These are questions from the Killer Math paper (from Nanyang Primary Prelim 2007) I talked about in my previous post. Well, at least it killed me, the following last 6 questions in the paper constituted 28 marks, and I got only 1 mark :(

Monica, post your working, I'm sure they're quite different from Brian's.

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Q48. A bus and a car travelled from Town X to Town Y. The bus left Town X at 1048pm and it took 5 hours to reach Town Y. The car started 30 min later than the bus and it took 4 hours to reach Town Y. At what time did the car catch up with the bus?

Let x be the distance from Town X to town Y.

Bus's Speed --> x/5h = 1/10 x/ 30min

Car's Speed --> x/4h = 1/8 x/ 30min

At 1118pm, Car travelled 0 x, Bus travelled 1/10 x

At 1148pm, Car travelled 1/8 x, Bus travelled 1/5 x

At 1218am, Car travelled 1/4 x, Bus travelled 3/10 x

At 1248am, Car travelled 3/8 x, Bus travelled 2/5 x

At 118am, Car travelled 1/2 x, Bus travelled 1/2 x

Car caught up with bus at 118am.

Ans: 1.18 am (answer given in testpaper is 1.18pm)

* I think there should be a better way to present the working than this, if anyone cares to give it a try, I'd very much appreciate it.

****************************************

Q47. At a school carnival, there were 520 more girls than boys. 1/8 of the girls and 20% of the boys left the carnival. In the end, there were 488 more girls than boys.

a) Did more girls or boys leave the carnival? How many more?

b) How many children were there at the carnival in the end?

a) 520-488 = 32

Ans: Girls, 32 more.

b) Let G and B be the number of Girls and Boys at first.

G = B + 520 -- (1)

7/8 G = 4/5 B + 488 --(2)

(1) - (2)

1/8 G = 1/5 B + 32 -- (3)

(1) divided by 8

1/8 G = 1/8 B + 65 -- (4)

(4) - (3)

3/40 B = 33

B = 440

G = 440 + 520 = 960

7/8 G + 4/5 B

= 7/8 (960) + 4/5 (440)

= 840 + 352

= 1192

Ans: 1192

***************************************

Q46 Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio of 3:1. In the end, Azman and Bala had 780 and 480 marbles left respectively. How many marbles did Azman have at first?

Let A, B and C, be the number of marbles Azman, Bala and Chongfu had at first.

A = 5/4 C

4/5 A = C -- (1)

C = 8/5 B -- (2)

Substitute (1) into (2)

4/5 A = 8/5 B

A = 2B -- (3)

Let x be the number of marbles lost

A - 3x = 780 -- (4)

B - x = 480 -- (5)

Substitute (3) into (4)

2B - 3x = 780 -- (6)

(5)x2

2B - 2x = 960 -- (7)

(7)-(6)

x = 180

From (4)

A - 3(180) = 780

A = 780 + 540 = 1320

Ans: 1320

*********************************

Q45 A rectangular tank measuring 60cm by 35cm by 40cm is half-filled with water. If Tap A is turned on, it will take 6 min to fill the remaining half of the tank to its brim. Tap B drains water from the tank at a rate of 12 litres per min. How long will it take for the tank to be filled to 1/8 of its capacity if both taps are turned on at the same time?

Tap A fills up 1/2 of the tank in

--> ((60x35x40)/2)cm3/6 min

= (84000/2)cm3/6 min

= 42000cm3/6 min

= 7000cm3/min

The tank loses 12000 - 7000 --> 5000cm3 of water every minute.

Difference between 1/2 and 1/8 of the tank

--> 3/8 (84000)

= 10500 x 3

= 31500cm3

Time taken to fill the tank to 1/8 of capacity

--> 31500/5000

= 315/50

= 63/10

= 6.3 min

Ans: 6.3 min

**********************************

Q44 The tickets for a show are priced at $10 and $5. The number of ten-dollar tickets available is 1 and 1/2 times the number of five-dollar tickets. 5 out of 6 ten-dollar tickets and all the five-dollar tickets were sold. The ticket sales amounted to $5600. How much more would have been collected if all the tickets were sold?

Let T and F be the number of ten and five-dollar tickets available respectively.

T = 3/2 F -- (1)

50/6 T + 5F = 5600 -- (2)

(1)x2/3

2/3T = F -- (3)

(3)x5

10/3 T = 5F -- (4)

Substitute (4) into (2)

50/6 T + 10/3 T = 5600

70/6 T = 5600

1/6 T = 80

T = 480

F = 320

Amount of money collected if all tickets are sold

--> 10T + 5F

= 4800 + 1600

= 6400

Extra amount collected

--> 6400 - 5600 = 800

Ans: $800

******************************

Q43 The shaded figure is made up of 4 quarter arcs of radius 10cm. Find its area (take pi=3.14).

There's actually a diagram of the kinda cut-out circle; if anyone's really interested, just go to this link to the testpaper, it's Q43.

Area of circle

--> 3.14 x 10 x 10

= 314

Side of square

--> Sqrt(10x10 + 10x10)

= Sqrt200

Area of square

--> Sqrt200 x Sqrt200

= 200

Area of 4 arcs

--> 314 - 200

= 114

Area of 1 arc

--> 114/4

= 28.5

Area of shaded part

--> 200 - 2(28.5)

= 200 - 57

= 143

Ans: 143cm2

*Not sure if that cut-out part of the circle is called an arc though, is it an arc or sector?

