Discursive / Argumentative Model Essay #3

“Money can’t buy happiness.” What are your views?

Can you imagine living without money in this day and age? Is it even possible to survive without money in today’s materialistic and cash-driven world? It has been said that money makes the world go round. Hence, it is no wonder that money has become the central focus of many people’s lives. Everyone seems to be working tirelessly for money. Even students are studying hard so that they can get a well-paid job and earn lots of money in future. Although I think money cannot buy happiness, it is something that we cannot live without.

It is clear that money cannot buy happiness as many people who work hard and long every day for money are often very unhappy. Most of them do not even have time to spend their hard-earned money due to heavy workload or long working hours. They have no time or energy for leisure activities and needless to say, their family and friends hardly get to see them too. This can make them feel lonely and depressed. Thus, working hard for money does not bring happiness but instead misery in this case.

Worse still, money is often the main culprit that ruins relationships. People frequently fight over money and this can become a very serious problem, whether it is between friends or family members. For instance, it is not uncommon to hear of family members fighting over inheritance or longtime business partners squabbling over money-related matters. In some cases, ugly lawsuits ensue and relationships are destroyed forever. What then is the point of having lots of money when there is no one to share it with?

However, from a different perspective, money can sometimes make one happy. For some, earning enough money to pay their monthly bills and put food on the table makes them happy. For others, it could be saving up enough money to buy things of their interests or go on a dream vacation. Having some savings instead of living pay cheque to pay cheque also gives one peace of mind. After all, a person cannot possibly be happy if he or she is constantly worrying about running into financial difficulties. Hence, money does buy happiness where one’s survival is concerned or when he wishes to satisfy his wants.

Mark Twain once said, “The lack of money is the root of all evil.” I agree with him as no one can survive without money in this day and age. Like it or not, money matters and one’s financial situation has a direct bearing on his happiness. That said, money does not guarantee contentment. Money often rears its ugly head and ruins relationships. One also has to make sacrifices such as lack of family time in the pursuit of wealth and material comforts. Therefore, to be happy, I think one must realise that there is more to happiness than money.

Secondary 3, 2017, English Tuition

The Family of Real Numbers – Integers

Enjoy this excerpt from Tutor Leon’s Secondary 1 Math tuition class. 😊

Tutor Leon: Can anyone tell me what real numbers are? Or… what type of numbers are considered real? Or… if you can’t explain it in words, you can give me examples of what real numbers are.

Student Ethan: I know, I know… they are not fake numbers! [Class giggles]

Tutor Leon: Haha… very funny, Ethan. But… it’s actually kinda true! “Fake numbers” do exist! [Bewildered look on everyone’s faces 😮  ]

Student Ethan: Huh!?!? Sure or not, Cher?

Tutor Leon: Well… put it this way – numbers that are NOT real do exist. However, we don’t call them fake numbers. They are called imaginary numbers. For now, you do NOT need to concern yourself with imaginary numbers as they are beyond your O-level syllabus. [Sigh of relief from the class] For secondary level mathematics, numbers that you deal with are ALL real. For now, just know that besides real numbers, imaginary numbers also exists. Ok?

The Entire Class: Ok!!

Tutor Leon: So… back to my original question, what are real numbers? [Class ponders… 🤔  ]

Tutor Leon: How about this. You can think of real numbers as a family of numbers, just like how your immediate and extended families are made up of various members like your father, mother, brothers, sisters, uncles, aunties, cousins, etc. So what are the different types of numbers that belong to the real number family? Megan, what do you think?

Student Megan: Err… 1, 2, 3, 4, 5 … and so on?

Tutor Leon: Hmm… that’s not a bad start. Yes, real numbers include the numbers 1, 2, 3, 4, 5 and so on. Can you tell me what is the largest number you can think of?

Student Riley: Gazillion!! Just kidding… hahaha… err… I think it’s called infinity? 😬

Tutor Leon: That’s a decent answer, Riley! You’re kinda right. There are an infinite number of real numbers. However, infinity is NOT an actual number, but rather the idea that something is endless. Meaning that real numbers go on and on forever and ever. Does that make sense? [Class nods in unison] Ok, so the next question is… does anyone know what the numbers 1, 2, 3, 4, 5 and so on are called?

