This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

Thursday, January 31, 2008

MGS (Paya Lebar) Pri School P6 Math CA1 2006 (Q47)

The areas of Figure A and Figure B are equal. Figure A is made up of a square consisting Rectangles P, Q and 6 similar and smaller rectangles. Figure B is another square made up of 4 similar rectangles and Rectangle P. The area of Rectangle Q is thrice the area of each small rectangle.

a) Find the area of Figure 1
b) Find the length and breadth of Figure 2



Area of Figure B is = 12 cm x 12 cm = 144 square cm.


The length and breadth of Rectangle Q is

Length = 9 cm
Breadth = 4 cm

Wednesday, January 30, 2008

The Four Seasons

PSLE Science textbooks explain that the Earth’s revolution round the Sun causes the 4 seasons. However, many of these books do not appear to explain that the tilt of the Earth’s axis is also a contributory factor.

In Figure 1 below, note that the Earth’s axis is not vertical but tilted at an angle away from the vertical line. The sun’s rays will cause half of the Earth to experience day, while the other half to experience night.

Figure 1

Imagine a place on Earth marked “A” in the Fig 1 above. "A" will experience night. As the Earth rotates, A will move towards A1. The dotted line between A and A1 is the path taken by the place marked “A”, as the Earth rotates.

Note that the dotted line between A and A1 has a longer period of day, as compared to the night. This causes the parts of the Earth marked between A to A1 to experience summer.

At the same time, the place on the Earth marked “B”, will move towards B1 as the Earth rotates. Also note that the dotted line between B and B1 has a longer period of night, as compared to the day. This causes the part of Earth marked between B to B1 to experience winter.

The Earth revolves round the sun once every year. This means that in 6 months, the sunlight will fall onto the Earth from the opposite direction.

Figure 2

In Figure 2, we have a different diagram showing the Earth 6 months later. Since the earth takes 12 months to revolve around the Sun, in 6 months, it makes only half a revolution. This causes the sunlight to fall onto the Earth from the opposite direction.

It can be seen that the parts of the Earth marked between A to A1 will now experience a longer period of night, as compared to the day. This now means that the parts of the Earth marked A to A1 will experience winter.

Again, at the same time, the parts between B and B1 will experience a longer period of day, as compared to the night and hence, will experience summer.

From these 2 diagrams, we can see that when the Northern hemisphere experiences summer, the Southern hemisphere will experience winter and vice-versa.

The 4 seasons is thus caused by the Earth's revolution around the Sun and the tilt of the Earth's axis.

Tuesday, January 29, 2008

Handling Comprehension (Open Ended) Questions

Comprehension (Open Ended) Section accounts for 20 marks out of a total 200 in the English PSLE Paper. That makes up 10% of the whole paper. Unfortunately, this section is where students lose most marks in English Paper 2. As such, it is important to pay close attention to this very important section.

There are many ways to approach Comprehension (Open Ended) Section. However, I find that the most effective way is to read the questions before reading the passage. By reading the questions first, you focus on what is asked, rather than what is in the passage itself.

Hence, with your focus on what is asked even before reading the passage, you will be able to pinpoint the answer when you start reading the passage – a clear advantage over those who read the passage before reading the questions.

Here is an example. Let us read the questions and see if we understand the story even before reading the passage itself.

Questions from the Comprehension Open Ended Section of Ai Tong School P5 English SA1 2004.

Q1. How were the men feeling while they were on the landing craft?

The key phrase that gives us a good hint is “landing craft”. Landing crafts are not civilian vehicles. These vehicles are used by the military and/or rescue mission parties. As such, we can tell that “the men” may be from the military or some rescue team either on a mission or under going training.

The above demonstrates that even without reading the passage, simply by reading the questions first, we already have an idea of what the passage is about.

Q2. Explain in your own words the phrase “betraying of inner feelings” in the first paragraph.

Q3. What was the relationship between Vince and Eddie?

We are introduced to 2 men. Vince and Eddie. Again, without even reading the passage yet, we know that there are 2 characters at least, in this passage.

Q4. How did the British differentiate their planes from those of the enemies?

The words “enemies” and “British” are dead giveaways. This is the first conclusive piece of information that tells us that this story may be about a war scenario. For students who have read widely, they may even be able to relate this background to World War 2 or the Falklands War, where the British made contact with enemy planes.

Q5. What does the word “them” in the fourth paragraph refer to?

Q6. Do you think that Vince and Eddie were proud to be part of the British army?

Question number 6 confirms that the 2 men are serving the British military during a war period.

Q7. Which word in paragraph 7 tells you that the soldiers moved in a group in the water?

The key words “moved in a group in the water” suggest that the soldiers are infantry men. Again, students who read widely will know that infantry men move in groups in such terrain.

Q8. Why did the soldiers “believe they had seen their last day”? (third last paragraph)

A hint that this may be a life and death situation, which aptly fits a war scenario.

Q9. What do you think happened to Eddie in the end of the passage?

Q10. Who helped Eddie when he lost his balance? Why do you think so?

By reading all the ten questions, we can reasonably conclude that:

1. This is a war scenario.

2. The story is seen from the British perspective.

3. It could be about World War 2 or the Falklands War.

4. While the story is about the British at war, it centres on two individual soldiers, Vince and Eddie, their relationship and their fate.

It can be seen very clearly that if you were to read the questions before reading the passage, you would have collected some very important information.

You are now be in a better position to spot the answers in the passage because you will be on the lookout for the information you have already gathered from the questions.

Now compare the passage below and see if the information we have gathered from the questions tallies with the passage itself.

The Comprehension Passage

The mass of helmets lurched backwards as the landing craft plunged into the dark water. Sea spray glistened on the surface of everything it touched, catching the light of the artillery fire. Private Eddie Hagen glanced at the faces of the men around him. Some were praying, while others held pictures or mementos of sweethearts and family before carefully tucking them away inside their pockets. The rest stared into the unknown, their faces expressionless, betraying no inner feelings.

