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Why Do We Learn Average?

We learn different Mathematics concepts in Primary school. For Primary students, do you expect them to understand why they are learning average? Or percentage? Yes, they do not understand the reasons behind and when they face difficulties, they give up.

As parents or educators, when we are teaching the children, it would be better if we can explain the reasons behind why they are learning different Mathematics concepts and how they can apply the concepts in real life. Below is an example of buying a commodity, using different Mathematics concepts learnt at school:

Concept 1: Weight

1 kg of the commodity costs S$ 9780.00. As a small investor, you can only buy 10 g at a time. How much does 10 g of the commodity cost?

1 kg = 1000 g => S$ 9780.00

10 g => S$ 97.80

Concept 2: Average

Unfortunately, the price goes down and you wish to reduce the risk of losing more money. Thus, you buy another 10 g at S$ 96.90 and another 10 g at S$ 94.50.

The average price for 10 g = (S$ 97.80 + S$ 96.90 + S$ 94.50) / 3

= S$ 96.40

This concept is called average down in investment term, where it is commonly used for buying stock and/or commodity, such as gold, silver, etc.

Concept 3: Money

(a) At the end of the year, the price has gone up to S$ 9710.00 per kg. You are thinking if you can make money by selling all the 30 g of commodity that you have. The maintenance fee is S$ 20.00.

At the first glance, the price of S$ 97.10 per 10 g is not profitable because you first bought the 10 g at S$ 97.80. But after averaging (concept 2), you only spent averagely S$ 96.40 for 10 g.

Another factor to consider is the maintenance fees. You need to subtract the maintenance fees to get the total money won or lost:

For this example, the total money invested = S$ 96.40 x 3 = S$ 289.20

When you sell the 30 g of the commodity, you get = S$ 97.10 x 3 = S$291.30

Without considering the maintenance fees, you think that you have made S$ 2.10 from this investment. After subtracting the maintenance fees, you actually lose S$ 17.90 from this investment.

(b) After the calculation from (a), you know you are losing money, so you wait for the commodity price to go up further. After six months, the price has gone up to S$ 9920.00 per kg. The maintenance fee is S$ 20.00. You are thinking if you can make money by selling all the 30 g of commodity that you have.

The total money invested = S$ 96.40 x 3 = S$ 289.20

When you sell the 30 g of the commodity, you get = S$ 99.20 x 3 = S$297.60

Similarly, you need to subtract the maintenance fees to get the total money won or lost:

S$ 297.60 – S$ 20.00 = S$ 277.60

Again, after considering the maintenance fees, you are still lost of S$ 11.60, even though the price has gone up to S$ 9920.00 per kg.

As you can see, a simple example link three different concepts. Children will appreciate the concepts better if they can see the linkage and also the real life application.

Disclaimer: This post is not encouraging children and / or adults to invest blindly. This is only a simple example where you can use the knowledge learnt in real life. Investment in real life is more complicated and involves more risks.

Primary Mathematics Notes

Some parents have been complaining about Primary Mathematics. They say nowadays Primary Mathematics is not “pure” Mathematics anymore. They say that the Mathematics questions are more like playing with word games, if you do not understand the questions, you cannot solve the questions. Nonetheless, we can still solve the “word games” and score high in Mathematics! In addition, the terms are universal, you can keep this note for Secondary Mathematics too.

Caution: Though the wordings used in this post are commonly found in the Mathematics questions, each question is unique and may vary. The most important thing is to read and understand the questions. Treat each question on a case-by-case basis. If you face any problem on Mathematics questions, please feel free to contact me at wendy@joyfulyue.com

Below are some of the common words used in Primary Mathematics questions:

1. as … as = same

Jenny is as tall as Kenny. That means both Jenny and Kenny have the same height.

Variation version:

(a) Jenny has twice as many candies as Kenny. That means if Jenny has 6 candies, Kenny has only 3 candies. In algebra, Jenny’s candies = 2 x Kenny’s candies.

(b) When x is doubled, find y. That means when x = 2x.

2. -er than, the difference of => use subtraction (-)

Kenny has $50 more than Jenny. That means the difference of the amount of money between Kenny and Jenny is $50, most questions can be solved using subtraction.

Kenny is taller than Jenny by 2 cm. That means the difference of the height between Kenny and Jenny is 2 cm and Kenny is taller.

3. altogether, the sum of => use addition (+)

How many flowers are there altogether? The question is asking you to add all the flowers mentioned in the question.

What is the sum of money? The question is asking you to add all the money value mentioned in the question.

4. Mathematics language

(a) Subtract 5 from 9 => 9 – 5

(b) A bag cost $5.00, how much does it cost if Jenny buys 3 bags? => $5 x 3

Below are the concepts that must be understood by Primary students so that they can tackle more difficult questions:

1. Percentage

2. Ratio

3. Average

4. Bar modelling

5. Algebra (This concept will be taught in more details in Secondary school, thus the understanding of the concept is of utmost importance)

In a nutshell, understanding the concepts is the most important thing to learn in Mathematics. Once you have understood, solving more questions will reinforce the understanding and A* is on the way!