## Homeschool Math Challenging Puzzles

The questions listed are also very suitable as PSLE Challenging Math Problem Sums.

Basically, for Grade 2-4, they are very challenging.

For Grade 6 (Primary 6, 12 year old students), they are challenging math questions.

Do give it a try and see if your child can solve it!

## Homeschool Math Challenging Questions

Mathtuition88 will be starting a series of Homeschool Math Challenging Problems, aimed at age 8 to 10 (Grade 2 to 4).

This series is targeted at kids age 8 to 10 who are strong / gifted at mathematics and wish to further stretch their potential. It is also useful for children who may not be strong in math at the moment, but have a keen interest in math nonetheless.

In particular, it is very suitable for the following purposes:

• Preparation for GEP (Gifted Education Programme) screening and selection tests
• Puzzles for kids interested in math but find school work too easy.
• PSLE challenging Math problem sums. The questions are also well within the PSLE Math Syllabus, and will be challenging to Primary 6 students as well.

This series of questions will follow the Singapore Math syllabus for Grade…

View original post 66 more words

## Homeschool Maths Puzzles with Answers: The “Average” Question

The average of 5 numbers is 73. When 2 numbers were removed, the average decreased by 3. What is the average of the 2 numbers that were removed?

This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:

• Preparation for GEP (Gifted Education Programme) screening and selection tests
• Puzzles for kids interested in math but find school work too easy.

This is literally an “average” question. 😛 The word “average” appears 3 times.

The trick is to focus on the total instead.

The total of the 5 numbers is: 73×5=365.

After removing 2 numbers, the average is 73-3=70.

Hence, the total of the 3 remaining numbers is: 70×3=210.

We can then conclude that, the total of the 2 removed numbers is:

365-210=155.

Hence, the average of the 2 removed numbers is: 155/2=77.5 or 75 1/2.

## Hardest Questions in Additional Mathematics (A Math)

Additional Mathematics questions can range from standard all the way to super challenging among the secondary schools in Singapore.

Certain schools (such as IP schools), and also some schools such as Anderson, Chung Cheng High School, are well known for setting hard A Math papers.

Note that even though top schools set hard A Math papers, it is not often the case that top schools teach or prepare well their students for the tests! Often, the teachers in school teach at a basic level (due to time constraints or other factors), but still test at an advanced level. Hence, many students in top IP schools are not well prepared for their school’s tests (unless they have excellent self study skills or have a parent or tutor to guide them). It is not uncommon for a student in a top IP school to be failing his/her math tests due to the above phenomena (difficult tests which do not match what is taught in school).

Some of the more difficult types of questions in the A Math syllabus are listed below.

## Algebra

1. Conditions for ax^2 + bx + c to be always positive (or always negative).
This type of question has potential to be very tricky. Somehow, many students will assume wrongly that b^2-4ac is always positive as well (where it should be the opposite).
2. Partial Fractions with Improper Fractions.
Only top schools tend to test improper partial fractions. Many students will miss out long division or make mistakes along the way.
3. Binomial Theorem.
Many students have serious problems with this topic. Also, not many seem to know that ${n\choose 2}=\frac{n(n-1)}{2}$.

## Trigonometry

• Sketching of Tangent graphs.
90% of all sketching questions are on Sine or Cosine. Only top schools will set tangent sketching questions, and many students will be caught unaware.
• Half-angle formula sin(x/2) or Quadruple angle formula sin(4x)
Top schools like to test half-angle formula, many students who have not seen such questions will be stuck.

## Integration

• Finding area to the left of the curve, i.e. $\int x\,dy$.
Most schools kind of brush off this type of questions during teaching. But it is a hot topic for testing among top schools. Hence, students will have a hard time solving it if they lack practice for this type of questions.

## Cool Math Games

Some games are fun but not educational.

On the other hand, some games are educational but not fun!

This very popular website Cool Math Games is a combination of fun and educational!

## Benefit of Cool Math Games

• Their games are all browser-based, there is no need to download anything. It can be played on your Internet Explorer or Chrome browser.
• They have a wide range of different games, ranging from Numbers, Logic, Trivia, and Strategy.
• Their games are kid-friendly and educational.

## Cool Math Games Example

This games “Swap Sums” is suitable for lower elementary school kids (age 5-10). It starts off easy, but the later stages are actually quite challenging. For example, the stage below actually requires some thinking to get it right.

## Cool Math Games Review

Children naturally love to play games. When I was a child, my favorite activity was to play computer games. Hours can just fly by when playing games. When playing games that are educational at the same time, it can hugely benefit a child in terms of increasing his/her interest in the subject.

Hence, parents are encouraged to let their child play educational games, such as Cool Math Games, to relax as well as to learn. Most children learn better when the content is fun and engaging.

## School holiday activities for children stuck at home

Due to the circuit-breaker, most children are unfortunately stuck at home during their school holidays. Other than playing computer games, this article suggests other educational and fun activities for children and their parents: School holiday fun at home: Kids can go online to stargaze, study about animals, do science experiments.

The live stargazing activity of Science Centre sounds quite fun: https://www.facebook.com/183389296588/videos/2534433140205259/

Most of the activities are open to children outside Singapore as well!

## Slow and Steady Snail (Homeschool Math Favorite Challenging Puzzles)

This is a favorite type of homeschool math challenging puzzle — The Snail question.

Question: An aquarium is 47 cm deep. A snail starts at the bottom of the aquarium. Each day, during the daytime the snail climbs up 8 cm, and during the nighttime the snail slides down 3 cm. How many days will it take for the snail to climb out of the aquarium?

This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:

• Preparation for GEP (Gifted Education Programme) screening and selection tests
• Puzzles for kids interested in math but find school work too easy.

Solution:

A tempting answer would be 10 days. This is a trick! Those who get the answer “10 days” reason like this: each day the snail moves a net distance of 8-3=5 cm.

Hence, 47/5=9 R 2.

At the end of the 9th day, the snail moved 45 cm. Thus, rounding up will give 10 days as the answer. However, there is a tricky part to the question!

The correct answer is 9 days.

We can do a list:

Day 1 — 5 cm

Day 2 — 10 cm

Day 3 — 15 cm

Day 8 — 40 cm

Day 9 day time — 40 +8 = 48cm > 47 cm !!!

The snail is already out of the aquarium on Day 9!

## Canon Most Ink Efficient Printer

Just bought this printer (Canon PIXMA G5020, which is listed in Singapore as Canon PIXMA G5070). It is ideal for home use for students and working professionals.

• Very efficient “ink tank” system. The ink refill system is by bottles of pure ink liquid instead of cartridges.
• Design for high volume printing at low running cost
• Compact size and dimensions (Approx. 403 x 369 x 166 mm for factory configuration,  Approx. 403 x 695 x 356 mm when Output/ADF trays extended)
• Dual paper loading (you can load paper on the rear tray as well as the front tray). If you retract the rear tray, the printer becomes even more compact (just 16.6cm tall).
• High speed (for inkjet): ISO standard print speed (A4): up to 13.0ipm black / 6.8 ipm colour
• Supports wireless connection to computer as well as smart phone.
• Automatic Duplex

Overall, this is the ideal printer for work from home, as well as homeschool purposes. It is even more ideal for those who don’t want additional features such as scanner and fax. By not having those features (which you may not need), it has a very economical affordable cost. Especially when you factor in the long term savings from cheap and long-lasting ink refills.

