachers and tutors, there’s nothing to be ashamed of if at first or second reading, they’re clueless how to tackle these nonroutines. Yes, they do appear in mid- or final-year exams arguably as a social filter to separate the nerd from the herd, but once math educators and homeschoolers know how to approach these questions from the right angle, before long, these math problems would become routine to them.

The 4F’s of Mathematical Problem Solving

Few math teachers and writers would admit that (school or olympiad) math involves lots of fears, false starts, frustrations, and failures. The sooner parents and homeschoolers (and their children and grandchildren) are aware of this oft-unspoken problem-solving process or ritual, the pressure or expectation level for all parties ought to go down significantly in reducing any unnecessary mental or mathematical stress.

Pain is (always) part of the joy of creative mathematical problem solving—the no-pain-no-gain mantra is axiomatic in math at all levels.

Geometrically & perseveringly yours

© Yan Kow Cheong, October 16, 2023.

* When the wallet-friendly title was out of print, a senior editorial staff emailed me that he’d pay me a cosmetic S$150 to buy the copyrights. I never bothered to reply to his laughably ridiculous suggestion. I wouldn’t be surprised that they’d since plagiarized the content to be used and reused for other purposes.

Expensive-Cheat Singapore Math Books

In recent years, a certain genre of mathematics titles had flooded the Singapore assessment (supplementary) market to meet the needs and wants of kiasu parents, who want to ensure that their children have a competitive edge over their peers.

One conspicuous series of such assessment titles in our local bookstores is published by Amazing Books. The Primary 1 - 3 titles (selling from $8.00 to $9.90) are written by a certain Newton Wong, while Primary 4 - 6 titles (selling from $11.00 to $12.50) are written by an Ernest Wong—it’s hard to confirm whether the writers are ghosts or not. These supplementary titles generally cost as much as a Ministry of Education (MOE)-approved primary textbook—however, they're value-for-money titles, if you're agnostic as to whether copyrights have been safeguarded or not.

Wallet-friendly titles that may meet the
mathematical needs and wants of kiasu parents

Indeed, there is much to be gained from writing these assessment titles, as compared to, say, authoring an MOE-approved textbook which goes through the tedious reviewing exercise by the Ministry of Education, the approving body of Singapore textbooks. 

Critics (mainly authors of traditional assessment books) arguably claim that these “cheat-expensive books” or "expensive-cheat books," as they’re called in local educational publishing, are nothing but a rehash of faintly modified past exam questions from the top or popular schools in Singapore.

High Price, Low Content

Another category of expensive-cheat titles involves those whose contents don't justify their selling prices—titles that over-promise and under-deliver. Come with quality paper, some look pretty good in form but shy of substance. 

Note however that the use of the word “cheat” doesn’t in any way suggest that the writers had plagiarized the contents, although it’s not uncommon for teachers and tutors to suspect that in some cases plagiarism could have inadvertently taken place. 

At best, these expensive-cheat titles provide information for readers new to the subject matter at a high price; at worst, these titles are copycats of pirated test papers or canned contents that have been put in a form that are readers-friendly.


Piracy Goes Online

Here is a typical ad spammed probably to tens of thousands of homes every few months:

