Importance of 100%

Here is another question that my students always have problem with.

Allan had 40% more money than Ben. Charles had 20% more money than Allan. When Charles spend $1680, his amount of money decreased by 50%. Allan and Ben each spent 20% of their money. How much money did three of them left altogether?

The key for this question is to let Ben be 100% and be careful with Charles' percentage.

        84% --> $1680
        1% --> $20
        Total 276% --> $5520

The common mistake is the highlighted part - finding the percentage for Charles. 

Students normally just add 20% to Allan's 140% to find Charles. But this is wrong because Allan is not 100%.

**Note: We can only add the percentage directly when the base is 100% 

Importance of reading model

My student asked me this question:

If Alex uses his money to buy 8 similar notebooks, he will still have $6 more than Bella. If Bella uses some of her money to buy the same 8 notebooks, she will have $70 less than Alex. How much is the cost of 1 notebook?

This question can be solved easily using model.

16 notebooks + $6 --> $70

16 notebooks --> $64

1 notebook --> $4

Problem sums, even complex sums, can be solved easily using model drawings.  This is so as model drawing simplifies the problem and the pictorial representation helps pupils interpret the sum in a more comprehensible manner.   

However, the use of model drawing is just one of the many other heuristic strategies used in problem solving.  We will be sharing more effective methods, taught in Singapore Schools and we improvise them, to help you better guide your child in their Math homework.