**From: Madam Ser, Parent**

*Dear Sir *

*We refer to the UNIT TRANSFER METHOD Primary 4 book, Chap 2, Q8*

**Mrs Gan is changing the water in her fish tank.**

**If she uses a 4-litre pail to fill the tank, 4 litres of water will overflow.**

**If she uses a 2-litre pail to fill the tank, she will need another 3 more pails of water. **

**How many litres of water are needed to fill the fish tank.**

*The answer provided by the book indicates that the fish tank’s capacity is “16 litres”*

*However, when we work backwards :*

*Case 1: If fish tank’s capacity is 16 litres, that means that Mrs Gan used 4 pails of 4 litres each to fill the tank. The amount of water available to Mrs Gan was 20 litres, so, 4 litres would overflow.*

*Case 2: If fish tank’s capacity is 16 litres, that means that Mrs Gan used 8 pails of 2 litres each to fill the tank. If the amount of water available to Mrs Gan was 20 litres, so, there would still be an excess of 4 litres*

*Please clarify.*

**From desk of Sunny Tan……..**

**Case 1:** If fish tank’s capacity is 16 litres, that means that Mrs Gan used 4 pails of

4 litres each to fill the tank. The amount of water available to Mrs Gan was 20 litres, so, 4 litres would overflow.

**Comment:** Therefore the number of pails used is 5 pails.

**Case 2:** If fish tank’s capacity is 16 litres, that means that Mrs Gan used 8 pails of 2 litres each to fill the tank. If the amount of water available to Mrs Gan was 20 litres, so, there would still be an excess of 4 litres

**Comment 1:** If she use 8 pails of 2-litre each, she will fill up the tank completely, she

will not need another 3 pails, this assumption is invalid as it contradicts the question.

**Comment 2:** If the amount of water available to Mrs Gan was 20 litres, so, there

would still be an excess of 4 litres

This assumption is invalid. Case 1 and Case 2 scenarios are if..and if…, the two events never took place. Therefore we cannot assume that 20 litres of water, that is available in Case 1 is equal to that in Case 2.

** Comment 3**: Number of pails = 5 pails.

Total volume = 5x2 =10 litres

The capacity is 16 litres

Therefore she need extra 6 litres, which is 3 additional pails.

-----------------------------------------------------------------------------------------------------------------

**From: Madam Ser, Parent**

*Dear Sir *

*Thank you for your explanation.*

*The model that we created as below:*

* U : No. of 4-litre pails*

*P : No. of 2-litre pails*

*Capacity of tank = 4U*

*4 litres that overflowed = 1 pail = 1U*

*Therefore, 4U = 16 litres*

*Check : *

*2P + 6 litres = 4U = 16 litres*

*Therefore, P = 5 pails of 2-litre each, resulting in shortage of 6 litres (3 pails of 2-litre each)*

*Please advise if the above interpretation is correct. Else, please help provide working.*

*Thank you.*

**From desk of Sunny Tan……..**

I noticed from your model, the U and P is the same.

In fact, this fact can be established in the beginning, that is the number of pails used in both scenarios Case 1 and Case 2 are the same.

Thus, it is unnecessary to introduce P, too many unknown variables may confuse the child.

Let define: 1u = represents the number of pails

2 u = 10

1u = 5 (5 pails)

Either use

case 1: 4u – 4 = 4x5 – 4 =16

case 2: 2u + 6 = 2x5 + 6 =16

Hope this helps.

** *** *