Problem solving is at the heart of MYP Mathematics. The criteria reward more than the ability to reproduce a method: they reward the reasoning that lets you start a question when the route is not obvious, work through it clearly, and explain what your answer means. This guide sets out a practical approach to problem solving in MYP Maths, from understanding the problem through to checking and communicating your conclusion.

A note on terminology. This guide uses the current IB MYP Mathematics assessment criteria. Problem solving draws most directly on Criterion B (Investigating patterns), Criterion C (Communicating) and Criterion D (Applying mathematics in real-life contexts), but the reasoning involved also strengthens Criterion A (Knowing and understanding). Confirm the exact level descriptors for your year against your school's published rubrics.

Understanding the Problem

Most problem-solving marks are lost at the start, not the end. Before you calculate, make sure you understand what the question is asking. Read the problem more than once. The first read gives you the gist; the second read should be slower, with attention to what is given, what is defined, and what is being asked.

A useful habit is to restate the problem in your own words. If you cannot restate it, you have not yet understood it. Ask yourself: what is the situation? What information am I given? What am I being asked to find or to decide? What constraints apply?

Many errors come from answering a slightly different question from the one asked. A clear statement of the problem, in your own words, is the cheapest way to avoid that.

Identifying the Information

Once you understand the question, identify the information you have to work with. List what is given explicitly, and note any relationships or definitions the question provides. Watch for:

Explicit values and variables. Numbers, measurements, defined quantities.
Relationships. Any formula, definition or rule the question establishes.
Conditions and constraints. Limits on the domain, assumptions, or restrictions on the situation.
What is implied but not stated. Some problems expect you to bring a definition or relationship from the course.

Writing the given information down, in a small list or a labelled diagram, makes the next step much easier. It also reduces the chance that you overlook a piece of information that turns out to matter later.

Choosing a Strategy

With the problem understood and the information identified, the next step is to choose a strategy. There is rarely a single correct strategy; there are strategies more or less likely to work for a given problem. Useful strategies include:

Try a simpler case. If the problem is general or abstract, look at a specific simple version to build intuition.
Draw a diagram. Many problems become clearer when represented visually, especially in geometry, rates and functions.
Identify the relevant mathematics. Name the topics or methods that might apply. Even unfamiliar problems are built from course content.
Work backwards from the target. Ask what you would need to know to answer the question, then what you would need to know to know that, and so on until you reach what you have.
Look for a pattern. In investigation-style problems, computing a few cases often reveals a structure.
Set up an equation or model. In applied problems, translating the situation into mathematics is often the key step.

Do not wait for the perfect strategy. A partial attempt on a promising path is better than waiting for the ideal idea, because the attempt often reveals the path forward.

Showing Reasoning

In MYP Maths, the reasoning matters as much as the answer. A correct answer with no working earns only part of the credit, because the criteria reward the communication of mathematical thinking. Show your reasoning by:

Stating what you are finding at each step. A line of working should not appear without context.
Showing the key steps, not every arithmetic detail, but enough that a reader can follow.
Using correct notation consistently, including units where relevant.
Connecting each step to the next so the reasoning flows logically.
Explaining any decision to use a particular method, model or formula where it is not obvious.

Clear reasoning is a skill that improves with practice. The more often you set out your thinking explicitly, the more natural it becomes, and the easier it is for a reader to award the communication and reasoning marks your work deserves.

Checking Your Work

Checking is not a luxury step at the end; it is part of problem solving. A few habits catch most errors:

Re-read the question. Did you answer what was actually asked, including any conditions or units?
Check the reasonableness of the answer. Does the magnitude, sign and unit make sense in context? An answer that feels wrong usually is.
Substitute back. Where possible, put your answer back into the original situation to see if it fits.
Try a second method. If you can solve the problem more than one way, agreement between methods is strong evidence the answer is right.
Watch for premature rounding. Rounding too early changes later results; round at the final step unless instructed otherwise.

A student who checks systematically catches errors that a student who does not check loses. Over a whole assessment, the difference is significant.

Explaining Conclusions

The conclusion is where you connect your answer back to the question. A conclusion is not just a number; it is a statement of what the number means in the context of the problem. A strong conclusion:

Answers the question that was asked, in the terms the question used.
Includes units and context where the problem is applied.
States any conditions or assumptions that affect the answer.
Acknowledges limits where the model or method has them, particularly in Criterion D tasks.