“This is it, Buddy!” Eddie managed a smile in return for the hearty slap on his shoulder and twisted around to acknowledge a friend.

“We’re finally going to get the Japanese!” Vince grinned down at Eddie. “Remember, buddy, stick with me. We’ll both do just fine. Besides, your sister never will never marry me if I let anything happen to you.”

At this moment, both men were distracted by an explosion which sent more spray into the craft. The roar of airplanes filled the sky. As the planes passed overhead, the black and white “invasion” stripes painted on them could be seen. The marking let the British know that these were their own, for protection against their anti-aircraft guns. The soldiers watched them as they made their way over the cliffs.

Eddie recalled the time when Vince and him signed up for the British army at the same time. After basic training, the two strutted like peacocks before family and friends. As full-fledged fighting men, they would now join in the fight against the Japanese.

Suddenly, the barking of orders from the platoon leader interrupted Eddie’s thoughts. The back wall of the craft crashed into the water and the throng of men moved forward. Plunging into the icy water, the British soldiers gasped as the cold wetness penetrated their clothing. The dark, green depths caused many to stumble, already weighted down with excess gear. This, combined with the mortar fire aimed at them from the top of the cliffs, caused many to believe they had seen the last day.

As Eddie struggled toward the shore, a bullet pierced through the man in front of him, causing him to fall backward. He looked into the lifeless eyes before the sea covered the soldier’s face and claimed his spirit.

A second later, Eddie felt a sharp pain in his side. Before losing his balance, he felt a strong arm lifting him up.

So was the information collected from the questions, before we read the passage accurate? Did you have the feeling that you have "read this passage before"? That's because you have read the questions first, giving you some very important clues as to what the passage is about.

The trick here is that while you are reading the passage, take note of the "familiar" pieces of information you gathered earlier. Those pieces of information hold the key to your answers to the comprehension questions.

For example, for Q1, How were the men feeling while they were on the landing craft? Have you noticed that in the passage, you noticed a familiar scenario when you read this part of the passage?

The mass of helmets lurched backwards as the landing craft plunged into the dark water. Sea spray glistened on the surface of everything it touched, catching the light of the artillery fire. Private Eddie Hagen glanced at the faces of the men around him. Some were praying, while others held pictures or mementos of sweethearts and family before carefully tucking them away inside their pockets. The rest stared into the unknown, their faces expressionless, betraying no inner feelings.

The question asks, "How were the men feeling...." That means you are expected to describe the men's feelings and emotions.

So now in your own words, you have to answer Q1, based on the information above. When people pray, hold mementos of loved ones and "stare into the unknown", what do these actions tell you? Are they happy? Sad? Aniticipative? Worried? Enthusiatic? Anxious?

Repeat the above process for the rest of the Comprehension Questions. In this way, you can improve your Comprehension Open Ended Section scores.

Monday, January 28, 2008

MGS (Paya Lebar) Pri School P6 Math CA1 2006 (Q46)

Mrs Ng spent $180 on pens and files. The ratio of the amount of money she spent on blue pens, red pens and files was 4 : 5 : 1. Blue pens were bought at 4 for $1. The number of red pens she bought was 1/3 of the number of blue pens. The number of files was 3/8 of the number of red pens.

a) How much did she spend on blue pens?
b) How many red pens and files did she buy altogether?


Q(a) How much did she spend on blue pens?

10 units ----- $180
1 unit ----- $18
4 units ----- $18 x 4 = $72

Answer: She spent $72 on blue pens.

Q(b) How many red pens and files did she buy altogether?

4 blue pens cost $1.
Mrs Ng spent $72 on blue pens.
$1 ----- 4 blue pens
$72 ----- 4 blue pens x 72 = 288 blue pens

Number of red pens bought was 1/3 the number of blue pens.
1/3 x 288 = 96 (red pens)

Number of files bought was 3/8 of number of red pens.
3/8 x 96 = 36 (files)

Total number of files and red pens -----
96 + 36 = 132

Answer: She bought a total of 132 files and red pens.

Sunday, January 27, 2008

Another two more forum letters pertaining to the Sec 5 / ITE debate

Two more forum letters from the Straits Times forum dated 25 Jan 2008.

Put students' self-esteem before school rankings

Let students decide after hearing out school heads

More on Primary 6 Algebra

You can check the syllabus of P6 PSLE Maths pertaining to Algebra.

Refer to this link from the website of the MOE .

Below is a screenshot of page 32 taken from the above link.

Click on image to enlarge

Saturday, January 26, 2008

Algebra allowed but not encouraged

Using Algebra for PSLE Maths is perfectly legal. The student would not be penalized. However, Algebra taught in P6 is very basic. It is not deep enough to solve many of the Section C questions found in PSLE Maths. As such, teachers usually do not encourage students to use Algebra. Instead, heuristics are encouraged.

In P6, only the 4 operations of Algebra is taught. Students are not taught how to use Algebra to solve Section C type questions, which cognitive skills are needed.

As such, if students were use Algebra without being taught how to apply them in actual Section C questions, they may fumble along the way.

Here is an example how Algebra can be used to solve a P6 question.


Ricci saved $200 from her salary and spent the rest. She spent 1/9 of the expenditure on a blouse, $40 on a scarf and the rest on books. The amount spent on the scarf was $20 less than that spent on the blouse. What was her salary?


Let $n be her salary

Since she saved $200, she would have $n - $200 left to spend.

Amount spent on blouse was 1/9 x ($n - $200) = $(n – 200)/9

Amount spent on scarf was $40. But we know scarf was $20 less than blouse, which means blouse cost $60.

Cost of blouse….