Student Riley: Cher, you mean numbers have names?

Tutor Leon: Sort of… just like how in science, in order to make sense of things around us, we categorise or classify different types of animals, plant life, etc. So the same applies to numbers, especially since there are an infinite number of them. To help us understand numbers better. Wouldn’t it make sense to categorise the different types of numbers?

Student Riley: Guess so… err… so what are the numbers called?

Tutor Leon: Good question! 😉  Numbers starting from 1 then 2, 3, 4, 5 and so on are called natural numbers.

Student Megan: Natural numbers? Why natural?

Tutor Leon: Another good question! Do you remember the time when you were much younger, as a toddler, when you were learning your ABC’s and of course learning how to count? [Class nods] Didn’t we all start counting from 1, 2, 3, 4, 5 … [Class nods again] Exactly! It’s simply the most natural way for most of us to count numbers… hence natural numbers. Sometimes natural numbers are also known as counting numbers.

The Entire Class: Oorrrhh…

Tutor Leon: So imagine that the real number family started with natural numbers but was still not a complete family yet. More numbers were added to the real number family. Any idea what comes before 1?

The Entire Class: Zero!!

For more insights on the origins of the number 0, please read “History of Zero“.

Tutor Leon: Spot on! Yes, then the number 0 joined the family. However, since zero is NOT natural, we had to think of another category to call numbers from 0, 1, 2, 3, 4, 5 and so on. Can anyone tell me what these numbers are called?

Student Ethan: Artificial numbers!! Hahaha… [Class giggles]

Tutor Leon: That’s a little corny, Ethan. Come on, seriously, what are these numbers called?

Student Ethan: 😝

Student Megan: Whole numbers!

Tutor Leon: Bingo!!

Student Ethan: Wah… steady lah… 👍

Student Megan: 😏  Just guessing.

Tutor Leon: If it was a guess, it was an intelligent guess. Well done, Megan. With the number 0, the number family was finally made whole. In other words, numbers starting from 0, 1, 2, 3, 4, 5 and so on are called whole numbers. Is that it? Are there no other numbers in the real number family? Or perhaps are there other numbers smaller than zero? Hint… hint. 😉

Student Ethan: I know… I know… really… really… it’s negative numbers! Negative 1, negative 2, negative 3 and so on.

For more information on the origins of negative numbers, please read “History of Negative Numbers“.

Tutor Leon: Very good! That’s absolutely right! So… the question is: Are negative numbers natural?

The Entire Class: NO!!

Tutor Leon: Are negative numbers whole numbers?

Student Riley: Hell no!

Tutor Leon: So… what are numbers …-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 … and so on categorised as?

Student Megan: I can’t quite remember… but I think it’s “inter” something.

Tutor Leon: You are very close. Anyone else wants to try?

Student Riley: In… ter… jar??

Tutor Leon: Good try… almost there! They are called… integers. I-n-t-e-g-e-r-s. In-te-gers.

Student Megan: Yah… yes… yes… integers!!

Tutor Leon: So now that we know a negative whole number is an integer. Is a positive whole number an integer?

The Entire Class: Yes!!

Tutor Leon: That’s right! Numbers 1, 2, 3, 4, 5 and so on are ALL integers. How about zero? Is the number 0 an integer?

Student Ethan: Yes. Confirm! Zero is an integer.

Student Megan: I disagree! Zero is errr… errr… hmmm… actually I’m not sure. I don’t think zero is negative, or is it considered positive?

Tutor Leon: Awesome! I’m glad you guys are giving it more thought. Zero… is… an… integer! Yes, some do get confused as integers are often related to negative and positive numbers. How you can think about zero is that it is a special integer that is neither positive nor negative. Does that make a little more sense to you?

The Entire Class: Yesss!

Tutor Leon: Ok, great! Let’s summarise…

Tutor Leon then summarises with the diagram below and continues with a more in-depth Q&A session on real numbers with the math class.

To be continued…

Stay tuned for future blog posts on other real number family members, such as non-integers (i.e. fractions and decimals), rational/irrational numbers and last but not least, prime numbers.