If you do want copier, fax and scanning features, then you can consider the Canon PIXMA G7020 instead, which is basically the Canon G5020 with the additional features.

## The Enigma of the Erasers (Homeschool Math Challenging Puzzles)

Dan has 745 red, green, blue and yellow erasers.

If the number of red erasers is tripled, the number of green erasers is halved, the number of blue erasers is decreased by 39, and the number of yellow erasers is increased by 48, there will be an equal number of erasers for each of the colors.

How many erasers are there for each of the colors?

This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:

• Preparation for GEP (Gifted Education Programme) screening and selection tests
• Puzzles for kids interested in math but find school work too easy.

Solution

Let the number of red erasers be 1 unit:

R -> 1u

3R -> 3u

This means that the number of green erasers must be 3u x 2 = 6u.

G -> 6u

(This is so that after the green erasers are halved, it is also 3u.)

B -> 3u+39

Y -> 3u-48

Hence,

R+G+B+Y = 13u – 9 = 745

13u = 754

1u = 754/13 = 58.

Hence, the number of erasers for each color are:

R = 1u = 58

G = 6u = 348

B = 3u+39 = 213

Y = 3u-48 = 126

## Pinterest Update

Previously, I tried using the automatic Pinterest RSS Feed but to no success. I even tried posting on the WordPress.com forum but again it did not address the problem. (To be fair, this is probably a problem on the Pinterest side.) Hence, the conclusion is that currently the WordPress.com to Pinterest automatic posting does not seem to work. (It apparently works for WordPress.org users according to my search on Google.)

Thus, I have manually added some pictures from Mathtuition88 (including reblogged content) onto Pinterest. Feel free to share it!

Manually adding pictures onto Pinterest is quite tedious and time-consuming. I will be monitoring how much effect Pinterest has, in terms of channelling traffic.

## The Secret of the Sweets (Sweet Distribution Problem)

Mrs Smith has some sweets to distribute to her students. If she gives each student 3 sweets, she will be left with 24 extra sweets. If she gives each student 5 sweets, she will be short of 42 sweets.

How many sweets does Mrs Smith have?

This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:

• Preparation for GEP (Gifted Education Programme) screening and selection tests
• Puzzles for kids interested in math but find school work too easy.

Solution

This is quite a tricky problem for Grade 2-4 students. The main problem is that the number of sweets, as well as the number of students is unknown! Many students will not know how to even start solving such questions.

We can reason as follows:

From 3 sweets each to 5 sweets each is an increase of 5-3=2 sweets each.

From having 24 extra sweets to being short of 42 sweets is a difference of 24+42=66 sweets.

Hence, to cause the above difference, there must be a total of 66/2=33 students!

Then, we can conclude:

33 students x 3 sweets each = 99 sweets

99+24=123 sweets altogether.

We can also check our answer using another method:

33 students x 5 sweets each = 165 sweets

165-42=123 sweets.

## Anubias tied too tightly

I think one of my Anubias rhizomes died (rotted) due to it being tied too tightly. The Anubias rhizome is supposed to be hard and green, if it is soft or brown, something is wrong.

For Anubias, the rhizome is the most important part of the plant, if it is dead, the whole plant will die.

Another reason for the Anubias rhizome rotting is the dreaded Anubias disease, but I don’t think it is the case here because another rhizome just next to the rotted rhizome is perfectly healthy.

Hence, the conclusion is that the Anubias rhizome most likely died from being tied too tightly by the string. It was at the back of my tank so I didn’t really notice it at first. I only noticed it when I saw a new leaf sprout out from the rotting rhizome, but the new leaf melted soon after. Usually, when new leaves melt, it is a sign of something wrong. Upon taking the entire Anubias plant out, I then realized that the rhizome had turned mushy.

The original Anubias was tied (by the seller) with thick string. I don’t really blame them for tying too tight because it is not easy at all to tie Anubias (too loose and it will not stay in place). I cut off the old string, threw away the rotted rhizome, and re-tied the healthy Anubias lightly with sewing thread.

Probably the same problem can occur for Java Fern, Bucephalandra, the rhizome may rot if tied too tightly.

## Hikari Shrimp Cuisine Review

I find this Hikari Shrimp Cuisine quite good. The pellets are quite small sized so you can control exactly how much you want to feed (down to each individual pellet).

## How to feed Hikari Shrimp Cuisine Pellet (without fish snatching it away)

This was something that perplexed me for a long time. My fish would grab any food meant for the shrimp, leaving close to nothing left for the slower moving shrimp.

The solution I found was to:

1. Put the Hikari Shrimp Cuisine pellets in a small container with tank water.
2. Crush the pellets (I just use my finger).
3. Stir to “dissolve” the pellets a little. Stirring also helps the pellets to sink.
4. Pour the water with “dissolved” pellets back into the tank.

You may switch the order of steps 1 & 2 if you like (I find it easier to crush the pellets when wet).

The main reason why this works is because:

• Hikari Shrimp pellets are sinking (this is very important since shrimp can only eat sinking pellets that reach the floor).
• By crushing the pellets into powder, it is virtually impossible for the fish to snatch all the shrimp’s food.
• Some, if not most, of the powder will reach the tank floor, where the shrimp can find and eat it.

Another way to feed shrimp exclusively is the usage of a shrimp feeding tube and feeding dish.

## How much Hikari Shrimp Cuisine Pellets to feed

This depends on how many shrimp you have, and also your tank setup. Ideally, shrimp such as cherry shrimp or Amano shrimp can survive on algae and biofilm. Hence, if your tank is well planted, you only need to feed lightly. Personally, I only feed the shrimps once a week, at around 2 Hikari Shrimp pellets per shrimp.

If your tank is bare (no plants), you need to feed more, maybe once every day or once every two days.

Supplementing with Hikari Shrimp food is good because it contains essential minerals like copper (shrimp need small amounts of copper) and other minerals that can help shrimp molt.

## Stickers Math Question

Abby, Brian, Charles, Dennis and Eason have 50 stickers altogether.

Abby has the most stickers — she has 12 stickers.

In second place (tied) are Brian and Charles.

In third place is Dennis.

In fourth place is Eason, with 6 stickers.

How many stickers does Dennis have?

This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:

• Preparation for GEP (Gifted Education Programme) screening and selection tests
• Puzzles for kids interested in math but find school work too easy.

For this type of questions, the easiest way to do is “trial and error”, also known as “guess and check”.

Firstly, lets check how many stickers B, C, and D have together:

50-12-6=32

 B C D Total (B+C+D) Comments 9 9 14 32 Wrong! Since D is more than A 10 10 12 32 Wrong! Since D is tied with A 11 11 10 32 Correct! 12 12 8 32 Wrong! Since B, C is tied with A

For guess and check, the most important thing is to be systematic, rather than guess wildly. For instance, we can systematically increase our guesses for B, C.

We can see that the only logical answer is:

B= C=11

D=10

This is something quite interesting. Possibly a very good idea for many bloggers — kill two birds with one stone (write a book while developing a blog).

We know many of you love your blogs, and gleefully publish photos and posts without thoughts to reuse your work in other forms. But we know some wonder: could this be a book? Recently we wrote about how a WordPress.com blogger scored a book deal for You Are Not So Smart. But what if you want to do it all yourself?