Top Schools' Test Papers (Yr 20XX) on CD 

Hi Parents Give your child a head-start at school by Practice Doing Top Schools' Test Papers This will help your kids to Score !!! *Primary 1  -  Primary 6 ( SA1 & SA2 papers ) *Data is in scan-in PDF format *English, Maths, and Science *Answers also provided *Only $5 per subject !( Min order 3 subjects @$15 only ) **3-Year Series : P5 SA2 / P6 Prelim ( Yr 20XX - 20XX )     3 yrs x 3 subjects @$15 only ( total about 50 sets testpapers ) **Also available : Sec.1 - 4 SA2/Prelim  Maths :( Yr 20XX ) @ $10/subject Call Now !! XXXX XXXX * NB *  To unlist pls click < HERE > thank you. A kiosk outside a shopping mall, selling past exam papers from allegedly top schools. Plagiarism Begets More Plagiarism Grade 4 questions that mimic those set by teachers in "top schools"—these "model answers" are quasi-edited "solutions." It’s an irony that while many fly-by-night writers had modified questions from the top schools’ exam papers with cosmetic changes; yet, often times, some teachers from these same schools are equally guilty in lifting up large chunks of content from assessment titles, by photocopying and distributing entire chapters to their students and fellow colleagues. Plagiarism begets new levels of intellectual theft. Unscrupulous vendors know too well that the MOE would find it hard to crack down on these perpetrators of piracy. After all, few parents could detect the authenticity of these questions—whether or not they’re really set by teachers from allegedly top schools. Most questions look challenging to the clueless parents, who would buy anything which would help their children do well in the subject.  Two Wrongs Don't Make a Right If half-baked or poorly edited solutions isn't much of an issue, these tips-and-tricks titles may appeal to some students who can't afford private tuition. Lest their children lose out vis-à-vis their peers, most kiasu parents wouldn’t give a second thought to buying these pirated sets of exam papers. The rationalization is that since the MOE refuses to sell them, they’ve little or no choice but to procure them from illegal vendors. The means to laying their hands on these sought-after papers justifies the end—that these non-routine questions would prepare the child confidently for his or her school test or exam. With home delivery service of these syndicated or pirated papers at no extra costs, parents can now feel less guilty, as they could avoid being seen buying these illegal papers in public. And for IT-savvy consumers, they’d now order these papers online, at a cheaper price, if they want an electronic version of them. A Copycat of Top Schools’ Exam Papers A grades 7-8 supplementary title that may be suitable for drill-and-kill specialists—it's priced at S$24.95 in retails outlets. Unknown to many of these authors, the international mathematical community of mathematics educators often poke fun at the poor quality of our local assessment or supplementary mathematics titles. Many writers have probably not read what math educators out of Singapore are saying about their dear titles, especially when they're marketed overseas.  Leaving poor design and linguistic blunders aside, these expensive-cheat local titles are often an embarrassment to the image of Singapore mathematics publishing, as the nation strives to become an educational and publishing hub in Asia. In recent years, it's an open secret that questions from so-called top schools are actually the works of syndicates, which recruit Indian and mainland Chinese nationals, and cash-strapped undergraduates, to write math questions that mimic those posed by teachers from top schools. The Works of Syndicates No one is surprised that these expensive-cheat titles are a few folds pricier than the traditional assessment titles. These often ill-written supplementary titles, which make unverifiable claims to parents and teachers, will continue to thrive if the authorities don't get down to verifying the authenticity of the questions, and as long as the consumers continue to purchase them, pretending that they’re unaware that they're MOE-copyrighted materials. While the MOE authorities should take a share of the blame pie for not making schools' test papers available for sale, very often, it’s those teachers with an entrepreneurial spirit who are probably the source of these copyrights infringements. Who can have access to these exam papers if students and outsiders are not allowed to take them out of the school compound? The non-routine questions are suitable for grades 5-6 students, but the solution methods sometimes lack rigor, and a number of them are poorly presented and edited.  Although there is no formal investigation on these assessment titles claiming to contain contents that match the questions commonly set by Singapore's top schools, it doesn’t take a DNA scientist to figure out that most of these assessment papers were probably lifted up from test questions, which have undergone some cosmetic rewriting to avoid being caught (or sued) for blatant infringement of copyrights. The sale of most past exam papers from government schools is officially illegal; yet, every local knows how and where to buy them. The public knows that schools and the MOE don’t have the resources to sue the guilty parties. It wouldn't be surprising that some education officers are themselves part of the piracy syndicate. How would syndicates have had access to those past exam papers in the first place had they not been leaked out by teachers or school personnel themselves? Indecent Photocopying Over the years, I’ve personally heard from a number of assessment authors who had complained to the MOE that some top schools’ HODs had blatantly plagiarized their contents to be used in workshops and seminars, or that some teachers had made an indecent number of copies for an army of students. Of course, the standard answer from the MOE was that they’d look into the matter, and before you know it, the whole saga has faded away.  As long as we pay lip service to the intellectual rights of math writers and authors, and the infringement of  copyrights is condoned among teachers and students, the future of math publishing in Singapore doesn't look too bright. In fact, the quality of future Singapore math titles is likely to suffer further, as more and more non-math graduates are recruited as math editors in local publishing houses.  © Yan Kow Cheong, May 29,  2013.