PSLE Math Question on Ratio

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Read : Parents up in arms again over PSLE Mathematics paper.

My two cents – Firstly, if all the smart students can solve all the problems then who will be the smarter and who will be the smartest ? Secondly, the question mentioned in the article is ‘nothing new’ as similar ones can be found in exam papers from ‘top ten schools’. (The most recent – ACS Prelim 2009 Q16)

In my classes, we call this type of questions, ‘Before – After’. Typically, an initial ratio, percentage, fractions is given (Before). Then something happen – sweets eaten, marbles lost, wateva! Finally, the end ratio, percentage, fractions is given. (After).

For my students, I teach them both methods but I highly recommend the ‘X-method’ (Algebra) for solving ‘Before-After’ questions. Modals can be time consuming!

There are two ways to solve the problem.

1) Modal Method (Step-by-Step Solution)

Step 1 : Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim.

psle1

Step 2 : Jim ate 12 sweets and Ken ate 18 chocolates.

Step 3 : The ratio of Jim’s sweets to chocolates became 1:7 and the ratio of Ken’s sweets to chocolates became 1:4psle2

Step 4 : Focus on the two BLUE parts. Both the BLUE parts (Jim’s Sweets & Ken’s Sweets) are the same because from the question, ‘Ken bought some sweets and gave half of it to Jim’. This means Ken and Jim have equal share of the sweets.

The modal can be redrawn to look like this:

psle3a

Step 5 : Focus on the GREEN parts. Both GREEN parts (Jim’s chocolates and Ken’s chocolates) are the same because from the question, ‘Jim bought some chocolates and gave half of it to Ken’. This means Ken and Jim have equal share of the chocolates.

7u = (12 + 1u) + (12 + 1u) + (12 + 1u) + (12 + 1u) + 18

7u = 48 + 4u + 18

7u – 4u = 48 + 18

3u =66

1u = 22

Ken bought : (12 + 1u) + (12 + 1u) = (12 + 22) X 2 = 68

Ans : 68 sweets.

2) Algebra

Step 1 : Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim.

This means Jim and Ken both has 1 unit of chocolate and 1 unit of sweets.

Jim                       Ken

1s :  1c                1s  :  1c

Step 2 : Jim ate 12 sweets and Ken ate 18 chocolates

Jim                       Ken

1s – 12 : 1c          1s : 1c – 18

Step 3 :   The ratio of Jim’s sweets to chocolates became 1:7 and the ratio of Ken’s sweets to chocolates became 1:4

Jim                       Ken

1s – 12 : 1c          1s : 1c – 18

X                   X           (This is what I coined the ‘X’-method, a common lingo in my class)

1 :  7             1 : 4

Equation 1 : 7s – 84 = 1c

Equation 2 :  4s = 1c – 18 or 4s + 18 = 1c

Solving the two equations simultaneously

7s – 84 = 4s + 18

7s – 4s = 18 + 84

3s = 102

s = 34

2s = 34 x 2 = 68

Ans : 68 sweets


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4 Comments

  1. arion  •  Oct 11, 2009 @18:21

    This question is not logical at all!!
    Math question must be set based on a logical background,

    e.g. for bad question: Peter need 10 seconds to trim one of his finger nail using the nail clipper, how many finger nails can Peter trim in 5 minutes?

    Back to the First question, using the Modal Method:

    If Ken is a kid, his parents will not allow him to buy 68 sweets.

    If Ken is a rich boy and his parents dont care how he spend his pocket money. Ken want to eat 18 chocolate now, he could just buy them rather than get the sweet first later exchange his sweet with his little buddy Jim.
    (you can argue on these but that will lead you to a similar debate of the above e.g. question)

    If Ken is not a kid, he must be a complete idiot who commit such an action, or he could be a math geneius without logical mind set. (so is the person who came up with this Math Question.)
    To those geneius, please note that maths is not simply about numbers and calculation, maths also consist of thinking, logic and application.

  2. Janice  •  Oct 12, 2009 @01:21

    I agree. Math questions should be logical application. Maybe ‘During a barter trade, Jim and Ken exchanged eggs for buns …… ‘Geniuses’ who are able to solve the problem could just be those who have been adequately exposed to such questions by their teachers/tutors.

  3. Exasperated  •  Oct 12, 2009 @06:21

    I like the comments above. The Singapore system does not differentiate smart children from not so smart. it differentiates the hardworking from the not so hardworking. It differentiates the parents as well, those who will devote time or not devote time , to educate and nuture and “force” in my case, the children into a structured system that requires them to work hard. It’s not a measure of intelligence. An IQ test would have done that sufficiently. You are right that if the child is sufficinetly exposed to the questions, eg, 10 year series, top school papers, a hardworking kid that did all that will do better than a smart kid who understood but did less and thus did not encounter such questions…(unlucky in that case). When the kid grows up and get out of the education system, so many other factors come into play. The smart kid who did worse in school, may end up doing better in life because he is smart and knows how to deal with real problems in life rather than created “problem sums” in school.

    Sigh what to do? I just wish the educators out there will relax abit and let our children grow up happily, so that depression and stress will not be the one of the top ailments in Singapore.

  4. teeeeecher  •  Oct 13, 2009 @18:02

    I agree that the question is nothing new. Personally, I feel that your model is not well drawn. If drawn clearly, it explains the question better than simultaneous equation.

    There is a reason why simultaneous is only taught on the secondary level. Use what they are taught in school and apply that in their problem solving instead of introducing harder stuff. Makes teaching easier for you, but learning more difficult for them.

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