## Thursday, April 30, 2009

### When kids trump adults

When Monica emailed me a couple of days back to ask about this question from Nanyang Prelim 2008 (I didn't do this paper, but Brian did) that stumped her, I bugged her to try that school's Killer 2007 paper, cos that paper totally slayed me.

Brian and I did the Nanyang Prelim 2007 paper together at the end of last year. At the time, I sensed that he wasn't happy to be left alone to do work while the rest of us were either playing (Sean), watching TV (Ed) or surfing the internet (me).

He was not focussed at all, kept making silly mistakes. So I started sitting together with him, doing the tests together. He relished the competition (or maybe it was just about Equal Misery), and was so focussed and made far less careless mistakes.

Our relationship improved so much then. He was so good after that, not so snappy and angry, and not always upset with Sean. But Sean got neglected a lot. And after a while, I stopped sitting together with him, cos lost momentum, plus he is able to work alone now and even checks his work as best as he can, using all the time allocated.

And I haven't blogged about a major spat we had a week plus ago, basically bottom-line is he wants to do his own revision, Mom's not needed anymore. Yes, I've become dispensable.

Back to the killer paper, I remember after the first hour or so, just sitting there waiting for him to complete his paper, cos I was done. Done as in FRIED; I couldn't do almost ALL of the questions in Section C.

Brian got about 80 on that paper. And Model Mum Monica? She got 73, that's not Band 1, and she is an A* calibre mathematician. Monica calls me out on this in her post about this exam paper, so since I've revealed my dismal results there, I'll also reveal it here.

I got a GRAND total of 55 marks! How ridiculous is that??

Yesterday, when Monica told me she got more than 70, I thought, hmmm, it's been some months, I think I've gotten better at this, so I tried doing the paper again, and got less than 50! I got Brian to try again and this time, he got 93 even though he said he had forgotten all the questions.

Why did I do worse after all these months while Brian did better? The difference between Brian and I is that since end-2008, he has been practising on more papers and I haven't. He's also taken part in a couple of math competitions which seemed to have helped a lot in his mathematical thinking, even though those are American competitions.

So let that be a lesson to all, use it or lose it! And parents reading this, know just how tough things are for our kids these days, and cut them a little bit of slack every now and then. As I commented in Mon's post, I have the utmost, greatest, respect for Singapore kids. This is only Math, I'm sure all the other subjects are equally, if not more, demanding.

Brian and I did the Nanyang Prelim 2007 paper together at the end of last year. At the time, I sensed that he wasn't happy to be left alone to do work while the rest of us were either playing (Sean), watching TV (Ed) or surfing the internet (me).

He was not focussed at all, kept making silly mistakes. So I started sitting together with him, doing the tests together. He relished the competition (or maybe it was just about Equal Misery), and was so focussed and made far less careless mistakes.

Our relationship improved so much then. He was so good after that, not so snappy and angry, and not always upset with Sean. But Sean got neglected a lot. And after a while, I stopped sitting together with him, cos lost momentum, plus he is able to work alone now and even checks his work as best as he can, using all the time allocated.

And I haven't blogged about a major spat we had a week plus ago, basically bottom-line is he wants to do his own revision, Mom's not needed anymore. Yes, I've become dispensable.

Back to the killer paper, I remember after the first hour or so, just sitting there waiting for him to complete his paper, cos I was done. Done as in FRIED; I couldn't do almost ALL of the questions in Section C.

Brian got about 80 on that paper. And Model Mum Monica? She got 73, that's not Band 1, and she is an A* calibre mathematician. Monica calls me out on this in her post about this exam paper, so since I've revealed my dismal results there, I'll also reveal it here.

I got a GRAND total of 55 marks! How ridiculous is that??

Yesterday, when Monica told me she got more than 70, I thought, hmmm, it's been some months, I think I've gotten better at this, so I tried doing the paper again, and got less than 50! I got Brian to try again and this time, he got 93 even though he said he had forgotten all the questions.

Why did I do worse after all these months while Brian did better? The difference between Brian and I is that since end-2008, he has been practising on more papers and I haven't. He's also taken part in a couple of math competitions which seemed to have helped a lot in his mathematical thinking, even though those are American competitions.

So let that be a lesson to all, use it or lose it! And parents reading this, know just how tough things are for our kids these days, and cut them a little bit of slack every now and then. As I commented in Mon's post, I have the utmost, greatest, respect for Singapore kids. This is only Math, I'm sure all the other subjects are equally, if not more, demanding.

## Tuesday, April 28, 2009

### Singapore Math: RGPS Prelim 2008

I'll be sharing problem sums Brian has done and please continue to give your feedback. Posting the sums also means we are able to refer to these questions when the real exam draws near. I'm only posting the questions that I would find difficult if I had to do them and/or those that he couldn't do. These are from Raffles Girls Primary School Preliminary Exam 2008.

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Q41. Tank P, a rectangular tank measuring 40cm by 35cm by 25cm was 4/5 filled with water. Tank Q, a rectangular tank measuring 30cm by 30cm by 40cm, was 3/8 filled with water. The water from Tank P was then poured into Tank Q to its brim. How much water was left in Tank P?

Volume of water in Tank P at first

--> 40 x 35 x 25 x 4/5 = 28000

Volume of water in Tank Q at first

--> 30 x 30 x 40 x 3/8 = 13500

Volume of water poured from Tank P to Tank Q

--> (30 x 30 x 40) - 13500

= 36000 - 13500

= 22500

Volume of water left in Tank P

--> 28000 - 22500 = 5500

Ans: 5500 cm3 (ans key says 5500 ml)

***************************

Q43. Some identical cubes were placed in a container as shown below. 1120cm3 of water was poured in to fill the container to its brim. Water was then drained out of the container and stopped when the water level is at the height of the bottom layer of cubes. Given that 352cm3 of water is left in the container now, find the height of the container.

