3 Types of Problem Sums To Master Before The Math PSLE Paper

August 16, 2022

Often making headlines, Singapore’s Primary School Leaving Examination (PSLE) Mathematics paper is known to be a challenging one.

There are many types of questions students may encounter during PSLE math preparation. Out of the two papers, however, students typically struggle the most with problem sum questions in Paper Two, especially when they involve multiple steps. Every question requires a different approach to solve it correctly, so your child needs to be familiar with them.

The good news is that while the questions may change, the methods to solve them are the same. Here are three types of problem sum questions your child will have to master before the math paper.

1. Constant Total/Internal Transfer

The total usually remains the same in Constant Total/Internal Transfer concept questions so students ought to make use of this critical information.

Example question: Alex and Betty have pens in the ratio of 5 : 4. If Alex gives 20 pens to Betty, they have an equal amount of pens. How many pens does Betty have in the end?

Step 1: Make Alex’s and Betty’s total to be the same.

A : B : Total (Before)

5 : 4 : 9

10 : 8 : 18


A : B : Total (After)

1 : 1 : 2

9 : 9 : 18

Step 2: Find the difference between Alex’s starting and ending amounts.

10u – 9u = 1u

Step 3: Find one unit.

1 unit = 20 pens

Step 4: Find Betty’s amount at the end.

9 units = 180 pens

2. Gap/Difference Concept

The Gap/Difference concept is based on the difference between two variables. Typically, the difference (e.g. time or age) will remain constant while the variables change.

Example question: John’s mother gave John and Kevin an equal amount of money. John spent $20 each day and Kevin spent $25 each day. When Joe had $157 left, Kevin had $82 left. How much did Kevin receive?

Step 1: Find out the difference spent between John and Kevin each day.

$25 – $20 = $5

Step 2: Find out the difference between John and Kevin at the end.

$157 – $82 = $75

Step 3: Find out the number of days.

$75 ÷ $5 = 15 days

Step 4: Find out how much Kevin spent over 15 days.

15 X  $25 = $375

Step 5: Add the remainder left.

$375 + $82 = $457

3. Remainder Concept

Remainder concept problem sums typically test the students’ knowledge about fractions.

Example question: Ali had some sweets. He gave 178 sweets to his friend and 2/5 of the remainder to his mother. He then gave 1/3 of the remainder sweets to his neighbour and had 256 sweets left. How many sweets did he have at first?

Step 1: Find out the number of sweets left before he gave to his neighbour.

2 units 🡪 256 sweets

1 unit 🡪 256 ÷ 2= 128 sweets

3 units 🡪  128 X 3 = 384 sweets

Step 2: Find out the number of sweets left before he gave to his mother.

3 units 🡪 384 sweets

1 unit 🡪 128 sweets

5 units 🡪 128 X 5 = 640 sweets

Step 3: Find out the initial amount before he gave to his friend.

640  + 178 = 818 sweets

Master Mathematics With MindChamps’ Math Enrichment Courses

It is important to focus on mastering the above three types of problem sum questions during PSLE revision to give your child the best chance of success.

The good news is that MindChamps Enrichment Singapore has Mathematics enrichment courses available from P1 to P6 to help your child achieve mastery level for PSLE Math .knowledge essential for PSLE. For P6 students, our PSLE –The Champion Mindset Way programme will reinforce concepts and hone answering techniques to further boost their PSLE preparation for success.

Using the 3-Mind Approach, at MindChamps we help to nurture our students’ critical thinking skills and teach them how to spot patterns instead of using the rote learning method. Find out more about our Math classes by booking a visit to the nearest MindChamps Enrichment centre or contact us today to find out more.