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:-
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?