$(n – 200)/9 = $60
$(n - 200) = $60 x 9
$n - $200 = $540
$n = $540 + $200
$n = $740

Since $n represents her salary, it means her salary was $740.

Note that there are no diagrams or models used. Every step has to be envisioned in the mind. In the above, you must be able to see that 1/9 of the expenditure is equivalent to the cost of the blouse, which is also equivalent to $40 more than the cost of the scarf . P6 students are not trained to do that using Algebra.

P6 students are however trained in heuristics. Now compare how the same question is done, using heuristics, as demonstrated in the link below.

Tao Nan School P5 SA2 2006 Math Question (Q47)

So to answer the question, “Is Algebra allowed in PSLE Maths?”, the answer is yes, it is, but it is not encouraged.

Friday, January 25, 2008

MGS (Paya Lebar) Pri School P6 Math CA1 2006 (Q45)

Tim, Tom and Kat have a certain number of books. If Tim gives 8 books to Tom, he will have half as many books as Tom. If Kat gives 15 books to Tom, both of them will have the same number of books. If Tom has 40 books at first, how many books do Tim and Kat have altogether at first?


Tom at first ----- 40 books

If Tim gives Tom 8 books
Tom ----- 40 books + 8 books = 48 books
Tim will have half of Tom ----- 48 books divided by 2 = 24 books

Therefore (at first) Tim will have
24 books + 8 books he gives to Tom ----- 32 books at first

If Kat gives Tom 15 books
Tom ----- 40 books + 15 books = 55 books
Kat will have same number of books ----- 55 books

Therefore (at first) Kat will have
55 books + 15 books she gives to Tom ----- 70 books at first

Tim and Kat at first will have
32 books + 70 books = 102 books.

Answer: Tim and Kat will have a total of 102 books at first.

Thursday, January 24, 2008

Question on Phases of the Moon

In yesterday’s post, we created a 28-day chart in order to calculate the phases of the moon. In this post, we will apply what we have learnt to answer an actual Science question on phases of the moon.


Rashid observed a full moon on 6 January. When will he most likely observe a full moon in February?

(1) 5 February
(2) 15 February
(3) 25 February
(4) 5 and 22 February

Using the 28-day chart, we count 28 days from 6 January.

28 + 6 = 34

Since January has 31 days, we minus 31 days.

34 – 31 ----> 3 February

Hence, Rashid would be likely to observe a full moon on 3 February. However, in the multiple choice question above, there is no 3 February. The closest date is 5 February. We therefore take the answer to be (1) 5 February.

Note: The answer (4) 5 and 22 February is not accepted because it takes 28 days for every full moon to appear and 22 February is only 17 days after 5 February.

Wednesday, January 23, 2008

Calculating the Phases of the Moon

The first Science topic taught in P5 in most schools is the Solar System. Of all sub-topics within this topic, Phases of the Moon gives students the most headache. Most students find difficulty in calculating the dates of the phases of the moon.

Here is a quick and simple method to make sure you get your dates right.

The moon revolves round the earth in 28-day cycles. In order to calculate the phases of the moon, we must therefore use a 28-day chart.

Note that in Figure 1 below, the beginning of the cycle is “Day 0” and ends at “Day 28”. It does not start at “Day 1” because if you were to start at Day 1 and end at Day 28, you will be creating a 27-day cycle instead of 28.

Days 0 represents the beginning of the cycle, while Day 28 represents the end of the cycle. It also must be noted that Day 0 of the current month is also Day 28 of the previous month. Likewise, Day 28 of the current month, is Day 0 of the next month.

Since Day 28 is the last day of the cycle, Day 14 is considered mid-cycle. Day 7 is hence right in middle of the beginning and mid-cycle, while Day 21 is the middle of the mid-cycle and the end of cycle.

Let us look at Figure 1 again. We start with a full moon at Day 0. At the end of the cycle, Day 28 will also have a full moon. Since Day 14 is mid-cycle, we will experience a new moon. Day 7 is between full moon and new moon, which means, we will experience half moon. Day 21 is between new moon and full moon, which also means we will experience half moon. Note that the half moon on Day 21 is a mirror image of Day 7’s half moon.

Figure 1

We can use actual dates to calculate. Let us suppose that a full moon was spotted on 26 July.

The next full moon will be 28 days from 26 July.

26 days + 28 days = 54 days.

But we know that there is no such thing as 54 days in a month. The last month was July, which has 31 days. We need to subtract 31 days from 54.

54 – 31 = 23

Therefore, the next full moon will be 23 August.

We can also calculate when the new moon will occur. A new moon occurs 14 days after a full moon. Hence,

26 days + 14 days = 40 days

40 – 31 = 9

Therefore, the new moon will occur on 9 Aug.

The half moons are 7 days from 26 July and 9 Aug.

Your turn now. Study Figure 2 below. Can you calculate the various dates? Try to make an attempt before checking the answers.

Figure 2

Answers for Figure 2:

Day 28 (next new moon) – 17 Dec.
Day 21 (half moon) - 10 Dec
Day 14 (full moon) – 3 Dec
Day 7 (half moon) - 26 Nov

Now try this one. No answers are given this time.

In tomorrow's post, we will take a look at an actual Science question on phases of the moon, and apply what we have learnt today, to answer that question.


Update: Related post

Tuesday, January 22, 2008

MGS (Paya Lebar) Pri School P6 Math CA1 2006 (Q44)

In the figure not drawn to scale, PQRS is a parallelogram, PX = PY and YXQ is a straight line. Find
(a) Angle PQY
(b) Angle YPS


(a) Find Angle PQY

Angle QPS + Angle PSR = 180 degrees because PQRS is a parallelogram.

Therefore, Angle SPQ = 180 degrees – 125 degrees = 55 degrees.

Angle PQY = 180 degrees – 95 degrees – Angle SPQ

= (180 – 95 – 55) degrees = 30 degrees

Answer: Angle PQY is 30 degrees.

