Bar models, explained for parents

The "model drawing" method in Singapore maths — and why your child draws rectangles

If your child's workbook is full of rectangles and you were never taught this way, this guide is for you. The bar model isn't extra work — it's the thinking, drawn out.

What a bar model is

A bar model turns the numbers in a word problem into rectangles whose lengths stand for amounts. Instead of holding "Ali has 7 more than Siti" in their head, the child draws it — and once it's drawn, the sum to do usually becomes obvious.

It was developed in Singapore in the 1980s and is now the backbone of how primary schools here teach word problems. The point is simple: you can't solve what you can't see.

The three models your child will meet

1. Part-whole — "parts make a total"

There are 35 stickers. 14 are red and the rest are blue. How many are blue?

2. Comparison — "one has more than the other"

Ali has 7 more stickers than Siti.

3. Before-after — "something changed"

Ali had some stickers. After giving away 8, he had 15 left. How many did he start with?

A real P3 problem, worked through

Ali and Siti have 35 stickers altogether. Ali has 7 more than Siti. How many stickers does Siti have?

Many adults reach for algebra here. A P3 child draws:

1. Take away the extra: if we cut off Ali's "7 more", both bars become the same length. 35 − 7 = 28.
2. Now the bars are equal: two identical bars make 28, so one bar is 28 ÷ 2 = 14. That's Siti.
3. Check: Ali = 14 + 7 = 21, and 21 + 14 = 35. ✓

That "remove the difference, then share equally" move is one children reuse for years — the same drawing solves P5 ratio problems and, eventually, becomes the algebra they meet in secondary school. A bar labelled "?" is a variable; the child just doesn't know the word yet.

How to help at home (even if you were never taught this)

• Ask them to draw it, not solve it. "Show me the bars" is more useful than "what's the answer?" — if the drawing is right, the answer usually follows.
• Every bar needs a label. Who it belongs to, what's known, and a ? on the thing being asked. An unlabelled model is where most marks are lost.
• Let them narrate. "This bar is Ali, this part is the 7 more…" — a child who can talk through their model understands it; one who can't has copied a shape.
• Don't teach them algebra instead. It feels faster to you, but schools mark the model, the method builds the intuition algebra later formalises, and mixing methods mid-stream confuses more than it helps.

Common mistakes to watch for

• Bars wildly out of proportion. A model is a sketch, not a scale drawing — but the "7 more" bar shouldn't be drawn longer than the main bar. Rough proportion keeps thinking honest.
• No question mark. If nothing is marked "?", the child solves for the wrong thing — very common in two-step problems.
• One bar when the story compares two things. "More than / fewer than" almost always needs two bars, one above the other, lined up on the left.
• Jumping to the sum too early. The classic: seeing "gave away" and subtracting before drawing. The model exists precisely to slow that reflex down.

Practise the word problems free

StudyLab has word problems at every level from P1 to P6 — the same story shapes bar models are built for: part-whole, comparison, and change. Free, no ads, no sign-up, and every question explains its answer.