### Mathematical Monday ~ Fractions

J likes fiddling with my math manipulatives. He has discovered how to add fractions with my fraction discs and strips.

 1/4 + 1/2
 Change 1/2 = 2/4. Now 1/4 can be added to 2/4.

Recently, he asked me how 1/3 can be added to 1/4. "Thirds cannot be changed to fourths and fourths cannot be changed to thirds," he said. I told him to change both to something else. What about twelfths? I asked. He was soon able to tell me that 1/4 is equal to 3 twelfths and 1/3 is equal to 4 twelfths. We did not have our manipulatives with us then, but the pictures below illustrate what I have just discussed.

 1/3 + 1/4
 Change 1/3 to 4/12 and 1/4 to 3/12. Now 4/12 and 3/12 can be easily added.
I think J's earlier contact with the fraction resources has helped him to visualise fractions. I was too excited to stop teaching altogether and so I proceeded to discuss multiplication of fractions with him. What is 1/2 of 1/2? I asked. J ventured a few guesses, but was not able to get the answer. Undeterred, I drew the following picture. The purple part was drawn first.

Me: Can you see half here? (point to shaded purple part)
J: Ah ha.
Me: Now, what is half of this?
J: Oh! 1/4. I knew it!
Me: 1/2 of 1/2 is also the same as 1/2 x 1/2. You can also get 1/4 by multiplying 1 by 1 in the numerator and 2 by 2 in the denominator.

We tried 2 more examples and J got the correct answer. He was also able to draw pictures similar to what I have drawn above.

When I taught product of 2 fractions in school last time, I folded a piece of paper into 2 equal parts and shaded one part to represent 1/2. I further folded that 1/2 into 2 equal parts to show that 1/2 of 1/2 is 1/4. Some pupils did not understand how the folding was related to 1/2 x 1/2. Perhaps the pictorial representation is clearer.

I guess I am a geek, but Maths is exciting. :)

### Minsu in Yilan

My family has just spent three days and two nights in Yilan county and I was grateful for the escape from the hustle and bustle of city life. I chose a minsu in a remote area in Dongshan and although we needed a driver to get to all our destinations, I loved my choice!

When we were in Yilan, the sun was scorching in the day and the temperature went up to 34 degrees. The children were most delighted when we arrived at our minsu in the evenings. They had reason to celebrate as the minsu owners had decorated the rooms to attract young clientele like them.

Our room on the first night had a swing with a teddy bear and lots of toys. The bath tub overlooked the paddy field and both children took turns to soak in it. There was also a mini kitchen for little chefs and Little An went on the slide with Lightning McQueen many many times.

We moved to another room on our second night. The minsu had about eight beautifully decorated rooms and we were spoiled for choice. Our second room, which was in…

I was feeling disgruntled with the Singapore education system recently. Application for DSA starts in May and I have been asking people around me about their opinions of the secondary schools their children are studying at.

It was not the first time I heard about students in IP schools being taught higher level content without being given the basics. One common grouse was that the teachers assumed that the students already had the foundational knowledge and thus did not scaffold the learning of the students. Someone told me that her secondary one son's book list contained secondary four science books. Another friend told me he was asked to help his neighbour's son with his math homework as the boy's teacher (from a reputed IP school) did not teach the content necessary for the homework to be completed. I have no experience in this but I certainly hope that IP schools are using the time saved from preparing for the O levels to equip students with 21st century skills rather …

### Fraser's Hill with Kids

We spent 6 days and 5 nights on Fraser's Hill. Before the trip, I looked up Tripadvisor and saw that there were not many activities listed. Nevertheless, we had many unplanned lessons on nature and it helped that Lyn and our fellow travellers are bird enthusiasts who are able to identify feathered creatures readily.

Here are some of the activities which we enjoyed:

1) Birdwatching

Armed with binoculars and DSLRs, we spotted a number of birds commonly found on Fraser's Hill.

2) Boating

The older kids in our party enjoyed the paddle boats at Allan's Water so much that each of them went twice. Little An and another toddler could not go as the height requirement was 107 cm so they could only watch their older siblings while enjoying some snacks. It cost RM9 to hire each boat for 15 minutes, but I suspect that we were given extra time and the kids were grateful. I got quite tired paddling and steering the boat but still enjoyed the tranquil surroundings.

3) Strawberry Picking

N…

### Korea Trip Day 1 ~ N Seoul Tower

My last trip to Korea was in June 2007 and we had joined a tour group. This time, I was audacious enough to lug my five-year-old on a free and easy trip there in the cold month of March, knowing only two Korean words. Before the trip, I was gaping at the temperature charts (which showed that the temperature would range between -2 and 12°c during our trip), wishing that the country would heat up while we were there. I also added to the sales figures of Uniqlo by stocking up on its Heat tech products.

All my worries were unfounded. Our outer jackets (mine was a lightly padded one from Uniqlo while hers was a little more puffy one from Decathlon) managed to keep us warm throughout the trip. On most days, we wore three layers (extra warm Heat tech thermals, a shirt or jumper and our jackets) and we were comfortable.

The airport buses were easily located. We took Bus 6015 to Myeongdong and located our hotel after a short walk. What I was not prepared for was that Google maps do not provide…

### Mama

This post is dedicated to my grandma, who passed away on 2 May 2019.

She was an amazing woman. Her husband had left her and she single-handedly brought up five children. One of them is a professor in the USA and the others are respectable in their own ways. She did not have much education and had to hold down more than one job to make ends meet.

It was impressive how she managed to be my brother's and my main caregiver till we reached teenage. She became a grandma at the age of 49. My brother and I are only 1.5 years apart in age. Imagine the number of diapers she had to manage each day and the number of milk feeds she had to prepare! She would also have to deal with unexplained tears or tantrums. She made sure we read books and taught herself to write the letters of the alphabet. I remember her saying proudly that both the grandchildren she raised were scholarship holders. Although I attribute the scholarships to God's blessings, I must thank her indeed for somehow instilling…