(b) Find Angle YPS

Angle SPX = Angle SPQ – Angle QPX
= 55 degrees – 32 degrees
= 23 degrees

Angle PXY = 180 degrees – 95 degrees – Angle SPX
= (180 – 95 – 23) degrees
= 62 degrees

Angle PYX is also 62 degrees because triangle PYX is an isosceles triangle.
Angle PZY = (180 – 95) degrees = 85 degrees

Angle YPS = 180 degrees – Angle PZY – Angle PXY
= (180 – 85 – 62) degrees
= 33 degrees

Answer: Angle YPS is 33 degrees.

Monday, January 21, 2008

MGS (Paya Lebar) Pri School P6 Math CA1 2006 (Q43)

Last year, the ratio of the number of boys to the number of girls in a chess club was 5 : 3. After 5 boys and 9 girls joined the club this year, the ratio became 5 : 4. How many girls were there in the chess club at first?


20 units + 20 ----- 15 units + 45
20 units – 15 units ----- 45 – 20
5 units ----- 25
1 unit ----- 25 divided by 5 = 5

(Girls at first) 3 units ----- 5 x 3 = 15

Answer: There were 15 girls at first.

Two more forum letters on the Sec 5 - ITE debate

Principal's tone to Sec 5 students plainly wrong

Individual counselling would have been better

Both articles were published in the Straits Times Forum, dated 19 Jan 2008.

Thursday, January 17, 2008

Building a vocabulary base

There are many ways to build a student’s vocabulary base. In the era of the internet, it is now much easier than ever before!

Here is a step-by-step guide on how to build a vocabulary base, using IT and the internet.

Step 1 - Look for articles found in online newspapers and take note of “new words” you may come across. It is better to pick local news, as such news are easily related to, compared to world economics or finance.

Here is an article with the “new words” highlighted in bold, taken from the Straits Times

Loan-shark syndicate busted, 5 suspects held

THIS year's first break-up of a loan-shark syndicate saw the suspected leader and four henchmen - all with suspected secret society links - rounded up on Tuesday night.

Six illegal moneylending syndicates were busted last year.

On Tuesday, all five suspects were picked up in raids on two coffeeshops along Keong Siak Road, part of a seven-hour island-wide operation by the Criminal Investigation Department.

Various premises in Bukit Timah, Woodlands and Toa Payoh were searched and about $2,800 in cash, mobile phones, various ATM cards and suspected debtors' records were uncovered.

Seven poles, five parangs and one dagger were seized in the Keong Siak Road raids.

The 53-year-old alleged mastermind and his associates - three men and a woman, all aged between 28 and 40 - are Singaporeans and believed to have been running the illegal operation for over a year.

More than 200 people may have borrowed sums of money ranging from $500 to $10,000 from the syndicate, which gives out $150,000 in loans every month.

CID deputy director Ng Ser Song said those who defaulted on repayment with interest were harassed with threatening phone calls.

Investigators, however, did not think the weapons recovered were used to harass debtors. Instead, Assistant Commissioner Ng suggested the suspects may have secret society connections. The weapons were possibly stored for use in gang fights.

There were 277 arrests for illegal moneylending and its related activities from January to September last year, 17 shy of the number of people arrested in the whole of 2006.

In the same nine months last year, there were 7,438 reported cases of illegal moneylending and related activities such as harassment.

Meanwhile, a youth turned himself in on Tuesday after his picture - together with three others whose images were caught on CCTV cameras - was released by the police on Monday.

Police believed they were involved in illegal loan-shark activities.

Yesterday, no plea was taken from Ong Kah Soon, 17. He is accused of splashing iodine on an HDB unit in Bedok Reservoir Road together with another man on Dec 17 last year.

Ong, who has highlighted hair, and his accomplice, are said to have been acting on behalf of an illegal moneylender known as Ah Beng.

Ong has been remanded for a week for further investigation. His case will be mentioned next Tuesday.

If found guilty of harassment, a first-time offender faces a fine of between $4,000 and $40,000 or three years' jail or both plus not more than four strokes of the cane.

In the above article, the following “new words” have been noted –


Take note of the “theme” of the article. It can be seen that the article above is about crime and money lending, which is organized by a group of criminals.

Step 2 – go to

Key in the new words above, one at a time and hit “search”. As can be seen from the screenshot below, there are 11 returned results for the word "syndicate".

Click on image below for a clearer view.

The first 4 of the 11 results for "syndicate" are as follows.

1 . a group of individuals or organizations combined or making a joint effort to undertake some specific duty or carry out specific transactions or negotiations: The local furniture store is individually owned, but is part of a buying syndicate.

2. a combination of bankers or capitalists formed for the purpose of carrying out some project requiring large resources of capital, as the underwriting of an issue of stock or bonds.

a) an agency that buys articles, stories, columns, photographs, comic strips, or other features and distributes them for simultaneous publication in a number of newspapers or periodicals in different localities.

b) a business organization owning and operating a number of newspapers; newspaper chain.

4. a group, combination, or association of gangsters controlling organized crime or one type of crime, esp. in one region of the country.

Next, compare the sentence in the news article, with the definitions given above. The sentence in the article reads, “THIS year's first break-up of a loan-shark syndicate saw the suspected leader and four henchmen -”

It can be seen that result # 4 above, returned by, describes the above perfectly. This definition also fits the “theme” of the article, which is about crime and organized groups.

Step 3 – putting your hard work in a database.

A spreadsheet is the perfect place. Below is an illustration of how it is done

Click on image below for a clearer view.

Repeat the procedure for the rest of the new words.

You can target perhaps 25 new words per week. In a month, that would be 100 words. As the database grows, since you are using a spreadsheet, you can sort it according to alphabetical order, converting your spreadsheet into a “mini” dictionary.

