This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

Monday, November 26, 2007

Mathematics – The “Compounding” Subject

Mathematics is considered a “compounding” subject. Foundation topics are introduced at the early stage. Other topics, which are highly dependent on the knowledge of foundation topics, are then introduced at a later stage. This means that if a student does not have a good grasp of earlier topics, he/she will have problems with topics that will be taught later.

For example, if a student does not understand foundation topics like Fractions or Decimals, he/she will have problems with topics like Ratio, Averages, Percentages, Rate etc, which will be introduced later. Maths is hence, called a “compounding” subject because if the student does not know his earlier topics, the problems will start compounding as time goes by.

It is therefore important to know that for a student to do well in Mathematics for his/her PSLE, he/she must have a strong foundation in Mathematics right from the very start, ie – from Primary One. The later the student works towards understanding Maths, the more difficult it would be for him/her to do well in his/her P6 PSLE Maths.

The flip side to this is that a "compounding” subject has benefits. You can use your knowledge attained in past topics to solve questions set for a current topic. Here is one example.

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Question –

The distance between Town A and Town B is 450 km. A car started from Town A and travelled towards Town B at a speed of 45 km/h. At the same time, a bus started from Town B and travelled towards Town A at a speed of 30 km/h. What was the distance they each travelled when they passed each other?
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Obviously, the above topic is Speed. You will see that in the above example, you will be able to use a previously taught topic, which is much easier than Speed, to solve the question. In this case, we will use Ratio instead of Speed.

Since the car travelled at 45 km/h and the bus at 30 km/h, the ratio between the distances covered by the car and bus during any same period is 45:30 or 3:2.

This means that 5 units (3 units for car and 2 units for bus) ---> 450 km.

5 units ----- 450 km
1 unit ----- 450 km divided by 5 units = 90km
3 units (car) ----- 3 units x 90 km = 270 km covered by car (Answer)
2 units (bus) ----- 2 units x 90 km = 180 km covered by bus (Answer)

As it can be seen from the above example, although the question is a Speed question, knowledge that has been acquired in the topic of Ratio is used instead. This method is simpler, easier to grasp and has a less tendency on the part of the student to make calculation errors, compared to if knowledge on the topic of Speed had been used instead.

A student who has a strong foundation in earlier topics is definitely much better off than his/her peers who may not have such a foundation. He/she will be able to use his/her knowledge acquired in past topics to help solve questions that are set in current topics.

Maths is a “compounding” subject. You need to have a strong grasp of earlier topics to be able to do well in topics that are taught later.

It is a mistake to think that you can “catch up” with your P3 and P4 Maths, when you are in P5 and P6.

Likewise, it is a mistake to think you can catch up with your P5 Maths, when you are in P6.

The later you start strengthening your foundation in Maths, the more difficult you will find Maths as a subject, when you sit for your PSLE.

keentolearn said...

Mr. Song,
Good Afternoon

I understand that you have stopped taking questions from the public. I am not looking for detailed solution, but wish to seek clarification on

a) whether problems with rest period are included in PSLE exam

b) In such problem, should the rest period be considered when calculating the average speed using the formula, Total Distance/Total Time?

For example
Sarah travelled for 1 h from Town A to Town B at a speed of 60km/h. She rested in Town B for 10 min. After that, she continued travelling for 20 min to Town C at a speed of 45km/h. Find Sarah’s average speed for the whole journey.

Excel Eduservice said...

Yes, in this case, average speed includes the rest period. Note that you are to find Sarah's average speed for the whole journey.

keentolearn said...

Dear Mr.Song