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A friendly flat-vector scene of three stacked bars of different lengths, one with a small extra block on the end, beside a bowl of sweets, in IllumiTutor navy and amber on an off-white background.

Combining Part-Whole and Comparison

Drawing a total and a comparison into one model, mixing equal units with extra known bits.

⏱ 6 min · 🎯 4 things to master

You have met the part-whole model (one bar, a total) and the comparison model (two bars, a difference). The trickiest PSLE problems hand you both at once: a total to share, and comparisons between the shares. The skill is to draw them into a single picture using equal units plus the odd extra bit — then collect everything into a total number of units and find one unit.

Parents: let your child decide who is "1 unit" before revealing. The "Method tip" boxes name the move a marker rewards — turning the words into units plus extras, then a single total.

By the end you'll be able to take a three-quantity problem and build one combined model that solves it. Let's combine them.

Units plus an extra bit

The trick is to choose the smallest quantity as , then write everyone else in terms of it. Some shares are a clean number of units ("twice as many" is 2 units). Others are a number of units plus a fixed extra ("8 more than Ben" is 1 unit + 8). Drawing that little extra block on the end is what lets a total and a comparison live in one model.

🤔 Predict first: Ben has some sweets. Amy has 8 more than Ben. If Ben is 1 unit, how do you draw Amy?

One total of units

Try it. Three children share 90 sweets. Amy has 10 more than Ben. Carol has twice as many as Ben. Make Ben 1 unit. Then Amy is 1 unit + 10, and Carol is 2 units. Altogether that is 1 + 1 + 2 = 4 units, plus the extra 10, and it all adds to 90. Step one unit until the three bars total 90.

Share 90 sweets three ways

Predict first: Counting only the units (ignore the extra 10), how many units are there in total?

Here is the working. The total is 4 units + 10 = 90, so 4 units = 90 − 10 = 80, which means 1 unit = 20. Ben has 20, Amy has 20 + 10 = 30, and Carol has 2 × 20 = 40. Check: 20 + 30 + 40 = 90.

Choosing your unit

Always make the smallest share 1 unit, so every other share is a whole number of units (no fractions of a unit to juggle). If one person is "3 times another", that person is the big one — the other is your 1 unit.

🤔 Predict first: David has 3 times as many marbles as Eddy, and Faith has 12 more than Eddy. Who should be 1 unit?

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

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

  1. Ben is 1 unit. Amy has 7 more than Ben. How do you draw Amy?

  2. Three shares are 1 unit, 1 unit, and 2 units, plus a fixed extra of 5, totalling 85. What is 4 units worth?

  3. In the question above, what is 1 unit?

  4. David has 3 times as many marbles as Eddy. Who is best chosen as 1 unit?

  5. Two numbers add to 50. The bigger is 6 more than the smaller. What is the smaller number?

  6. Alan, Bob and Carl share $135. Bob has twice Alan, and Carl has $15 more than Alan. How much does Alan get?