As a blogger who has authored several successful books with publishers, and who works on WordPress.com, I recently self-published a book based entirely on posts from my blog. I wanted to see what I could learn, and I’m here to share it all with you.

The book I self-published is called Mindfire: Big Ideas for Curious Minds. It’s a collection of my best essays from my WordPress blog at scottberkun.com, where I write about ideas, creativity and leadership. The book has done well, and has often been in the top 100 books on philosophy and other categories on amazon since it was published.

There are four questions I often get asked by other bloggers.

This is the wrong way to start. A book is a different reading experience than a blog, and to “shape” a blog into a book assumes words are like clay, where you can shove them into any shape you like. A book is a longer reading experience, and every chapter, or every page, needs to line up in a readable way with the others. It will take some effort to rework  material written for a blog to fit well together as a book. Don’t start with the assumption you’ll include every single post on your blog, or keep them in the chronological order they were written.

The first step is to make two lists: possible posts and possible concepts. You might discover a book concept that’s strong, but you only have 10 or 12 posts that fit. That’s ok. You can always choose to write more. Of course the theme of your entire blog could be the theme for a book, but consider other concepts too.

I went back to the beginning and made a list of posts that might be good enough to include. I made a separate list of possible book concepts. One concept I saw in some of my posts was intelligent provocation: asking big questions and offering intelligent and entertaining answers. I filtered the list based on that concept, and arrived at 45 possible posts.  Then I hired an editor to help refine the list, and the result was 30 posts that, while all written independently, fit together into an excellent read.

There are services like Blurb or Blog2print that will take your WordPress.com blog and build a book from it. If your WordPress blog is self-hosted, and not on WordPress.com, you might take a look at Anthologize, a plugin that automates the process of converting your blog into an e-book. But these services do nothing to shape your work into a great read. No software can do this for you.  There is an enormous distance between a ‘book’ and a ‘book someone will enjoy reading’ and that distance is closed only by your hard work.

Plan to take a draft version of your book and ask people to read it. Ask for feedback on improving the order of posts, or which posts don’t fit. You’ll notice people expect tighter and more careful writing in a book, compared to reading posts online. It’s acting on this feedback that makes the difference between a book that feels like a book, and a book that feels like a bunch of random posts thrown together. Revise posts, or write new material, to develop the book into a singular strong narrative. I asked for volunteers on my blog for people to give feedback on the drafts and their input was a key part of making the book so strong.

### 2. How do you actually (self) publish a book?

To go the traditional route, you’ll need to reach out to publishers or agents and try to find one that’s interested. This takes significant effort beyond writing the book itself. In all cases, traditional or self-published, the hardest part is writing and editing an excellent book. If you’re dedicated to your book, self-publishing can allow you to focus your energy on making the book better, rather than in searching for someone to give you a chance you can give yourself.

If you already have a well edited manuscript, you are most of the way there: the technical parts of self-publishing are surprisingly easy. You take your complete manuscript, after it has been copyedited and reviewed by an editor, and convert it to a PDF. With a PDF in hand, there are many services that will convert your PDF to a print or digital book for you.

For Mindfire, I used Lightning Source for the print edition, and a service called BookBaby to manage the digital editions.  These services list the book on amazon.com, and it can be purchased like any other book on amazon.com, including KindleiBook and other digital versions. It doesn’t cost much: maybe a few hundred dollars. If you choose to only produce a digital version, it can be much cheaper.

The more work you do, the cheaper the services are. If you are willing to hire your own editor and cover designer, or do those tasks yourself, and take care of details like getting an ISBN number, you can user services like  Lightning Source or CreateSpace to simply print and distribute he book. But if you want to hire people to help you, services like CreateSpace and Lulu.com let you pay them to take care of many steps on your behalf.

### 3. Why would people buy a book if the content is free on the blog?

The rise of the iPad and Kindle have proven the demand for longer reading experiences, experiences longer than what the web provides. A compilation of your work offers a deeper experience than what people get through your blog alone. Blogs are fantastic for small to medium length reading experiences, but to consume 40 or 50 posts without interruption, posts that are chosen to fit together on a specific theme, you need something else. A book is a better experience for this kind of continuous reading.

### 4. How can I use my blog to help the book succeed with the book?

If you involve your readers as your produce the book, they will naturally help spread word when it’s done. Using polls I asked my readers to help pick the title, to give feedback on several rounds of cover designs, and many other decisions. This attracted new readers curious about how books are made, and allowed me to collaborate with my readers on the book, increasing their interest in seeing it finished and released.

It’s counterintuitive, but giving the book away for free for a time helps a new book, and your blog, tremendously.

### 5. What’s the first step to take?

You’re a blogger: start by blogging about it. Ask your readers if they’re interested in helping you work on a book. Post your list of book concepts and see what they think. Perhaps there’s an author, editor or designer who reads your work that can lend their expertise. Take a careful look at the work you’ve already written and start thinking about what concepts might match.

## Marbles Math Question

Aaron and Bob had some marbles in a box.

At first, Bob had thrice as many marbles as Aaron.

Aaron sold 5 marbles and Bob bought another 35 marbles.

Then, Bob had 5 times as many marbles as Aaron.

How many marbles were there in the box at first?

This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:

• Preparation for GEP (Gifted Education Programme) screening and selection tests
• Puzzles for kids interested in math but find school work too easy.

Solution:

This question can be solved using the “units” method, and “working backwards”.

At the end, Bob had 5 times as many marbles as Aaron.

We write:

Aaron –> 1u

Bob –> 5u

Next, we work one step backwards (before Aaron sold 5 marbles and Bob bought another 35 marbles.)

Aaron –> 1u + 5

Bob —> 5u – 35

Now, we calculate what is 3 times of Aaron (thrice of Aaron’s marbles):

3 times of Aaron –> 3u + 15

We can conclude that:

3u+15 = 5u-35

We may draw the above model, after which we can conclude that:

2u –> 15+35=50

1u —> 25

Hence, Aaron had 1u+5 = 30 marbles at the start.

Bob had 5u-35 = 90 marbles at the start.

In total, there are 30+90= 120 marbles at first.

Ans: 120

## Homeschool Math Challenging Questions

Mathtuition88 will be starting a series of Homeschool Math Challenging Problems, aimed at age 8 to 10 (Grade 2 to 4).

This series is targeted at kids age 8 to 10 who are strong / gifted at mathematics and wish to further stretch their potential. It is also useful for children who may not be strong in math at the moment, but have a keen interest in math nonetheless.

In particular, it is very suitable for the following purposes:

• Preparation for GEP (Gifted Education Programme) screening and selection tests
• Puzzles for kids interested in math but find school work too easy.
• PSLE challenging Math problem sums. The questions are also well within the PSLE Math Syllabus, and will be challenging to Primary 6 students as well.

This series of questions will follow the Singapore Math syllabus for Grade 3 students, covering the following topics:

1. Whole Numbers
2. Fractions
3. Money
4. Measurement (Length, Mass, Volume)
5. Time
6. Area and Perimeter (rectangle/square)

Although the syllabus above is elementary, we are choosing the toughest math questions (while still remaining in the framework of the syllabus). Hence, the title of the series is “Homeschool Math Challenging Puzzles for Grades 2-4”!

As far as possible, the questions will be categorized under: https://mathtuition88.com/category/homeschool-math-challenging-puzzles/

## GEP Test Format

There is limited information on the GEP Test Format on the official MOE website:

### IDENTIFICATION OF PUPILS FOR THE GEP

The entry point into the GEP is at Primary 4.

