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A friendly flat-vector scene of two bars labelled before and after with an arrow showing a piece moving from one to the other, beside a couple of coins, in IllumiTutor navy and amber on an off-white background.

The Before-and-After Model

Drawing a before state and an after state, and spotting when a transfer keeps the total unchanged.

⏱ 6 min · 🎯 4 things to master

Lots of PSLE problems have a story with two moments in time: how things were before, and how they are after something happened. The trick is to draw both states and then ask the most powerful question in the whole model method: what stayed the same? For one big family of problems — when one person simply gives some of their amount to another — the answer is that the total never changes. That is the before-and-after model, and the idea behind it is called the constant total.

Parents: let your child slide the transfer and notice the total staying fixed before they read the answer. The "Method tip" boxes name the reasoning a marker rewards — here, "the total stays the same".

By the end you'll be able to draw a before and after model, see that an internal transfer keeps the total constant, and use it to solve "they become equal" problems. Let's see it move.

Before and after

A shows the starting amounts. An shows them once the story has played out. Drawing both side by side makes the change obvious — you can literally see what moved.

The most important kind is a transfer: one person gives some of their amount to another. Nothing comes in from outside and nothing is thrown away — the amount just moves between them. So the two amounts change, but added together they stay exactly the same.

🤔 Predict first: Adam has $30 and Ben has $18. Adam gives $5 to Ben. What is their TOTAL amount after that?

The total stays the same

Here is the model in action. Adam has $30 and Ben has $18. Adam gives some money to Ben until they have equal amounts. Slide the transfer and watch two things: the bars rebalance, but the total sticks at $48 the whole time. Find the transfer that makes them equal.

Adam gives Ben money until they are equal

Predict first: When Adam gives money to Ben, what happens to their TOTAL?

Because the total $48 never changes, "equal amounts" means each ends with 48 ÷ 2 = $24. Adam went from $30 to $24, so he gave away $6. Check: Ben went from $18 to $24, which is also $6. It balances.

Spot what stays the same

Not every before-and-after problem keeps the total constant. The skill is to read the story and decide what is unchanged:

  • One person gives to another (nothing enters or leaves) → the total stays the same.
  • Money is spent or received from outside → the total changes.
  • The same amount is added to both → the difference stays the same (you'll meet this in the constant-difference note).

Drawing the before and after models is what makes the unchanged quantity jump out at you.

🤔 Predict first: Two sisters have $80 altogether. The older gives the younger some money. After that, how much do they have altogether?

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

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

  1. Priya gives some of her stickers to Raj. What stays the same?

  2. Two friends have $100 altogether. One gives the other $15. What is their total now?

  3. Amir has $50 and Ben has $20. Amir gives Ben money until they are equal. How much does each have at the end?

  4. In the question above, how much did Amir give Ben?

  5. Which situation does NOT keep the total constant?

  6. Lena and Mei have 48 sweets altogether. Lena gives Mei 6 sweets and now they are equal. How many did Lena have at first?