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In “Why Do We Learn Average?”, we learn 1 kg = 1000 g. As adults, we understand the concept of 1 kg = 1000 g, which means if I carry 1000 bags weighting 1 g each, it means I carry a total weight of 1 kg. But children are confused when they see “g” and “kg”.
Below are the pictures showing equivalence of the weight by using weighting scale, to help children to understand better:
(a) The weighting scale is balance. Thus, we know the weight on the right is equal to the weight on the left. That means if I have 10 bags weighting 1 g each, I have a total weight of 10 g.
(b) The weighting scale is balance. With the 10 g each bag from example (a), I fill 10 bags. So, I have 10 bags with 10 g each.
10 x 10 = 100
Thus, I have a total weight of 100 g.
(c) The weighting scale is balance.
With the 100 g each bag from example (b), I fill another 10 bags. So, I have 10 bags with 100 g each.
10 x 100 = 1000
Thus, I have a total weight of 1000 g, which is also equivalent to 1 kg.
On the other hand, if I just have many bags of 1 g, for 1 kg, I will have 1000 bags of 1 g each.
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.