Table of Contents
1. Part-Whole Model
In P3, this model is mainly used for basic addition and subtraction. By P4, the phrasing becomes less direct, and students must think critically about the relationships between parts and wholes without explicitly solving for “1 unit.”
Example
There are a total of 8650 red and blue marbles in a box. After 2500 red marbles are added, the number of red marbles become 5700. How many blue marbles are there in the box?
Step 1: Read and write (draw model)
Step 2: Obtain Evidence: Link up information
Write Number Statements
1u = 5 700 – 2 500
= 3 200
Step 3: Solve the Mystery: Read the Math Qn Again
Blue = 8 650 – 3 200
= 5 450 (Ans)
There are 5 450 blue marbles in the box.
2. Comparison Model (Before and After, More Than/Less Than)
Many students struggle with this type of comparison model. Often, they draw two separate models and do not know how to merge them into one.
Mirroring the model is also very important. You can once again see the increase in depth when applying the same
comparison model concept in P3 and P4.
This model becomes trickier as students now need to combine two models into one and mirror them correctly.
Visual reasoning and spatial awareness become crucial at this stage.
Example
1. After Andy gave Rick 2 450 pebbles, he had 6 790 more pebbles than Rick.
How many more pebbles did Andy have than Rick at first?
Step 1: Read and Write (Draw Model)
Step 2: Obtain Evidence: Link up information
Make changes to the units in the models.
Step 3: Solve the Mystery: Read the Math Qn Again
Write Number Statements
Difference (At first) = 2450 + 6790 + 2450
= 11 690 (Ans)
Andy had 11 690 more pebbles than Rick at first.
3. Set Approach (Multiplication and Division)
Set approach is a very commonly tested concept in upper primary P5 and P6. In P4, students are introduced to basic set approach concepts to help them understand the fundamentals of sets — with and without remainders.
This is also a very real-world application-based concept that students must master.
What parents can do is to use real-world examples to have conversations with your child.
For example: You are buying muffins at a store and see a “Buy 5 Get 1 Free” offer. If you want 24 muffins for a party, how many sets should you buy?
Simple examples like these help prepare your child to understand the concept better when taught formally in school.
(A) Basic division without remainder
Example
Janet packed 132 cookies equally into 6 boxes.
How many cookies were there in each box?
Solution:
132 ÷ 6 = 22 cookies
There were 22 cookies in each box.
(B) Division with remainder
Example
Janet packed 200 cookies equally into 6 boxes and had some cookies left over.
(a) How many cookies were there in each box?
(b) How many cookies were left over?
Solution:
200 ÷ 6 = 33 R 2 cookies
a) There were 33 cookies in each box.
b) There were 2 cookies left over.
(C) Set Approach + Quantity x Value (QxV)
Example
Tip: Find 1 set
A chair has 4 legs. A stool has 3 legs. Lincoln has three times as many chairs as stools.
There are 105 legs altogether. How many chairs does Lincoln have?
1 set = 3 chairs + 1 stool
= (3 × 4) + (1 × 3)
= 15 legs
105 ÷ 15 = 7 sets
Chairs = 7 × 3 = 21 (Ans)
4. Assumption / Supposition Method
Assumption / Supposition Method is introduced in P4 to build logical thinking and structured working. In P3, students may still use guess-and-check, but from P4 onwards, this approach becomes essential.
The assumption method helps students make a starting assumption (e.g., assume all items are equal) and adjust based on clues given in the question. It improves labelling, reasoning, and accuracy.
- Missing or incorrect labels can lead to final answer mistakes.
- Hard to distinguish problem types when many adjustments are needed.
- Students may struggle with abstract ideas without concrete examples.
It’s essential that students label their assumptions carefully and check their reasoning as they go along.
Example
Each adult ticket costs $8. Each child ticket costs $5.
Sean buys 10 tickets and spends $74.
How many adult tickets did Sean buy?
Method 1: Guess and Check (to revise P3)
Method 2: Assumption / Supposition Method (Must do this method)
To-B-So-Opposite
- Total → 10 × 5 = 50
- Big gap → 74 – 50 = 24 (Total shortage of adults)
- Small gap → 8 – 5 = 3 (Difference between adult and child cost)
- Opposite (No. of tickets) → 24 ÷ 3 = 8 (Ans)
There are 8 adult tickets.
