Life long sharing . . .

Archive for May 2013

Created the Kosa Kata document for Ling. Those are words from her textbook that she finds difficult to memorize the meaning. Ya, BM is getting tougher for them.

Sharing it here, and can reuse when Ying is Std 2 next year.


Another nice exercise from this book casco_vocab: an exercise about “Happy” 🙂




Another topic I like about in this book is Pascal’s Triangle. 

You can get so many things out of it.



The first diagonal is always ‘1’.

The second diagonal is a list of counting numbers.

The third diagonal has the triangular numbers (as explained above).

And the forth diagonal has the tetrahedral numbers.



If you add the number by rows (horizontal sum), you will get the power of two.

e.g. Adding the first row, which is only 1, is equal to 20

Adding the second row, 1 + 1 = 2, is equivalent to 21

Adding the second row, 1 + 2 + 1 = 4, is equivalent to 22

and so on, as depicted in the picture above.


And also, if you want to get the sum of the counting numbers, e.g. 1 + 2 + … + 10,  go to number ’10’ in the second diagonal, and move down one row to the right, (as highlighted in blue), you will get the sum, which is 55.

Cool isn’t it ?

Another nice one from the book 《假如数学消失了》 maths-disappear0001 is this magic trick Sam showed to his friends:




Take a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a loop. Then Sam instructed his friend to start drawing a line in the middle of the strip non-stop.

Now, his friend commented, ” Strange, I didn’t remove my pen from the strip. I was drawing continuously inside the stripe, but didn’t know starting when, I started to draw outside the stripe !  And I continued, I drew on the inside again .. And at the end, I drew both the outside and inside of the stripe/ring. Unbelievable!”

This is the Mobius Strip or Mobius Band discovered by the German mathematicians.

And if you take a pair of scissors and start cutting according to the line drawn, guess what, at the end, you will get ….. ONE BIG LONG LOOP.  Ya, not two small loop.

I did this with my girls this holiday. They have fun 🙂


This is an interesting book I found in 商务书局:《假如数学消失了》, a translation from a Canadian book: “The Great Number Rumble: A Story of Math in Surprising Places”. A book recommended and read by Chinese teenagers (I even saw comments from children in upper primary).


The story started when the Mayor of the town Jeremy stayed announced the abolish of Math class in all schools. “When the schools in Jeremy’s town ban math, there are loud cheers from the kids. Even his teachers happily toss their textbooks. But Jeremy’s best friend Sam, a self-proclaimed mathnik, sets out to prove that math is not only important, but fun.

Through this character ‘Sam’, the author explained the importance and the amazing side of Math in our life. Actually I was quite ‘surprised’ as there are quite a number of Math concepts or theories mentioned in the book that I also didn’t know or learn last time.

For e.g. the 黃金比例 (Golden ratio) :

The Greek letter phi (\varphi) represents the golden ratio. Its value is:

\varphi = \frac{1+\sqrt{5}}{2} = 1.61803\,39887\ldots.

Many 20th century artists and architects have proportioned their works to approximate the golden ratio—especially in the form of thegolden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing

In the book, Sam was trying to show the Golden ratio exists even in the nature world, using a spiral shell.


And in between each chapters, the author slipped in some history and stories about those famous ancient mathematicians, like this one from the famous Greek mathematician Archimedes 阿基米德:


According toVitruvius, a votive crown for a temple had been made for King Hiero II, who had supplied the pure gold to be used, and Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density. While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying “Eureka!” (Greek: “εὕρηκα!,” meaning “I have found it!”).

A week ago, while taking her lunch, Ling stopped and said, “Mummy, I don’t think I am beautiful, especially after I wear specs.” … I forgot what was my reaction then.

Today in the car, while driving, I told Ying that someone said her drawing was beautiful, and she replied, “My drawing might be beautiful, but I am not beautiful.”

Oh dear oh dear, this is not something I expect it to come so fast. And vanity is one thing I don’t want you two to pick up at all. Was a bit stunt and don’t know how to react. But I knew I could not just keep quiet this time.

“Do you think Mummy is beautiful ?” thinking that they might say no.

“Yes” both of them replied. What a silly question.

“Even with all this pimple and holes on my face ?”

“Yes,” Ying said.

“Then, do you think 阿麻 is beautiful ? ”

“Eh … yes, ” a hesitate yes this time from the girls.

“How about 爷爷 ? Is he beautiful ? ”

The girls started giggling and trying to correct me that I should use handsome.

“You know what I am trying to ask. So, with all the wrinkles on his face, do you think 爷爷 is beautiful ?”

“Not really .. ” Ying answered.

“Then, 爷爷 has to be always upset and dig a hole to hide since he is not beautiful, ”

The girls laughed out loud.

“You have a kind heart, you are a good person, you do good things, you should feel good about yourself, even when you are old, you are still beautiful. Just like how you see 阿麻, 爷爷 and me. Beauty is not just how you look from the outside. ”

Ai ya, I also don’t know what I was talking about… so ‘deep’, don’t know how to teach them.


Dedicating one of Mummy’s favorite song to you,  by James Blunt, assuming he is singing to you two, my angels

“You’re beautiful, You’re beautiful,  You’re beautiful, It’s true…”

One day last week, Ying finished her homework quite fast, and straight she took out a piece of recycle paper and start drawing and colouring. Normally she would have chit-chat a lot with her sister, but not that afternoon.

That night, when she was tidying her school bag, she came to me with the piece of recycle paper, and a cheerful smile on her face.

“Teacher said there is a drawing and colouring competition, organized by Colgate, ” she handed me the piece of A4 paper.

“Teacher said must draw a face with a wide smile showing the teeth, ” she explained to me pointing to her drawing.

“And must write ‘Senyuman Ceria Saya’ on it,” she ended.


Ai ya,.. I should have paid more attention and found out what she was doing then, I could have corrected her and asked her to draw on a proper drawing paper. But now it’s kind of late, almost their bed time. Didn’t think she had enough time to redo everything. But still I tried to ask her if she wanted to do it. If yes, I would let her stay a bit late, later than usual.

“Dear, I think you might need to draw on a proper drawing paper. Do you want to do that ?” I tried to ask nicely, not to hurt her feeling.

“Hmm…. I think let me ask my teacher tomorrow.” She answered, still very optimistic.

The next day, she told me teacher said cannot, must use an A3 drawing paper. I asked her if she wanted to redo. She said it’s ok, she would just keep her drawing. She didn’t sound upset at least.


Mummy is keeping your drawing here. And Mummy is very proud of you for being environmental friendly.

You won my


May 2013

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