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11 Common Types of Problem Sums

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Basic Prerequisite Knowledge

1) Modeling Method

The current approach to learning math in Singapore primary schools is through the math

model method. Under this approach, students are required to draw math modelsthat illustrate the questions. For lower primary students, modeling might seemunnecessary but the skills being mastered will come in handy at upper primaryleel where problem sums becoming more challenging.

Trial !uestion

"ane has #$% o& the stamps 'li has. They hae ( stamps altogether. *ow many stampsdoes "ane hae+

#

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#) uess and -heck

uess and -heck is a problem/soling strategy that students can use to solemathematical problems by guessing the answer and then checking that the guess&its the conditions o& the problem. For e0ample, the &ollowing problem would be

best soled using guess and check

/ -onstruct table

/ Fill in the headings

/ now what you hae

/ -heck results

Trial !uestion

2usra went to her grand&ather3s &arm. *er grand&ather has chickens and goats on his &arm.She asked him how many chickens and how many goats. 2ecause her grand&atherlikes mathematical pu44les, he told her that his animals had #5 heads and 56 legsand &rom that in&ormation she could calculate the number o& chickens and thenumber o& goats. 7& you were 2usra, how would you sole the problem+

8

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Type 1: Remainder Concept

9ery o&ten such questions hae the word :remainder; in them or ask about the totalamount o& something gien by the remainder. Most o& the time, remainder conceptquestions test the knowledge o& &ractions. *aing strong model drawing skills would be

use&ul in handling such questions.

Sometimes, it will be easier to conert decimal, percentage, ratio into &raction be&oreattempting such kind o& questions.

Sample uestion

"ude can buy 8 noels with 1$< o& his money. *e can buy 5 noels and # dictionaries withhis remaining money. 7& he wants to buy only dictionaries with all his money, howmany dictionaries can he buy

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!1. =inston can buy < towels with #$% o& his money. *e can also buy < towels and 8 T/shirts with his remaining money. *ow many T/shirts can he buy with all his moneyi& he wants to buy only T/shirts+

%

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!" Repeated #dentity Concept

>epeated 7dentity conceptproblem sums commonly &eature one unknown or ariable as apoint o& re&erence &or other unknowns. *ence, the units method is used to sole theseproblem sums.

Sample uestion

'lbert, 2ill and -arsen hae 16 stamps. 'lbert has twice the number o& stamps 2ill hasand -arsen has thrice the number o& stamp 'lbert has. *ow many stamps does 2ill hae+

5

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!1) Flora paid ?15# &or 8 skirts and # blouses. @ach blouse cost 8 times as much as askirt. *ow much did a skirt cost+

(

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$" %qual Concept

@qual -oncept problem sums compare &ractions or percentages &rom di&&erent unknowns,but which represent equal amounts.

Sample uestion

Mrs Foo had 1A5 mangoes and pears at her stall. '&ter selling some mangoes and pears,she had 1$8 o& the mangoes and 1$< o& the pears le&t. The number o& mangoes andpears le&t were the same. *ow many mangoes did she hae at &irst+

6

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!1) Miss Tay bought #A black and blue pens. '&ter giing away #$% o& the black pensand 1$8 o& the blue pens, the number o& black and blue pens le&t were equal. *owmany blue pens did she hae at &irst+

A

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&" Pattern Concept

Battern concept problem sums are among the most challenging, as they require studentsto recogni4e arying number patterns that may inole more than one arithmeticoperation.

*ere, you will need to &ind the relation between the pattern number and the number o&matchsticks usedCBattern Dumber E 8 1). Grder o& operations is also important &orgetting the right answer.

7t would usually be a number pattern or picture pattern

Sample uestion

Study the pattern belowHPattern 1 Pattern ! Pattern $

Ca) -omplete the table below.

Battern Dumber1#8ichard and Beter had the same amount o& saings. '&ter >ichard spent ?1(% andBeter spent ?6%, Beter had thrice as much money le&t as >ichard. *ow much saings didboth o& them hae altogether+

#8

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