Let C be the volume of each cube.

3(6C + 352) = 10C +1120

18C + 1056 = 10C +1120

8C = 64

C = 8

Side of a cube ---> 2 cm

Height of container ---> 2 x 3 = 6 cm

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Q 44. There were 186 adults in an auditorium. When 7/12 of the men and 4/9 of the women left the auditorium, the total number of adults who remained became 90. How many men were there in the auditorium at first.

Let m and w be the number of men and women respectively.

m + w = 186 (1)

5/12 m + 5/9 w = 90 (2)

(2) x 36

--> 15 m +20 w = 3240 (3)

(1) x 20

--> 20 m + 20 w = 3720 (4)

(4) - (3)

--> 5 m = 480

m = 96

Ans: 96 men

*****************************

Q45. A car, travelling at a constant speed, took 9 hours to travel from Town Y to Town Z. A lorry, travelling at a constant speed, took 18 hours to travel from Town Z to Town Y. Both vehicles started at the same time and they met when they were 180km from Town Z.

a) Find the distance between the two towns.

b) Find the speed of the car.

There's a little diagram in the solution so I took a picture of his working. The answers are slightly out of the camera's focus but they are (a) 540km (b) 60km/h.

********************************************

Q48. Joanne had some twenty-cent coins and fifty-cent coins in a box. The percentage of the number of twenty-cent coins was 40% of the total number of coins Joanne had. Joanne took out 10 fifty-cent coins and put in twenty-cent coins of the same value. The percentage of the number of twenty-cent coins then became 50% of the total number of coins Joanne had. What was the amount of money in the box?

Let t and f be the number of twenty and fifty cent coins at first respectively.

3t = 2f ---- (1)

f - 10 = t + 25

f = t + 35

2f = 2t + 70 --- (2)

Substitute (2) into (1)

3t = 2t + 70

t = 70

f = 105

20t + 50f = 1400 + 5250 = 6650

Ans: $66.50

************************************

Brian got Q46 wrong, and the solution turned out to be relatively simple to understand.

Q46. In Box A, the ratio of the number of blue balls to the number of green balls was 4:1. In Box B, the ratio of the number of blue balls to the number of green balls was 2:3. The total number of balls in Box A was twice the total number of balls in Box B.

a) What was the ratio of the number of blue balls in Box A to the number of green balls in Box B?

b) When 40 green balls were moved from Box A to Box B, the ratio of the number of blue balls to the number of green balls in Box B became 5:8. How many green balls were there in Box B at the end?

This is the solution given in the answer key:

a) Box A --> G:B --> 1:4 --> 2:8

Box B --> G:B --> 3:2

Ans: 8:3

b) After 40 balls moved from Box A to Box B

Box B --> G:B --> 5:8 --> 16:10

Compare Before G:B --> 3:2 --> 15:10

1U --> 40

16U --> 640

Ans: 640 green balls

****************************

Q41. Tank P, a rectangular tank measuring 40cm by 35cm by 25cm was 4/5 filled with water. Tank Q, a rectangular tank measuring 30cm by 30cm by 40cm, was 3/8 filled with water. The water from Tank P was then poured into Tank Q to its brim. How much water was left in Tank P?

Volume of water in Tank P at first

--> 40 x 35 x 25 x 4/5 = 28000

Volume of water in Tank Q at first

--> 30 x 30 x 40 x 3/8 = 13500

Volume of water poured from Tank P to Tank Q

--> (30 x 30 x 40) - 13500

= 36000 - 13500

= 22500

Volume of water left in Tank P

--> 28000 - 22500 = 5500

Ans: 5500 cm3 (ans key says 5500 ml)

***************************

Q43. Some identical cubes were placed in a container as shown below. 1120cm3 of water was poured in to fill the container to its brim. Water was then drained out of the container and stopped when the water level is at the height of the bottom layer of cubes. Given that 352cm3 of water is left in the container now, find the height of the container.

Let C be the volume of each cube.

3(6C + 352) = 10C +1120

18C + 1056 = 10C +1120

8C = 64

C = 8

Side of a cube ---> 2 cm

Height of container ---> 2 x 3 = 6 cm

*****************************

Q 44. There were 186 adults in an auditorium. When 7/12 of the men and 4/9 of the women left the auditorium, the total number of adults who remained became 90. How many men were there in the auditorium at first.

Let m and w be the number of men and women respectively.

m + w = 186 (1)

5/12 m + 5/9 w = 90 (2)

(2) x 36

--> 15 m +20 w = 3240 (3)

(1) x 20

--> 20 m + 20 w = 3720 (4)

(4) - (3)

--> 5 m = 480

m = 96

Ans: 96 men

*****************************

Q45. A car, travelling at a constant speed, took 9 hours to travel from Town Y to Town Z. A lorry, travelling at a constant speed, took 18 hours to travel from Town Z to Town Y. Both vehicles started at the same time and they met when they were 180km from Town Z.

a) Find the distance between the two towns.

b) Find the speed of the car.

There's a little diagram in the solution so I took a picture of his working. The answers are slightly out of the camera's focus but they are (a) 540km (b) 60km/h.

