How to Solve the Helen and Ivan Coin Problem: A Parent-Friendly Guide

Quick Answer: To solve the Helen and Ivan coin problem, use the comparison method: look at what is the same between the two children (their total number of coins) and what is different (how many of each coin type they have). The mass difference comes entirely from the difference in the number of heavier coins. Multiply the difference in heavier coins by the mass difference per coin, and the answer appears — without any complex algebra or lengthy calculations.

This guide is written for parents who want to understand the problem enough to help their child, not to become PSLE math experts. No algebra, no advanced math terminology — just clear reasoning that you can use at the study table.

Solving the Helen and Ivan problem means recognising that when two people have the same total number of items, any difference between them comes from swapping one type for another — you only need to count how many swaps happened and multiply by the effect of each swap.

A Simpler Analogy: Oranges and Apples

Imagine Helen and Ivan each have ten fruits — some oranges, some apples. Helen has six oranges and four apples. Ivan has four oranges and six apples. Both have ten fruits total. An orange is 50g heavier than an apple. Who has the heavier bag, and by how much?

Do not calculate the weight of oranges and apples separately. Instead, compare: Helen has two more oranges than Ivan (6 vs 4). For each extra orange, Helen's bag is 50g heavier. So Helen's bag is 2 × 50g = 100g heavier. Done. This is exactly the logic behind the Helen and Ivan coin problem — just with coins instead of fruit and with specific numbers from the exam paper.

The Core Insight: Focus on What Is Different

The most powerful problem-solving technique your child can learn is this: when comparing two things, find what is the same and ignore it. What is the same contributes equally to both sides and cancels out when you subtract. Only what is different between the two sides matters.

In the Helen and Ivan problem, the same thing is the shared coins — the lighter coins both children hold in equal numbers, and the heavier coins they hold in equal numbers. Strip those away in your mind, and you are left with a much simpler problem: one child has a few extra heavier coins, and the other has a few extra lighter coins. The entire difference comes from those extra coins.

Teaching Your Child: Three Steps

Step 1 — Read together: Read the problem aloud with your child. Ask them to underline what is the same in both scenarios (same total number of coins) and circle what is different (the breakdown of which coins). This identification step is where many students lose their way — they jump to calculation before they understand the structure.

Step 2 — Visualise: Draw two circles on a piece of paper representing Helen's and Ivan's coin collections. Shade the coins that are the same, leaving the different ones unshaded. The unshaded coins are the only ones that matter. This visual step makes the comparison heuristic concrete.

Step 3 — Calculate the difference: Count the unshaded coins. If Helen has five more heavier coins than Ivan, and each heavier coin is 3g more than each lighter coin, the mass difference is 5 × 3g = 15g. Write the answer with a clear explanation of the reasoning — PSLE markers reward method marks, and a well-explained answer is more likely to earn full credit.

What If Your Child Still Does Not Get It?

If the comparison method does not click, try the "secret swap" approach. Tell your child: "Imagine I secretly take one lighter coin from Helen and swap it with one heavier coin from Ivan. Now Helen's collection is heavier by the mass difference between the two coin types, and Ivan's is lighter by the same amount. If I do this twenty times, the total difference is twenty times the per-coin mass difference." This reframing helps some children who struggle with the abstract comparison.

If neither approach works, step back and practise comparison problems with smaller numbers and simpler contexts — fruit, stationery, food items. Build the comparison intuition before returning to the exam-level problem.

FAQ

Is it okay to solve the problem a different way?

Yes, as long as the method is mathematically valid and the reasoning is clearly shown. The comparison method is the most efficient, but students who solve the problem correctly using a different heuristic or a systematic listing approach will receive full marks. The marking scheme rewards correct reasoning, not conformity to a single method.

How long should my child spend on a question like this in the exam?

If the heuristic is immediately clear, the question should take two to three minutes. If your child reads the question and does not see the path forward within 30 seconds, they should move on to other questions and return to this one at the end. Spending 10 minutes struggling with one question is rarely the right exam strategy, regardless of how many marks it is worth.

Should I teach my child algebra to solve these questions?

Not unless they are already comfortable with algebraic thinking. The MOE primary syllabus is designed around heuristics, not algebra, and teachers assess accordingly. Introducing algebra may confuse a child who has not yet developed the abstract reasoning that algebra requires. Stick with the heuristic methods their school teaches — they are the right tools for the exam.

Where can I find more practice questions like this?

Your child's school should provide practice papers that include heuristic-based problem-solving questions. MOE-approved assessment books labelled "Problem-Solving" or "Heuristics" are widely available. The key is variety: work through questions that require different heuristics so that your child builds a broad toolkit rather than mastering only one problem type.

Summary

The Helen and Ivan problem is not about advanced math — it is about seeing the structure behind a word problem. The comparison heuristic — ignore what is the same, focus on what is different — solves it cleanly. Helping your child develop this structural thinking, and ensuring their English reading skills are strong enough to parse the problem correctly, is the best preparation you can provide. iWorld Learning strengthens the English comprehension and analytical reading skills that support accurate problem interpretation in Math and beyond. Explore our primary school English programmes at Tanjong Pagar and Somerset, or contact us to discuss your child's needs.