How to Write a Perfect Maths Internal Assessment

It is no secret that Maths IA is one of the central elements of your assessment, and perhaps, the most challenging one. On one hand, it allows you to take the role of an independent researcher, because you are free to choose the research topic and methodology yourself. On the other hand, the responsibility of working autonomously is tremendous. 

How do you know how to write a high scoring Maths Internal Assessment if you have never done it before? A big mistake can cost you up to 20% of your final grade.

TutorsPlus and our IB Maths tutors, and IB examiners are here to help. In this guide, we’ll explain the requirements, structure, and format of a high-scoring IA Maths report. 

What is the Maths Internal Assessment?

The Maths Internal Assessment is an integral part of your IB Maths course contributing 20% to your overall score regardless if you are at SL or HL. This comprehensive assessment allows you, as a student, to showcase your understanding of mathematical concepts.

But the IA isn’t just about knowing your Mathematics. It’s about being able to solve real-world problems. To complete the assignment, you need to come up with a question, collect data, analyse it using appropriate mathematical techniques, and draw meaningful conclusions. Therefore, your analytical skills come into play as well.

The freedom to choose your own IA Maths topic lets you take a closer look at the areas of Maths that you find particularly interesting. You can investigate anything – from intricate patterns in nature to hidden mathematical secrets within your favourite sport – as long as there is an element of Mathematics in it.

According to IBO, the Maths Internal Assessment should be 12-20 pages long and correspond to the level of difficulty of the course. Typically, students need 10-15 hours to complete their IAs.

What are the Scoring Criteria?

A well-written Internal Assessment can bring you 20 marks distributed across 5 criteria:

• Presentation;
• Mathematical communication;
• Personal engagement;
• Reflection;
• Use of mathematics.

Communication (4 marks)

The topic of your IA takes centre stage. The key is to tell it clearly, concisely, and in a well-organised manner. You should stick to the recommended 12-20 pages of content – substance is a priority here, not a length. Remember, the examiners are looking for your mathematical exploration, not a novel.

Graphs, tables, and diagrams should be embedded within the text instead of appendices. This creates a smoother reading experience for the examiners and helps them clearly track your train of thought. Don’t forget to acknowledge the work of others by citing sources and including a proper bibliography.

Mathematical Presentation (3 marks)

This criterion implies your mathematical understanding. You need to define key terms wherever necessary, relying on textbooks or reputable journal articles. And don’t forget to reference them!

It is also important to speak the language of Maths confidently. To do so, make sure to utilise appropriate notation, symbols, and terminology. At the same time, you should avoid overly complex language, as it can backfire and reveal a lack of understanding. It is also important to maintain professionalism, so don’t use informal slang or jargon.

But you’ll know that your IA can’t be just plain text. Instead, when appropriate, it should include formulas, diagrams, tables, charts, graphs, or models. These visual aids support your understanding of the topic. All the visuals must be made by you (not just downloaded) and feature clear labels and titles.

Personal Engagement (4 marks)

Arguably the trickiest criterion, it requires you to show your personal connection to the topic through your writing.

First of all, you need to speak in the first person to show your ownership of the project and your genuine interest in the subject.

Second, don’t shy away from sharing the challenges you faced along the way. This not only outlines your progress overcoming obstacles, but also demonstrates your determination. You can also mention your emotions (did the results of your exploration surprise you?) as they communicate your personal involvement.

Finally, you need to make sure your work showcases your growth as a mathematician. So, don’t forget to highlight the mathematical concepts you’ve learned. Along with this, you can specify how this exploration has broadened your understanding and skills.

Reflection (3 marks)

Have you reached unexpected conclusions? It is not always a bad thing to prove yourself wrong. Sometimes, unexpected results can be the most valuable learning experiences. The key to learning from your mistakes is to analyse the reasons behind them and how you could improve your methods in hindsight.

But don’t forget to celebrate your successes as well. Did you prove your hypothesis, find an optimal solution, or successfully model a challenging concept? Then explain the strengths of your work while also pointing out weaknesses or areas of improvement.

Furthermore, you should consider exploring alternative approaches and the ways they might have influenced the outcome.

In addition, you may discuss the broader implications of your work. Ensure to point out if you believe that your findings can contribute to a wider understanding of the topic or explain how your research can be applied to other areas.

Use of Mathematics (6 marks)

Contrary to popular belief, scoring high on this criterion doesn’t require complex mathematics. Remember the IBO’s recommendation: use mathematics “commensurate with your level.”

In fact, being too ambitious and choosing a level that exceeds what might be expected of a high school student can be detrimental. 

For instance, you can take a syllabus topic and explore it beyond the covered depth. Or you could apply your knowledge to a new scenario, such as using differentiation to model a bottle flip.

Optional modules within your course can be a valuable source of inspiration. As a Standard Level student, you can explore Higher Level optional modules, for example, graph theory using Dijkstra’s and Kruskal’s algorithms. Remember, the examiners are more interested in how you demonstrate your understanding and knowledge, not just the complexity of the chosen mathematical concepts.

Last but not least, all your calculations must be relevant to answering the research questions and error-free.

How Can I Get a High Score?

Now that you know the Maths IA criteria, let’s see what you should do to score high.

Find an Maths IA Topic that Sparks Your Curiosity

We can’t stress enough the importance of finding the right Maths IA topics. It isn’t just about meeting the Personal Engagement criterion. It is also about being enjoyable as you’ll be dedicating significant time and effort to this project. Avoiding boredom and staying motivated is crucial for achieving a high mark.

