Bus Fare, Then and Now

The Rule of 72 is a formula used to estimate the number of times a number (X) has to be compounded at a certain percentage in order for the number (X) to double.  It is often used in the financial world to estimate inflation.  The easiest way to understand this is to look at a series of examples:

72  =  2  x  36 
Price doubles in 2 years if compounded at 36% annually.
Price doubles in 36 years if it’s compounded at 2% annually.

72  =  7.2 x 10 
Price doubles in 7.2 years if it’s compounded at 10% annually.
Price doubles in 10 years if it’s compounded at 7.2% annually.

72  =  12 x 6
Price doubles in 12 years if it’s compounded at 6% annually.
Price doubles in 6 years if it’s compounded at 12% annually.

Let’s apply this to a real life case:

This was my bus pass.  The monthly travel bus pass for tertiary students in 1990 cost $27.  30 years have passed and the same now costs $55.50.  The price has roughly doubled.  We can estimate the annual price increase (compounded) by applying the Rule of 72:

72  =  2.4  x  30

In financial lingo, we can say that bus fare has increased by 2.4% annually over the last 30 years.  Numbers don’t lie, but they are meaningless.  Only when context is attached to numbers will they begin to make sense and cause people to react.

Whether or not 2.4% inflation on bus fare is an acceptable figure, is not only a a discussion for the economic and political departments in academia, but also for you to have with your children.  If bus fare continues to inflate at 2.4% annually, what does it mean and how will it affect your lives?  What other factors do you need to consider to make the conversation more meaningful?  Income growth, interests rates, and what else?

Virtual or real money, online games or Grab, your children are confronted with money issues.  They are not too young to learn about money and how it works. Teach them to use the calculator and don’t let tedious computation get in the way of learning the important lessons.  The ability to make sense of numbers is different from the ability to compute numbers.


Little Ethan straightening out and reaching further with a friend’s help.

Friends sit on each other.  They stretch and straighten each other up.  They cause pain to each other, then massage each other to relieve the pain.  Friends laugh and play together.  They share fun and vulnerabilities.  They can trust each other because each is trustworthy.  As a result, both emerge stronger, more flexible and with the gumption to reach further because they know that someone is watching out for them.

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Fun-filled Music Conversations: My Son’s Ukulele

The ukulele I’m playing in this video belongs to my son.  I bought it for me, but I gave it to him as a birthday gift knowing that I’ld be the one enjoying it.  What sort of a horrid mum would buy her son a present that’s meant for herself?  Me! 🤣

But seriously, what better way to give your child the gift of music than to create an environment and culture for music appreciation to take place?  Here’s the truth: your child is a sponge, the younger he is, the more absorbent.  Whatever type of music you listen to, or sing, or play, or learn, and in whatever languages, your child will be absorbing them all, whether you like it or not!

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Our Usual Jam Session

Our Usual Jam Session

My friend Penny visited us one day and insisted on recording this part of our homeschool journey because she was amused by our routine. As it was usual for my son and me to do music together, we didn’t think it was anything special.  Anyway, little Ethan was sufficiently persuaded by Auntie Penny’s amusement to play for her camera.  I’m sharing this video with the other Auntie Pennys who might be curious about the stuff we did with so much time in our hands, and why we had so much fun.

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The Lunar Calendar

Counting time with 5 elements and 12 animals.

Fun facts about the lunar calendar and its naming conventions:

The Chinese built a 12-year cycle represented by twelve animals into a larger cycle of five elements:  metal, water, wood, fire, earth.  The animal changes every year, but the element changes every two years.  We are presently in the year of the Metal Rat – the first element paired with the first animal!  After this will come the year of the Metal Ox, followed by the Water Tiger, then the Water Rabbit, and so on.  The year of the Water Rat will arrive in 12 years.

12 animals x 5 elements = 60 years.

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The Real Life Challenge

Math in Real Life

 The Ministry Of Education writes in its Mathematics Syllabus for primary education, about their goal to raise students who understand math in real life.  It is a good objective, but I wonder how they expect their teachers to carry that out when a large part of real life takes place outside the classroom.  Multiply that problem across a class of 40 students, with each having his own unique “real life” experiences, and you will understand how difficult that task is. Is it possible for even the best math teacher to engage all her students in real life math within the limited periods of Math lessons?  What is math in “real life” in the first place?

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Facing My Dark Side

Facing My Dark Side
Facing My Dark Side

I named my first hamsters Bo Bo and Cha Cha, after my favourite dessert.  Cha Cha died at his 1 month old birthday party after being dropped from a height of 1.5 metres.  I grieved and cried for days over the loss of a loved pet. I was fifteen then.

Bo Bo lived on to have many babies with male hamsters that I borrowed from my friends.  The population in my little cage grew and I had lots of fun with that project.  Eventually, I grew lazy and got distracted with other interests, neglecting my little darlings despite constant reminders from my mom.

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Adapting To A New Body

Growing up, I recall one strange day when I crashed my head into a low hanging horizontal beam of the block of flat where I lived.  I’ve run below that beam a thousand times with no problem, until that day.  It wasn’t obvious to me that I had grown taller.

As a mom of 2 boisterious little boys, I used to grab them by the arms when they misbehaved.  They would struggle to free themselves of my hold, but I was strong enough to overpower them.  But one strange day, the same struggle with the elder son resulted in me being knocked over.  It wasn’t obvious to him that he had grown bigger and stronger. The same happened with my younger son.

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