IB Math Internal Assessment Solved: A Guide for Math AA and AI Students

Wait so you’re telling me I have to write an assignment…for Maths?! How do I even come up with a topic? Do I need to ‘invent’ new math? How on earth am I supposed to score well on this assessment?

In this guide, we will share our tried-and-tested winning formula for both Math Analysis and Approaches (Math AA) students and Math Applications and Interpretations (Math AI) students to succeed in your Math Internal Assessment.

Topic Selection:

When selecting a topic, it is always great to start with an area of interest to make it easier to add elements of personal engagement (this will become apparent later, when we take a look at the marking criteria).

This may be a particular sport, hobby or extracurricular activity which you participate in. Some popular examples include basketball, football, swimming, business/economics, music or even mangoes (yes, I have seen a Math IA on mangoes).

Now you may be thinking “this is the most generic and useless advice I have ever received” but from here, we can get more specific based on which Math course you are undertaking. For Math AI students, your course is heavily focused on statistics and statistical testing, while Math AA students have far more content on modelling, functions, trigonometry and calculus.

So the trick from here is to take your chosen field, let’s say for example we choose football, and try to connect the mathematical topics to this area of interest:

But how do I get from ‘Football’ to these ideas?!

Well the starting point is to consider what kind of questions do we often ask in real life? In the case of football, one might ask whether teams should be spending more money on new transfers or developing young talent? Or perhaps whether players should shoot ‘low and hard’ or ‘high with placement’ on penalties? Starting with these questions, we can then ask whether we can use any of our Mathematical knowledge to investigate an answer!

Finally, the process of narrowing in on a topic is reliant on two factors – applicability of Mathematical tools and availability of data. You must be able to apply the Mathematical tools that you have learned throughout the IB in your IA, and you must also consider whether the data you need for your exploration is publicly available or can be personally collected.

Writing the Internal Assessment:

It can often be difficult to start writing the Math IA. What do I write first? What calculations should be done in advance? How do I even know if the Math is going to work?!

First, plan out the IA, particularly all the tools, tests and Mathematical calculations to be completed. We then recommend you complete all the ‘Math work’ in the IA before commencing any substantial writing, as you may find that the tools which you originally planned are not relevant or that the data cannot be found or collected accurately. This means that data collection (whether this is through online research or directly) is the first step, followed by performing the calculations for the IA. After this is completed and you are satisfied that the calculations have been performed well and the conclusions from your tests provide enough content for an interesting discussion, we can then start writing the IA itself.

While the structure of the IA varies between course and even between particular topics, a broad framework would be:

1. Introduction and Rationale – Introduce the topic and your rationale for writing the IA

2. Aim/Approach – Outline the aim of your IA and how you will be approaching your topic

3. Data Collection – Explain how you collected your data, define any key terms/assumptions and present your data

4. Main Body – The main body of the Math IA will depend on the focus questions built within your topic and the particular tools which you will employ

5. Conclusion and Evaluation – Present the conclusions of your IA and evaluate strengths/limitations

The IB Marking Criteria – Writing for Success:

Wait, hold on a minute. So should my IA be just a presentation of calculations? How much working do I need to show? Do I need to explain the tools or is it assumed knowledge?

To answer these questions, let’s delve into the marking criteria and take a look at what they really want from you.

Criterion A: Presentation (4 Marks)

Your IA needs to look clean, coherent and well-organised. It must have well-constructed diagrams to assist clarity when necessary. Importantly, to hit the top band, it must not only be coherent and well-organised but concise.

This means that when presenting calculations, do not repeat all steps each time you do a new calculation, if the steps have previously been explained. For example, if you are calculating the mean, median and mode for a series of datasets, show an example calculation for the first value but present the remaining findings in a table without showing working for all of them.

Criterion B: Mathematical Communication (4 Marks)

Communicating mathematics is very difficult. Your biggest asset in the Math IA will be diagrams, tables and charts which can accompany your text.

Other elements of this criterion to note include defining all key terms and variables (and remaining consistent throughout the IA), using the correct notations, symbols and terminology and showing your line-by-line working to set out your proofs.

Criterion C: Personal Engagement (3 Marks)

You can easily score 1 or 2 marks in this criteria by merely relating your chosen topic to your own personal experiences and motivations. For example, the conclusions of an IA about football may be useful to implement in your own footballing.

However, to maximise your marks in this criterion, you need to demonstrate personal engagement in the way you approach the task. Implementing creative ways of collecting data, utilising tools or even applying your data can all contribute to this criterion.

Criterion D: Reflection (3 Marks)

One common misconception about this criterion is that you can ‘throw in some reflection at the end in the evaluation section’. This approach will not allow you to score more than 1/3, as this criterion requires both ‘substantial evidence’ (i.e. throughout the entire IA) of ‘critical reflection’.

Some ways to integrate this include continuously linking back to the aims of the exploration (e.g. explaining how each conclusion you draw can be applied to your aim/the real world), commenting on new discoveries that you make as you are making them and commenting on not only the results but the tools, calculations and approaches you have taken.

One tip from us is to always write as though you are discovering everything for the first time, almost like a journal/logbook; for example, you may complete the first section and note that the result appears to support a particular hypothesis, although you will need to complete further calculations to be sure.

Essentially, reflect on your results as they appear, their meaning to your aim, the strengths and limitations of the tools you are using, and your own ‘thoughts’ which pop up throughout the writing process.

Criterion E: Use of Mathematics (6 Marks)

In my opinion, this criterion is very poorly named as it is not only your ‘Use of Mathematics’ which is being awarded marks but your understanding of the math which you are using. For example, compare the wording for a 3/6 and a 6/6 in this criteria:

3/6: Relevant mathematics commensurate with the level of the course is used. Limited understanding is demonstrated.

6/6: Relevant mathematics commensurate with the level of the course is used. The mathematics explored is correct. Thorough knowledge and understanding are demonstrated.

‘Relevant’ mathematics refers to tools which support the development of the exploration toward the completion of its aim – this also indicates that we should be justifying WHY we are using particular tools prior to using them and only using a tool if it contributes to our aims. However, you’ll notice that using relevant mathematical tools commensurate with the course is merely a prerequisite to scoring half marks in this criterion. So where do the other marks come from?

Well firstly, you need to use it correctly. It does not need to be perfect to score in the top bracket, however it must not detract from the flow of the mathematics or lead to an unreasonable outcome.

More importantly, you need to show knowledge and understanding (and this must be thorough to score 6/6). So what exactly does this involve? You must:

1. Justify the use of each mathematical tool (e.g. Why are we using this tool and how will it help us investigate the aim)

2. Explain how the tool works (e.g. If calculating Pearson’s Correlation Coefficient, not only explaining the process of calculating the coefficient using the formula but explaining how the formula works)

3. Interpreting what our results mean (e.g. What is the formal conclusion and what is the relevance to our aims)

In essence, to score highly in this criterion, you need to dive back into your Mathematics textbook or class notes and read that one section that no one ever pays much attention to – the part that explains why formulas work, how they are derived and what you are actually doing when you are substituting values into these formulas. Ultimately, this IA was designed by the IB to assess two overarching principles: firstly, your ability to take the mathematical concepts, tools and theories and apply them to a real-world problem and secondly, to prompt students to reflect upon and delve into the intricacies of the mathematical content which they are learning.

And that’s it, everything you need to know to succeed in your IB Math Internal Assessment for both Math AI and Math AA students! If you are still struggling to get started, write or generally unsure about how exactly to succeed in this task, reach out! Our team of successful IB tutors are well-equipped to assist with the IB Math IA and are able to work with you from topic selection to final completion of this task.