********************************************

Q48. Joanne had some twenty-cent coins and fifty-cent coins in a box. The percentage of the number of twenty-cent coins was 40% of the total number of coins Joanne had. Joanne took out 10 fifty-cent coins and put in twenty-cent coins of the same value. The percentage of the number of twenty-cent coins then became 50% of the total number of coins Joanne had. What was the amount of money in the box?

Let t and f be the number of twenty and fifty cent coins at first respectively.

3t = 2f ---- (1)

f - 10 = t + 25

f = t + 35

2f = 2t + 70 --- (2)

Substitute (2) into (1)

3t = 2t + 70

t = 70

f = 105

20t + 50f = 1400 + 5250 = 6650

Ans: $66.50

************************************

Brian got Q46 wrong, and the solution turned out to be relatively simple to understand.

Q46. In Box A, the ratio of the number of blue balls to the number of green balls was 4:1. In Box B, the ratio of the number of blue balls to the number of green balls was 2:3. The total number of balls in Box A was twice the total number of balls in Box B.

a) What was the ratio of the number of blue balls in Box A to the number of green balls in Box B?

b) When 40 green balls were moved from Box A to Box B, the ratio of the number of blue balls to the number of green balls in Box B became 5:8. How many green balls were there in Box B at the end?

This is the solution given in the answer key:

a) Box A --> G:B --> 1:4 --> 2:8

Box B --> G:B --> 3:2

Ans: 8:3

b) After 40 balls moved from Box A to Box B

Box B --> G:B --> 5:8 --> 16:10

Compare Before G:B --> 3:2 --> 15:10

1U --> 40

16U --> 640

Ans: 640 green balls

### Singapore Math: NYPS 2008 Speed Question

Another Speed question, this one from Nanyang Primary's 2008 Prelim paper (Qn 47).

Lily is meeting a friend at a certain time. If she drives at 80km/h, she will be 1/3 h late. If she drives at 60km/h, she will be 3/4 hour late. How long will the journey take if she drives at 90km/h?

**************************************

Brian's working (refined for this post):

At 80km/h or 240km/3h --> 20 min late

At 60km/h or 240km/4h --> 45 min late

Difference in time taken is 1 hr or 60 min per 240km.

60 min --> 240km

25 min --> 25/60 x 240 = 100km

Time taken at 90km/h

--> Distance divided by speed

--> 100km/90km/h = 1 1/9 h

************************************************

I worked the solution out by Algebra:

Let D be distance and T be time taken

D / (T + 1/3) = 80

D = 80T + 80/3 ---> (1)

D / (T + 3/4) = 60

D = 60T + 45 ---> (2)

(1) - (2)

20T = 55/3

T = 55/60 ---> (3)

Substitute (3) into (2)

D = 55 + 45 = 100km

When Lily drives 90km/h:

T = D/90 = 100/90 = 1 1/9 hr

**********************

Lily is meeting a friend at a certain time. If she drives at 80km/h, she will be 1/3 h late. If she drives at 60km/h, she will be 3/4 hour late. How long will the journey take if she drives at 90km/h?

**************************************

Brian's working (refined for this post):

At 80km/h or 240km/3h --> 20 min late

At 60km/h or 240km/4h --> 45 min late

Difference in time taken is 1 hr or 60 min per 240km.

60 min --> 240km

25 min --> 25/60 x 240 = 100km

Time taken at 90km/h

--> Distance divided by speed

--> 100km/90km/h = 1 1/9 h

************************************************

I worked the solution out by Algebra:

Let D be distance and T be time taken

D / (T + 1/3) = 80

D = 80T + 80/3 ---> (1)

D / (T + 3/4) = 60

D = 60T + 45 ---> (2)

(1) - (2)

20T = 55/3

T = 55/60 ---> (3)

Substitute (3) into (2)

D = 55 + 45 = 100km

When Lily drives 90km/h:

T = D/90 = 100/90 = 1 1/9 hr

**********************

## Friday, April 24, 2009

### Rollerblade® Rollerblades

New rollerblades for the boys by Rollerblade®. Yes, there's actually a brand called Rollerblade®, didn't know that, did you? And this exact model is the one I bought for both of them; on sale mah...looks fierce huh :)

Bought protective gear including helmets too. Pocket very holey and burnt now.

So we're (and by we I mean the boys, of course I'm not rollerblading, siao ah!) all set for spring/summer skating! Watch out!!

## Tuesday, April 21, 2009

### Books for (my) Boys

Okay, for those with boys, these are books your kids might like. Most of these are Brian's books, Sean reads very little fiction. Where available, I've provided links to the books' website so you can find out more if you want. Brian's reading is limited to a few genres so check this excellent site for links to more authors of other books for boys; the site was recommended by blog reader Sandy (Thanks!).

Brian has just finished reading the Percy Jackson series by Rick Riordan; there are 4 books in all, 1) Lightning Thief 2) Sea of Monsters 3) Titan's Curse 4) Battle of the Labyrinth, a 5th (The Last Olympian) will be released next month, . Half-blood demi-God Percy Jackson, son of Poseidon, fights Kronos, the evil Titan King, who's out to destroy the Greek Gods.

One of Brian's favourite reads is The Eragon series, 1) Eragon 2) Eldest 3) Brisingr, the author Christopher Paolini is writing a 4th one, title yet to be revealed. A kind of review by Brian here.

Brian bought the book on the left, Saving the world and other extreme sports, by James Patterson at his school's bookfair last year and he started on MaximumRide: The Final Warning today. Very much a boy's book, I wouldn't have given it a passing glance looking at the cover.

