How to Unpack Multi-Step Maths Word Problems

Start with the situation, before the arithmetic

To unpack a multi-step word problem, first retell what happens, identify how the quantities relate, and represent those relationships. Then calculate and check the answer against the story. The useful question is not simply “Which operation goes with this word?” It is “What quantity do I need, and how can the information help me find it?” A student might calculate accurately yet answer a different question because an intermediate result looks like a finished answer.

The official PSLE Mathematics syllabus for examination from 2026 includes interpreting information, applying mathematical understanding in different contexts, reasoning, and selecting strategies. Those objectives give a reason to practise explaining relationships alongside calculations. The sequence in this note is an original practice framework, rather than a required examination method. It can be shortened for a straightforward problem or revisited when a representation reveals something the learner missed. There is no promise that one diagram will suit every question.

Retell the story and name the unknown

I begin this example by putting the situation into everyday language: there is a starting collection, some bookmarks are kept for another activity, and the rest are shared. This retelling preserves the order of events. It also separates “bookmarks for the workshop” from “bookmarks for the groups”. Before using any number, ask the learner to finish the sentence “I need to find the number of bookmarks …”. The final words, “each reading group receives”, matter.

Next, attach a meaning to each number. Eight counts boxes; fifteen counts bookmarks in one box; twenty-four counts bookmarks reserved; six counts groups. None of those numbers alone is the answer. If the learner is uncertain about “sets aside”, clarify that phrase with counters or a simple sketch before introducing an operation. Reading support here is part of understanding the problem. Asking for a retelling should reveal uncertainty, not become another sentence the child must memorise.

Connect quantities before choosing operations

There are three relationships to connect. Equal groups of fifteen make the starting collection. That collection splits into the reserved amount and the remaining amount. The remaining amount then splits into six equal shares. Each relationship answers a different question. Multiplication finds the starting number of bookmarks; subtraction finds what remains; division finds the number in one reading group’s share. This explanation gives every operation a job instead of using the numbers in the order they appear.

A word such as “remaining” can help a reader understand an event, but it does not identify every operation needed for the whole problem. Likewise, “each” appears both in a description of the original boxes and in the final sharing question. One occurrence helps describe equal groups; the other asks for one share. Read the full relationship. When a student suggests an operation, ask “What would that result count?” If the answer has no clear meaning, return to the story before calculating.

Choose a representation you can explain

For the first relationship, draw eight equal groups and label one group “15 bookmarks”. For the next, use a whole bar labelled “starting bookmarks”, divided into “24 reserved” and “remaining”. Finally, divide the remaining part into six equal shares. The drawings need not be to scale. They need labels that make the relationships readable. A short number sentence can accompany a sketch, particularly when drawing every individual bookmark would distract from the quantities.

Ask the learner to point to the unknown in the representation. If the question asks about one group, pointing to the whole remaining bar shows that the representation is not yet connected to the final question. This is a useful place to pause. An adult can ask “Which part is one group’s share?” without drawing the solution for the child. If the child prefers a labelled table or a clear sequence of equations, check that the same relationships remain visible.

Calculate one meaningful quantity at a time

Notice that 120 and 96 are useful results, but neither answers the final question. Writing a short label next to each calculation keeps its meaning available for the next step. The final response is “Each reading group receives 16 bookmarks.” The unit is bookmarks, rather than boxes or groups. If a learner writes 96 as the answer, ask them to read their label aloud: it describes all the bookmarks available for sharing, so another step is needed.

A calculation error and a relationship error call for different follow-up. A student who explains the equal sharing correctly but computes the division incorrectly needs to revisit that computation. A student who divides the starting collection without accounting for the reserved portion needs to revisit which bookmarks are available to share. Keeping working visible helps locate the point to discuss. Rewriting every line neatly is less useful than being able to explain why each line belongs in the solution.

Check the unit, the size, and the original conditions

First check the unit: the answer counts bookmarks in one group’s share. Then check its size. If nothing had been reserved, sharing 120 bookmarks among six groups would give 20 per group. Reserving some must make each share smaller, so 16 is plausible. This estimate does not prove the answer, but it would flag a result of 160. A reasonableness check should connect to this situation rather than rely on whether a number merely looks tidy.

Finally, reconstruct the starting amount. Six groups receiving 16 bookmarks use 96 bookmarks. Add the 24 reserved bookmarks to recover 120, which matches eight boxes of fifteen. This reverse check tests the original conditions with the proposed answer. For another problem, a useful check might compare a part with its whole, test a stated difference, or substitute a value into a relationship. Choose the check because it tests the story, rather than repeating the same calculation without reconsidering its meaning.

Keep parent practice small and specific

1. Start with one unfamiliar problem. Ask for a retelling and a statement of the unknown before asking for working. Let the child explain in ordinary language.
2. Choose one point to discuss: a number label, a relationship, a representation, or a check. Give time to revise that point before adding another question.
3. After solving, change one condition and predict what should happen. If more bookmarks are reserved while everything else stays the same, each group should receive fewer bookmarks.
4. Finish by asking which step was difficult to explain. Keep that question for the next practice session, and use a simpler example if the same relationship remains unclear.

The aim of this practice is an explanation that the learner can follow again: what is happening, what is unknown, and how each step moves towards it. A correct answer is useful evidence, but the explanation shows what to discuss next. When speaking with a tutor, bring the child’s original working and describe the step that became uncertain. That gives the conversation a concrete starting point without turning one question into a judgement about the child’s overall ability.