The model method — drawing problems as labelled bars — is Singapore's signature primary maths strategy, and it turns wordy PSLE problem sums into a picture a child can reason about. In our experience, many marks are lost not in the arithmetic but in not knowing where to start; the bar model tackles exactly that. This guide is from Ancourage Academy, whose primary Mathematics tuition teaches the model method step by step in small groups of 3–6 at Bishan and Woodlands.
This is a single-topic deep-dive — the bar-model companion to our broader PSLE maths heuristics guide (which covers all 12 problem-solving methods) and our PSLE maths tips. It also sets up the bridge from model drawing to algebra in secondary school.
If your child freezes on problem sums, Ancourage Academy's upper-primary Maths programme builds the model method from the basics — book a trial class (usually $18) for a diagnostic assessment.
What Is the Model Method in PSLE Maths?
The model method represents the quantities in a problem as rectangular bars drawn to relative size, so the relationships between them become visible and the unknown can be found by reasoning about units. It is central to the Singapore primary maths approach described in the MOE primary mathematics syllabus and supports the problem-solving demands of the PSLE Mathematics examination. The method works because it makes an abstract word problem concrete.
What Are the Two Types of Bar Model?
Almost every bar model is one of two structures — the part-whole model or the comparison model — and recognising which one a problem needs is the first decision.
| Model | What it shows | Typical wording |
|---|---|---|
| Part-whole | Parts combining into a total | "altogether", "in total", "the rest" |
| Comparison | Two or more quantities compared | "more than", "less than", "twice as many" |
In a part-whole model the parts sit end to end to form one whole bar; in a comparison model the bars are stacked to show the difference. Many multi-step problems combine both, but every step is still one of these two shapes.
How Do You Apply the Model Method?
The model method follows a fixed routine: read the problem, draw and label the bars, mark the unknown, then work out the value of one unit.
- Read carefully and identify what is known and what is being asked.
- Draw the bars to roughly the right relative sizes, choosing part-whole or comparison.
- Label everything — values, the difference, and a "?" for the unknown.
- Find one unit: use the numbers to work out the value of a single unit, then scale up to the answer.
The "find one unit" step is the engine of the method and is exactly the thinking that becomes algebra later — the unit is, in effect, the unknown x.
What Do Bar-Model Worked Examples Look Like?
Here are three worked PSLE examples — a comparison problem, a fraction problem and a before-after problem — each solved with the same routine: draw the units, find the value of one unit, then scale up to the answer. Seeing the unit reasoning in action is the fastest way to make the method click.
| Problem | Bar setup | Working and answer |
|---|---|---|
| Comparison: Ravi has 3 times as much pocket money as Siti; together they have $48. | Siti = 1 unit, Ravi = 3 units (4 units in total) | 4 units = $48, so 1 unit = $12 → Ravi = $36, Siti = $12 |
| Fraction (part-whole): 3/5 of the 40 pupils in a class are boys. | Whole bar = 5 equal units = 40 pupils | 1 unit = 8, so boys = 3 units = 24 and girls = 2 units = 16 |
| Before-after: Ann has $90 and Bala has $60. After each spends the same amount, Ann has twice as much as Bala. | The $30 difference stays constant; after spending, Bala = 1 unit and Ann = 2 units | Difference = 1 unit = $30 → Bala = $30, Ann = $60 (each spent $30) |
Notice the same three steps every time. The before-after example shows the decisive skill: spotting the quantity that does not change — here the $30 difference between Ann and Bala — and using it to anchor the two models against each other.
How Do Bar Models Handle Fractions, Ratio and Percentage?
The same bars extend naturally to fractions, ratio and percentage by dividing the bar into equal units.
- Fractions: split the whole bar into the number of equal parts the denominator gives, then shade the fraction.
- Ratio: draw one unit per share, so a ratio of 2 : 3 is a bar of 2 units beside a bar of 3 units.
- Percentage: treat the whole as 100% and divide the bar into the units the question needs.
