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The Part-Whole Model

The foundation of the model method — drawing one bar, splitting it into parts, and finding the value of one unit to unlock the answer.

⏱ 7 min · 🎯 4 things to master

Word problems can feel like a wall of words. The model method is how Singapore students turn those words into a picture they can actually solve — and it all starts here, with the part-whole model. The idea is simple: a big amount (the whole) is made up of smaller amounts (the parts). Draw one bar for the whole, split it into the parts, and the answer almost always falls out once you find the value of one unit.

Parents: let your child predict before they reveal each step. The blue dotted words are tappable definitions, and the "Method tip" boxes name exactly what a PSLE marker rewards in the working — not just the final number.

By the end you'll be able to read a problem, spot the whole and its parts, draw the bar, and find one unit to solve it. Let's build it up one piece at a time.

The whole and its parts

Every part-whole problem has two kinds of quantity. The is the total. The are the pieces that make it up. The golden rule is: the parts always add up to the whole.

So if you know all the parts, you add to find the whole. If you know the whole and all but one part, you subtract to find the missing part. That one sentence solves a huge number of P3 to P6 problems.

🤔 Predict first: A box holds 250 marbles. 90 are red and the rest are blue. To find the number of blue marbles, you should…

Splitting a bar into units

Here is where the model method gets powerful. Many problems give the parts as a number of equal units instead of plain numbers. A is one equal block. When you find what one unit is worth, you can find every quantity in the whole problem.

Try this one. A rope 240 cm long is cut into a short piece and a long piece. The long piece is 3 times as long as the short piece. Draw the short piece as 1 unit and the long piece as 3 units — together the rope is 4 units. Now slide until one unit makes the whole rope 240 cm.

Cut the rope: find one unit

Predict first: How many units long is the WHOLE rope?

Once you have 1 unit = 60 cm, the short piece is 60 cm and the long piece is 3 units = 180 cm. Check: 60 + 180 = 240 cm. It works.

Putting it together

The full routine for any part-whole problem is always the same four moves:

  1. Find the whole and the parts in the words.
  2. Draw one bar, split into the parts (use units when a part is "times" another).
  3. Add or subtract — or count the total units and divide to get 1 unit.
  4. Use 1 unit to answer the actual question.

🤔 Predict first: Aisha and Bala share $360. Aisha's share is twice Bala's. In units, how much is ONE unit worth?

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

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

  1. A jug holds 1500 ml of juice. 600 ml is poured out. Which operation finds how much is left?

  2. A ribbon is cut into a short and a long piece. The long piece is 4 times the short piece. How many units is the WHOLE ribbon?

  3. $420 is shared so that one share is 2 units and the other is 1 unit. What is one unit worth?

  4. There are 300 fruits: apples, oranges and pears. There are 110 apples and 95 oranges. How many pears?

  5. Two numbers add up to 240. The bigger is 3 times the smaller. What is the smaller number?

  6. A farmer has 540 animals: chickens and ducks. There are twice as many chickens as ducks. How many chickens are there, and what is the key first step?