Many marks are lost by stopping at a number when the question asked for a conclusion. Read the question one more time at the end and make sure your final line actually answers it.

Unfamiliar Problems

Unfamiliar problems, questions that frame known content in a way you have not seen, are a particular challenge because the first step is not obvious. They are also where the problem-solving skills above matter most. A repeatable method:

Read the whole problem before calculating. Understand what is given and asked before you start.
Identify which course topics are relevant. Even unfamiliar problems are built from course content. Name the topics.
Try a simple case. A specific or simplified version often reveals the structure.
Write down what you know. Definitions, given relationships and standard results. Sometimes the start of a solution appears when you list what is available.
Attempt a direction and commit. A partial attempt on a promising path is better than waiting for the perfect idea.
Use earlier parts of the question. Multi-part problems are structured; a result from one part is often intended for the next.
Check reasonableness and revisit. If a path stalls, reassess rather than abandon the question entirely.

The ability to start an unfamiliar question is itself a skill, and it improves only with practice. Seek out unfamiliar problems rather than practising only what you can already do.

An Illustrative Example

The following is an illustrative example, not from any specific assessment. Suppose a question asks you to investigate how the number of square tiles needed to frame a square picture grows as the picture grows, and to generalise the pattern.

A problem-solving approach:

Understand. The question is about a pattern in the number of tiles, and it asks for a general rule.
Try simple cases. Compute the number of frame tiles for a small picture, then a slightly larger one, then another. (Illustrative only: the actual numbers depend on the precise definition of "frame" in the question.)
Look for a pattern. Compare the numbers. Is the difference constant? Is there a relationship to the picture size?
State a conjecture. Propose a rule that fits the cases you have computed.
Test the conjecture. Check it against another case you have not yet used.
Justify the conjecture. Explain why the rule follows from the structure of the frame, at a level appropriate to your year.
Communicate. Set out the cases, the pattern, the conjecture, the test and the justification clearly, with correct notation.

This is the kind of reasoning Criterion B rewards. The point is not the specific answer; it is the process of noticing, conjecturing, testing and justifying.

Common Mistakes in MYP Maths Problem Solving

Rushing the first read. Misreading the question is the most common source of lost marks.
Starting to calculate before understanding. Calculation without understanding produces answers to the wrong question.
Showing only the final answer. Without working, reasoning and communication marks cannot be awarded.
Stopping at the number. A conclusion that does not answer the question in context loses marks.
Giving up too early on unfamiliar problems. Many problems become approachable after a simple case or a different strategy.
Not checking. Avoidable errors that a check would catch are a common cause of lost marks.
Poor notation and labelling. Missing units, unlabelled diagrams and inconsistent symbols cost communication marks.

How MYP Maths Tutoring Can Help

Problem solving responds well to targeted work with a tutor. A tutor can help you build the habit of understanding before calculating, choose strategies, set out reasoning clearly, and practise the unfamiliar problems that stretch your thinking. If you would like focused support, see our MYP Maths tutoring in Hong Kong.

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MYP Maths Problem-Solving FAQs

Why does working matter if my answer is right? MYP Maths criteria reward reasoning and communication, not just the final answer. A correct answer with no working earns only part of the credit.

What do I do if a problem looks unfamiliar? Read it fully, identify the relevant course topics, try a simple case, write down what you know, and start a partial attempt. See the method above.

How is problem solving assessed in MYP Maths? Across the criteria, particularly B (Investigating patterns), C (Communicating) and D (Applying mathematics in real-life contexts). See our assessment criteria guide.

How do I get better at problem solving? Practise unfamiliar problems, not only routine ones; set out your reasoning deliberately; and review your mistakes to find patterns in where you lose marks.

Should I memorise strategies? Strategies are useful, but the underlying skill is the habit of understanding, choosing and reasoning. Memorised strategies help less than practised thinking.

Can a tutor help with problem solving? Yes. Problem solving responds well to targeted work. See our MYP Maths tutoring in Hong Kong.

For more, see our assessment criteria guide and Standard vs Extended guide. Browse all MYP Maths resources, MYP resources or MYP tutoring in Hong Kong.

MYP Maths Problem-Solving Guide