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.

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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What Is 1 Centimetre?

Jotter Book

How do you like this page in my son’s jotter book?  It was a doodle produced during a continuous conversation about Length, a story I wrote about in Chapter 10 of Fun-filled Math Conversations With Your Child. You can see how much I enjoyed doodling and how much he disliked colouring. It was important that I taught him to translate the information floating inside his head into a readable and writable form on paper so that others can understand him.  This is called literacy.  Exams are paper-based after all.

The process went like this:

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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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