From Channel News Asia
As requested by some students, here is one possible workout for the solution.
Question
Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim's sweets to chocolates became 1:7 and the ratio of Ken's sweets to chocolates became 1:4. How many sweets did Ken buy?
Solution
Chocolates ----- C
Sweets ----- S
Jim bought 2 units of chocolates ----- C, C
Ken bought 2 units of sweets ---- S, S
Jim gave 1 unit of chocolates to Ken and Ken gave 1 unit of sweets to Jim.
Jim ----- S, C
Ken ----- S, C
Jim ate 12 sweets and Ken ate 18 chocolates.
Jim ----- S – 12; C
Ken ----- S; C – 18
Jim’s sweet to chocolate ratio 1:7. Therefore for number of sweets to be same as number of chocolates, multiply sweets by 7.
C ----- 7 x (S – 12)
C ----- 7S – 84
Ken’s sweet to chocolate ratio 1:4. Therefore, for number of sweets to be same as number of chocolates, multiply sweets by 4.
4 x S ---- C – 18
4S ---- C – 18
From Jim, (C ----- 7S – 84), replace Ken's C....
(Ken) 4S ----- C - 18
4S ----- (7S – 84) – 18
4S ----- 7S – 102
3S ----- 102
1S ----- 34
Number of sweets Jim had at first
2 units of sweets ----- 2 x 34 = 68
Answer: 68 sweets.
Saturday, October 10, 2009
Parents up in arms again over PSLE Mathematics paper
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10 comments:
i think best way to help all the kids understand math is to teach them calculus at an earlier age. It is the fundamental of math. With that they can solve any question they want using ways they are comfortable at. This question can be solve almost instantly by writing out 2 equations. 2 unknowns 2 equation :)
Hi! compo: String of 1 big balloon: 90cm/2 = 45cm String of 1 small balloon: 120cm/5 = 24 cm difference in the length of string: 45-24=21 cm how much longer if they have the same number of big balloons and small balloons: 105(small balloons more) x 24= 2520 cm The number of big balloons that will cause this difference: 2520/ 21 = 120 Number of big balloons: 120 balloons Number of small balloons 120+105=225 balloons Total: 120+225= 345 balloons
Hi Mr Song
What is your opinion about PSLE 2009 Maths?
Did your students find it easy or difficult?
My opinion is that this paper is weird i most of my teachers predicted that there will be hard patterns , big numbers etc etc,
but there isn't the hardest question turned out to be the Jim and Ken,that question's number are quite small <100.
The angle question was like impossible for me .
There is no pattern in that paper .
No age question .
There is calculator .
Unique huh ?
My opinion for Jim abd Ken's question is that it's quite simple if your school had practised on external transfer etc etc and equations.
jm
I feel that the solution you've presented for the Jim and Ken question doesn't fully utilise the model diagram method. I've solved the question by drawing models and it's not too bad. But then under exam conditions, people cannot think properly, so that's why it's still difficult.
Some students found the PSLE OK so far, others said the Maths was a little difficult.
WTH IT WAS ACTUALLY THAT EASY?OK I TELL U MY METHODS
7(Jim)=4(Ken)+18
1(Ken)=1(Jim)+12
1(Jim)=1(Ken)-12
7(Jim)=7(Ken)-84
18--84=102
7(Ken)-4(Ken)=3(Ken)
3(Ken)=102
1(Ken)=34
1(Ken)=1/2 of sweets bought
34x2=68#
Model is actually very simple.
Make the big unit into small unit + 12.
You then find the small unit.
Then you get the answer.
Whatever method you use the basis for solving the problem required the student to have a good understanding in substitution, which will lead to simultaneous equation. The question is this one of the topic which they are being taught. If yes good, if not why the question is set in the first place.
umm.... i'm not trying to show off but it was actually easy :
Sweets : Choclates
Jim 1u+12 7u
Ken 1p 4p+18
So if you can see 1p actually equals to 1u+12 so 4p+12 equals to 4p+66.Then 3u+66,1u=22,22+12=34,34x2=64
Thats it easy
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