Because fractions, ratio and percentage all describe proportional relationships, one consistent bar picture lets a child move between them — a major reason the method is so powerful for the upper-primary syllabus.
What About Before-and-After Problems?
Before-and-after problems — where quantities change partway through — are solved by drawing two bar models, one for the situation before the change and one for after, and comparing them. These are among the hardest PSLE problem sums, but the two-picture approach makes the change visible: what stayed the same (the "constant") is the key to unlocking them. Identifying the unchanged quantity, then aligning the two models against it, turns a confusing problem into a clear comparison.
The Most Common Model Method Mistakes
In our primary Maths classes at Ancourage Academy, a handful of recurring errors cause most avoidable mark loss with the model method.
| Mistake | Why it happens | How to fix it |
|---|---|---|
| Not drawing the model | Trying to do it all mentally | Always draw — the picture is where the marks are found |
| Unequal units | Drawing units of different sizes | Keep every unit the same width within a model |
| Wrong model type | Forcing part-whole onto a comparison | Check the wording: "altogether" vs "more than" |
| Forgetting to find one unit | Jumping to the answer | Work out one unit first, then scale up |
| Misaligned before-after bars | Not spotting the constant | Identify what stays the same and align the two models to it |
Why the Model Method Builds Algebraic Thinking
The model method is not just a primary trick — it is concrete algebra, and the "one unit" a child solves for is the same idea as the unknown in a secondary equation.
- One unit = x: finding the value of a unit mirrors solving for an unknown.
- Smooth transition: students who understand bar models adapt to algebra faster. See our model-to-algebra bridge guide.
- Lasting habit: drawing to understand a problem helps right through secondary maths.
A Study Plan for the Model Method
Build the method in order: the two model types, then fractions and ratio, then before-after problems.
- Weeks 1–2 — the two models: drill part-whole and comparison models on whole-number problems.
- Weeks 3–4 — fractions and ratio: practise dividing bars into equal units for fractions and ratio.
- Weeks 5–6 — percentage: apply the whole-as-100% bar to percentage problems.
- Weeks 7–8 — before-after: tackle two-model problems, focusing on the unchanged quantity, under timed conditions.
Ancourage Academy's P5 and P6 Mathematics programmes teach the model method on this progression in small groups of 3–6. Book a trial class (usually $18) for a diagnostic, or WhatsApp us with any questions.
Common Questions About the PSLE Maths Model Method
What is the model method in PSLE maths?
The model method, often called the bar model, is a visual problem-solving strategy in which the quantities in a word problem are drawn as rectangular bars sized in proportion to one another. Seeing the relationships as a picture makes it clear how to find the unknown, usually by working out the value of one equal unit and scaling up. It is a cornerstone of the Singapore primary mathematics approach and is central to tackling PSLE problem sums.
What is the difference between a part-whole and a comparison model?
In a part-whole model, two or more parts are placed end to end to form a single whole bar — used when a problem talks about a total or "the rest." In a comparison model, two bars are drawn one above the other to show how much bigger or smaller one quantity is than another — used for wording like "more than," "less than" or "twice as many." Recognising which structure a problem needs is the first and most important step.
Can the bar model be used for fractions, ratio and percentage?
Yes. Because fractions, ratio and percentage all describe proportional relationships, the same bar can be divided into equal units to handle each — a whole split into parts, two quantities compared, or a before-and-after change. For fractions, split the bar by the denominator; for ratio, draw one unit per share; for percentage, treat the whole bar as 100%. Using one consistent picture across all three is a major reason the model method is so effective for the upper-primary syllabus.
How does the model method help with secondary algebra?
The model method is concrete algebra. When a child works out the value of "one unit" in a bar model, they are doing exactly what algebra does when it solves for an unknown such as x. Students who understand bar models therefore make a smoother transition to writing and solving equations in secondary school, because the underlying reasoning is the same — only the notation changes from bars to symbols.
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