Vocabulary building is an important part of your English. To expand your vocabulary, you need to read, and take note of new words. Keep working on this and soon you will be able to improve your English vastly.

Minister’s comment is really no comment

The Sec 5 “ITE route” saga continues.

Principal's ITE advice 'had to be delivered'


“THE tone of a principal's message to Secondary 5 students may not have gone down well, but it was one that had to be delivered, for the students' sake, a minister said yesterday.

This message was that Sec 5 students who stay on to do the O levels instead of applying to the Institute of Technical Education (ITE) will find it a tough road ahead.

Minister of State for Education Lui Tuck Yew said students and parents need to know that 40 per cent of Sec 5 students will not do well enough at the O levels to qualify for polytechnic…..

…..Rear-Admiral (NS) Lui said the Ministry of Education preferred not to prescribe to principals what they can or cannot say, or what their tone should be, since they knew their students better.”

The crux of the parents’ complaint is not whether ITE route is the better route or not. The crux of the issue is the manner and timing of those words by the principal.

Was it necessary to flash the individual girls’ results with an overhead projector? What happened to confidentiality and privacy?

Furthermore, if the principal truly had the interest of the girls at heart, why were they not told last year – before the deadline for application of higher courses at ITE?

The minister’s words appear to be nothing more than damage control. He appears to hope to be perceived he is involved in the matter, yet washes his hands, when he made no comments on the above two issues, which are the parent’s main complaints.

Instead, he chooses to say, “(It is) important to separate tone from substance of message” – a non-issue with the parents.

MGS (Paya Lebar) Pri School P6 Math CA1 2006 (Q40)

The ratio of the amount of savings that Lisa had to the amount of savings that Andrea had was 8 : 5. They decided to share the cost of a Sony playstation in the ratio of 3 : 1. Lisa used half of her savings to pay for her share and Andrea paid $120 for her share. What was their total savings after paying for the playstation?


Ratio in which Linda and Andrea shared was 3 : 1.

(Lisa) 3 units
(Andrea) 1 unit ----- $120

Therefore Lisa,
3 units ----- 3 x $120 = $360

But $360 is half of Linda’s savings.
Therefore Lisa’s total savings ----- $360 x 2 = $720

Ratio of Lisa’s savings to Andrea’s was 8 : 5.
We also know that Lisa’s savings was $720.

Their savings after paying for the playstation

$360 + $330 = $690

Answer: They had a balance of $690 in total.

Wednesday, January 16, 2008

Wrong way to motivate, Mdm Principal!

I support the school system in Singapore. I always tell parents that our teachers and principals are well trained and children and teenagers in Singapore a lucky lot. No matter what the shortcomings of any teacher or principal, I have always stood for them, explaining to parents and students that they are just doing their job.

Of late, I have to admit that this job I have undertaken is not easy, considering how some of the very educationists I have been supporting, are doing the education system and themselves a big disfavour.

Last week, a principal from an unnamed girls’ school told her Sec 5 students to take the ITE route. What probably hurt the girls most was that their results were flashed in full view, using an overhead projector.

The principal’s reply was that it was to “motivate” the girls. In my opinion, that reply is hollow. As an educationist, she should know that is no way to motivate her Sec 5 students.

Nothing is more demoralizing for a student, already streamed in a class that is considered weak, than for a principal to tell her, that she cannot make the grade.

An overhead projector was used, allowing detailed results to be seen in full view for everyone to see. It was also stressed that a 100% pass from the girls was expected. The girls cannot be faulted, if they read the message, that the school’s image of getting a 100% pass, is more important than the individual girls’ results.

No amount of explanation given by the principal after such an incident can repair the damage done.

It now appears that the unnamed girls’ school is not the only school that has the principal who is trying to discourage Sec 5 students from attempting the O Level route. (I have inserted the article in full at the end of this post.)

It may be true that some schools advise the Sec 5 students to take the ITE route, because in the opinion of the teachers and principal, these students may be better off at ITE. However, there is a right way of giving advice and there is a wrong way of giving advice.

The manner of “advice” given by principal of the unnamed girls’ school is very telling. She has made it known she expects a 100% pass. Furthermore, her words, 'Some...who don't qualify for poly will end up in the ITE anyway, so they might as well go direct to the ITE', indicate that she was more interested in her school’s image, rather than the girls’ welfare.

Educationists are supposed to be the professionals in our education system. As professionals in the education system, how a principal or teacher speaks, advises, or even carry out his or her duties, must be done in a professional manner.

For years, I have been defending teachers and principals whenever parents pick their shortcomings. Today, I have to draw the line. If a supposed professional acts unprofessionally, I shall not defend her action. The parents of the Sec 5 girls have every reason to be fuming and complaining.


From the Straits Times
Jan 16, 2008

4 in 10 in Normal stream can't get into poly

Parents are upset by schools' advice to weaker students, but principals say they mean well

FOUR in 10 Secondary 5 Normal stream students put through the O-level mill each year fail to make it to the polytechnics.

This comes to 3,600 out of 9,000 such students who do not make the cut.

Of the 3,600, half end up at the Institute of Technical Education (ITE), with the rest hitting the job market, going to private schools for diploma courses or repeating the O levels.

These figures explain why schools advise their weaker Normal stream students to take the ITE route even if they have made it to Secondary 5.

Following a report in which the head of an un-named girls' school was said to have told one of her Sec 5 classes they might as well apply now for places in the ITE as they were unlikely to do well in the O levels at the end of the year, more than 20 other angry parents wrote to The Straits Times saying their children had also been told this by their principals and teachers.

The parents were upset, saying advice put in this way could further dent the self-confidence of Normal stream teenagers who, as it is, take a year longer than Express stream students to reach the O levels.