5. Multiples (Listing Method)
Multiples (Listing method) is introduced in P4, where students are taught how to list systematically using tables. This becomes a foundation for more advanced methods such as excess and shortage. It’s a challenging concept to master but essential for future problem types.
Important points to take note:
- Proper and clear headers
- Equations must be written clearly and carefully as there are many computations involved
- Look at the correct row when solving — poor labelling or organisation often leads to careless errors
Example
Lincoln has some sweets.
If he packs them in groups of 4, he will have 2 extra sweets.
If he packs them in groups of 7, he will need another 2 sweets.
What is the least number of sweets Lincoln has?
Solution:
Listing Method
STEP 1: List the Multiples of 4
STEP 2: Add 2 to the Multiples of 4
STEP 3: List the Multiples of 7
STEP 4: Subtract 2 from the Multiples of 7
STEP 5: Find the Common Number (in step 2 and step 4) = Number of Sweets
Lincoln has 26 sweets. (Ans)
| 1 gp | 2 gp | 3 gp | 4 gp | 5 gp | 6 gp | 7 gp | 8 gp | 9 gp | 10 gp | 11 gp | 12 gp | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Groups of 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| +2 extra | 6 | 10 | 14 | 18 | 22 | 26 | 30 | 34 | 38 | 42 | 46 | 50 |
| Groups of 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| –2 short | 5 | 12 | 19 | 26 | 33 | 40 | 47 | 54 | 61 | 68 | 75 | 82 |
6. Listing method (Involving Lowest Common Multiple (LCM)
Listing Method (involving Lowest Common Multiple – LCM) is very similar to the previous listing method, but with a key difference: students must not only list the numbers but also identify the Lowest Common Multiple (LCM).
This is a more advanced application of the listing strategy. Students must understand what an LCM is, and how to apply it to real-world context questions. It’s a concept that requires precision and logical structure.
Important points to take note: (Points 1–3 are similar to number 5 question)
- Proper and clear headers
- Equations must be written clearly and carefully as there are many computations involved
- Look at the correct row when solving — poor labelling or organisation often leads to careless errors
- Identify that it’s a question asking to find the LCM and apply it
Example
Jack goes to the library once every 3 days. Mary goes to the library once every 5 days.
If they first met on 7th October, on which day would they meet again next?
| Listing Method | Multiples | 3 | 6 | 9 | 12 | 15 | 18 |
|---|---|---|---|---|---|---|---|
| Multiples Table | Multiples of 3 | 3 | 6 | 9 | 12 | 15 | 18 |
| Multiples of 5 | 5 | 10 | 15 | 20 |
Find the Common Number (from both rows above) = 15 days
They will meet again after 15 days.
L.C.M. of 3 & 5 = 15
7th Oct ➜ 22nd Oct (Ans)
7. Excess and Shortage
In p4, students may still prefer using the listing method despite it being tedious and easy to make mistakes as its easier to understand and its less abstract.
Its ok to use the listing method in p4 in the beginning to really understand the concept behind why is there and addition or subtraction for each value.
However its important to transit to the excess and shortage method once they had mastered it as questions will get more challenging as they move on to p5
and the listing method will not be very ideal for such questions.
Example: Some apples are to be shared among some children.
If each child gets 5 apples, there will be 24 apples left.
If each child gets 8 apples, there will be 6 apples short.
- (a) Find the number of children.
- (b) Find the number of apples.
Solution:
Method 1: Listing Method
| Num of children | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 5 apples each | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| +24 left | 29 | 34 | 39 | 44 | 49 | 54 | 59 | 64 | 69 | 74 | 79 | 84 |
| 8 apples each | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| -6 short | 2 | 10 | 18 | 26 | 34 | 42 | 50 | 58 | 66 | 74 | 82 | 90 |
(b) Number of apples = 74 (Ans)
Method 2: Excess + Shortage
SUMMARY
3 Scenarios
Case 1: Excess + Shortage
Case 2: Excess – Excess
Case 3: Shortage – Shortage
Big gap = 24 + 6 = 30
Small gap = 8 − 5 = 3
Number of children = 30 ÷ 3 = 10 (Ans)
Number of apples = (10 × 5) + 24 = 74 (Ans)
There are 10 children and 74 apples.