Pupils are identified for the GEP through a two-stage exercise in Primary 3.

Stage Month Participants Papers
Screening August Primary 3 pupils enrolled in government and government-aided schools English Language

Mathematics

Selection October Only shortlisted pupils will be invited to the Selection stage English Language

Mathematics

General Ability

For the screening test, the duration for each paper is around 1.5 hours.

For the selection test, there are traditionally two papers of 2.5 hours each:

• Paper 1: English paper and a General Ability paper
• Paper 2: Maths paper and another General Ability paper

In August every year, the cohort of P3 students is invited to sit for a GEP screening test. The test is not compulsory but all children are encouraged to go for it. The test comprises an English and a Maths paper, about 1½ hours each.

Out of the cohort of approximately 50,000 kids, some 3,000 pupils (about 6%) are shortlisted for the GEP selection test.

The selection test takes place over two days in October, the first comprises an English paper and a General Ability paper, about 2½ hours in total. The second consists of a Maths paper and another General Ability paper, also about 2½ hours altogether.

## GEP Test Syllabus

Officially, the GEP Test can only test within the Primary 3 syllabus. (This is more relevant for Math than English. For English, it is more open-ended, they can test advanced GEP vocabulary like “cantankerous”.)

For example, technically they are not supposed to test “speed” questions since that is a Primary 5 topic. Similarly, they are not supposed to test area/perimeter of circle questions, or even area/perimeter of triangle questions.

Hence, the GEP Math Test Syllabus (according to the official Primary 3 syllabus) includes:

1. Whole Numbers
2. Fractions
3. Money
4. Measurement (Length, Mass, Volume)
5. Time
6. Area and Perimeter (rectangle/square)
7. Angles (basic concepts of right angle, acute angle)
8. Perpendicular & Parallel Lines (basic concepts)
9. Bar graphs

The above topics may seem deceptively easy. However, even for a simple topic like fractions, it is possible to test a question like the GEP Screening Test Question Sample: The Tap Question, which may stump many secondary school students.

Related posts:

## Mosquito Rasbora & Neon Tetra

Mosquito Rasbora (Boraras Merah / Phoenix Rasbora) can live peacefully together with neon tetras!

The neon tetras mostly ignore the smaller mosquito rasboras, except maybe during feeding time where they try to snatch the food. There has been zero aggression between the mosquito rasboras and the neon tetras.

Mosquito Rasbora are surprisingly clever and have distinct personalities. One of my mosquito rasbora prefer to hangout near the top of the water together with the neon tetras, while another prefers to swim low near the roots of plants.

## Jeff Bezos: How do you say no to annoying meeting requests?

How do you respond:

1. A) Yes, I’ll definitely meet with you.
2. B) No, I won’t meet with you.
3. C) Tell you what. Call so and so and they’ll work something out.
4. D) Quietly resolve to become a shut-in.
5. E) Something else (fill in the blank)

Quite interesting to see Jeff Bezos’s answer (Option C).

Unfortunately this option only works for higher level executives who have a secretary/admin staff?

## “Toxic environment” in Elite Secondary School (Singapore)

Just came across this Facebook post (originally by Pamela Lim):

For convenience, the post is reproduced below. Although the school is not explicitly named, it is quite easy to guess from the description which school it is! (It is probably a school that “offers a highly accelerated mathematics and science curriculum integrated with language, arts, humanities, sports, in a modular system.”)

Case study:

Anthony’s PSLE result was sterling and he got into an elite of elite secondary school, one that promises more than academic rigor, their high school credits can be used as credit transfers into a top university in Singapore.

Needless to say, it is a sought after secondary school, and the kids are studying 3-4 years ahead of their age peers in the areas they specialize in.

The celebration was short-lived. Within six months, the parents reached out to me. The high IQ child has school refusal problems. So I got our counselors involved to see how we can help.

Our advice was to remove him from a toxic environment where kids are often driven to a place where they feel deflated, over challenged and unaccomplished. We feel he should go to where his gifts are appreciated, where he can score well and his self-esteem is high. On the side, we promised to offer enrichment that will challenge and stimulate his intellectual needs. We felt he needed both social and intellectual support, and since he cannot get them both in the same place, we suggest splitting them.

Not unexpectedly, the parents and child felt that it was a ‘waste’ to give up a prestigious school, so they stayed. Yesterday, we received another call. In the six months since we last spoke, the child moved to an international school, and now refuse to go to the new school as well. In fact, he is refusing to get out of the house, so can we send in some psychologist.

To be honest, I don’t think we can ‘rescue’ a child like that, no matter how much they offer to pay us. He is only 14, and just 2 years ago, he was acing his cohort, happy about his situation, full of confidence of his future.

Just a disclaimer that “Toxic Environment” is a subjective term, one man’s meat can be another man’s poison. However, the fact of the matter is that many schools (especially elite schools like IP schools) do have high academic stress. The level of the internal tests in top IP schools is much higher than ‘O’ level standard. It is quite common for top students in PSLE to “fail” those tests in the elite IP schools, especially if they can’t adapt quickly to the style of tests.

Most notably, in top IP schools, what is tested in exams is quite often not taught in class! Students are expected to extrapolate the basic material taught in class, to tackle the tough questions in exams. Basically students need to 举一反三！(The teacher teach you one thing e.g. 1+1=2, the student needs to extrapolate and deduce for yourself 3 other things e.g. 1+2+3+…+99+100=5050.)

Needless to say, only minority of students (even in top schools) are capable of the above. Hence, that is why self-learning in the form of challenging assessment books or tuition has become quite popular as it is one way of overcoming the “teach simple, test difficult” style in top secondary schools or JCs.

Recommended books:

## Paul Krugman Masterclass Review

Paul Robin Krugman is an American economist who is the Distinguished Professor of Economics at the Graduate Center of the City University of New York, and a columnist for The New York Times. His notable awards include the Nobel Prize for Economics!

Students studying economics in high school or university are highly recommended to watch his Masterclass lessons (link to Masterclass website). It is always good to listen to insights from masters who have experienced economics at the highest level.

Prof. Krugman is also the author of a university level textbook titled Economics (co-written with Robin Wells):

He also writes several popular economic books for laymen, such as The Return of Depression Economics and the Crisis of 2008, where he predicts that the world’s economy is sliding into a deep recession (recall he is a Nobel Prize winner in Economics, not just any “bogus” author!). He also gives tips on how to avoid catastrophe in this case.

A detailed video review of Paul Krugman’s Masterclass is available below:

Link to his masterclass here: Masterclass Official Website (Krugman Economics)

## IP Math Syllabus (Integrated Programme Mathematics)

Students and parents new to IP (Integrated Programme) may be confused on what is the Mathematics syllabus of IP Math. Indeed, it is very confusing as every school has its own syllabus. In general, the syllabus as a whole is not that different from ‘O’ level Mathematics, but the order in which the school teaches is unique to each school.

In general, the topics can be divided as follows, following the famous assessment book “Mathematics (Integrated Programme)” by Wong-Ng Siew Hiong who is a teacher at RI. This is one of the very few IP Math books available in local bookstores.

