Why Bar Models Earn Marks
The bar model is the single most powerful tool in Singapore primary math. It turns abstract problem sums into pictures your child can manipulate. Examiners actively reward it: a clearly drawn bar model with correct units typically earns method marks even when the final answer is wrong. Parents who think bar models are old-fashioned should look at the working space on the latest PSLE Math paper — there is a reason it is generous.
The Three Bar Model Types You Need
Almost every PSLE problem sum reduces to one of three bar model patterns.
1. Part-Whole
A whole bar is split into parts. You are usually told the whole and one or more parts, and asked for the missing part. Most P1 to P3 questions use this.
2. Comparison
Two or more bars are drawn side-by-side, with one longer than the other. The difference between bars is the key quantity. Common from P3 onwards, especially in age, money, and quantity problems.
3. Fraction or Ratio of a Whole
A bar is divided into equal units to represent fractions or ratios. The hardest variant — fraction of the remainder — is a PSLE staple in the last five questions of Paper 2.
Worked Example 1: P3 Part-Whole
Question: Aiman, Bala, and Chloe shared $84 among themselves. Aiman received $12 more than Bala. Chloe received twice as much as Bala. How much did Chloe receive?
Drawing the Bar Model
Picture three horizontal bars stacked, all aligned at the left edge.
- Bala's bar: one unit (call it `u`).
- Aiman's bar: one unit `u` plus a small extra block of $12 attached on the right.
- Chloe's bar: two units `u` placed end to end.
Solving It
Add the units and the extra $12.
- Total units: 1 (Bala) + 1 (Aiman) + 2 (Chloe) = 4 units
- Total extra: $12
- 4 units + $12 = $84
- 4 units = $84 − $12 = $72
- 1 unit = $72 ÷ 4 = $18
- Chloe = 2 units = $36
Common Mistakes
- Forgetting to subtract the $12 before dividing — students often divide $84 by 4 directly.
- Drawing Aiman's bar with the extra $12 underneath rather than attached, which obscures the structure.
- Stopping at "1 unit = $18" and circling that as the answer because they forgot the question asked for Chloe's share.
Worked Example 2: P4 Comparison
Question: Daniel had 84 more stickers than Esther. After Daniel gave 18 stickers to Esther, Daniel still had 28 more stickers than Esther. How many stickers did Daniel have at first?
Drawing the Bar Model — Before
Two bars, one above the other.
- Esther's bar: a length we will call `E`.
- Daniel's bar: the same length `E` extended on the right by an extra block labelled 84.
Drawing the Bar Model — After
After Daniel gives 18 to Esther, Esther's bar grows by 18 and Daniel's bar shrinks by 18.
- Esther after: `E` + 18
- Daniel after: `E` + 84 − 18 = `E` + 66
Wait — the question says the gap is 28. Let us solve it properly.
Solving It (The Cleaner Way)
The total transferred from Daniel to Esther is 18, but this changes the gap by 2 × 18 = 36 (Daniel loses 18, Esther gains 18).
- Original gap: 84
- New gap: 84 − 36 = 48 — but the question says 28.
The lesson: always check that 2 × (amount transferred) reduces the gap correctly. If your numbers do not match, you have either misread the question or copied wrong.
Common Mistakes
- Reducing the gap by 18 instead of 36. The transferred amount affects both bars.
- Drawing only one "after" model and trying to reason without the comparison.
- Mixing up "Daniel had more" with "Daniel gave more" — circle the verbs in the question before drawing.
Worked Example 3: P6 Fraction of Remainder
Question: Faiz had some marbles. He gave 1/4 of them to his brother. He then gave 2/5 of the remainder to his sister. He had 36 marbles left. How many marbles did Faiz have at first?
Drawing the Bar Model
Start with one long bar representing the original total. This is the trickiest model — work in stages.
- Stage 1: Divide the original bar into 4 equal units. Shade 1 unit (given to brother). The unshaded 3 units are the remainder.
- Stage 2: Take just those 3 units and redraw them as a new bar divided into 5 equal smaller units (because 2/5 of the remainder goes to the sister). Shade 2 of those 5 small units.
- Stage 3: The unshaded 3 small units of the second bar represent the 36 marbles left.
Solving It
- 3 small units = 36 marbles
- 1 small unit = 12 marbles
- The full remainder = 5 small units = 60 marbles
- The remainder is 3/4 of the original total, so:
- 3/4 of original = 60
- Original = 60 ÷ 3 × 4 = 80 marbles
Common Mistakes
- Treating "2/5 of the remainder" as "2/5 of the original" — this is the single most common P6 error and costs 3 to 4 marks every time.
- Not redrawing the remainder as a new bar — students try to subdivide the original 4-unit bar by 5, which is messy and error-prone.
- Forgetting to convert back from the remainder to the original total at the final step.
A Few Practical Tips for Drawing
The drawing itself matters. Examiners give marks for correctly labelled models even when the answer is wrong.
- Use a ruler. A wobbly bar suggests careless work to the marker.
- Label every section. Names, fractions, dollar amounts — all clearly written above or below.
- Show the question mark. Place a small `?` above the bar segment you are solving for. It anchors your thinking.
- Keep the bars to scale where possible. A "$12 extra" block should look smaller than the main unit, not the same size.
When Algebra Replaces Bar Models
By upper P6, some students start substituting algebra for bar models. This is fine, but bar models still have an edge in PSLE because they earn method marks even when the algebra goes wrong, surface fraction-of-remainder errors visually, and are explicitly rewarded under the MOE syllabus. Most AL1 scorers can do both, and choose the bar model when the problem involves remainders or comparisons.
What to Do This Week
- Pick one fraction of remainder problem from your child's last paper and redraw it together using the two-stage method above.
- Make a rule: every problem sum at home this week is solved with a bar model first, algebra second.
- Photograph your child's neatest bar model and pin it on the fridge — visible standards become normal standards.