Sponge ME, Maths Tuition (Singapore)

English Vocabulary – Top 5 Bizarre Terms by Students

1  Oftenly (instead of ‘often’)

  • Student’s sentence: People who smoke oftenly are more prone to lung cancer.
  • Get it right: People who smoke often are more prone to lung cancer. (‘Often’ and ‘frequently’ are synonyms, BUT unlike ‘frequently’, ‘often’ DOES NOT end with ‘ly’.)

2  Oning (instead of ‘switching on’ or ‘turning on’)

  • Student’s sentence: I was oning the TV when the phone rang. 
  • Get it right: I was switching on the TV when the phone rang. (‘On’ is NOT a verb! Use phrasal verbs like ‘switch on’ or ‘turn on’.)

3  Betterer (instead of ‘better’)

  • Student’s sentence: She is betterer at science than her sister.
  • Get it right: She is better at science than her sister. (There’s no such word as ‘betterer’. The correct comparative adjective is ‘better’.)

4  More worse (instead of ‘worse’)

  • Student’s sentence: My results are more worse this time.
  • Get it right: My results are worse this time. (‘Worse’ is a comparative adjective, so there’s NO NEED for ‘more’.)

5  Agreeded (instead of ‘agreed’)

  • Student’s sentence: Everyone agreeded that it was a good plan.
  • Get it right: Everyone agreed that it was a good plan. (‘Agreed’ is the past tense of ‘agree’. There’s no such word as ‘agreeded’.)

🤣  🤣  🤣  🤣  🤣

Sponge ME, English Tuition (Singapore)

Personal Recount Model Essay #3

Write about a time you did not take the advice someone had given you and you regretted it.

Our school’s photography club was headed towards Lower Pierce Reservoir for a field trip. Upon arrival, our CCA teacher-in-charge, Madam Toh announced, “You have two hours. Meet here at four-thirty!” I hurried off with my best friend, Albus. Our mission that day was simple. We were having a competition and the best picture with the most apt caption would win a prize. I was determined to win the “Best Photographer Award”. The flora and fauna at Lower Pierce Reservoir was stunning. Birds were twittering away gaily on the trees, bees were humming and dancing in the flower beds and the leaves on the tree branches were swaying gently in the breeze. I closed my eyes and felt the breeze caressing my face.

“Harry, let’s take a picture of that tree!” Albus suggested, pointing at an umbrella-shaped tree which was nearby. Just then, I saw a troop of playful monkeys near some shrubs. Having rarely seen monkeys, I was naturally excited. I found them so adorable and charming. A few smaller-sized monkeys were intimidated by Albus’ and my presence and scurried away. However, there was one bold monkey which was unperturbed by humans and shot us a curious look. The monkeys all looked scrawny and hungry. I saw a couple of them rummaging through the dustbin. My heart wrung with sympathy for them. Remembering that I had some leftover sandwiches from recess, I zipped open my bag and fished out my lunch box.

Albus seemed to have read my mind. “Harry, you are not going to feed the monkeys, are you?” That sign clearly states not to feed the monkeys!” Albus reminded me, his eyebrows creasing into a frown. I brushed off his concern and edged closer to the monkeys. “Harry, steer clear of those monkeys! They might become aggressive!” Albus advised. Once again, I shrugged off my friend’s warnings. Anyway, what could a mere small monkey do to me?

With a piece of bread in my hand, I edged closer towards one of the monkeys which was nearest to me. The monkey seemed to have noticed me and when it spotted the piece of bread, it started scuttling towards me. Albus looked worried and warned me again. “Harry, no!” I looked back at Albus nonchalantly. I was sure I knew what I was doing. The puny creature could not possibly do any harm to me. The monkey looked more curious and friendly than belligerent. Its piercing green eyes were fixed on the food which it was about to get.

I stretched out my hand and offered the piece of bread to the monkey, which wore a look of happiness. It swiftly snatched the bread over, which disappeared down its throat in two seconds flat. Then it stared at me, as if thanking me for the delectable treat. Victorious looks spread across my face as I whipped around and looked triumphantly at Albus. “See, Albus. It’s harmless. It’s all right to feed the monkeys!” I exclaimed proudly. Albus just sighed. My best friend still looked concerned. From my school bag, I pulled out a packet of potato chips, which was my snack.

