Here’s a scenario that plays out in living rooms across Singapore every week. Your child sits down with a PSLE Math practice paper, breezes through Paper 1, and then hits Paper 2. The first problem sum looks manageable. The second one, too. But by the third or fourth question, they’re stuck, not because they can’t do the arithmetic, but because they can’t figure out what the question is actually asking them to do.
This is the reality of PSLE Mathematics. The exam doesn’t just test whether your child can calculate. It tests whether they can read a problem, identify the underlying concept being tested, and choose the right approach to solve it. And that’s where most students struggle.
At BrightMinds Education, we’ve been teaching PSLE Math since 2008, and one of the most effective frameworks we use is built around 11 core concepts that appear again and again in PSLE Math problem sums. These aren’t random categories we invented, they reflect the recurring patterns that SEAB uses to design questions across topics like Fractions, Ratio, Percentage, Whole Numbers, and more.
When your child can recognise which of these 11 concepts a question is testing, they’re no longer guessing. They have a starting point, a strategy, and a clear path to the answer.
Let’s walk through each one.
Why Concepts Matter More Than Memorisation
Before we dive in, it’s worth understanding why this approach works.
PSLE Math Paper 2 is worth 55 marks and consists of short-answer and long-answer problem sums ranging from 2 to 5 marks each. The questions are deliberately designed so that students cannot simply apply a memorised formula. They need to understand the relationship between the pieces of information given, figure out what’s changing and what’s staying the same, and then select the most efficient method to solve the problem.
Our teaching approach at BrightMinds follows three steps: understand the concept being tested, analyse the content of the problem sum, and choose the best method to solve it. The 11 concepts below form the foundation of that first step, and once your child internalises them, they’ll approach every problem sum with far greater clarity and confidence.
Concept 1: Remainder Concept
What it is: Problems where something is divided, spent, or given away in stages, and the question involves the “remainder” or “what’s left” after each stage.
How to spot it: Look for the word “remainder” or phrases like “the rest,” “what was left,” or “of the remaining.” These questions usually involve fractions or percentages being applied one after another.
Example: Sarah had some stickers. She gave 2/5 of them to her sister and 1/3 of the remainder to her brother. She then had 80 stickers left. How many stickers did Sarah have at first?
How to solve it: The key technique here is the branching method, working through each stage of the problem sequentially. Your child traces what fraction is left after each “give away” step, expresses the final amount as a fraction of the original, and then works backwards.
After giving away 2/5, Sarah has 3/5 left. Of that remainder, she gives 1/3 away, keeping 2/3 of the remainder. So she has 2/3 × 3/5 = 6/15 = 2/5 of her original amount. If 2/5 of the original equals 80 stickers, then the original amount is 80 ÷ 2 × 5 = 200 stickers.
Why students get it wrong: They try to add the fractions directly (2/5 + 1/3) instead of recognising that the second fraction applies to the remainder, not the original total.
Concept 2: Repeated Identity Concept
What it is: Problems where two or more relationships share a common item. The “repeated identity” is the quantity that appears in more than one comparison.
How to spot it: The question gives two separate ratios or fraction comparisons that share one common item. For example, “A is 2/3 of B” and “B is 1/4 of C.”
Example: Devi has 2/3 as many stamps as Ling. Ling has 1/5 as many stamps as Kumar. If the three of them have 120 stamps altogether, how many stamps does Devi have?
How to solve it: Identify the repeated identity, in this case, Ling appears in both comparisons. Express all three quantities in terms of the same unit. If Ling = 5 units (so Kumar = 25 units, since Ling is 1/5 of Kumar), and Devi = 2/3 of 5 = 10/3 units. Then find the total in units and solve.
The trick is making the repeated item have the same value in both ratios, so everything can be compared directly.
Why students get it wrong: They set up two separate ratios but forget to make the common item the same number of units before combining them.
Concept 3: Equal Concept
What it is: Problems where two different fractions or ratios of different items are equal to each other.
How to spot it: Phrases like “1/3 of A is equal to 1/4 of B” or “after the change, both had the same amount.”
Example: 1/3 of the number of boys is equal to 2/5 of the number of girls. If there are 44 children altogether, how many boys are there?
How to solve it: Since 1/3 of Boys = 2/5 of Girls, we can write Boys/3 = 2 × Girls/5. This means Boys = 6 units and Girls = 5 units when we make the equal portions the same (both equal 2 units). So Boys = 6u, Girls = 5u, but we need to check: 1/3 of 6u = 2u, and 2/5 of 5u = 2u. Correct. Total = 6u + 5u = 11u = 44 children. So 1u = 4, and Boys = 6 × 4 = 24 boys.
Why students get it wrong: They don’t equate the fractions properly and end up comparing unlike parts.
Concept 4: External Transfer with Unchanged Quantity (Constant Part)
What it is: A “before and after” problem where one item’s quantity changes but the other stays the same.
How to spot it: Only one side of the ratio changes. For example, some cars leave a car park but the number of motorcycles stays the same.
Example: The ratio of cars to motorcycles in a car park was 10 : 3. After 154 cars left, the ratio became 3 : 2. How many cars are left?
