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How to Solve Problem “before and after” PDF Print E-mail
Written by Administrator   
Tuesday, 13 December 2011 02:40

Prepare for PSLE Math

– How to Solve Problem “before and after”

 

GreatMinds School Math Department

 

1. Introduction

The No.1 type of challenging question in PSLE Math is the “before and after” question which involves ratio, fraction and percentage. This type of the question becomes the No.1 challenging questions due to two reasons: (1) students may still have difficulties in the concepts of ratio, fraction or percentage; (2) students are not able to organize the much information into the ‘before” and “after” situation. Below are some of the typical questions which show how they are similar and how they can be solved using “ratio”, “model” and “algebra” method. The comparison on these three methods has also been discussed.

 

 

2. Three pieces of information in “before and after”

 

E.g. 1

The ratio of the number of pencils to the number of sharpeners in a box was 1:2. When 9 more pencils were added into the box, the ratio became 5:4. How many pencils and sharpeners were there in the box at first?

The question is designed base on three pieces of information:

(1) Use ratio, or fraction, or percentage to state the “before” situation, like

The ratio of the number of pencils to the number of sharpeners in a box was 1:2

(2) Also use ratio, or fraction, or percentage to state the “after” situation, like

the ratio became 5:4

(3) There is changes to link “before” and “after”, like

When 9 more pencils were added into the box

           Similar questions (E.g. 2-5) are shown below and the 3 pieces of information is also highlighted.

 

 

           E.g. 2

          Mira was sitting for her driving theory test which consisted of multiple choice questions. By the first hour, she completed 2/5 of the questions. After another half an hour, she managed to answer another 14 questions and the ratio of questions that were answer to those that were unanswered became 3:1. How many questions did the theory test consist of?

 

E.g. 3

In the Art club last year, 40% of the members were boys. After 45 girls left the club this year, the ratio of the number of boys to the number of girls in the club became 4:3. How many children were there in the Art club last year?

 

Such type of the questions can be as simple as the above questions whose appear in P5, they can also be very complicated as below appears in P6 and PSLE.

 

E.g. 4 (PSLE-2008)

box X and Box Y contained only blue and red pens. In Box X, the ratio of the number of blue pens to the number of red pens was 5:4. In Box Y, the ratio of the number of blue pens to the number of red pens was 5:1. there were 3 times as many pens in Box X as in Box Y.

(a) what was the ratio of the number of blue pens in Box X to the number of red pens in Box Y?

(b) when 66 red pens were put into Box Y, the ratio of the number of blue pens to the number of red pens in Box Y became 3:5. How many red pens were there in Box Y then?

 

E.g. 5 (PSLE-2009)

Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1:7 and the number of sweets and chocolates Ken had were in the ratio 1:4. How many sweets did Ken buy?

 

3. Methods to solve “before and after”

In order to solve this type of questions, “ratio”, “model” and “algebra” method are introduced.

Below is the example shows how to use the three methods to solve Q1 and Q2.

 

E.g. 1

The ratio of the number of pencils to the number of sharpeners in a box was 1:2. When 9 more pencils were added into the box, the ratio became 5:4. How many pencils and sharpeners were there in the box at first?

 


 

 

E.g. 2

Mira was sitting for her driving theory test which consisted of multiple choice questions. By the first hour, she completed 2/5 of the questions. After another half an hour, she managed to answer another 14 questions and the ratio of questions that were answer to those that were unanswered became 3:1. How many questions did the theory test consist of?

 


 

 

 

 

 

 

4. Limitation of “ratio” and “model” method

Some of the similar questions can be solved using “ratio” method. If Q1 is modified as below, then “ratio” method is not suitable for that question.

 

E.g. 6

The ratio of the number of pencils to the number of sharpeners in a box was 1:2. When 9 more pencils and 6 sharpener were added into the box and, the ratio became 5:4. How many pencils and sharpeners were there in the box at first?

 

The “model” solutions in Q1 and Q2 also show the limitation as they are totally different for two similar questions.

 

 

5. Conclusion

It is clear that “ratio” and “model” method shows very different approaching for Q1 and Q2, while “algebra” shows the same approaching for both questions and can make this type question be a simple one. Students should understand that all such five questions actually are the same type of question and they can be solved using the same method. “Ratio” and “model” method are taught for P5 but students are encouraged to use “algebra” in P6.

 

 

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