There are 6 books in the Artemis Fowl series by Eoin Colfer that Brian liked a lot earlier last year; not in any particular order they are 1)Artemis Fowl 2)The Eternity Code 3)The Arctic Incident, 4)The Opal Deception 5)The Time Paradox 6)The Lost Colony.

Brian found the book Flyte, part of the Septimus Heap series by Angie Sage in his teacher's classroom library in late 2007 and liked it enough to beg me to buy him the other books he had not read when we were in Singapore that Christmas. Four books in the series 1) Magyk 2)Flyte 3)Physik 4)Queste.

Three books in the His Dark Material trilogy by Philip Pullman, he's misplaced The Amber Spyglass, shown here are Northern Lights and Subtle Knife. These books look new cos they've been read just once. Haven't been re-read till they have dog ears so probably not a favourite.

Finally, books of good literary standing? Or maybe he likes them for narcissistic reasons, the protagonist shares his name. Following up on the popular award-winning book Hatchet, Gary Paulsen continues the Brian Saga series with Brian's Winter and Brian's Return.

Peter Pan, not by J.M. Barrie, but someone with a similar last name, famous humour columnist Dave Barry trying his hand at writing children's literature. Brian read this when he was in London, and I now see it's actually a trilogy. We have two of the three books, Peter and the Shadowthieves and Peter and the Starcatchers.

The Diary of a Wimpy Kid series is liked VERY much by both Brian and Sean. Sean actually chose one of these as an impromptu Christmas present when we were in MPH last year (it was really close to Christmas and I hadn't bought them presents yet). We bought the 2nd book later. And this last trip back, they begged me to buy the 3rd instalment when they saw it in Borders. But it was still the hardcover version and really expensive for a book like this, so I gave them a firm no. Told them to borrow from the school library if available or if the paperback comes out before then, I'll buy it for them. This series is obviously raking in the money for the authors/publishers as there's a 4th and 5th instalment in the making.

I put these two books together cos both come highly recommended by my friend Slim, whose boys read very widely. As you can see, one book has been read thoroughly, the other, not at all. Brian tried reading The Earthsea Quartet when I first got the book last year but he didn't like it. Not sure if he'll like it now. As for Captain Bluebear, I blogged about it here.

I think there are more books in the Inkheart series but Brian only read this one and have not wondered more about the book. It's been turned into a movie, I think.

For a time, Brian was hooked on Brian Jacques' Redwall Series. He's read them all save for the latest instalment which we saw at Borders, but still hardcover and so expensive. Laterlah...

And for both boys and girls, there's the Harry Potter series (our books are in Malacca) and shown here Chronicles of Narnia and Lord of the Rings trilogy. Aren't my LOTR books gorgeous? I got the books, which come in a case, for a very nice low price at one of the warehouse sales in Singapore. Brian tried reading LOTR but didn't like it enough to complete the first book.

Boys will also like books by Roald Dahl and Judy Blume. In Judy Blume's Tales of a 4th Grade Nothing, the protaganist has a very rascally little brother, so Brian can totally relate to the character. It's really quite funny.

In this pile are some animal-related stories that could appeal to boys, including Woof!, Rascal, Because of Winn-Dixie (oh, Brian just told me he didn't like this book, so...), Mrs Frisby and the Rats of Nimh, Old Yeller, The Pig who saved the world, and The Tale of Despereaux. The Phantom Tollbooth and Louis Sachar's Holes are books that Brian enjoyed a lot too.

My friend Monica has many posts on books, just click on the book label in her blog. Direct links here to her posts on Classic Book Series for Girls and Book series for boys. Hehe, very different from my list up there, which looks so un-cerebral in contrast.

Just added:

In the car on the way home from school just now, I saw Brian reading the book below, Firestar's Quest: Super Edition from the Warriors series by Erin Hunter. So I'll just add this to the list of books he likes to read, cos he's actually read 6 books from this series, not including this one.

Brian has just finished reading the Percy Jackson series by Rick Riordan; there are 4 books in all, 1) Lightning Thief 2) Sea of Monsters 3) Titan's Curse 4) Battle of the Labyrinth, a 5th (The Last Olympian) will be released next month, . Half-blood demi-God Percy Jackson, son of Poseidon, fights Kronos, the evil Titan King, who's out to destroy the Greek Gods.

One of Brian's favourite reads is The Eragon series, 1) Eragon 2) Eldest 3) Brisingr, the author Christopher Paolini is writing a 4th one, title yet to be revealed. A kind of review by Brian here.

Brian bought the book on the left, Saving the world and other extreme sports, by James Patterson at his school's bookfair last year and he started on MaximumRide: The Final Warning today. Very much a boy's book, I wouldn't have given it a passing glance looking at the cover.

There are 6 books in the Artemis Fowl series by Eoin Colfer that Brian liked a lot earlier last year; not in any particular order they are 1)Artemis Fowl 2)The Eternity Code 3)The Arctic Incident, 4)The Opal Deception 5)The Time Paradox 6)The Lost Colony.

Brian found the book Flyte, part of the Septimus Heap series by Angie Sage in his teacher's classroom library in late 2007 and liked it enough to beg me to buy him the other books he had not read when we were in Singapore that Christmas. Four books in the series 1) Magyk 2)Flyte 3)Physik 4)Queste.

Three books in the His Dark Material trilogy by Philip Pullman, he's misplaced The Amber Spyglass, shown here are Northern Lights and Subtle Knife. These books look new cos they've been read just once. Haven't been re-read till they have dog ears so probably not a favourite.

