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A friendly flat-vector scene of two stacked bars of different lengths with a bracket marking the difference, beside a few counting cubes, in IllumiTutor navy and amber on an off-white background.

The Comparison Model

Drawing two bars side by side to picture the difference, and using "times as many" to find the value of one unit.

⏱ 6 min · 🎯 4 things to master

Some problems are not about a total — they are about a gap. "How many more does Anna have than Ben?" "Who is taller, and by how much?" For these, you draw two bars, one under the other, and the answer is the bit that sticks out. This is the comparison model, the second model every PSLE student must own.

Parents: encourage your child to say which bar is longer before revealing. The "Method tip" boxes name the exact reasoning a marker rewards — especially the line "the difference is … units".

By the end you'll be able to draw two bars, mark the difference, and use "times as many" to find one unit. Here we go.

Two bars, one difference

In a comparison model you draw the two quantities as two separate bars, lined up on the left. The longer bar is the bigger quantity. The part of the longer bar that goes past the end of the shorter bar is the .

So if Anna has 12 stickers and Ben has 7, draw Anna's bar longer; the overhang is 12 − 7 = 5. That overhang is "how many more Anna has".

🤔 Predict first: A blue rope is 8 m and a red rope is 5 m. On a comparison model, what does the part of the blue bar that sticks out past the red bar show?

When the difference is in units

The model becomes a real shortcut when a problem says one quantity is a number of times another. Then each bar is drawn in equal units, and the difference is also a number of units. Find what those difference-units are worth, and you have one unit.

Try it. Devi has 3 times as many beads as Kai, and Devi has 120 more beads than Kai. Draw Kai as 1 unit and Devi as 3 units. The difference is 3 − 1 = 2 units, and that equals 120. Slide until one unit makes the difference equal to 120.

Beads: find one unit from the difference

Predict first: How many units is the DIFFERENCE between Devi and Kai?

With 1 unit = 60, Kai has 60 beads and Devi has 3 × 60 = 180. Check the gap: 180 − 60 = 120. Correct.

Comparison or part-whole?

How do you know which model to draw? Listen to the question:

  • Words like "in total", "altogether", "share" point to a part-whole model (one bar).
  • Words like "how many more / fewer", "longer", "the difference", "times as many" point to a comparison model (two bars).

Many harder problems use both — a total and a comparison — but you choose your first model by what the question is really asking.

🤔 Predict first: A pencil costs 4 times as much as an eraser. The pencil costs 90 cents more than the eraser. The difference of 90 cents is equal to how many units?

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

  1. On a comparison model, what does the part of the longer bar that sticks out represent?

  2. Sara has 5 times as many cards as Tom. In units, what is the difference between them?

  3. A is 3 times B. A is 80 more than B. What is the value of one unit?

  4. Which phrase tells you to draw a comparison model (two bars) rather than a part-whole model?

  5. A box of chocolates has 4 times as many milk chocolates as dark. There are 66 more milk than dark. How many DARK chocolates are there?

  6. Mia is 6 times as old as her baby brother and is 35 years older than him. What is the best first step?