Since the rollout of Singapore’s refreshed Mathematics syllabus in 2021 for Primary Schools, students in Primary 4 are now expected to engage with problem sums that require a deeper level of reasoning and application. This shift pushes students to not only grasp core Mathematical concepts but also apply them to different scenarios with confidence.
For many students and parents, the challenge isn’t always in the calculation but in identifying what type of Math problem sum they’re dealing with—and knowing the right method to use. Problem sums at this level test logical thinking, the ability to interpret relationships between quantities, and a clear understanding of Mathematical models.
Recognising these common structures early can help students build a strong foundation and approach even complex questions with clarity.
1. Visualising Differences: The Comparison Model Approach
The comparison model is a powerful visual tool often used in problem sums to help students understand the relationship between two quantities. Quite possibly one of the most basic methods, it involves drawing bar models of different lengths to represent the values being compared. By aligning the bars vertically, students can clearly see which quantity is greater and by how much. It’s especially helpful when one value is more or less than the other by a known difference.
Let’s look at an example.
Question:
Marcus collected 1,572 toy cars, and 324 more than what Joel collected. How many toy cars did Joel collect?
Solution Using the Comparison Model:
We treat Marcus’ quantity as the longer bar and subtract the difference:
1 Unit → 1572- 324 = 1248
So, Joel collected 1248 cars.
The visual model helps students avoid confusion when identifying which quantity is bigger and how to isolate the unknown. It also trains them to break problems down systematically—an essential skill for tackling more complex Math problem sums later on.
2. Hypothetical Scenarios: Solving with the Assumption Method
The assumption method—also known as the supposition method—is a strategic way to approach Math problem sums involving two types of items that contribute to a combined total value. It’s especially useful when the exact number of each item isn’t known, but the overall total is.
The key idea is to assume that all the items are of one type (usually the one with the smaller value), then compare the calculated total with the actual total to find the difference. This difference is then used to figure out how many items must be replaced with the other type to reach the correct value.
Question:
A school bought a total of 35 chairs and benches. Chairs have 4 legs each, while benches have 6 legs. Altogether, there were 170 legs. How many benches were there?
Solution Using the Assumption Method:
Step 1: Assume all 35 items are chairs.
35 × 4 = 140 legs
Step 2: Compare with the actual number of legs.
170 − 140 = 30 extra legs
Step 3: Each bench has 2 more legs than a chair.
30 ÷ 2 = 15 benches
So, the school bought 15 benches.
This method trains students to think logically through hypothetical reasoning—an important skill for tackling more complex problem sums as they progress.
3. Organising Units: The Grouping Concept Strategy
The grouping concept is especially helpful for Math problem sums involving equal sets of items sold or distributed in repeated combinations. This strategy requires students to first identify the composition and value of one complete group, then determine how many such groups are needed to reach a given total. It’s a common problem sum type that trains logical breakdown and proportional thinking.
Question:
A bookshop sold equal numbers of notebook sets, each containing 2 small notebooks and 1 large notebook. Each small notebook costs $3, and each large notebook costs $6. If the shop collected $144 in total, how many notebook sets were sold?
Solution:
Cost of 1 set = (2 × $3) + (1 × $6) = $6 + $6 = $12
Number of sets = $144 ÷ $12 = 12
12 notebook sets were sold.
This concept helps students visualise the grouping process clearly and apply multiplication and division meaningfully—two key skills for mastering Math problem sums in Primary 4.
4. Layered Quantities: Understanding Stacking Models
Stacking models are especially useful for solving Math problem sums involving items of different quantities layered together in one total. These questions often appear in real-world contexts—tickets, meal sets, purchases—where one type of item is priced or counted differently than another. The challenge lies in identifying the extra amount or quantity that one group contributes over the other, then working backwards to find the individual values.
Question:
Jamie bought 3 small notebooks and 2 large notebooks. A large notebook costs $4 more than a small one. If she spent $38 in total, how much does one large notebook cost?
Solution:
Step 1: Calculate the extra amount paid for the large notebooks.
$4 × 2 = $8
Step 2: Subtract the extra from the total amount.
$38 – $8 = $30
Step 3: This $30 is the cost of 5 small notebooks (3 small + 2 large, if they were all the same).
$30 ÷ 5 = $6 (cost of one small notebook)
Step 4: Add the $4 difference to get the cost of a large notebook.
$6 + $4 = $10
So, each large notebook costs $10.
Stacking models helps students visually and logically break down layered quantities—an essential strategy for mastering more complex Math problem sums.
5. Balancing Quantities: Solving Equal Stage Problems
Equal stage problem sums are a familiar feature in Primary 4 Math problem sums, typically involving two parties who start or end with the same quantity after a change—like giving away or receiving more items.
These questions often require careful model drawing and attention to key actions in the question. Words like “gave,” “bought,” “received,” or “left with” are important cues to track changes and find the balance point.
Question:
Lena had 64 stickers and Marcus had 28. After Lena gave away some stickers and Marcus received 12 more, they ended up with the same number. How many stickers did Lena give away?
Solution:
Step 1: Let’s find the difference between their original amounts:
64 – 28 = 36
Step 2: Marcus received 12 more, so the gap Lena must have closed is
36 – 12 = 24
Step 3: That means Lena gave away 24 stickers to make their totals equal.
By using model diagrams to visualise these shifts and focusing on how the numbers change before reaching the same amount, students can confidently tackle equal stage Math problem sums.
Mastering Primary 4 Math problem sums take more than just memorising steps—it’s about building the confidence to think critically and reason through different scenarios. Whether it’s drawing comparison models or using logical assumptions, these strategies equip students with the tools to tackle word problems effectively. With consistent practice and the right guidance, even the most challenging Math problem sums can become manageable.
At TLS Tutorials, we specialise in providing targeted support through our Primary School Math tuition centre in Singapore. Whether your child needs P3 Math tuition to help build fundamentals or is transitioning into upper Primary and needs P5 Math tuition classes to help tackle more complex problem types, our approach ensures that every student learns at their own pace, with clarity and confidence. Let us support your child in developing the problem-solving skills that will carry them through every stage of their academic journey.