Suddenly, I heard some monkeys chattering behind me. I turned around and almost jumped out of my skin. Dozen pairs of green eyes were staring at me. More monkeys had emerged from the shrubs and there were at least ten monkeys around us. Where did all these monkeys come from? I had no idea that my packet of potato chips was like a magnet to the ravenous monkeys. My heart started thumping frenetically, as if it was trying to ram its way out of my chest. The monkeys started screeching and all hell broke loose. Clearly, the monkeys’ target was my food. However, I was not going to give away my entire packet of chips. My mother only allowed me to indulge in junk food once a month, and my intention was to give a few chips to the monkeys and savour the rest myself. Oh-oh. How wrong was I! Within a few seconds, I was surrounded by a bunch of ravenous monkeys.

One bold monkey attempted to snatch the potato chips from my hand. I was not about to give up my favourite snack so easily. I tried to shoo the monkey away. Then unexpectedly, I let out a painful yelp. “Ouch!” The monkey’s sharp claws had dug into my flesh. I could feel an excruciating pain sear through my arm and I dropped my packet of chips. Instantly, the monkeys tore and ripped at the plastic wrapping. “Are you all right?” Albus asked me, a concerned look etched on his face.

“You were right Albus. I should have heeded your advice,” I mumbled softly, as regret gnawed at my insides. When we went back to the meeting point where Madam Toh was, she gave me a severe dressing down and our field trip ended abruptly. I was brought to the hospital for outpatient treatment. I was told by the doctor that if the scratches had gone deeper into my skin, I would require stitches. I was given an injection and two courses of antibiotics to complete. “You should have listened to Albus. He has always been more prudent than you!” Mother admonished me.

All these happened because I had not heeded my friend’s advice. If only I could turn back the clock. From that day onwards, I have always steered clear of monkeys. I had not expected the harmless-looking creatures to turn aggressive over food. Till today, horrors of that incident remain vivid in my memory. The “No Feeding The Monkeys” sign is there for a purpose and it was foolhardiness on my part to disregard it.

Secondary 1, 2016, English Tuition

English Vocabulary – Breakfast Talk

The subject of breakfast came up in class recently when the students were discussing the advantages and disadvantages of studying abroad.

Student A: Not everyone can adapt to the new environment. Everything is different from the weather to the food.

Student B: Ya lor, I don’t like to eat ‘ang-moh’ food, especially ‘ang-moh’ breakfast, so if I go ‘ang-moh’ country, sure die. 😝

Tutor Adeline: Interesting. Student B, what do you mean by ‘ang-moh’ breakfast?  (asking the obvious)

Student B: The bacon, ham and all that lah.

Tutor Adeline: And you don’t like them.

Student B: Yah, cos’ they are very unhealthy.

Tutor Adeline: I have to agree with you that a typical Western-style breakfast is a heart attack on a plate. *laughter* 🤣   Since we are on the subject of breakfast, does anyone know the difference between a continental breakfast and an English breakfast?

The entire class: *blank look* 😕

Tutor Adeline: Okay, here’s the difference:

Continental Breakfast

a light breakfast, usually consisting of tea or coffee, bread rolls, croissants and pastries

English Breakfast

a large or full breakfast, usually consisting of tea or coffee, bacon, ham, sausages, eggs and a variety of other cooked foods

Student B: What about American breakfast?

Tutor Adeline: Good question!

American Breakfast

a variant of English breakfast, often consisting of the same stuff; hash browns, pancakes and waffles are common in American breakfast

Student B: That’s why it is a heart attack on a plate! *laughter* 🤣

Tutor Adeline: Everything in moderation. It’s okay to indulge once in a while. I do love bacon and pancakes, so don’t curse me. Final question. What’s a power breakfast?

Student C: After eating will become very powerful? *seriously loud laughter* 🤣  🤣

Tutor Adeline: Very funny, Student C! 😏

Power Breakfast

a meeting that business people have early in the morning while they eat breakfast

Sponge ME, English Tuition (Singapore)

Geometry – Euclid, the Father of Geometry

Remember playing shape recognition games as a kid? These games often involve identifying and placing different shapes (circle, square, triangles, etc.) in the right slots. They help to develop our minds in determining different shapes, and are our first exposure to geometry! 

In broad terms, geometry is the branch of mathematics that deals with the measurements and relationships of lines, angles, surfaces and solids.