Finally, books of good literary standing? Or maybe he likes them for narcissistic reasons, the protagonist shares his name. Following up on the popular award-winning book Hatchet, Gary Paulsen continues the Brian Saga series with Brian's Winter and Brian's Return.

Peter Pan, not by J.M. Barrie, but someone with a similar last name, famous humour columnist Dave Barry trying his hand at writing children's literature. Brian read this when he was in London, and I now see it's actually a trilogy. We have two of the three books, Peter and the Shadowthieves and Peter and the Starcatchers.

The Diary of a Wimpy Kid series is liked VERY much by both Brian and Sean. Sean actually chose one of these as an impromptu Christmas present when we were in MPH last year (it was really close to Christmas and I hadn't bought them presents yet). We bought the 2nd book later. And this last trip back, they begged me to buy the 3rd instalment when they saw it in Borders. But it was still the hardcover version and really expensive for a book like this, so I gave them a firm no. Told them to borrow from the school library if available or if the paperback comes out before then, I'll buy it for them. This series is obviously raking in the money for the authors/publishers as there's a 4th and 5th instalment in the making.

I put these two books together cos both come highly recommended by my friend Slim, whose boys read very widely. As you can see, one book has been read thoroughly, the other, not at all. Brian tried reading The Earthsea Quartet when I first got the book last year but he didn't like it. Not sure if he'll like it now. As for Captain Bluebear, I blogged about it here.

I think there are more books in the Inkheart series but Brian only read this one and have not wondered more about the book. It's been turned into a movie, I think.

For a time, Brian was hooked on Brian Jacques' Redwall Series. He's read them all save for the latest instalment which we saw at Borders, but still hardcover and so expensive. Laterlah...

And for both boys and girls, there's the Harry Potter series (our books are in Malacca) and shown here Chronicles of Narnia and Lord of the Rings trilogy. Aren't my LOTR books gorgeous? I got the books, which come in a case, for a very nice low price at one of the warehouse sales in Singapore. Brian tried reading LOTR but didn't like it enough to complete the first book.

Boys will also like books by Roald Dahl and Judy Blume. In Judy Blume's Tales of a 4th Grade Nothing, the protaganist has a very rascally little brother, so Brian can totally relate to the character. It's really quite funny.

In this pile are some animal-related stories that could appeal to boys, including Woof!, Rascal, Because of Winn-Dixie (oh, Brian just told me he didn't like this book, so...), Mrs Frisby and the Rats of Nimh, Old Yeller, The Pig who saved the world, and The Tale of Despereaux. The Phantom Tollbooth and Louis Sachar's Holes are books that Brian enjoyed a lot too.

My friend Monica has many posts on books, just click on the book label in her blog. Direct links here to her posts on Classic Book Series for Girls and Book series for boys. Hehe, very different from my list up there, which looks so un-cerebral in contrast.

Just added:

In the car on the way home from school just now, I saw Brian reading the book below, Firestar's Quest: Super Edition from the Warriors series by Erin Hunter. So I'll just add this to the list of books he likes to read, cos he's actually read 6 books from this series, not including this one.

## Sunday, April 19, 2009

### Singapore Math: Speed without Models

Between now and October (if we do go ahead with the PSLE route), I'll need to figure out how to help Brian present his math working for Speed questions better. Trouble is I'm pretty bad at Speed questions myself.

The working he's done here is entirely self-concocted, he hasn't learnt this in school, I've not taught him any particular method cos I don't really know how to present answers for Speed questions either and obviously, he is not following the model method taught in Singapore assessment books.

The thing is he gets the answers right, it's just the working that needs refining, and some discipline on his part not to skip steps. Anyone else finds his working confusing? I've included his verbal explanation in Italic, but look at his working without reading his explanation and let me know how many marks he'd lose even if he gets the answer right, assuming each question is 5 marks. Suggestions for improvement, with method mostly intact, would be much appreciated.

1. Fandi took 3h to travel from town A to town B. On the way, he passed a motorcyclist who was travelling in the opposite direction at a uniform speed of 48km/h. 1 and 3/4 h later, Fandi reached town B while the motorcyclist was still 6km away from town A. Find the distance between the two towns.

Distance between meeting point and Town A

= (48 x 1 3/4) + 6

= 84 + 6

= 90

Fandi's speed

= 90km/ 5/4h

= 72km/h

Distance between both towns

= 72km/h x 3h

= 216km

Brian: The motorcyclist took 1 and 3/4 of an hour to travel from their meeting point to a point 6km away from Town A. So the distance between their meeting point and Town A is the motorcyclist's speed times 1 3/4h plus 6 which equals 90. 90km is also the distance that Fandi travelled from Town A to the meeting point. He took 1 and 1/4 of an hour to travel to the meeting point, so his speed is 90km per 5/4 of an hour, which equals 72km/h. He took 3 hours to travel from Town A to Town B, so the distance between the two towns is 72 x 3 = 216.

2. Richard left town A for town B at 10am. 3/4h later, Linus left town A for town B and overtook Richard at 1230pm. Linus arrived at town B at 105pm. At what time did Richard reach town B?

Let Richard's speed and Linus's speed be R and L respectively.

2 1/2 R = 1 3/4 L

5/2 R = 7/4 L

20 R = 14 L

L = 10/7 R

7/3 L = 10/3 R

Richard took 10/3 hours to reach Town B.

Richard reached Town B at 120pm.

