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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Recognising Quantities

Recognising Quantities

I want five.  I wish I was five.  It is five.  It has five.  There are five.  We say these sentences so often that we overlook the fact that they are incomplete.  Are you gritting your teeth now and mumbling to yourself, “Five what, monkeys?”  Because of the missing noun, many jokes emerge from such statements.  The fact is this:  numbers are adjectives, and they describe a quantity.  When you are counting to five with your fingers, fingers is a noun that you add to the adjective five to provide context. This change of perspective can bring new life to your math discussions! 

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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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My Dancing Queen

The Dancing Queen
Mom and me

 Mom taught me to do the cha-cha when I was little.  Back then, it was socially awkward for people to dance alone, thus making me a very available and convenient dance partner for Mom because she loved to dance.  Pa had made enough money in his career to afford a turntable and several records which provided Mom and me with the privilege of having music on demand, meaning we could dance repeatedly and whenever we liked, to an instrumental stereophonic soundtrack of Cherry Pink And Apple Blossom White with the trumpet leading the way.  (Click Here to hear how it sounded like).

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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 World That Didn’t End

Wild flowers blooming. The earth is more resilient than we credit it for.

I remember March 10, 1982.  I was 14 years old, sitting in class and waiting to die.  A periodical I had read some days earlier informed me that the world was ending THAT day.  I didn’t want to go to school because facing termination with my family was much more comforting than facing termination alone, but I went to school anyway.  In class, my attention drifted between the teachers, who appeared clueless that the world was about to end, and the anticipation of a loud bang, a dimming sun or quaking floor.  No excitement happened, the end didn’t arrive.  I was a little disappointed that the day was boring as ever, but mostly relieved that every person who mattered to me was still alive!  I now know that the ending of the world on March 10, 1982 was prophecised in a book titled The Jupiter Effect.

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Adding Colour to Math

Isn’t math so much clearer with colours? And alluring too!  You can now show your 8-year-old why the sum of odd numbers starting from one equals the square of the the number of terms.

Adding 1 Term   → 1 = 12
Adding 2 Terms → 1 + 3 = 22
Adding 3 Terms → 1 + 3 + 5 = 32
Adding 4 Terms → 1 + 3 + 5 + 7 = 42
Adding 5 Terms → 1 + 3 + 5 + 7 + 9  = 5 (See Diagram)
Adding 6 Terms → 1 + 3 + 5 + 7 + 9 + 11 = 62

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