How to solve it: Since motorcycles didn’t change, make the motorcycle units the same in both ratios. Before: Cars : Motorcycles = 10 : 3 → multiply by 2 → 20 : 6. After: Cars : Motorcycles = 3 : 2 → multiply by 3 → 9 : 6. Now motorcycles are both 6 units. The difference in cars = 20u − 9u = 11u = 154. So 1u = 14, and cars remaining = 9 × 14 = 126 cars.
Why students get it wrong: They forget to equalise the unchanged quantity before comparing.
Concept 5: Internal Transfer with Unchanged Total (Constant Total)
What it is: One person gives something to another person. The total amount between them doesn’t change, it just shifts from one to the other.
How to spot it: Phrases like “A gave B some amount” or “A transferred to B.” No items enter or leave the system.
Example: Ali and Bala had money in the ratio 5 : 4. After Ali gave Bala $20, they had equal amounts. How much money did Bala have at first?
How to solve it: Total stays the same. Before: 5u + 4u = 9u. After they’re equal: each has 9u ÷ 2 = 4.5u. But since we’re working with whole units, we can scale up. Before = 5 : 4 (total 9). After they’re equal, each has 4.5 parts of the original. Ali lost 0.5u, which equals $20. So 0.5u = $20, meaning 1u = $40. Bala had 4 × $40 = $160 at first.
Why students get it wrong: They confuse this with external transfer and don’t recognise that the total is unchanged.
Concept 6: External Transfer with Unchanged Difference (Constant Difference)
What it is: Both items gain or lose the same amount, so the difference between them stays the same.
How to spot it: This is the classic “age problem” setup. As time passes, both people age by the same number of years, so their age difference never changes. It also appears in questions where both parties spend or receive the same amount.
Example: Ryan is 33 years old and his son is 5 years old. In how many years will Ryan be three times as old as his son?
How to solve it: The age difference is 33 − 5 = 28 years, and this will always remain 28. When Ryan is 3 times his son’s age, the difference (which is 2 parts of the son’s age) equals 28. So the son’s age at that point = 28 ÷ 2 = 14. Since the son is currently 5, it will happen in 14 − 5 = 9 years.
Why students get it wrong: They try to set up complicated equations instead of recognising that the difference is constant and using it as the anchor.
Concept 7: External Transfer with Changed Quantities (Everything Changes)
What it is: Both items change by different amounts. Nothing stays constant, not the total, not the difference, not any individual part. These are typically the hardest problem sums in the paper.
How to spot it: Both sides of the ratio change and by different amounts. These questions often appear as the final 4- or 5-mark problems.
Example: Ali had 3 times as many sweets as Bala. After Ali ate 14 sweets and Bala received 22 sweets, they had the same number. How many sweets did they have altogether at first?
How to solve it: This requires the “Units and Parts” method. Before: Ali = 3u, Bala = 1u. After: Ali = 3u − 14, Bala = 1u + 22. Since they end up equal: 3u − 14 = 1u + 22. So 2u = 36, meaning 1u = 18. Total at first = 3u + 1u = 4 × 18 = 72 sweets.
Why students get it wrong: Because nothing is constant, students panic and don’t know where to start. The key is to express everything in units and let algebra do the work.
Concept 8: Pattern Concept
What it is: Problems that involve a sequence or repeating arrangement, where students must identify the rule governing the pattern and use it to find a specific term or total.
How to spot it: Questions about figure numbers, tile arrangements, shapes in a sequence, or any repeating structure.
Example: Figure 1 has 5 dots. Figure 2 has 8 dots. Figure 3 has 11 dots. How many dots are there in Figure 20?
How to solve it: Identify the pattern, the number of dots increases by 3 each time. The formula is: Number of dots = 5 + (Figure number − 1) × 3. For Figure 20: 5 + 19 × 3 = 5 + 57 = 62 dots.
Why students get it wrong: They try to list every single figure instead of finding the general rule. For larger figure numbers, this becomes impractical and error-prone.
Concept 9: Proportions Concept (Grouping)
What it is: Problems involving the total quantity of two or more types of items with different values, where students need to find how many of each type there are.
How to spot it: Often involves money (e.g., $2 coins and $5 notes), or items with different properties (e.g., tables with 4 legs and stools with 3 legs).
Example: A box contains a mixture of $2 coins and $5 notes. There are 40 items in total and their combined value is $131. How many $2 coins are there?
How to solve it: Use the supposition method (also called “guess and check” with logic). Suppose all 40 items were $2 coins. Total value = 40 × $2 = $80. The actual total is $131, which is $51 more. Each time we replace a $2 coin with a $5 note, the value increases by $3. Number of $5 notes = $51 ÷ $3 = 17. So $2 coins = 40 − 17 = 23 coins.
Why students get it wrong: They try random guessing instead of using the systematic supposition method, which is faster and more reliable.
Concept 10: Simultaneous Concept
What it is: Two equations with two unknowns, where students need to compare or combine the equations to find the value of each unknown.
How to spot it: Two different combinations of the same items with different totals. For example, “3 pens and 2 erasers cost $8” and “2 pens and 3 erasers cost $7.”