The principal of the girls' school said she was merely trying to give the girls a 'wake-up call' and impress on them the need to work hard to make it through the O levels. She also said the weaker ones among them were really better off going direct to the ITE.

One parent, Mrs Katherine Lim, a 48-year-old shop manager, realised on reading the report her Sec 5 son was not alone.

She said his teacher had 'poured cold water' on his ambition of studying sports management at a polytechnic by saying 'he was wasting his and her time in school'.

Mr Bryan Tan, 51, whose son was also advised to go to the ITE, said there was 'absolutely nothing wrong' with the ITE - his nephew had done well there - but he did not think his son was technically inclined.

Like some parents, he said he wished the school principal had not battered his son's self-confidence by predicting his failure in the O levels.

Principals told The Straits Times they mean well when they tell a student to go to the ITE.

Northland Secondary principal Gan Chee Hau said his teachers study a student's profile first. If students come to Sec 5 weak in mathematics and science, they are 'probably better off going to the ITE'.

Strong grades in maths and science are crucial for entry to the polytechnics.

But he added that his teachers guard against demoralising students and focus instead on their strong points when explaining why the ITE is better for them.

At Northbrooks Secondary, students more clearly cut out for the ITE are counselled even before they sit the N levels in Sec 4, said the school's vice-principal Yee-Toh Gek Khiaw.

She said students and their parents may be in the dark about the courses available there. They could also be unaware that some ITE students do make it to the polytechnics.

But principals point out that the tougher criteria for promotion from Sec 4N to Sec 5N will ensure that those who make it to Sec 5N are academically stronger and more likely to qualify for polytechnic places.

From next year, Sec 4N students must do well in at least five subjects including English and maths - up from three including English - to move on to Sec 5.

Parents like Mrs Lim welcome these changes, but say their effects will be a few years in coming.

She said: 'I agree most teachers mean well, but I hope once the parent and child decide on the O-level route, the school will give all the help and encouragement the child needs to do well in the O levels.'


Feel free to leave your comments.

MGS (Paya Lebar) Pri School P6 Math CA1 2006 (Q37)

I have 38 coins and they are made up of 50-cent and 20-cent coins. Their total value is $13.60. What is the ratio of the number of 20-cent coins to the number of 50-cent coins?


Assume all are 20-cent coins

38 coins x $0.20 = $7.60

But the total value is $13.60. This is $13.60 - $7.60 = $6 more, compared to if all 38 coins were 20-cents.

A 50-cent compared to a 20-cent coin has a value that is 30 cents more.

30 cents “more” ---- 1 (50-cent coin in place of a 20-cent coin)

10 cents “more” ----- 1 divided by 3 = 1/3

($6) or 600 cents “more” ----- 1/3 x 600 = 20 (50-cent coins)

If there are 20 50-cent coins, it means there are 18 20-cent coins.

Therefore the ratio of 20-cent coins to 50-cent coins is:

Answer: The ratio of the number of 20-cent coins to the number of 50-cent coins is 9:10.

Forum Letters from Straits Times

Two issues pertaining to the education system have been in the limelight the past weeks.

1. Teacher's pay
2. A principal's manner in handling Sec 5 students.

Here is an update.

Better pay for teachers not at odds with passion

Principal's words of advice to Sec 5 students ill-chosen

Both articles were published in ST Forum on 15 Jan 2008.

Tuesday, January 15, 2008

MGS (Paya Lebar) Primary School P6 Math CA1 2006 (Q36)

Linda paid $36.40 for 8 chocolate cakes and 14 muffins. The total cost of a chocolate cake and a muffin was $3.80. Leroy brought 2 chocolate cakes and 6 muffins. How much change would he receive if he paid the cashier $30?


1 cake + 1 muffin ----- $3.80


8 cakes + 8 muffins ---- $3.80 x 8 = $30.40

(Linda) 8 cakes + 14 muffins ----- $36.40

(8 cakes + 14 muffins) – (8 cakes + 8muffins) ----- $36.40 - $30.40

6 muffins ----- $6

1 muffin ----- $6 divided by 6 = $1

Cake therefore cost

1 cake + 1 muffin ($1) ----- $3.80

1 cake ----- $3.80 - $1 = $2.80

(Leroy) 2 cakes + 6 muffins ----- (2 x $2.80) + (6 x $1)

= $5.60 + $6 = $11.60

Change he received

$30 - $11.60 = $18.40

Answer: He received $18.40 change.

Saturday, January 12, 2008

Principal wants 100% pass, advises girls to take ITE route

From the Straits Times, dated 12 Jan 2008

Sec 5 class advised: Go to ITE instead


Principal tells students that they are unlikely to do well at O levels

A group of 27 girls in a Secondary 5 class in a mission school - which shall remain unnamed - were advised by their principal on the first day of school last week to seek transfers to the Institute of Technical Education (ITE), since they were unlikely to do well in the O levels this year.

To back her point, she even flashed the girls' detailed N-level grades on the board in class using an overhead projector; she also stressed that she wanted 100 per cent passes in her school.

The result: teens with punctured self-confidence and some fuming parents.

The girls, who had done well enough in last year's N-level examinations to get to Sec 5, were looking to repeat their good performance at the O levels this year and move on to the polytechnics.

Those with strong N-level results had a new option this year: They could have skipped Sec 5 and headed for higher-level technical courses at ITE, but the deadline for applications closed on Jan 2.

The Principal's Side of the Story

Principal's stance

THE school principal told The Straits Times yesterday she was merely trying to give her girls a 'wake-up call' when she spoke to them on the first day of school.

She confirmed that she had used an overhead projector to display the girls' results, but that it was to impress on them that they would have to work hard to qualify for a place in the polytechnics….

……When given the principal's side of the story, two of the parents interviewed said that if all she wanted was to give the girls a wake-up call, she could have done it differently.

One parent said: 'I would have preferred it if she had called the parents in and given them the hard facts, instead of destroying the confidence of the girls.'