Method 2 of excess and shortage is definitely a faster approach and lower chance of making mistakes. However this method is pretty abstract so the model drawing will help student to understand the concept better. Usually p4 students who can understand this method 2 are the advance learners.
8. Equal Concept
There are 3 types of equal concept in total,
- Equal beginning (At first)
- Equal ending
- Equal change
Equal concept is tested yearly in PSLE! Parents do take note. So it’s a concept that you must definitely master.
In P4, we first teach the Equal Concept on equal beginning. (At First)
Students are taught how to solve the question using a model.
Start off with a “Double Decker Bus”
2 types:
1) External Transfer
Example
Lincoln and Elyse had the same number of marbles at first. Lincoln gave away 20 marbles and Elyse gave away 50 marbles. Lincoln then had 3 times as many marbles as Elyse at the end. How many marbles did Lincoln and Elyse each have at first?
Step 1: Search for Clues (Read and Write)
Step 2: Obtain Evidence Clues (Look and loop up information)
2 units = 50 – 20
= 30
Step 3: Locate the key (Find 1 unit)
1 unit = 30 ÷ 2
= 15
Step 4: Solve the Mystery (Read the Qn to solve)
At first = 50 + 15
= 65 (Ans)
Each of them had 65 marbles at first.
2) Internal Transfer
Concept: Equal Concept + Internal Transfer
Example
Diana and Amy had an equal amount of money at first.
Diana gave Amy $120. Amy then had 5 times as much money as Diana.
How much money did Diana have at first?
Step 1: Search for Clues (Read and Write)
Step 2: Obtain Evidence Clues (Look and loop up information)
4 units = $120 × 2
= $240
Step 3: Locate the key (Find 1 unit)
1 unit = $240 ÷ 4
= $60
Step 4: Solve the Mystery (Read the Qn to solve)
At first = $60 + $120
= $180 (Ans)
Big gap = 24 + 6 = 30
Small gap = 8 − 5 = 3
Number of children = 30 ÷ 3 = 10 (Ans)
Number of apples = (10 × 5) + 24 = 74 (Ans)
There are 10 children and 74 apples.
9. Equal Concept – Equal Change
The next part of the Equal Concept series is Equal Change. In these questions, the same amount is either added to or subtracted from both parties, yet the difference between them stays the same.
Students are taught to draw a model to represent these changes clearly. They learn to add to or cut from the front part of the model to reflect what is given or taken away.
There are three common scenarios in Equal Change questions:
- Same amount given away
- Same amount received
- Same age gap or difference over time
By drawing and adjusting the model accurately, students can better understand the logic behind the question and solve it with confidence. Visualizing the movement of quantities helps solidify the concept and reduces careless errors.
1. Same amount given away
2. Same amount received
3. Age gap
10. Equal Concept – Equal Ending
The final part of the Equal Concept series is Equal Ending. In these questions, students are taught to use model drawing to represent the situation clearly.
We guide students to start with a “double-decker bus” model—two horizontal bars stacked one above the other—to show the comparison between the two subjects.
This model helps students visualize how the values align at the end of the scenario, even if the starting points or changes along the way were different. Understanding and applying this model correctly allows students to solve these questions with greater confidence and accuracy.
As with all Equal Concept types, identifying keywords and choosing the correct model are essential steps toward solving the problem effectively.
1. External Transfer
2. Internal Transfer
For all 3 types of Equal Concept questions — Equal Beginning, Equal Change, and Equal Ending — students must:
- 💡 Identify and distinguish the type of Equal Concept used in the question
- 📏 Draw the correct model (usually Double Decker Bus) to visualize the problem
- 🔗 Understand how the parts of the question link together to choose the right solving method
This is a challenging but powerful concept to master. With practice and the right guidance, students can learn to spot the clues and keywords that point to the correct method.
