Helen and Ivan PSLE Question Answer: A Step-by-Step Walkthrough

Quick Answer: The complete answer to the Helen and Ivan question has two parts: (a) Helen has more money because she has more of the heavier, more valuable coins, and (b) the mass difference is calculated by multiplying the difference in the number of heavier coins by the per-coin mass difference — no algebra or simultaneous equations needed. The full solution takes only a few lines of clear working when the comparison heuristic is applied correctly.

This walkthrough presents the full answer as a student should write it in the exam, with each step explained. It also shows the common errors that cost marks and how to structure working to maximise method marks.

The Helen and Ivan PSLE answer demonstrates that the comparison heuristic — identifying what two scenarios share, removing those common elements, and calculating the difference from what remains — produces a clean, efficient solution that a P6 student can complete in under three minutes with full working shown.

The Problem Restated

Helen and Ivan each have a collection of coins. Both have the same total number of coins. Helen has more 50-cent coins, and Ivan has more 20-cent coins. The 50-cent coin is heavier than the 20-cent coin by a given amount. You are told the total mass of one child's coins. Find: (a) who has more money, and (b) the mass difference between their two collections.

Part (a): Who Has More Money — Full Working

Identify the value of each coin. The 50-cent coin is worth 30 cents more than the 20-cent coin. Since Helen has more 50-cent coins than Ivan, and both have the same total number of coins, Helen must have fewer 20-cent coins — one fewer 20-cent coin for each extra 50-cent coin. The net value difference for each swapped coin is 50 cents minus 20 cents, which is 30 cents in Helen's favour. Multiply this per-coin value difference by the number of extra 50-cent coins Helen holds. Helen has more money by this amount.

A student should write: "Number of extra 50-cent coins Helen has = [difference]. Value difference per pair of swapped coins = 50¢ − 20¢ = 30¢. Total extra value = [difference] × 30¢ = [amount]. Therefore, Helen has more money."

Part (b): The Mass Difference — Full Working

Apply the same comparison logic to mass. For each extra 50-cent coin Helen has (and correspondingly each extra 20-cent coin Ivan has), the difference in mass is the mass of one 50-cent coin minus the mass of one 20-cent coin. Multiply this per-coin mass difference by the difference in the number of heavier coins.

A student should write: "Difference in number of 50-cent coins = [difference]. Mass difference per swapped coin pair = [given mass difference]. Total mass difference = [difference] × [given mass difference] = [result]. Helen's coins are heavier by [result]."

Why This Solution Earns Full Marks

PSLE Math markers look for four things: correct identification of the concept or heuristic used, clear numerical working that shows each step, a logical flow from given information to answer, and the correct final answer with appropriate units. This solution structure delivers all four. The marker can see at a glance that the student recognised the comparison structure, set up the comparison correctly, executed the arithmetic accurately, and stated the conclusion clearly.

A common mistake is writing only the final numerical answer — "60g" — with no working. This risks losing method marks even if the answer is correct. Another common mistake is attempting to solve for the mass of each coin individually using simultaneous equations, which is mathematically valid but unnecessarily complex and prone to arithmetic errors under time pressure.

How to Practise Writing Full-Mark Answers

Students should practise writing out their reasoning in complete sentences, not just number statements. A helpful exercise: have your child solve a heuristic-based problem, then explain their solution to you verbally. If they cannot explain it clearly, they probably do not understand it deeply enough to earn full method marks. This verbalisation practice — sometimes called "think-aloud" — builds the metacognitive skills that both improve problem-solving and produce clearer written working.

FAQ

How long should this answer take to write in the exam?

Two to three minutes for a student who recognises the comparison heuristic immediately. The working for each part is only a few lines. If a student spends more than five minutes on this question, they are likely using an unnecessarily complex approach or are stuck. In that case, the right strategy is to move on and return at the end if time permits.

Would a student lose marks for using a different method?

No, as long as the method is mathematically valid and the reasoning is clearly shown. The comparison method is the most efficient, but model drawing, systematic listing, or even a basic algebraic approach would earn full marks if executed correctly and explained clearly. The PSLE marking scheme rewards correct reasoning, not conformity to a single approved method.

Is it necessary to state which heuristic was used?

Not in those exact words. A student does not need to write "I used the comparison heuristic." But the working should make the comparison logic visible — for example, by subtracting the common coins and focusing on the difference. A marker should be able to see the reasoning without needing to guess what the student was thinking.

What if my child gets the right answer but with messy working?

Messy but logically complete working will still earn most or all method marks. Illegible or disorganised working that makes it hard for the marker to follow the reasoning may lose marks, particularly if the marker cannot tell whether a step was reasoned correctly or was a lucky guess. Encourage your child to write clearly, label their steps, and present their solution as if explaining it to someone else.

Summary

The Helen and Ivan question has a clean, efficient solution when the comparison heuristic is applied. Students who show clear reasoning — identify the heuristic, set up the comparison, execute the arithmetic, state the conclusion — earn full marks. The most important exam technique for heuristic-based questions is to make thinking visible on the page. iWorld Learning's PSLE English programmes strengthen the structured writing and analytical thinking skills that help students present clear, logical working across all subjects. Learn more about our primary school English courses or contact us at Tanjong Pagar or Somerset.