Any comments from anyone?

Ai Tong School P5 Math CA1 2006 (Q48)

Alfred sold thrice as many $5 T-shirts as $10 T-Shirts. He also sold twice as many $10 T-shirts as $20 T-shirts. He collected $160 more from selling $5 T-shirts than from selling $20 T-shirts.

a) How much money did he collect from selling $5 T-shirts?
b) How many T-shirts did he sell altogether?


He collected $160 more selling $5 T-shirts than from selling $20 T-shirts.

6 units – 4 units ----- $160

2 units ----- $160

1 unit ----- $160 divided by 2 = $80

Q(a) How much money did he collect from selling $5 T-shirts?

6 units ----- 6 x $80 = $480

Answer: He collected $480 from selling $5 T-shirts.

Q(b) How many T-shirts did he sell altogether?

($5 T-shirts) ----- $480
$480 divided by $5 = 96 (T-shirts)

($10 T-shirts)
4 units ----- 4 x $80 = $320
$320 divided by $10 = 32 (T-shirts)

($20 T-shirts)
4 units ----- 4 x $80 = $320
$320 divided by $20 = 16 (T-shirts)

Total number of T-shirts sold

96 + 32 + 16 = 144

Answer: He sold 144 T-shirts altogether.

Friday, January 11, 2008

Ai Tong School P5 Math CA1 2006 (Q47)

Monica, Vanessa and Angeline share 3 packets of sweets among themselves. Each packet contains 180 sweets. Monica takes 90 sweets while Angeline takes 3 times as many sweets as the total number of sweets Vanessa and Monica receive. If Vanessa is to get the same number of sweets as Angeline, how many sweets must Angeline give to her?


4 units + 90 + 270 ----- 540
4 units ----- 540 – 270 – 90 = 180
1 unit ----- 180 divided by 4 = 45

Vanessa has 45 sweets (1 unit)
Angel has 3 units + 270 -----
(3 x 45) + 270
= 135 + 270
= 405

Angel has 405 – 45 = 360 more than Vanessa

Therefore, she has to give -----
360 divided by 2 = 180

Answer: Angeline has to give 180 sweets to Vanessa.

Thursday, January 10, 2008

Ai Tong School P5 Math CA1 2006 (Q46)

Joyce is paid $1.10 for every calculator she sells. She receives a bonus of $20 for every 150 calculators she sells. How many calculators must she sell to earn $1002?


1 calculator ----- $1.10
1 group of 150 calculators ----- (150 x $1.10) + bonus
= $165 + $20
= $185

5 groups of 150 ----- $185 x 5 = $925
6 groups of 150 ----- $185 x 6 = $1110

Therefore, to earn $1002, she has to sell 5 groups of 150 calculators plus….

$1002 - $925 (her pay for 5 groups of 150)
= $77

1 calculator ----- $1.10
$77 divided by $1.10 ----- 70 individual calculators

Total number of calculators that she has to sell

5 groups of 150 + 70
= (5 x 150) + 70
= 750 + 70
= 820

Answer: She has to sell 820 calculators to earn $1002.

Wednesday, January 09, 2008

Ai Tong School P5 Math CA1 2006 (Q45)

Jug X contains 4 times as much syrup as Jug Y. Sam adds 500ml of syrup to Jug X and 2 450 ml to Jug Y. Now the two jugs have the same amount of syrup. What is the total amount of syrup in the jugs now?


3 units ----- 2450 – 500 = 1950

1 unit -----1950 divided by 3 = 650

Total ----- 5 units + 500 + 2450

= (5 x 650) + 500 + 2450

= 3250 + 500 + 2450

= 6200

Answer: The total amount of syrup now is 6 200 ml

Tuesday, January 08, 2008

Ai Tong School P5 Math CA1 2006 (Q43)

Mrs Li had $10 more than Mrs Devi. Mrs Li spent all her money on 12 plates while Mrs Devi used all her money to buy 8 cups at $1.65 each and 4 plates. Find the cost of 1 plate.


Adding both Li’s and Devi’s items and cost, we get

2 units + $10 ----- 12 plates + 4 plates + 8 cups

2 units ----- 16 plates + (8 cups x $1.65) - $10

2 units ----- 16 plates + $13.20 - $10

2 units ----- 16 plates + $3.20

1 unit ----- (16 plates + $3.20) divided by 2

1 unit ----- 8 plates + $1.60

(Li) 1 unit + $10 ----- 12 plates

8 plates + $1.60 + $10 ----- 12 plates

$11.60 ----- 12 plates – 8 plates

$11.60 ----- 4 plates

1 plate ----- $11.60 divided by 4 = $2.90

Answer: One plate cost $2.90.

Monday, January 07, 2008

Another Article on Teachers' Pay

From the Forum Section of the Straits Times, dated 4 Jan 2008

The writer is of the opinion that pay tied to performance for teachers is not a good idea.

There's a reason it's called 'public service'

Excerpts -

"Public service requires a different aptitude, ethos and capacity, and emphasises empathy, altruism, selflessness and a strong sense of purpose in contributing to the community. It carries with it a heavy emotional investment, often difficult to quantify in monetary terms. The strongest motivation for such an endeavour would be to affect positively the next generation by being role models, and to improve significantly the condition of others, or society as a whole.

Public service includes the sectors of education, health care, social services and the civil service. Monetary rewards rank (or should rank) low, and often departures from public service have more to do with disenfranchisement, disillusionment and low trust environments, where individual contributions are not valued or individuals do not feel invested in the overall direction or purpose of the organisation.

In other words, poor motivation and poor work dynamics, distinct from pay, may be a more critical root cause to address.

In the private sector, a completely different set of circumstances is at play. In a free market economy, competitive salaries and performance-linked bonuses rank high in the decision-making process of job selection, and in motivating profitable behaviours.

