What Maths Problem Solving Actually Requires
Problem solving is the part of maths that cannot be bypassed. A child can memorise multiplication tables, learn the formula for the area of a triangle, and practise column subtraction until it is automatic — but none of that guarantees they can solve a multi-step problem they have not seen before. That ability is separate, and it develops through specific habits of mind rather than through content knowledge alone.
This matters in almost every maths context your child will encounter, from Year 5 word problems to GCSE reasoning questions to 11 plus assessments. The question of how to improve maths problem solving skills is therefore one of the most practically important questions a parent can ask — and the answer is more specific than “do more practice.”
Start with Reading the Problem
A significant proportion of errors in maths problem solving happen before a child has written a single digit. They read a question once, quickly, and begin working — often on the wrong thing. Slowing down the reading process is one of the most direct ways to improve accuracy.
Encourage your child to read a problem at least twice before doing anything else. On the first read, they are simply understanding what is being described. On the second, they should be asking: what is actually being asked? What do I know? What do I need to find?
This two-pass reading habit is not about being slow. It is about not spending effort solving the wrong problem.
Draw Before You Calculate
The bar model method — central to Singapore maths — is one of the most effective tools available for developing genuine problem-solving ability. Rather than jumping straight from a word problem to a number sentence, children are taught to represent the structure of a problem visually first.
Consider a straightforward Year 5 problem: “Together, Amara and Ben have 84 stickers. Amara has three times as many stickers as Ben. How many does Amara have?” A child working purely with numbers may struggle to find an entry point. A child who draws one bar for Ben and three equal bars for Amara immediately sees that there are four equal parts totalling 84, each part is 21, and Amara has 63.
The drawing is not a shortcut — it is the thinking made visible. Once the structure is clear, the arithmetic follows naturally. You can watch this technique demonstrated across a range of problem types on our YouTube channel, including examples from 11 plus and GCSE papers.
The broader principles behind this approach — sometimes called CPA, or concrete-pictorial-abstract — are explored in depth on the Bar Model Company website, which offers resources for parents and teachers wanting to understand why visual modelling is so effective.
Build the Habit of Checking
Children who struggle with problem solving often stop as soon as they have an answer. Children who consistently score well have learned to ask one further question: does this answer make sense?
This is not the same as rechecking arithmetic. It is a higher-level habit — reading back the original question and confirming that the answer actually addresses what was asked, and that the magnitude of the answer is reasonable. If a question asks how many bags can be filled and the answer is 3.7, something has gone wrong. If a percentage is greater than 100 in a context where that makes no sense, the checking habit catches it.
Building this habit takes deliberate practice. After completing a problem, encourage your child to read the question again and say, in their own words, what the answer means. This one step catches a surprising number of errors.
Work Backwards and Use Estimation
Two underused strategies in school maths are working backwards from a known answer and using estimation to bracket a reasonable range before calculating.
Working backwards is particularly valuable for checking: if you know the final answer should be correct, can you reverse the steps and arrive back at the information given? This is particularly effective for ratio and proportion problems, where working backwards confirms whether the method was structurally sound.
Estimation is most useful as a planning tool — doing a rough version of a calculation before the precise one to check the answer will be in a plausible range. Children who estimate instinctively before calculating are far more likely to catch errors caused by misplaced decimal points or incorrect operations.
Practise with Unfamiliar Problems
One of the most common traps in maths preparation is working only with familiar problem types — questions that look like ones already practised. This develops confidence with known formats but does not build genuine problem-solving ability. The problems that matter most — 11 plus questions, GCSE reasoning tasks, scholarship assessments — are specifically designed to be unfamiliar.
Exposure to varied, unfamiliar problem types is therefore an essential component of any structured preparation. The aim is not to have seen every problem type before the exam. It is to have developed the flexibility to work through an unfamiliar problem systematically, without panic, using the reasoning skills that have been practised in more structured contexts.
This is why our approach to secondary maths tuition and our 11+ programme both prioritise variety over volume — we deliberately include problem types children have not seen, in a supported environment where mistakes are part of the learning process rather than something to avoid.
The Role of Structured Support
Parents often ask whether a child can improve their problem-solving skills independently, through book practice at home. The honest answer is: to some extent, yes — but with significant limitations. Self-directed practice tends to consolidate existing habits rather than develop new ones. A child who habitually skips the reading stage, or who has settled on an ineffective method for a particular type of problem, will not naturally self-correct through more of the same practice.
A tutor who specialises in mathematical reasoning can identify exactly where a child’s approach is breaking down — not just what they are getting wrong, but why. This diagnostic work is what allows targeted improvement rather than general practice. At Singapore Maths Academy, our tutors are qualified teachers trained in the Singapore mastery method, working with small groups of around four to five children to provide the close attention that makes a significant difference to reasoning development.
We work with children across a wide range of year groups and abilities — whether they are preparing for the 11 plus, building foundations for GCSE, or simply developing the kind of mathematical confidence that will serve them well across all their studies. To find out more about how we can support your child’s problem-solving skills, get in touch with our team.
A Note on Resilience
Problem solving requires a tolerance for uncertainty. Children who have been trained to expect immediate answers — who have mainly practised questions with clear, single-step routes — often disengage when a problem does not resolve quickly. Building the capacity to sit with an unsolved problem, try an approach, and try another if the first does not work, is as important as any specific technique.
This resilience develops through experience of exactly this process — attempting unfamiliar problems in a supportive environment, with feedback that is specific about what went wrong and constructive about how to approach it differently. You can read more about how we structure this kind of purposeful practice in our guide to 11 plus maths word problems.
The skills that make a strong maths problem solver — careful reading, visual thinking, systematic checking, resilience — are not innate. They are learnable. With the right structure and support, most children can develop them significantly.