PSLE Math Paper 2: Mastering Ratio & Fraction Model Methods

Why Ratio & Fractions Are the New Paper 2 Battleground

For years, the hardest questions in PSLE Math Paper 2 were built around Speed. Families practised distance-time-speed problems obsessively, bought booklets dedicated to them, and had tutors drill them every session.

That chapter is now closed.

From the 2026 PSLE cohort onwards, the topic of Speed has been completely removed from the Primary 6 Mathematics syllabus. It now sits in the Secondary 1 curriculum instead. This is not a minor adjustment — it is a full topic removal.

What this means is that Ratio and Fraction model questions are now the undisputed hardest topic in PSLE Paper 2. They always were difficult, but with Speed gone, every mark that used to come from multi-step speed questions now comes from complex ratio and fraction problems.

For parents wondering why their child "knows ratio" but still cannot solve Paper 2 questions — this guide is for you.

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The Three Model Methods You Must Master

There are three distinct model types that appear in PSLE Paper 2 ratio and fraction questions. Each one looks different, trips students up differently, and requires a specific drawing approach.

They are:

1. ▸Repeated Identity (Same Total) — When two ratios share the same quantity, use units to link them.
2. ▸Constant Difference — When one quantity doesn't change as another changes.
3. ▸Equal Concept (Fraction of Ratio) — When fractions and ratios appear in the same question.

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Method 1: Repeated Identity (Same Total)

What It Is

This strategy is used when a problem gives you the ratio of two groups before and after a change, and asks you to find a quantity. The key insight is that one of the groups stays the same — it is the repeated identity that links both ratios.

Example Question

Peter and Mary shared some cards. The ratio of Peter's cards to Mary's cards was 2 : 5. After Peter received 24 more cards, the ratio became 2 : 3. How many cards did Mary have?

Step-by-Step Solution

Step 1: Identify what stays the same. Mary's cards did not change. Mary is the repeated identity.

Step 2: Make Mary's units equal in both ratios.

Before: Peter : Mary = 2 : 5 After: Peter : Mary = 2 : 3

Find the LCM of 5 and 3, which is 15.

Step 3: Find the difference in Peter's units. Peter gained: 10 − 6 = 4 units → this represents the 24 cards received.

Step 4: Find the value of 1 unit. 4 units = 24 cards → 1 unit = 6 cards

Step 5: Solve for Mary. Mary = 15 units = 15 × 6 = 90 cards

(Check: Peter before = 6 × 6 = 36. Peter after = 36 + 24 = 60. Ratio after = 60 : 90 = 2 : 3 ✓)

Drawing the Model

Peter (Before: 6u)
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
Mary (Before: 15u)
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
Peter (After: 10u)
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
+24 cards (4u)
Mary (After: 15u)
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit

1
Identify the repeated quantityMary's cards remain unchanged.
2
Find LCM for Mary's unitsLCM of 5 and 3 is 15.
3
Scale Peter's before unitsBefore: Peter = 2 × 3 = 6 units
4
Scale Peter's after unitsAfter: Peter = 2 × 5 = 10 units
5
Calculate the unit differencePeter's change = 10u - 6u = 4u
6
Find the value of 1 unit4u = 24 cards, so 1u = 6 cards
7
Calculate Mary's total cardsMary = 15u = 15 × 6 = 90 cards

What Students Get Wrong

• ▸Forgetting to scale both ratios to make the constant quantity equal.
• ▸Jumping to arithmetic without drawing the model first.
• ▸Not identifying which quantity is repeated (unchanged) between before and after.

Parent Tip

Ask your child: "Which person or thing did not change in this problem?" If they can answer that, the rest follows naturally. The repeated identity is always the key.

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Method 2: Constant Difference

What It Is

This strategy is used when the difference between two quantities stays the same, even as one or both quantities change. It is very common in age problems and "before/after transfer" problems.

Example Question

A mother is 4 times as old as her daughter now. In 6 years' time, the mother will be 3 times as old as her daughter. How old is the daughter now?

Step-by-Step Solution

Step 1: Draw the current model.

Let daughter's current age = 1 unit. Mother's current age = 4 units.

Daughter (Now: 1u)
1 unit
Mother (Now: 4u)
1 unit
1 unit
1 unit
1 unit

The age difference = 4u − 1u = 3 units (this never changes — it is the constant difference).

Step 2: Set up the future model.

In 6 years: Mother = 3 × Daughter. So in 6 years, the ratio of Mother : Daughter = 3 : 1. The difference = 3 parts − 1 part = 2 parts.

Step 3: Equate the differences.

Since the age difference never changes: 2 parts = 3 units

Daughter (Future: 1.5u)
1.5 units
Mother (Future: 4.5u)
1.5 units
1.5 units
1.5 units

1
Find current age differenceMother (4u) - Daughter (1u) = 3 units
2
Find future age differenceMother (3 parts) - Daughter (1 part) = 2 parts
3
Equate the constant difference2 parts = 3 units -> 1 part = 1.5 units
4
Compare Daughter's age changeDaughter grows from 1u to 1.5u (increase of 0.5u)
5
Connect change to years0.5u = 6 years -> 1u = 12 years
6
Calculate Daughter's current age1u = 12 years old

Daughter is currently 12 years old.