Brian: If you put it algebraically, you're only given one piece of information which is 2 1/2 R = 1 3/4 L (2 1/2 and 1 3/4 are the number of hours R & L travelled respectively when they met) so all you can do is compare the two variables. Since Linus took 2 and 1/3 hours (or 7/3 h) to reach town B, you have to find out how long Richard would take to get there.

3. Two towns, X and Y, were 156 km apart. Tom started to travel from town X to town Y at an average speed of 54km/h. At the same time, Peter also started to travel from town Y to town X. After travelling for 1 and 1/3h, they passed each other on the way. Find the average speed of Peter.

Tom's speed

= 54km/h

= 72km/ 1 1/3h

Peter's speed

= (156 - 72)km/ 1 1/3h

= 84km/ 1 1/3h

= 63km/h

Brian: I'm trying to find out the distance Tom has travelled when Tom and Peter met. Then subtract that distance from 156. That would be the distance that Peter had travelled by the time they met, and from this you can find Peter's speed.

The working he's done here is entirely self-concocted, he hasn't learnt this in school, I've not taught him any particular method cos I don't really know how to present answers for Speed questions either and obviously, he is not following the model method taught in Singapore assessment books.

The thing is he gets the answers right, it's just the working that needs refining, and some discipline on his part not to skip steps. Anyone else finds his working confusing? I've included his verbal explanation in Italic, but look at his working without reading his explanation and let me know how many marks he'd lose even if he gets the answer right, assuming each question is 5 marks. Suggestions for improvement, with method mostly intact, would be much appreciated.

1. Fandi took 3h to travel from town A to town B. On the way, he passed a motorcyclist who was travelling in the opposite direction at a uniform speed of 48km/h. 1 and 3/4 h later, Fandi reached town B while the motorcyclist was still 6km away from town A. Find the distance between the two towns.

Distance between meeting point and Town A

= (48 x 1 3/4) + 6

= 84 + 6

= 90

Fandi's speed

= 90km/ 5/4h

= 72km/h

Distance between both towns

= 72km/h x 3h

= 216km

Brian: The motorcyclist took 1 and 3/4 of an hour to travel from their meeting point to a point 6km away from Town A. So the distance between their meeting point and Town A is the motorcyclist's speed times 1 3/4h plus 6 which equals 90. 90km is also the distance that Fandi travelled from Town A to the meeting point. He took 1 and 1/4 of an hour to travel to the meeting point, so his speed is 90km per 5/4 of an hour, which equals 72km/h. He took 3 hours to travel from Town A to Town B, so the distance between the two towns is 72 x 3 = 216.

2. Richard left town A for town B at 10am. 3/4h later, Linus left town A for town B and overtook Richard at 1230pm. Linus arrived at town B at 105pm. At what time did Richard reach town B?

Let Richard's speed and Linus's speed be R and L respectively.

2 1/2 R = 1 3/4 L

5/2 R = 7/4 L

20 R = 14 L

L = 10/7 R

7/3 L = 10/3 R

Richard took 10/3 hours to reach Town B.

Richard reached Town B at 120pm.

Brian: If you put it algebraically, you're only given one piece of information which is 2 1/2 R = 1 3/4 L (2 1/2 and 1 3/4 are the number of hours R & L travelled respectively when they met) so all you can do is compare the two variables. Since Linus took 2 and 1/3 hours (or 7/3 h) to reach town B, you have to find out how long Richard would take to get there.

3. Two towns, X and Y, were 156 km apart. Tom started to travel from town X to town Y at an average speed of 54km/h. At the same time, Peter also started to travel from town Y to town X. After travelling for 1 and 1/3h, they passed each other on the way. Find the average speed of Peter.

Tom's speed

= 54km/h

= 72km/ 1 1/3h

Peter's speed

= (156 - 72)km/ 1 1/3h

= 84km/ 1 1/3h

= 63km/h

Brian: I'm trying to find out the distance Tom has travelled when Tom and Peter met. Then subtract that distance from 156. That would be the distance that Peter had travelled by the time they met, and from this you can find Peter's speed.

## Saturday, April 18, 2009

### Sean's first time rollerblading

Spring is really here. So yesterday, I dug out Brian's old pair of in-line skates and had Sean give them a try. Thanks to his ice-skating lessons in school, he is actually able to rollerblade immediately. This is a video I took today of Sean rollerblading, he looks tipsy, like he's had too much to drink, BUT trust me, this is wayyyyy better than how Brian fared 4 years ago. The boys are not the sportiest kids around.

## Thursday, April 16, 2009

### Guitar Lesson No 10

Last year, I was told by a couple of mothers about this wonderful Russian guitar teacher, Alexander, who was giving their boys lessons. I was very interested but this teacher's slots were all full. It was only when Minako, my Japanese friend, left Moscow at the end of last year that her boy Dennis' slot became available.

So Brian started his weekly lessons (an hour each week) after we returned to Moscow from winter break this year. He's really enjoyed lessons with Alexander, who is such an encouraging teacher. To mark Brian's 10th lesson with Alexander today, I've recorded him playing The Beatles' Blackbird.

So Brian started his weekly lessons (an hour each week) after we returned to Moscow from winter break this year. He's really enjoyed lessons with Alexander, who is such an encouraging teacher. To mark Brian's 10th lesson with Alexander today, I've recorded him playing The Beatles' Blackbird.

## Wednesday, April 15, 2009

### Buh-bye Wonder Bread!

The sandwich bread above is dubbed by my friends here in Moscow as Wonder Bread. Why? Cos even after a few months, the bread remains soft. Imagine how much preservatives go in there. But this has been what I've been feeding the family the past year or so. I did try buying bread with shorter expiry dates, but my fussy pots complained that the bread was too dry/hard, and I ended up tossing the 'healthier' bread cos no one would eat them.