## Secondary 3 IP Math Syllabus

1. Geometrical Properties of Circles
3. Matrices & Simultaneous Equations
4. Quadratic Functions, Inequalities & Roots of Equations
5. Sets
6. Relations & Functions
7. Indices & Surds
8. Exponential, Logarithmic & Modulus Functions
9. Polynomials & Partial Fractions
10. Graphical Solutions & Transformations
11. Circular Measure
12. Plane Geometry
13. Coordinate Geometry & Equations of Circles
14. Linear Law
15. Trigonometry
16. Further Trigonometry

## Secondary 4 IP Math Syllabus

1. Binomial Theorem
2. Probability
3. Statistics
4. Vectors
5. Differentiation Techniques
6. Differentiation and its Applications
7. Integrated Techniques
8. Applications of Integration
9. Integration Applications — Area and Kinematics

## Cheap alternative to Dyson Vacuum (Xiaomi DREAME V9 Pro)

Though Singapore is a relatively rich country, many people still find Dyson Vacuum Cleaners unaffordable since it is well over a thousand dollars.

Fortunately, there is a cheap and good alternative to Dyson Vacuum Cleaners (with many positive reviews): Xiaomi DREAME V9 Pro. (Some people actually claim that it is more powerful than Dyson vacuums! See the video at the end of this post.)

For example, an actual review by a Singaporean states:

My friend got it for her 3-room flat and she said this vacuum cleaner not bad. She gave me the courage to purchase it as I have been considering for a long time. After I received it, a test-out session became vacuum the whole house (it still has 1 bar battery when it arrived). The maneuvering is smooth, which let me vacuum the whole 4-rm flat effortlessly. I am a lady, so it should be fine for most people. Thumbs up!

[S$219.00](▼46%)Xiaomi DREAME V9 Pro Cordless Vacuum Cleaner | 20 000 Pa Suction Power | Long Battery Life WWW.QOO10.SG It is almost compulsory for every household in Singapore to have a vacuum cleaner, since our hot and humid climate makes dust mites grow and reproduce very fast if we don’t vacuum away the dust. In addition, many young children tend to have some form of childhood asthma in Singapore. Do read all the reviews of the Xiaomi cordless vacuum cleaner before making your decision! For international buyers, you may find the Xiaomi Dreame V9 on Amazon as well: Dreame V9 Pro Cordless Vacuum Hyper Clean Cordless Cleaner, Super for All Carpet and Hardwood Floor Stick Vacuum with Powerful Digital Motor, Handheld with Rechargeable Lithium Ion Battery Below is the YouTube reviewer who claims that the Xiaomi Dreame V9 is more powerful than Dyson in terms of suction: ## Sellfy free account to be discontinued Just received some news from Sellfy: Hi there, We have important news about your Sellfy account and your store https://sellfy.com/mathtuition88 You have been on our transaction fee only plan (Legacy plan) since you signed up for Sellfy. We are truly thankful for being with us all this time! Due to considerable technical adjustments in our platform and supporting services, we are forced to discontinue the Legacy plan on February 1st, 2020 and switch into supporting subscription-based plans only https://sellfy.com/pricing/. We no longer offer Legacy plan for new users since March, 2016. Most likely, we won’t be continuing with Sellfy after February 1st, 2020. Hence, this is the last 1-2 months to purchases math notes/material from our online store: https://sellfy.com/mathtuition88 if you are interested. Thank you for the support! ## Forest Man of India Previously, I blogged about the Mountain Man of India: Mountain Man Motivational Story Today, I learnt that there is also a Forest Man of India. By planting one tree a day (for many years), Jadav Payeng (a.k.a Forest Man of India) has planted a forest bigger than Central Park in New York! This principle of doing small things everyday also applies to students and learning. By doing one Math question per day, at the end of one year, a student would have completed 365 Math questions! This would be a considerable amount that would certainly help to boost the student’s Math grade and also Math understanding. ## Python Online Courses for Teenagers/Adults If your child is interested in a Computer Science/Data Science career in the future, do consider learning Python beforehand. Computer Science is getting very popular in Singapore again. To see how popular it is, just check out the latest cut-off point for NUS computer science, it is close to perfect score (AAA/B) for A-levels. According to many sources, the Singapore job market (including government sector) is very interested in skills like Machine Learning/ Deep Learning/Data Science. It seems that Machine Learning can be used to do almost anything and everything, from playing chess to data analytics. Majors such as accountancy and even law are in danger of being replaced by Machine Learning. Python is the key language for such applications. I just completed a short course on Python: Python A-Z™: Python For Data Science With Real Exercises! The course fee is payable via Skillsfuture for Singaporeans, i.e. you don’t have to pay a single cent. (You have to purchase it first, then get a reimbursement from Skillsfuture.) At the end, you will get a Udemy certificate which you can put in your LinkedIn profile. The course includes many things from the basic syntax to advanced visualization of data. It teaches at quite a basic level, I am sure most JC students (or even talented secondary students) with some very basic programming background can understand it. The best programming language for data science is currently Python. Try not to learn “old” languages like C++ as it can become obsolete soon. Anyway the focus is on the programming structure, it is more or less universal across different languages. Related posts on Python: ## American Health Concerns that many are unaware of America (and prosperous European countries like UK and France), being 1st world countries, are sometimes concerned about “First World Problems” that most other countries do not have time/energy/money to care about. Two health concerns that are very popular in America, but virtually unknown in most Southeast Asian countries are: ## Vaccines Health Concerns Although the main research linking MMR Vaccines to Autism has been retracted, many Americans, including President Donald Trump, have expressed their concern about vaccines. There are many anecdotal stories from parents whose children are doing well developmentally, until the day they took the vaccine where strange effects happened, including autistic regression. Read here about a Nature article on “The real issues in vaccine safety”. By the way, Nature is the top science journal in the world, it is considered a tremendous achievement for any professor to publish in Nature. The main author behind the MMR-Autism link, Andrew Wakefield, has published his version of the story in his book called “Callous Disregard”. He has been called a fraud, but yet many people do believe in his theory. Notably, in his retracted paper Wakefield did not claim that vaccines cause autism, he just investigated the link and basically said that more research needs to be done. His punishment was very severe (lost his UK doctor’s licence; he spent a decade earning his Gastroenterologist specialist degree), and some people believe it to be a conspiracy theory backed by the billion-dollar vaccine pharmaceutical giants. “We have identified a chronic enterocolitis in children that may be related to neuropsychiatric dysfunction. In most cases, onset of symptoms was after measles, mumps, and rubella immunisation. Further investigations are needed to examine this syndrome and its possible relation to this vaccine.” (Andrew Wakefield’s paper’s final conclusion.) Basically, vaccinations rely on a phenomenon called “herd immunity”, it requires at least 90-95% of the population to be vaccinated in order for it to be successful. Hence, many people dropping out of the vaccinations can cause the “herd immunity” to be lost, which may be dangerous. On the other hand, vaccines contain dangerous ingredients like preservatives and viruses, and even used to contain a mercury compound called thimerosal, which no doubt is something unnatural that you wouldn’t want to put in your body. Due to the vaccine controversy, thimerosal has now been discontinued in most vaccines. ## Gluten In Southeast Asia, I would say that more than 90% of people do not know what gluten is (though they eat it everyday). In Laymen’s terms, it is a type of protein that is found in wheat, barley, rye, etc. In America, many people have been tested to have gluten sensitivity, causing digestive problems such as Crohn’s disease or Celiac disease. Again, similar to vaccines, most people have no problem at all eating gluten, but in a selected minority of the population, it can cause severe problems. The digestive system is said to be a “second brain”, (see The Strange Location of Your Second Brain). It contains a lot of neurotransmitters. Hence, many scientists have started to notice the gut-brain connection. Read this Harvard article that links anxiety and depression to digestive (gut) problems. Hence, for people with gluten sensitivity or allergy, gluten can be the starting trigger for their other problems like depression/anxiety. It has also been linked to ADHD and even schizophrenia. Check out this book (1,001 positive reviews) on the connection between the gut (digestive system) and the brain: Watch what Donald Trump has to say about vaccines: ## Maths Tuition Blog We have revamped our Maths Tuition Blog at: https://mathtuition88.blogspot.com/. It now features a “sticky” Home Page that showcases some useful JavaScript Apps. We have also increased the font size for easier reading. For instance, our most popular App is the App to calculate JC Ranking Points: https://mathtuition88.blogspot.com/2015/03/calculate-uas-points.html. ## Nalgene Bottle Singapore Since Singapore is such a hot country, it is important for students and adults to keep hydrated to avoid heatstroke. One of the most popular and best brands of water bottles is Nalgene, which is made in the USA. It is BPA free, which is very important to avoid drinking toxic plastic particles that may leach into your water. (I think by now Singaporeans know it is not good to reuse Coca Cola bottles as your water bottle; 10 years ago it was very common to do that.) It is quite hard to find Nalgene bottles in supermarkets. NTUC Fairprice, Giant does not seem to carry them in their stock. Interested buyers may purchase Nalgene bottles from Qoo10 (see image link below). Do choose this store as it has many positive reviews, it has an actual store in Pasir Ris, but buying online would be much more convenient. [S$12.00](▼74%)[GHSGIFTS]Nalgene Water Bottle / WIDENARROW mouth/BPA Free / Small water Bottle – 500ml / 1000ml / 1500ml