Euclid-of-AlexandriaGreek Mathematician, Euclid (fl. 300BC) is often referred to as the father of geometry. The standard geometry most of us learn in school today is also known as Euclidean Geometry.

Euclid put together all the knowledge of the earlier mathematicians and wrote Elements, a mathematical and geometric treatise consisting of 13 books. 

Known as one of the most successful and influential works in the history of mathematics, Elements served as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.

Sponge ME, Maths Tuition (Singapore)

Top 10 Commonly Misspelt English Words

1. a lot (NOT alot) — Two words just like ‘a bit’ and ‘a little’!

2. embarrass (NOT embarass) — Double ‘r‘ because when you are embarrassed, you go really red!

3. interest (NOT intrest) — We should spell interest with an ‘e‘ because when we are interested in something, we are full of enthusiasm.

4. restaurant (NOT restuarant) — ‘a before u‘ because the appetiser always comes first!

5. environment (NOT enviroment) — It is vital that we spell environment with an ‘n‘ just as it is vital that we conserve nature.

6. recommend (NOT recommand) — Think re + commend. The prefix re = ‘back’ or ‘again’. To commend = to praise someone or something. So think of recommend as commending again.

7. argument (NOT arguement) — Let’s just say that people often get into arguments because of the E word: ego. Therefore, drop the e‘ and stop arguing!

8. committee (NOT comittee, or commitee, or committe) — Think commit + tee. It will really tee the committee off if you do not commit yourself to spell this word correctly.

9. maintenance (NOT maintainance) — Always remember that the tenant is responsible for the maintenance of the rented apartment.

Finally, here’s the most commonly misspelt word in the world:

10. definitely (NOT definately) — I will give you a definite answer now. The word is definitely spelt with an ‘i‘!

Sponge ME, English Tuition (Singapore)

Fun with Maths – Why Seven is so Awesome

  1. Most people can generally hold around seven numbers in their working memory for a short period of time (Miller’s law), which explains why our telephone numbers are mostly seven digits (excluding the country and area codes).
  2. Several sleep studies have found that seven hours is the optimal amount of sleep, not eight!
  3. There are seven colours in the rainbow: red, orange, yellow, green, blue, indigo, and violet.
  4. The ‘Seven Seas’ (as in the idiom ‘sail the Seven Seas’) is an ancient phrase for all the world’s oceans: Arctic, North Atlantic, South Atlantic, Indian, North Pacific, South Pacific, and Southern (or Antarctic).
  5. There are seven continents in the world: Africa, Europe, Asia, North America, South America, Antarctica,and Australia.
  6. Seven is used 735 times in the bible (54 times in ‘Revelation’ alone)! If we include ‘sevenfold’ and ‘seventh’, the number jumps to 860!
  7. And of course, seven is a prime number. 😉

Happy Seven! 😀

Sponge ME, Maths Tuition (Singapore)

Happy Year of the Monkey from Sponge ME 2016

May the new year bring you everlasting happiness and success in whatever you do. Happy Chinese New Year! 🙂

Please note: We’ll be taking a break over the festive season from 8 Feb 2016 to 15 Feb 2016. Classes will resume from 16 Feb 2016 onwards. Thank you.

English Spelling – Dessert vs Desert

Dessert (double s)

Definition: sweet food eaten at the end of a meal

Example: I will have a cupcake for dessert. 

Desert (one s):

Definition: a large area of land that has very little water and very few plants growing on it

Example: The Sahara is the largest desert in the world. 

Sponge ME, English Tuition (Singapore)

What are Prime Numbers?

Meet the Numeric Celebrity – Prime Numbers

That’s right, primes are quite the celebrity and not just in Hollywood movies. 😉  Here’s an excerpt of primes being featured in the movie, “Contact” where scientists discover an alien signal composed of… yes you’ve guessed it, prime numbers!

As seen in the movie, the aliens chose to send a long string of prime numbers to prove that their message was intelligent and not of natural origin. So why use prime numbers? What so special about primes?

What are prime numbers?