An overemphasis on salary incentives to attract or retain talent in public service may, in the long run, be detrimental to motivating the right behaviours, or worse, attracting people not suited for public service."


Related Articles:
Teachers' pay to be pegged closer to performance
Performance-linked pay more harm than good

Ai Tong School P5 Math CA1 2006 (Q41)

Gary has thrice as many stamps as Joel. The total number of stamps Gary and Joel have is twice that of Jackson. The three of them have a total of 210 stamps. How many more stamps does Gary have than Joel?


6 units ----- 210

1 unit ----- 210 divided by 6 = 35

2 units ---- 2 x 35 = 70

Answer: Gary has 70 more stamps than Joel.

Saturday, January 05, 2008

Ai Tong School P5 Math CA1 2006 (Q40)

Tom and Joan have 125 books. Tom and Sammie have 305 books. If Sammie has 3 times as many books as Joan, how many books does Tom have?


Sam ----- 3 units
Joan ----- 1 unit

Tom + Joan (1 unit) ---- 125

Tom + Sammie (3 units) ----- 305

“Tom and Sammie” has more books than “Tom and Joan”
305 books – 125 books = 180 books.

The 180 extra books are due to the 2 extra units “Tom and Sammie” have, as compared to “Tom and Joan”. Therefore,

2 units ----- 180
1 unit ----- 180 divided by 2 = 90

Tom + Joan (1 unit) ---- 125

Tom + 90 ----- 125

Tom ----- 125 – 90 = 35

Answer: Tom has 35 books.

Thursday, January 03, 2008

Ai Tong School P5 Math CA1 2006 (Q39)

Lincoln visited a farm where he saw some cows and ducks. There were 75 of them. He then counted the legs of the animals and found that there were 220. How many animals of each type were there in the farm?


If we assume all the animals were ducks

75 animals x 2 legs ----- 150 legs

But there were 220 legs. A cow has 2 “more legs” than a duck.

220 legs – 150 legs ----- 70 “more legs”

2 “more legs” ----- 1 cow

1 “more leg” ----- 1 divided by 2 = ½

70 “more legs” ----- ½ x 70 = 35

If there were 35 cows, the number of ducks were

75 – 35 = 40

Answer: There were 35 cows and 40 ducks.

Wednesday, January 02, 2008

Has gifted scheme benefited society?

From the Forum Section of the Straits Times, 2 Jan 2008

Has gifted scheme benefited society?


"It is hardly surprising that GEP graduates achieve significant academic and professional success, given their intellectual ability. I believe Mr Lim was more concerned, as I am, with whether GEP graduates have harnessed their formidable intellectual prowess and ability - enhanced by the GEP - to benefit society.

As the GEP goals include teaching students 'to develop a strong social conscience and commitment to serve society and nation' and 'to develop moral values and qualities for responsible leadership', the public would be more interested to know if the best educational resources bestowed on graduates have borne fruit for society in general.

Has the GEP instilled in them a desire to give back to society what it has invested in them? If the lavish educational investment has not paid dividends for society as a whole, then the GEP has failed in the most important regard."

Any comments?

Performance-linked pay more harm than good

Straits Times Forum, 1 Jan 2008

Performance-linked pay more harm than good

I REFER to the recent news about pegging teachers' pay package to performance.

Though it is commendable that the Government is trying to attract more teachers to the profession by paying them well and ensuring that hardworking outstanding teachers are rewarded monetarily, I feel that there are better ways to ensure that they stay in the teaching profession.

Rewarding workers with better bonuses and salary is just one of the many ways to retain workers. Often, an understanding principal and co-operative colleagues also contribute immensely to reasons why teachers stay on in their jobs. A positive vibrant working environment has always been an attraction for workers to continue contributing. Regular positive feedback is also vital in any organisation.

In a buoyant employment market where teachers are often employed on a contractual basis, the ability to get them to renew their contracts has to be done creatively.

Many teacher friends I know are not really attracted to the profession for the salary, but for honourable reasons. They really want to change the lives of their students. Often, their ambition is crushed either by a stifling school environment or an overbearing principal.

I have also heard that some teachers have little room to implement their own teaching style. There is a lot of red tape plus politics, especially in an environment where many colleagues want to score points by 'out-teaching' one another for a better appraisal.

The performance-pegged bonuses, though commendable, may create too much tension in the school environment, when teaching should primarily be a vocation that practitioners do out of love. If a teacher carries out his job with the intention to perform well to gain more bonuses, then teaching may not be the right profession for him.

Principals should not grade teachers well just because they do what is demanded of them. Many will then follow the crowd and do the necessary just to achieve above-average appraisals.

Often, outstanding teachers do more than is required of them. I remember a primary school teacher who visited students who were absent and even raised funds for families in need. Though their teaching was average, they motivated students to do better through their love and care.

Gilbert Goh Keow Wah

Hubei, China

Related Articles (updated on 7 Jan 2008):
Teachers' pay to be pegged closer to performance
Another Article on Teachers' Pay

Ai Tong School P5 Math CA1 2006 (Q38)

A handkerchief cost $4. A towel cost 3 times as much as the handkerchief. If Mrs tan paid $216 for the 28 items, how many handkerchiefs did she buy?


For every 1 towel Mrs Tan buys in place of 1 handkerchief, she has to pay “$8 more”.

If we assume all 28 items bought were handkerchiefs

$28 x 4 = $112.

But she paid $216. This means she paid $216 - $112 = $104 more.

$8 “more” ----- 1 (towel)

$1 “more” ----- 1 divide by 8 = 1/8

$104 “more” ----- (1/8) x 104 = 13 (towels)

If she bought 13 towels, the number of handkerchiefs bought was

28 items – 13 towels ---- 15 handkerchiefs

Answer: She bought 15 handkerchiefs.