Example: 3 files and 2 books cost $60. 2 files and 3 books cost $70. Find the cost of 1 file.
How to solve it: Multiply the first equation by 3 and the second by 2 so that the books term matches: 9 files + 6 books = $180, and 4 files + 6 books = $140. Subtract: 5 files = $40. So 1 file = $8.
Alternatively, students can add both equations: 5 files + 5 books = $130, so 1 file + 1 book = $26. Then substitute back to find each.
Why students get it wrong: They don’t realise they need to make one of the unknowns the same before subtracting. This is a stepping stone to formal algebra in secondary school.
Concept 11: Gap and Differences Concept
What it is: Problems where two people start with different amounts and spend or earn at different rates, creating a “gap” that either closes or widens over time.
How to spot it: Two scenarios with different rates of spending, earning, or distributing.
Example: Mei gave each student 8 stickers and had 15 stickers left over. If she had given each student 11 stickers instead, she would be short of 12 stickers. How many students are there?
How to solve it: The difference in stickers per student is 11 − 8 = 3. The total difference in outcome is 15 + 12 = 27 (going from 15 extra to 12 short). Number of students = 27 ÷ 3 = 9 students.
Why students get it wrong: They don’t see the connection between the “excess and shortage” and the per-unit gap. Once they understand that the total swing is caused by the per-unit difference multiplied by the number of items, this concept clicks.
How These 11 Concepts Map to PSLE Topics
One reason students find problem sums challenging is that the same concept can appear across completely different topics. For instance, the Constant Part concept might show up in a Ratio question one year and a Fractions question the next. The numbers and context change, but the underlying logic is identical.
Here’s how the concepts typically map to the main PSLE Math topics:
Fractions and Decimals, Remainder Concept, Equal Concept, Repeated Identity
Ratio and Percentage, All four External Transfer types, Internal Transfer, Constant Part, Proportions
Whole Numbers, Simultaneous Concept, Gap and Differences, Pattern
Algebra, Simultaneous Concept, Pattern, Everything Changes
Speed and Distance, Constant Difference (objects moving towards or away from each other), Everything Changes
When your child practises problem sums, encourage them to label each question with the concept being tested before attempting to solve it. Over time, this habit transforms problem-solving from a stressful guessing game into a structured, repeatable process.
The BrightMinds 3-Step Approach to Problem Sums
At BrightMinds, we teach every problem sum using a simple three-step framework:
Step 1, Identify the concept. Read the question carefully. What’s staying the same? What’s changing? Is there a remainder, a transfer, a pattern, or a comparison? Match it to one of the 11 concepts.
Step 2, Analyse the content. What topic is the question from, Fractions, Ratio, Percentage, Whole Numbers? What information is given, and what are you asked to find? Draw a model, set up units, or create a table to organise the information.
Step 3, Choose the best method. Bar models, units method, branching, supposition, or algebraic approach, pick the method that fits the concept and the numbers given. Then solve, check, and present the working clearly.
During our PSLE Math Intensive Revision Course, students practise more than 60 problem sums across all 11 concepts. Each question is specially prepared by our head Math teacher to reflect the style and difficulty of actual PSLE papers. Our students don’t just learn how to solve individual questions, they learn how to recognise what any question is asking and respond systematically.
As one of our former students, Nur Insyirah from Madrasah Alsagoff Al-Arabiah, shared after our course: “I can solve more questions easily now. I learnt new Maths concepts such as the Proportions concept, Gap and Differences concept, External and Internal Transfer concept.” She went on to score an A for PSLE Maths.
What Parents Can Do at Home
You don’t need to be a maths expert to help your child get better at problem sums. Here are some practical things you can do.
Print a “concept checklist.” Write down all 11 concepts on a sheet of paper. After your child completes each practice paper, have them label every problem sum with the concept it tests. This builds recognition speed over time.
Focus on one concept per week. Instead of doing random practice papers, dedicate each revision session to a specific concept. Spend a week on Remainder Concept questions, then a week on Internal Transfer, and so on. Depth beats breadth.
Review mistakes by concept, not by topic. If your child keeps getting Ratio questions wrong, dig deeper. Are they struggling with Constant Part? Constant Difference? Everything Changes? The problem might not be “Ratio” as a whole, it might be a specific concept within Ratio that needs attention.
Let your child explain their thinking out loud. If they can talk through why they chose a particular method, they understand the concept. If they can only show you the steps without explaining the reasoning, they may be relying on memorisation rather than genuine understanding.
The Bottom Line
PSLE Math problem sums don’t need to be intimidating. Behind every challenging question lies one of these 11 concepts. When your child learns to recognise the concept, the question stops being a mystery and becomes a structured puzzle with a clear path to the answer.
At BrightMinds Education, we’ve been teaching these 11 concepts to Woodlands students since 2008. Our small class sizes of 10 to 12 students ensure that every child gets the attention they need to build genuine understanding, not just surface-level familiarity with worked solutions. If your child is preparing for the 2026 PSLE and needs help mastering problem sums, we’d love to work with them.
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