WWW.QOO10.SG

For our international readers, Nalgene is also available on Amazon:

## National Geographic Kids Review

National Geographic Kids is a nice magazine that kids will love. Kids have a natural interest in animals/birds/dinosaurs, and this will inspire them to start reading, and learn about animals at the same time. Animals are a key topic in Science and will be tested in PSLE eventually. PSLE requires students to know the difference between mammals, birds and reptiles, and also certain insects.

Note that the National Geographic Kids is for around age six. Many Singapore students are more advanced in reading, and in fact they can move on to the adults’ National Geographic magazine if they are interested.

Especially if your child is gifted or in the GEP, at age 9 they should be poised to read the adult version of National Geographic to learn more advanced vocabulary and scientific concepts. (For gifted students, the kids version of the magazine may be too simple.)

For students interested in Geography, the National Geographic Atlas of the World, Tenth Edition is an excellent book to learn all about the Earth. A piece of trivia is that the chess world champion Magnus Carlsen could memorize the entire atlas when he was just a little kid. “Magnus was able to recall the areas, population numbers, flags and capitals of all the countries in the world by the age of five. Later, Carlsen had memorised the areas, population numbers, coat-of-arms and administrative centres of “virtually all” Norwegian municipalities.”

## ‘I refused to meet my son’s JC teacher after the 1st meeting with her’

Excerpt: “I refused to meet my son’s JC teacher after the 1st meeting with her after 1st half of JC1. She focused the whole conversation on my son’s grades and that he will fail eventually. She was very superficial all the way and kept reminding me that it’s a prestigious school. I told her it’s just the 1st 6 months, too early to judge anything. My message to all parents, trust your kids and give them moral support and space. They have enough from these so called teachers who just worry about the school reputation and not the kid’s potential.”

## Preschool Math Tuition Books and Toys

There seems to be an increasing demand for kindergarten Maths tuition for children of ages 2-6. (I have received many such requests lately.) Many parents are worried that their child may lose at the “starting line” which is Primary 1, hence are preparing beforehand during the ages of 2-6.

Possibly, at this age the best way to learn is through play, that is why Math Toys are very useful.

Skoolzy Rainbow Counting Bears Toy is suitable for age 2, 3, 4, 5 or 6 year old preschoolers to learn to add, count, sort & stack.

Goodnight, Numbers is an award-winning bestselling bedtime story for kids, that help them familiarize with numbers.

The Pattern Blocks and Boards toy is useful for developing pattern recognition and visualization skills; all very useful skills when it comes to the GEP Logic Section at age 9. PSLE has some very tough visualization questions on nets of cubes, only children with strong visualization skills will be able to solve them. It is notoriously hard to train for such questions (though there are some tips and techniques), it is almost like either you see it or you don’t.

Times Tables would be the most challenging Math for children of the age group 3-6. Hence, early mastery of this subject will give your child a headstart to learn other more advanced math.

This 4-in-1 book bundle enables your child to learn about the alphabet, shapes, colors, math, as well as animals.

This LEGO (Duplo) set teaches numbers, basic math skills, and includes fun activity cards. Very educational and fun toy.

## iPhone XR Price Reduction (Singapore)

Apple (US) has already started some form of price reduction for the iPhone XR, though only for trade-ins of iPhone 7 Plus. One can guess that their sales must be not as good as expected.

Though iPhone XR is indeed a good phone, the pricing of over S$1200 is absurd and unaffordable to the middle class. Note that the iPhone XR is supposed to be the cheapest model in the latest X-series. Even loyal fans of Apple are more likely to stick to older iPhone models like iPhone 7/8 than to upgrade. Other brands like Huawei and Samsung have much more affordable phones that are also decently good. Basically, it is not sustainable for Apple to keep increasing the price significantly for every new model. Otherwise, the iPhone 20 will cost like S$3000? A corollary to Moore’s Law is that electronic devices are supposed to get better (but cheaper) as time passes. One of the first Apple Macintosh cost US$2495 in 1984, which is around US$5694 when adjusted for inflation.

When will iPhone XR start price reduction in Singapore?

This case will be good for protecting your iPhone XR if you get it after the price reduction:

Spigen Tough Armor Designed for Apple iPhone XR Case (2018) – Black

## Christmas Present for Gifted Kids

This microscope set will be ideal for gifted children who are interested in biology, or science in general. Learning about the microscope is the first step towards the study of life sciences/medicine/biological sciences.

This set is made and endorsed by National Geographic, a popular science magazine in the US.

## Singapore Families with Many Children

In Singapore, having 5 kids is so rare that even the newspaper reports it!

Another related video is about raising 7 kids in modern Singapore:

This YouTube video is only a short excerpt, for those who want to watch the full series, it is available on Toggle, under the title of “Full House”.

Source 1: Starting a family of 7 in Singapore at the age of 21 (Family of 7 in this case means 5 kids and 2 adults apparently, not 7 kids.)

(These are two separate stories, the first is about a family with 5 kids, the second is with 7 children.)

It seems that the biggest worry for most families (be it big or small) is still their children’s education.

Quote:

Her husband’s absence or his relationship with their children, however, is not her biggest concern. “My greatest worry is Bryan. His PSLE,” she declared.

Her Primary 6 son seems to be more interested in playing – or fighting – with his siblings than in his coming examinations.

Said his mother: “He doesn’t really bother about his studies, but I can’t push him … because the more you push him, the more he doesn’t want (to listen).”

