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Relearning Maths Using The Singapore Model Method

Posted by on 24 April 2009

One of the challenges of being a working mother is finding the energy and patience to switch to ‘mommy mode’ at the end of a hectic day at the office. And for me, ‘mommy mode’ this week meant spending nights going through maths equations and word problems with OnlyGirl (9+) and RoundBoy (7+). They both go to a private school in KL that teaches both the Malaysian national curriculum and the Singapore curriculum for Maths and English. I’d have to tell you that, for the past 2 weeks, the Singapore curriculum has been giving my brain more workout than I can remember ever doing in a long, long time.

The concept is simple: use a ‘model’ or a diagram to illustrate the problem, then find a way to solve it. I find this method to be very effective because, first of all, it forces your child to understand the problem first, rather than simply remembering the method of calculating for the answer. Secondly, it helps the child solve problems that are quite complex in a much simpler way.

Let me show you what I mean through the following word problem:-

There are 160 apples and pears inside a box. If 1/2 of the pears is the same number as 5/6 of the apples, how many apples and pears are there?

Sounds rather complicated for a 9-year old, don’t you think? With the Singapore model method, the solution is actually maddeningly simple.

First, draw a diagram to illustrate the given data:-

model 1

Then, from the above diagram, we can deduce that 5/6 of the apples has 5 equal units:-


Ergo, if 5/6 if the apples is the same as 1/2 of the pears, that means 1/2 of the pears would have 5 units, as well:-


So if 1/2 of the pears have 5 units, then logically, the total number of pears would have 10 units. And the apples would have a total of 6 units:-


From this point on, all we have to do is add the total number of units:-

10 units Pear + 6 units Apples = 16 units

Then dividing the total number of fruits by the total number of units:-

160 / 16 = 10 fruits per unit

Therefore, we can easily conclude that there are:-

10 units x 10 fruits/unit = 100 Pears
6 units x 10 fruits/unit = 60 Apples

Simple, isn’t it?

The model method can be used for solving word problems involving discounts and percentages. Let’s take a look at this word problem:-

A set of patio furniture is on sale at a 23% discount. If the discount given is $690, how much is the selling price of the furniture set?

First off, we draw a simple diagram like so:-


From this model, we can see that $690 is 23% and that we need to find out the other 77% (which we calculated by subtracting 23% from 100%).

So…we start with what we know, i.e. based on what’s given in the word problem, which is:-

23% = $690

Now all we need to know is find out how much 1% is. How? By dividing 23% by itself, we reduce it to 1%. But we must also do the same thing with the other side of the equation, i.e.:-


which leads to:-


So now, we go back to the model.


In order to find out the patio set’s selling price after it’s been discounted, all we need to do is find out the value of the other 77% of the diagram. And how do we do it? Just multiply 77% with the value of the 1% that we calculated just a while ago.

77% = 77 x (the value of 1%)
77% = 77 x $30

77% = $2310

Now, had the question been “How much did the patio furniture set originally cost?”, all I needed to do would have been to multiply the value of 1% with 100, i.e.:-

100% = 100 x (the value of 1%)
100% = 100 x $30
100% = $3000

Meanwhile, as OnlyGirl wrestled with discounts and percentages, I found a fun and easy way of multiplying large numbers for RoundBoy — lattice multiplication. It made maths fun again…and gave him a much-needed boost in confidence.

There’s nothing quite as fulfilling as seeing your child’s eyes light up with understanding after you walk through the process with him/her. Plus, there’s the satisfaction of learning and mastering new techniques yourself.

With a nightly mental workout like this, who needs Sudoku?

16 Responses to Relearning Maths Using The Singapore Model Method

  1. Lola

    Because I could not get it, they would tell me “What a pity, Lola, you never learned this way during your school days:-)

    I would need this to poke my brain!

  2. Lola

    Thank you for this. I will relearn my maths this way :-)

  3. kg

    Mimi! mahina ako sa math ever since….that has been my weakness. i wonder if they invented this technique just now. that’s a good exercise to teach children who are having a hard time in math [like me]. :)

  4. mordsith

    that’s a nice technique! :) I am poor in math. I should have learned this many many years ago!

  5. odette

    i hate maths, except percentages and fractions. geometry and the rest of the numbers gang are hovering vaguely on the background. ^-^
    luckily, both civil service and lbp examinations i took mostly dwelt on percentages and fractions! you have a very effective teaching concept, you make it sound fun and easy!

  6. a-moms-diary

    Oh boy! I was struggling with the apples and pears question, till I saw your diagram. This is really a good method to teach children to think, instead of just memorising.

  7. ana

    Dear Mimi,

    Thanks for your blog about the model method. This will help me in my research.

    God Bless you!


  8. Mimi

    ana: i’m glad this post, which i wrote out as a pastime, helped you with your research. good luck!

  9. Yaggya

    Its quite interesting to see how Maths can be made more comprehensible by depicting the same through pictures. Thanks for the elaborate effort in depicting the same on ur blog. I am an Indian expat trying to find an appropriate school for my daughter now 3years old. Looking at International schools (Indian or British curriucilum). Both have their advantages and disadvantages. Also, searching for a school that follows Singapore curriculum in KL. Would you mind sharing (via email) which school/schools follow Singapore curriculum. Could you recommend a school for my child. The Indian system here is more towards rote learning but they tend to cover a huge syllabus as opposed to the British curriculum where the syllabus is less but understanding the concept is given more priority. Indian I am struggling to decide which school will be best for her. Since you have already gone through this stage, would u mind sharing and giving ur tips. Thanks in advance.

  10. alfchan

    Can you tell which school your children are attending? If find the fees for international school too expensive.

  11. Retha Tamashiro

    Hello! I have a hard time looking for this post, I am using it for my assignment, please don’t hesitate to make fresh interesting idea. expecting for your future writings. Thanks, Good Luck!

  12. anna

    Hi, are your children still studying in this school? Is it still good? I’ve heard that many private schools have a high turnover of teachers and that many are asking for money all the time. I’m looking for a good school for my daughter and am in a quandary. Please email me the name of the school. Many thanks!

  13. SC


    Could I find out the name of the private school that teaches Singapore based Maths and English curriculum for my kids?

    Many thanks in advance,

  14. Kana Vijay

    Turn words into two equations.No need for models.

    Solve using A for apple and P for pears ,you get P=
    100 and A=60.

  15. Kana Vijay

    If 2 3% is $690 then 100% is 690/23×100=3000..

  16. Kana Vijay

    Understanding is more important than memory as such a child should be encouraged to observe,think for themselves and see what can be drawn from the experience of observation,data collection in the mind ,and form a hypothesis , test it himself or herself ,it does not matter if failed but an experience of a life time no rota learning.Thats what I did on my own at my pre-school days of 4 years old and was encouraged to become an Engineer at my age of 5 years old by my late father.

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