Primes are the building blocks of all numbers. Think of prime numbers as atoms, just like in chemistry where we say that a water molecule is formed from two hydrogen atoms and one oxygen atom (notated as H2O). Likewise, the number 12 is the product of the prime factors 2×2×3 (notated as 22 3). So just like water can be decomposed into hydrogen and oxygen, all numbers can be decomposed into primes. Here are a few more examples:

  • 8 = 2×2×2 = 23
  • 20 = 2×2×5 =22 5
  • 180 = 2×2×3×3×5 = 22 32 5

This process of decomposing a number into its prime factors is called prime factorisation (a topic to be left for another time). Like atoms, prime numbers can’t be decomposed further or rather can’t be divided further, like 2, 3, 5, 7, etc. In other words, prime numbers are only divisible by 1 and itself, and a number that has more than 2 factors is known as a composite number. For example:

  • 2 = 1×2 (2 factors only) → Prime
  • 3 = 1×3 (2 factors only) → Prime
  • 4 = 1×4 or 2×2 (3 factors) → Composite
  • 5 = 1×5 (2 factors only) → Prime
  • 6 = 1×6 or 2×3 (4 factors) → Composite

At this point, you may be wondering – what about the number 1? Is it prime? Well, 1 is somewhat of a special case. If you think about it, 1 = 1×1×1×1×1… and this is where things get a little crazy. If you were to just consider the number of factors 1 has, it’s 1, which is also itself! So… is it prime? There is certainly a little more than meets the eye. 1 used to be prime, but it’s no longer prime. Haha… and the story of primes continue to unravel. To find out more, watch the short video below, where James Grime the Numberphile, concisely explains the Fundamental Theorem of Arithmetic (don’t worry, it’s just a fancy name – watch the video and all will become clear) and how it applies to 1 and prime numbers.

Cool right? Okay, so we now know that 1 is neither prime nor composite. It’s just the lonely one. Awww… poor 1. 😢

Well, is that all there is to prime numbers? Far from it! Here are a few more observations and interesting facts about prime numbers:

  • I’m sure you’ve noticed this. 2 is the only even number that is prime. The rest of the prime numbers are odd.
  • As numbers get larger, primes become less frequent and twin primes (see below) get even more rare.
  • In any case, we’ll never run out of prime numbers, as they are infinite. Any idea what’s the largest prime number ever discovered to date? Watch the final video below to find out.
  • Twin primes are pairs of primes that differ by two. The first twin primes are {3,5}, followed by {5,7}, {11, 13} and so on. It has been conjectured (meaning it’s never been proven) that there are infinitely many twin primes. This is known as the twin prime conjecture, a.k.a. Euclid’s twin prime conjecture.
  • Prime factorisation is hard work and when numbers get extremely large, you can imagine how tedious and slow it’ll be. ?
  • On top of this, primes do not have a pattern we can easily decipher, meaning there is no easy way to tell when the next prime number will appear. But that’s actually a blessing in disguise. Why? Read on to find out more.

Why are prime numbers so important?

Did you know that prime numbers are worth billions of dollars? 😲  Why are prime numbers so valuable to organisations, government agencies and companies like Apple, Google, eBay or Visa? Wondering how numbers can be worth even a single cent? Well, though prime numbers have little value in themselves, they are used in every credit/debit card transaction, including ATMs, online payments and even trading (e.g. stocks and shares) transactions totalling billions of dollars every day. In fact, prime numbers power the mathematics behind the cryptography (used for cyber security) of your WIFI connections, email accounts, blogs, Facebook, Twitter, etc.

To find out how primes combined with the difficulty of factoring large numbers are used to protect and secure our emails and payment transactions, please watch the short video below.

Aren’t prime numbers just fascinating? As Carl Sagan, author of the science fiction novel, “Contact” so eloquently pointed out – there is a certain importance to the status of prime numbers as the most fundamental building block of all numbers, which are in turn themselves the building blocks that help us understand our universe. 🤔  Regardless of how an advance alien life form may think or look like, one thing is for certain, if it understands the world around it, it most certainly understands the concept of primes.

Hope you found this article insightful and educational. Happy maths! 😁

Sponge ME, Maths Tuition (Singapore)

Oh… and if you are interested to find out what is the largest prime number ever discovered to date (Jan 2016), here is Matt Parker on the latest Mersenne Prime that holds the envious world record. Who knows? Maybe you might be the next record breaker for finding the “world’s largest prime”. Find out how it’s done and more in this video. Enjoy! 😉