Growing up dyslexic and recently diagnosed with hearing difficulties, Bryan has been struggling in school. And in a family of seven, it has been hard to devote attention and resources to just one child.

We did try giving them tuition. It did help, but it’s quite costly, so we cut down,” Mrs Lim said. “Nick and I are still … working out with teachers – taking (their) advice – how to handle him.

“But he’s a very stubborn boy, and he keeps everything to himself, so it’s kind of hard to get him to open up.”

His parents only want him to pass his subjects, but in his recent report card, he passed only his English out of three subjects.

“I did try, but … I always end up with only a few more marks (needed) to pass,” said the 12-year-old, who had to then promise his parents that he would do better or else they would take away his phone.

## The Most Accomplished 10-Year-Old (Gifted pupil)

Pan Annan is probably the most accomplished 10 Year-old student in Singapore, or perhaps even in the world.

Her list of accomplishments:

• International rhythmic gymnastics champion
• Youngest member of the Singapore National Youth Chinese Orchestra (SNYCO), where she plays the Pipa
• Raffles Girls’ Primary pupil

Any one of the above accomplishments is enough to stand out among 10 year-olds, and she has all of them! The most amazing is how she manages her time. I am familiar with Chinese Orchestra trainings, that alone is enough to account for quite a significant amount of time after school, since there is group practicing, sectional practicing, not to mention practicing alone. Possibly Chinese Orchestra alone adds up to a minimum of 5-10 hours per week.

Also, the workload from RGPS GEP is very demanding. Her schedule and timetable can only be achieved with 100% efficiency and focus. (She even does her homework in the car to maximize efficiency and save time.)

Parents may want to read my previous blog post on Book by Truly Gifted Kid (GEP Book), where a similarly prodigious child genius Moshe Kai Cavalin outlines his secret, with input from his mom on parenting. Also, as you can see, the standard for GEP students nowadays is very high, you may read Recommended Books for GEP Selection Test and How to Get Into GEP for some tips on how to do some foundational preparation for the GEP.

Sincerely all the best to Pan Annan for achieving her dreams of being a gymnastic champion.

Read more at: Channel News Asia

## Second Order Linear D.E. Summary

Homogenous D.E.
$y''+ay'+by=0$.

Solve the Characteristic Equation: $\lambda^2+a\lambda+b=0$.
Case 1) Two real roots $\lambda_1,\lambda_2$: $\implies \boxed{y=c_1e^{\lambda_1x}+c_2e^{\lambda_2x}}$

Case 2) Real double root $\lambda$: $\implies \boxed{y=c_1e^{\lambda x}+c_2xe^{\lambda x}}$

Case 3) Complex Conjugate root $\lambda_1,\lambda_2=-\frac{a}{2}\pm iw$, where $w=\sqrt{b-\frac{a^2}{4}}$: $\implies \boxed{y=e^{-\frac{a}{2}x}(c_1\cos wx+c_2\sin wx)}$

Non-homogenous D.E.
General solution of non-homogenous D.E.: $\displaystyle y=y_h+y_p,$ where $y_h$ is the general solution of the homogenous equation, and $y_p$ is the particular solution (with no arbitrary constants).

Method of Undetermined Coefficients (Guess and try method)
$y''+p(x)y'+q(x)y=r(x)$.

Only works if $r(x)$ is polynomial, exponential, sine or cosine (or sum/product of these).

Polynomial: Try $y$=Polynomial (e.g. $y=Ax^2+Bx+C$ or $y=Bx+C$.)

Exponential ($e^{kx}$): Try $y=ue^{kx}$, where $u$ is a function of $x$.

Trigonometric ($\sin kx$ or $\cos kx$): Convert to complex differential equation by replacing $y$ with $z$, replace $\sin kx$/$\cos kx$ by $e^{ikx}$.

Try $z=ue^{ikx}$, where $u$ is a function of $x$. After solving for $z$, take real/imaginary part of $z$ for cosine/sine respectively.

Method of variation of parameters
$y''+p(x)y'+q(x)y=r(x)$.

[Step 1)] Solve the homogenous D.E. $y''+p(x)y'+q(x)y=0$.

Get solution of the form $y_h=c_1y_1+c_2y_2$.

[Step 2)]
Let $\displaystyle u=-\int\frac{y_2r}{W}\,dx$ and $\displaystyle v=\int\frac{y_1r}{W}\,dx$ where $W$ is the Wronskian $\displaystyle W=y_1y_2'-y_1'y_2.$

Particular solution: $y_p=uy_1+vy_2$.

General solution: $y=y_h+y_p$.

Forced Oscillations
Let $F_0$ be the amplitude of the driving (external) force. If $F_0=0$, by Newton’s Second Law, $m\ddot{x}=-kx$, hence $\displaystyle \boxed{\ddot{x}=-\omega^2 x},$
where $\omega=\sqrt{k/m}$. The value $\omega$ is called the natural frequency.

If $F_0\neq 0$, then $\displaystyle \boxed{m\ddot{x}+kx=F_0\cos\alpha t},$
where $\alpha$ is the driving (external) frequency.

At resonance (when $\alpha=\omega$), $\displaystyle \boxed{x=\frac{F_0t}{2m\omega}\sin(\omega t)}.$

## Singapore Math Free Resources for Homeschool

Singapore Math is a popular resource for homeschooling children in the United States and many countries. Due to its challenging questions and unique methodology, Singapore Math prepares children for real math at higher levels.

We have curated some of the best Singapore Math Free Resources on the net:

1. https://thegoodgoatmomma.com/2014/10/17/free-singapore-math-curriculum-resources/
Has a good list of free resources including Curriculum and Tutorials.
2. https://singaporemathsource.com/resources/singapore-math-web-sites/
Some free online content to supplement Singapore Math.
3. https://www.freeeducationalresources.com/singaporemath/Singapore_Math.htm
This is an excellent treasure trove of free Singapore Math Worksheets (PDF).
4. https://www.onlinemathlearning.com/singapore-math.html
Many questions with worked solutions with Singapore Math Model method.
5. http://www.sgtestpaper.com/sgmath/
Includes questions modeled from real Singapore schools’ questions.

Do also read our most popular Singapore Math page to find out what is Singapore Math and what are its benefits.

## More schools to merge in 2019, JCs included

Seems like the declining population is quite serious indeed. Not too long ago there was another merger: 8 JCs to merge (i.e. 4 JCs to close down). “Merge” is just a nice way to say that the affected schools are closing down.

I think at this rate, quite a few jobs may be affected, like paediatrician (children’s doctor), childcare, and even tuition. I think a previous Today article mentioned the impact of declining population on the tuition industry.

The following Primary/Secondary schools will be merged in 2019:

Bendemeer Primary – from merger of Balestier Hill Primary and Bendemeer Primary

Casuarina Primary – from merger of Loyang Primary and Casuarina Primary

Cedar Primary – from merger of MacPherson Primary and Cedar Primary

White Sands Primary – from merger of Coral Primary and White Sands Primary

Damai Primary – from merger of East Coast Primary and Damai Primary

Jing Shan Primary – from merger of Da Qiao Primary and Jing Shan Primary

Junyuan Primary – from merger of East View Primary and Junyuan Primary

The merged secondary schools will be:

East Spring Secondary – from merger of East View Secondary and East Spring Secondary

Jurongville Secondary – from merger of Hong Kah Secondary and Jurongville Secondary

Yuhua Secondary – from merger of Shuqun Secondary and Yuhua Secondary

The merged schools will be located at the schools whose name has been chosen for the combined entities. For example, students from Loyang Primary will thus have to go to the existing Casuarina Primary School from 2019.