(Check: Mother now = 48. In 6 years: Daughter = 18, Mother = 54. 54 = 3 × 18 ✓)

What Students Get Wrong

• ▸Adding 6 to only one person's age instead of both.
• ▸Confusing "3 times older" with "3 times as old."
• ▸Drawing the wrong number of units in the future model because they forget the age difference is constant.

Parent Tip

For age problems, always write: "The difference in their ages is ___ and this never changes." This one line unlocks the entire solution.

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Method 3: Equal Concept (Fraction + Ratio in One Question)

What It Is

This is the most cognitively demanding model type in PSLE. A question will give you a fraction and a ratio that are linked to the same set of objects. The trick is to express both the fraction and the ratio in terms of the same units before drawing your model.

Example Question

There are red, blue, and green marbles in a bag. 1/4 of the marbles are red. The ratio of blue marbles to green marbles is 2 : 3. There are 90 marbles in total. How many blue marbles are there?

Step-by-Step Solution

Step 1: Use the fraction to find what is left.

Red = 1/4 of all marbles. Remaining (blue + green) = 1 − 1/4 = 3/4 of all marbles.

Step 2: Apply the ratio within the remaining portion.

Blue : Green = 2 : 3 → Total parts in the remainder = 5. So Blue = 2 out of 5 parts of the 3/4 portion.

Step 3: Calculate.

Blue = 2/5 × 3/4 = 6/20 = 3/10 of all marbles Blue = 3/10 × 90 = 27 marbles

Drawing the Model

Whole Bag (90)
Red (1/4 of total)
Remaining Blue + Green (3/4 of total)
Remaining (3/4)
Blue
Blue
Green
Green
Green

1
Find fraction of remaining marbles1 - 1/4 (Red) = 3/4 of bag
2
Determine parts of remainderBlue : Green = 2 : 3 (Total = 5 parts)
3
Express Blue as fraction of whole2/5 of 3/4 = 6/20 = 3/10 of total
4
Calculate number of blue marbles3/10 × 90 = 27 marbles

What Students Get Wrong

• ▸Applying the blue : green ratio to the total instead of only to the non-red portion.
• ▸Getting the fraction correct but then forgetting to multiply through.
• ▸Skipping the drawing and trying to do it mentally — this is where errors spike.

Parent Tip

Ask: "Does this ratio apply to EVERYTHING, or just to one part of the whole?" Help your child identify the subset before drawing.

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The 4-Step Ritual for Any Ratio/Fraction Model Question

For every Paper 2 model question, train your child to follow these four steps before writing any calculation:

1. ▸READ: Identify all the quantities. Underline the key numbers and relationships.
2. ▸IDENTIFY: Which model type is this? Repeated identity? Constant difference? Fraction + ratio?
3. ▸DRAW: Commit to drawing the model before computing. Even rough bars help.
4. ▸LABEL: Label each bar with units/fractions before solving.

This 4-step habit prevents the most common exam error: rushing to compute without understanding the structure of the question.

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Common Traps in PSLE Ratio Questions

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How Much of Paper 2 Is This?

With Speed absent from the syllabus, ratio and fraction model questions collectively account for an estimated 40–55% of Paper 2 marks (spanning 4-mark and 5-mark questions). This is not a peripheral topic — it is the heart of Paper 2 difficulty.

Students who can reliably execute all three model types will have a major structural advantage in the exam.

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A Note on Past-Year Papers

If your child is practising using 2024 or earlier past-year PSLE papers:

• ▸Speed questions in those papers are now off-syllabus — skip them.
• ▸Ratio and fraction questions remain fully relevant and should be prioritised.
• ▸Papers from 2023 and 2024 are the most representative of the current exam format.

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Practice Plan for the Next 8 Weeks

Building this over 8 weeks before the October exam gives most students enough repetition to pattern-match reliably under exam pressure.

Explore PSLE Ratio Practice → Start Your Free Trial →

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Frequently Asked Questions

Is Speed completely gone from PSLE 2026?

Yes. Speed (Distance-Time-Speed) has been fully removed from the Primary 6 Mathematics syllabus for the 2026 PSLE cohort. There will be no Speed questions. It is now taught in Secondary 1.

Which model method should my child learn first?

Start with Repeated Identity. It appears most frequently and builds the core habit of scaling ratios to match a common value. Once that is solid, move to Constant Difference, then Equal Concept.

My child draws models but still gets the wrong answer. Why?

Usually, the problem is in labelling — the drawing is there but the bars are not labelled correctly, or the "constant" quantity is not identified. Check whether your child is identifying the unchanged quantity before drawing. Also check: are they scaling both ratios to a common unit before comparing?

Can my child use algebra instead of models for PSLE?

For some questions, yes. But for PSLE Paper 2, the model method often gives the most direct solution path and is less error-prone for most P6 students. Algebra is introduced in Secondary 1 — for now, the model method is the tested and trusted exam approach.

How do I know which of the 3 model types to use?

• ▸If the problem says "before and after" with one thing unchanged → Repeated Identity
• ▸If the problem involves age gaps, or a difference that stays the same → Constant Difference
• ▸If the problem gives both a fraction AND a ratio for the same group → Equal Concept