Having said that, “enjoying the subject” is not enough. You need to seek a specific mathematical aspect to delve into. For instance, you might be fascinated with Renaissance architecture – why not explore its mathematical underpinnings (like proportions of planes or the golden section)? Here are our tips on how to choose your Maths IA topic. 

Adhere to the Marking Criteria

Keep IB’s marking criteria at hand throughout your work, constantly comparing your progress against the specified qualifiers. Your goal is to meet the requirements for each criterion, and you specifically need to consider the “full marks” descriptions.

Some of these criteria are rather subjective and it might be harder to understand what they entail. However, measurable criteria, such as proper notations or a certain bibliography format, can provide a solid foundation for your score.

Structure Your IA for Clarity

Your work must have concise and well-defined sections. A clear structure benefits both you and the examiner. By presenting your work in an easy-to-follow manner, you’ll help the marker understand your reasoning and potentially award higher marks.

There are no particular requirements when it comes to the structure of your IA. IBO encourages creativity and flexibility in your Maths IA. Having said that, the following format can help you structure your work more efficiently:

Reflect Throughout Your Exploration

Reflections on your results are an integral part of the conclusion. However, don’t wait till the end to showcase introspection. Instead, you might consider incorporating brief reflections after each result. These can be simple observations like “This result surprised me because…” or “This finding is interesting because…”.

Proofread Your Maths IA

The sheer volume of data, calculations, and equations in your Maths IA can easily lead to careless mistakes in notation, terminology, or even numbers. To minimise errors, you need to meticulously proofread your work.

If possible, ask someone else to do the same. Ideally, consider someone with strong maths skills, such as a Maths tutor or a friend who’s good with numbers. The more eyes review your work, the higher the chances of spotting errors.

Start Early

According to IBO’s estimations, students need 10-15 hours to complete their IAs. In reality, your research may take even more time. Data collection, processing, equation solving, typing, along with proofreading, revisions, and structuring, all require hours of work. That’s why you can’t just start a couple of days before the deadline. It’s best to begin working on your Maths IA as early as possible.

How to Format the Main IA Sections

Your work must have concise and well-defined sections. A clear structure benefits both you and the examiner. By presenting your work in an easy-to-follow manner, you’ll help the marker understand your reasoning and potentially award higher marks.

There are no particular requirements when it comes to the structure of your IA. IBO encourages creativity and flexibility in your Maths IA. Having said that, the following format can help you structure your work more efficiently:

Cover Page

Your Maths IA report begins with a cover page. It should introduce the key details of your work and you as its author, including:

• Mathematics course and level (for instance, Mathematics AA HL);
• Internal Assessment;
• The topic of your Internal Assessment;
• Your full name;
• Candidate number, i.e. your IB identification number consisting, as a rule, of three letters and three digits;
• Examination date (for instance, November 2024);
• School name and its code;
• Submission date;
• Page count.

Besides, some schools may require students to include an abstract, i.e. a 100-150-word summary of their work or/and a declaration of authenticity, i.e. a statement, that the report is neither plagiarised, nor copied from others. 

Try to make an introduction to your IA topic more personal. For example, you can connect it to your personal interests and explain why it sparked your maths.

Introduction

ematical curiosity. In addition, you should briefly outline your exploration’s direction without revealing too much detail.

Rationale

In this section, you need to justify your investigation. But don’t just restate your introduction. Instead, explain the specific mathematical concepts you’ll explore and how they address the chosen problem. You can also showcase examples, evidence, or preliminary calculations to justify your approach. If possible, you may briefly mention how your exploration relates to broader mathematical concepts or theories.

Aim

Here you should specify the goal of your exploration. However, instead of a vague “understanding of the topic,” you need to set clear, measurable objectives. For instance, “modelling the relationship between X and Y with an error margin of less than 10%.”

Main Body

This is the part where you show your calculations. But as we have already pointed out, Maths AI doesn’t just test your ability to use formulas and maths concepts. It also contributes to the development of fundamental skills, such as critical thinking. To demonstrate them, you can present different perspectives on solving the problem. It is beneficial to discuss and analyse alternative approaches even if they weren’t successful.

It is also critical to illustrate your calculations and reasoning with graphs, diagrams, and tables. Make them visually appealing and informative.

Conclusion

Don’t just summarise your findings, but explain their significance and how they align with your initial aims. Did you come across limitations, unexpected results, or difficulties? Then make sure to explain them as well as your approach to overcoming the issues.

Finally, the conclusive part of your IA may suggest future research questions, applications of your findings, and potential improvements for your work.

References

Proper referencing is one of the requirements of the ‘Mathematical Presentation’ criterion. Whenever you mention any sources, you worked with to support your background, theory, calculations, etc., you need to reference them. These could be textbooks, publications in scientific magazines, online databases, etc.

Please note that the proper referencing style depends on your school. Most commonly, it is either in-text citations (the so-called Harvard style) or a bibliography list. You must consult your teacher to find out which one to use.

Final Words about Maths IA

A properly structured Maths IA is important not only to meet the scoring criteria. It also helps to organise your thoughts and ideas, as well as gives you a well defined plan to follow. 

If you still struggle to write a Maths IA report your examiners will like, don’t hesitate to ask experts. Our knowledgeable IB Maths tutors have helped hundreds of students to reach their best. Whether you’re unsure about your research question, methodology, results, or simply require a professional opinion, we are always at your disposal. 

TutorsPlus and our tutors are available at 022 731 8148 and info@tutorsplus.com.

By Sara Lloyd

Sara has been an education consultant for TutorsPlus for 15 years, and is an expert on international IB education.  She is also a parent of two lively children.

Find a Tutor