Well, on my latest trip back to Singapore, I purchased the Zojirushi Bread Machine, which my friend Li Ping has been raving about and egging me to buy for months now. I was skeptical at first cos I already own a bread machine which never quite produced the kind of bread we like, ie, soft and fluffy ala Gardenia/Sunshine. The Zojirushi also costs a lot more than my old machine, so I took some time making the decision.

But no regrets at all! The Zojirushi machine works like a dream. It also takes up very little counter top space, is very quiet, and bakes 1 lb loafs, just right for us. Eddie is most fussy about bread, he likes them soft and fluffy, so if he says the bread tastes pretty good, then it's really incredibly good! Nothing to do with my ability at bread-making, it's entirely the machine's magic at work.

I've baked 3 different types of bread so far. The basic white bread using soft course.

Chocolate bread which didn't turn out aesthetically pleasing but which the boys liked enough to take as snack to school. Good by itself or with some Nutella on it.

And something I just baked today. Raisin bread, this one's really good, too bad Sean doesn't eat raisins.

Reviews of the breadmaker here. Retails at Takashimaya and Tangs for S$399 but I got it from Goh Ah Bee near Kovan MRT for S$295 all inclusive.

All in all, a worthwhile investment indeed. For once, I will not be chastizing my buddy Li Ping for making me spend money.

## Wednesday, April 08, 2009

### Getting Real with Virtual Mums

Six other mums and I met up today (okay a couple of days ago actually, this post is late cos I've just been so busy) for lunch at a fellow blogging mum's place. Oh, I'm back in Singapore this week.

Of the six, there was only one (Monica) whom I knew for 'real', two (Adeline and Cindy) I had met once for 'real' but only after knowing them 'virtually', and the other three are Adeline's friends whom I was meeting for 'real' for the first time, Ann, Sarah and Ai Lei.

Adeline was truly the hostess with the mostest LOL, and the rest of us mummies were beneficiaries of her excellent hosting skills. Mouth-watering to-die-for sushi, grilled kurobuta pork, lemon-flavoured cold noodles (it's shockingly delicious) and for the kiddos, spaghetti bolognese.

Kids in attendance were from left Gabriel (Ai Lei's boy), RK (Adeline's son), and my little monkey too. This is a nice picture of them, most of the other shots were....

...like this.

The moment I started snapping pictures, they immediately made silly faces. At the opposite side of the table was Sarah's girl Hannah. Too bad I don't have a clear snapshot of this sweet little girl, so well-behaved, sitting quietly while smiling good-naturedly at the silly antics of the monkeys across the dining table from her :)

Check out these mangoes that Cindy brought. So sweet...tropicalfruit-deprived Sean and I devoured most of the entire plate. And kind Ann also gave me the bag of mangoes she had brought along to take back. Brian loved them, thanks Ann!

We also had chocolates from Moscow, pretty aren't they? All these washed down with really fragrant tie guan yin, tea that Monica had brought back all the way from Beijing. How spoilt were we?! And what gluttons too :) Speaking for myself lah, don't so sensitive LOL!

I think I speak for all though when I say we all had a heckuva wonderful time. Great food aside, the company was also so much fun. We talked, laughed, talked, laughed and talked and laughed some more and totally forgot the time. Hours went by till Ann realised she really, really, REALLY, had to go. As Mon and I were taking a lift from her, we reluctantly dragged ourselves away too.

So my virtual friends, it's been swell getting to know all of you, and till the next time we meet again, thanks for keeping it real!

Of the six, there was only one (Monica) whom I knew for 'real', two (Adeline and Cindy) I had met once for 'real' but only after knowing them 'virtually', and the other three are Adeline's friends whom I was meeting for 'real' for the first time, Ann, Sarah and Ai Lei.

Adeline was truly the hostess with the mostest LOL, and the rest of us mummies were beneficiaries of her excellent hosting skills. Mouth-watering to-die-for sushi, grilled kurobuta pork, lemon-flavoured cold noodles (it's shockingly delicious) and for the kiddos, spaghetti bolognese.

Kids in attendance were from left Gabriel (Ai Lei's boy), RK (Adeline's son), and my little monkey too. This is a nice picture of them, most of the other shots were....

...like this.

The moment I started snapping pictures, they immediately made silly faces. At the opposite side of the table was Sarah's girl Hannah. Too bad I don't have a clear snapshot of this sweet little girl, so well-behaved, sitting quietly while smiling good-naturedly at the silly antics of the monkeys across the dining table from her :)

Check out these mangoes that Cindy brought. So sweet...tropicalfruit-deprived Sean and I devoured most of the entire plate. And kind Ann also gave me the bag of mangoes she had brought along to take back. Brian loved them, thanks Ann!

We also had chocolates from Moscow, pretty aren't they? All these washed down with really fragrant tie guan yin, tea that Monica had brought back all the way from Beijing. How spoilt were we?! And what gluttons too :) Speaking for myself lah, don't so sensitive LOL!

I think I speak for all though when I say we all had a heckuva wonderful time. Great food aside, the company was also so much fun. We talked, laughed, talked, laughed and talked and laughed some more and totally forgot the time. Hours went by till Ann realised she really, really, REALLY, had to go. As Mon and I were taking a lift from her, we reluctantly dragged ourselves away too.

So my virtual friends, it's been swell getting to know all of you, and till the next time we meet again, thanks for keeping it real!

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