🎯 Once the concept is identified, applying the correct model becomes easy — and solving becomes faster and more confident!
11. Solving Fraction Problem Sums (Addition & Subtraction)
Fractions can feel intimidating for many P4 students because they are abstract. Often, students don’t fully grasp that a fraction is simply a number (e.g., ½ = 0.5).
In fraction problem sums, it’s crucial to know:
- ➕ “More than” means Addition
- ➖ “Less than” means Subtraction
To solve fraction addition/subtraction, students need to be confident in:
- 📚 Times table proficiency
- 🔢 Finding Lowest Common Multiple (LCM) of different denominators
Example: To solve ½ + ⅓, students must know that the LCM of 2 and 3 is 6, and convert both to sixths: 3/6 + 2/6 = 5/6.
💭 Why Do Students Struggle?
- 🔍 Abstract thinking – Numbers like ½ or ¼ feel less intuitive without visual support
- ❌ Weak multiplication skills – LCM becomes difficult if times tables are shaky
- 🧠 Bridging concepts – They must apply P3 logic to a new fraction format, often across multiple steps
Solving fraction sums requires clear thinking, good number sense, and step-by-step guidance. With the right support and enough practice, students can build both confidence and stamina to master it!
Example:
12. Equal Fractions
Understanding equal fractions is an important stepping stone in mastering fraction problem sums. At BlueTree, students learn this in two stages:
(A) Model Approach
Students start by using visual models to represent equal fractions. This helps them understand why the numerators must be the same and builds a strong conceptual base.
(B) Abstract Method (Making the Numerators the Same)
Once students are confident with the model, they move on to a more efficient method—making the numerators the same using direct calculations. This step reduces errors and improves speed, especially when the models become too complex to draw.
By progressing from visual to abstract thinking, students gain both clarity and confidence in solving equal fraction problems efficiently.
13. Patterns (Using the Linear Equation Formula)
Pattern questions often involve a fixed increment or decrement between terms. To solve these efficiently, students are taught a linear equation formula that helps them identify the rule behind the pattern.
Once students master this formula, they will be able to tackle all fixed-pattern questions with ease — even if the sequence looks complex.
This method not only saves time but also builds confidence in handling number sequences logically and effectively.
14. Stack-Up Model
Students often feel intimidated when they see fractions in a question. At Bluetree, we use the “Read and Write” technique to help them break down the information and overcome this fear.
By carefully annotating the question—especially using arrows to highlight relationships—students can identify key values (e.g., bottle = 2u, jug = 3u). From there, they can draw a stack-up model and apply the unitary method to solve the problem confidently.
This technique turns what seems like a complex problem into a manageable, step-by-step process.
15. Age Questions (Difference Remains Constant)
When solving age-related problem sums, it is important for students to remember that the age difference remains constant over time. Using proper labels and drawing a model are crucial steps to avoid confusion.
Many students make mistakes in these questions because they either skip labeling or misinterpret the timeline. Labels such as “present age”, “years ago”, or “in X years” help students stay organized and make sense of the information given.
Clear labeling acts as a guide, keeping them on track and reducing careless errors.
16. Repeated Identity (Model Approach)
For repeated identity questions, students should always draw the common item at the start of the model. This strategy makes it much easier to visualize the relationships and solve the problem accurately.
A common mistake students make is skipping or misplacing the common item in their model, which often leads to confusion. With a correctly drawn and well-labeled model, these questions become straightforward and much less intimidating.
17. Units and Parts
Tip: always make opposite item the same to get rid of it
Conclusion: The P4 Milestone
Primary 4 marks a crucial turning point where students shift from basic arithmetic to more abstract problem-solving. This year lays the groundwork for upper primary math and PSLE success. It’s perfectly normal for students to find these new concepts challenging at first.
What matters most is consistent practice, guided support, and a willingness to learn from mistakes.
💡 To Parents: Your encouragement makes all the difference. Use everyday moments to spark math conversations and celebrate small wins.
🚀 To Students: Keep going! Every mistake is a step closer to mastery. With focus, practice, and the right techniques, you’ll become a problem-sum pro in no time.
