Model drawing: how to turn a word problem into bars

Model drawing is the method most Singapore students meet first and abandon soonest — usually right when it starts being useful. By P6 the problems have too many moving parts to hold in your head, and a bar model is what stops a hard question from becoming a guessing game.

The core idea is simple: a bar stands for a quantity, and equal units must be drawn equal. Everything else follows.

The two models

Almost every P5–P6 problem uses one of two shapes.

Part-whole — quantities combine into a total. Draw one long bar split into sections.

Comparison — quantities are measured against each other. Draw the bars stacked, aligned at the left edge, so the difference is visible as an overhang.

Choosing wrongly is the single most common reason a model “doesn’t work”. If the question says more than, fewer than, or times as many, it is a comparison model, even when a total is also given.

Worked example

Aisha and Ben share $120. Aisha gets $30 more than Ben. How much does Ben get?

“More than” tells you this is a comparison model. Ben is the smaller quantity, so make Ben 1 unit.

Now read the total off the drawing:

1u + 1u + 30 = 120
        2u   = 120 − 30
        2u   = 90
        1u   = 45

Ben gets $45. Aisha gets 45 + 30 = $75.

Always check against both facts in the question: 45 + 75 = 120 ✓, and 75 − 45 = 30 ✓. A model that satisfies only one is a model you’ve misdrawn.

When quantities are transferred

Transfer problems (“A gives B 24 stickers”) are where models earn their keep. The trick is to draw two models — before and after — and look for what didn’t change.

Raj has 3 times as many stickers as Mei. Raj gives Mei 24 stickers, and now they have the same number. How many did Raj have at first?

Before the transfer:

After Raj gives Mei 24, the two bars are equal:

Reading straight off the second drawing: Mei has 1u + 24, Raj has 3u − 24, and they are equal.

3u − 24 = 1u + 24
     2u = 48
     1u = 24

Raj had 3 × 24 = 72 stickers.

Check: Raj 72, Mei 24. After the transfer, 48 and 48 ✓.

Notice what made this work: the total never changed (96 stickers throughout). Spotting the quantity that stays constant is the key to most transfer problems.

Common mistakes

• Unequal units. If 1 unit is 2cm on the page, every unit must be 2cm. A sloppy drawing produces a wrong equation.
• Drawing the question instead of the structure. You are not illustrating stickers; you are showing how quantities relate.
• Forgetting to label. Mark the total, the difference and what 1 unit represents. Unlabelled models are where marks quietly disappear.
• Abandoning the model halfway. If you switch to mental arithmetic partway, you lose the method marks even when the answer is right.

Quick check

Draw a model for this, then solve it:

A rope is cut into two pieces. One piece is 4 times as long as the other. The longer piece is 96cm longer than the shorter. How long was the rope?

3u = 96
1u = 32

Rope = 1u + 4u = 5u
     = 5 × 32