## Highly Motivational Math Video (in Chinese)

This is actually one of the best motivational videos on Math I have seen. Unfortunately there is no English translation. It covers how useful Math is, and also some history of Math in ancient China. (It is rarely known, but China discovered negative numbers and calculated pi to high accuracy much earlier than in Western civilization.)

However, (according to the video), Math in ancient China went downhill in the Ming dynasty after it was scrapped from the imperial examination. Seems like removing Math from the examination syllabus is always a bad idea!

Finally, the video ends off with a note not to discourage budding mathematicians. Many budding mathematicians, will face strange looks from well-intentioned friends and society. Will learning math be useful or can it make money? Such thoughts can discourage people from learning mathematics (like the speaker himself).

By the way, at the start of the video, the speaker tells a humorous story of how he used Math to propose to his crush in England. This is related to my earlier post on Valentine’s Day Math on how to draw a heart using math.

## Uni Grads: Choosing the hawker life over the tried and tested route

Very nice to see their passion in cooking, and daring to choose the road less travelled. Do support them at their stall, Prawn Village, which currently at 20 Ghim Moh Road, #01-62, 199583.

SINGAPORE: They had not yet graduated from university, but like many of their peers, Joanne Heng and Chan Kheng Yee were already out and about looking for a full-time job. A posting on online portal Gumtree caught their attention, and they responded to the call for “interns” the very next day.

Like any job application, the two friends had to go through a job interview filled with questions about their sincerity, motivation and commitment to the position.

But this job required very different skill sets from your typical office job: Anson Loo, the person who made the post on Gumtree, was looking for young interns to help him run his hawker stall.

“I realised that there are young people who want to become hawkers, but face a lot of financial constraints,” said Anson, who sells prawn mee at Ghim Moh food centre. “So I thought, why not target young people with no experience, so I can give them the training from scratch?”

YOUNG AND INEXPERIENCED, BUT PASSIONATE

Of the seven who applied, Anson said Joanne and Kheng Yee fit his requirements the best. They were young, passionate and completely new to the hawker trade. And indeed, the two, who met while they were studying in the polytechnic, recalled bonding over a shared interest in F&B even as students.

## PSLE 181 to NUS Medicine (Miracle Story)

Quite an amazing story. The road from PSLE 181 to NUS Medicine is a long and arduous journey. Read how Mr Tan Jun Xiang, 22, managed to overcome the odds to enter the prestigious NUS Medicine faculty.

NUS Medicine is very hard to get in (even perfect scorers can get rejected). His overjoyed father “booked two tables at a restaurant and invited (his) relatives to celebrate.”

SINGAPORE – Mr Tan Jun Xiang, 22, is not your typical medical student who aced all his school examinations.

In fact, he scored only 181 points in the Primary School Leaving Examination (PSLE) and had to go into the longer five-year Normal stream in secondary school.

The polytechnic graduate, who made it to the prestigious medicine faculty at the National University of Singapore (NUS), is among the rare few who do not fit the mold.

When he was younger, he never thought he would go to university – much less the highly competitive Yong Loo Lin School of Medicine at NUS, where only about one in seven applicants get in.

So what sparked his stunning academic turnaround?

A few things: seeing how disappointed his parents were with his results, getting into the secondary school of his choice after an appeal and discovering that he could indeed do well if he put his mind to it.

## Math Books for Christmas

Wishing all readers a joyous Christmas ahead! Here are some ideas for a mathematical Christmas gift for your loved ones who are math lovers:

1)

This Christmas-themed Math book is the perfect gift for your child. According to Amazon, it is rated 4.5/5, and one reviewer even remarked that his 7 year old daughter loved reading it:

“I don’t write reviews normally but I was sitting in bed reading it when my 7 year old daughter snuggled up next to me to read it too – she would not let me turn the pages till she finished which was cute even though I had to wait.” (Amazon)

2)

This book is rated very highly on Amazon; it is one of the best sellers in the Math category. It is ideal for homeschoolers, and for Singaporean primary school students who want to learn in advance, during the school holidays. (American Middle School syllabus should be accessible to upper primary Singaporean students) It is written in a very interesting manner as well.

3)

This book is extremely popular in the United States. It is a #1 New York Times bestseller, as well as based on true history. “The phenomenal true story of the black female mathematicians at NASA whose calculations helped fuel some of America’s greatest achievements in space. Soon to be a major motion picture starring Taraji P. Henson, Octavia Spencer, Janelle Monae, Kirsten Dunst, and Kevin Costner.”

## Tessellations of Pentagons

Tessellation is a cool topic in primary level to PSLE math. Most students will enjoy it even if they hate other types of Math. It is a natural human instinct to be amazed at how different shapes can fit together perfectly to tile the plane.

Apparently, tessellation is going to be removed from the entire PSLE syllabus soon (see http://schoolplus.com.sg/primary-math-syllabus-2017/). That is certainly quite sad for many reasons.

Triangles and quadrilaterals (even irregularly shaped ones) can be easily tessellated. However for pentagons, it is less clear and some pentagons (including the regular pentagon) cannot be tessellated!

## 50 Life Lessons from an 80 Year Old

Quite interesting list. Wonder who is the 80 year old?

We absolutely love these pieces of advice from an 80 year old man.

1. Have a firm handshake.
2. Look people in the eye.
3. Sing in the shower.
4. Own a great stereo system.
5. If in a fight, hit first and hit hard.
6. Keep secrets.
7. Never give up on anybody. Miracles happen everyday.
8. Always accept an outstretched hand.
9. Be brave. Even if you’re not, pretend to be. No one can tell the difference.
10. Whistle.
11. Avoid sarcastic remarks.
12. Choose your life’s mate carefully. From this one decision will come 90 per cent of all your happiness or misery.
13. Make it a habit to do nice things for people who will never find out.
14. Lend only those books you never care to see again.
15. Never deprive someone of hope; it might be all that they have.
16. When playing games with children, let them win.
17. Give people a second chance, but not a third.
18. Be romantic.
19. Become the most positive and enthusiastic person you know.
20. Loosen up. Relax. Except for rare life-and-death matters, nothing is as important as it first seems.
21. Don’t allow the phone to interrupt important moments. It’s there for our convenience, not the caller’s.
22. Be a good loser..
23. Be a good winner.
24. Think twice before burdening a friend with a secret.
25. When someone hugs you, let them be the first to let go.
26. Be modest. A lot was accomplished before you were born.
27. Keep it simple.
28. Beware of the person who has nothing to lose.
29. Don’t burn bridges. You’ll be surprised how many times you have to cross the same river.
31. Be bold and courageous. When you look back on life, you’ll regret the things you didn’t do more than the ones you did.
32. Never waste an opportunity to tell someone you love them.
33. Remember no one makes it alone. Have a grateful heart and be quick to acknowledge those who helped you.
34. Take charge of your attitude. Don’t let someone else choose it for you.
35. Visit friends and relatives when they are in hospital; you need only stay a few minutes.
36. Begin each day with some of your favourite music.
37. Once in a while, take the scenic route.
38. Send a lot of Valentine cards. Sign them, ‘Someone who thinks you’re terrific.’