InertiaLearning

Internal Assessment Guide

IB Mathematics Analysis & Approaches HL

This is a complete guide to writing a great Internal in 2022.

So if you want to get a 7 on your IB Math AA HL Internal, then this guide is perfect for you.

Let’s dive right in.

The Internal Assessment in Mathematics Analysis and Approaches HL counts for 20% of your final IB score and is the easiest method to achieve an outstanding mark. This guide will direct you through every critical step of this journey so you end with a superior product.

Criterion Breakdown

In order to begin the process of writing your Internal Assessment, you must first understand how you are being graded. Below, you will find a summary of each of the criterion and what to emphasize in order to score well in each.

Criterion Name

A: Communication

B: Mathematical Presentation

C: Personal Engagement

D: Reflection

E: Use of Mathematics

Maximum Marks

4

3

4

3

6 IB Language

This criterion assesses the organization and coherence of the exploration. A well-organized exploration includes an introduction, has a rationale (which includes explaining why this topic was chosen), describes the aim of the exploration and has a conclusion. A coherent exploration is logically developed and easy to follow.

Use appropriate mathematical language (notation, symbols, terminology), defining key terms, where required, use multiple forms of mathematical representation, such as formulae, diagrams, tables, charts, graphs and models, where appropriate.

This criterion assesses the extent to which the student engages with the exploration and makes it their own. Personal engagement may be recognized in different attributes and skills. These include thinking independently and/or creatively, addressing personal interest and presenting mathematical ideas in their own way

This criterion assesses how the student reviews, analyses and evaluates the exploration. Although reflection may be seen in the conclusion to the exploration, it may also be found throughout the exploration.

This criterion assesses to what extent students use mathematics in the exploration. Students are expected to produce work that is commensurate with the level of the course. The mathematics explored should either be part of the syllabus, or at a similar level or beyond. It should not be completely based on mathematics listed in the prior learning.

InertiaLearning Summary

Clarity of your explanations
Organized structure – introduction that describes aims of investigation, bodies outlining arguments, well rounded, summarizing conclusion that links back to introduction

Accurate mathematical language – notation, symbols, terminology
Utilizing words such as “factored out” rather than “cancel”
Define key terms! – There might be things that you understand that an IB grader might not, especially with personalized topics
Mathematical representations can help improve understanding – graphs, charts, diagrams etc.
Ensure that labels are provided – axes, diagrams etc.

Ensure that your investigation is independent and unique – describe struggles, challenges, limitations, and extensions you brainstormed and experienced
Provide your own commentary – this is not a textbook!
Continue to personalize your topic – if writing about modeling the path of a baseball, maybe you add a component about the fastball pitch because it’s your signature pitch
Never say: “I have always been interested in…” It comes off as fake and unrealistic

Noting the reasons for which you chose that specific mathematical technique or concept – is it effective? More useful than others?
Are there weaknesses, limitations, errors – similar to a science internal assessment
Is your solution/investigation unique, effective, replicable in the real world?
In short, examine the paper you just wrote!
Can be done throughout the paper (specific sections may have individual reflections) but should be concentrated within the conclusion

You answered the questions and topics that you outlined in the introduction, utilizing relevant, IB level math
Demonstrate understanding of the math you’re using
You are writing a math internal, make the math good!

Step 1: Choose A Topic

The most critical decision on your Internal Assessment journey is determining your topic.

Your topic must be chosen carefully and strategically as it will be what the entire paper builds off of and is graded in itself within the personal engagement and communication sections.

For Mathematics AA HL the Criterion explicitly state that topics explored should extend existing curriculum and serve as a method to provide depth of understanding.

While difficult topics do have their place within the Internal Assessment, choosing a simpler topic may create a more well-rounded investigation as you will be able to demonstrate your understanding to a greater extent with a topic you wholly understand.

Additionally, your topic should possess real-world application and be relevant within today’s society in order to discuss the relevance of your investigation.

Topics that work

Topics that don't work

Modelling

Works wonderfully with topics like finance, architecture, and physics-based investigations. Can highlight personal engagement

Sports

These topics tend to be too focused on the physics aspect, unless it is a data-based analysis

Sequences and Series

Allows investigation into the basics of mathematics with topics like Number Theory. Best for the purists

Probabilities in Video Games

Either becomes too simple or too complicated depending on the game

Codes and Ciphers

An interesting and different topic for the grader to read and will achieve mathematical depth

Projectile Motion

Extremely common topic, especially when it is not a data-based investigation

Need more inspiration? Check out this extensive list of possible Internal Assessment Topics.

Step 2: Research and Development

Before you should even think about starting your paper, you should do at least 2 hours of research about your idea.

The point of doing research is to establish and ensure the validity of the topic, and to delve into and improve your mathematical understanding.

As said earlier, the understanding, or Criterion E, is worth the greatest number of marks.

The worst thing you can do is to simply start your paper without having any manifested ideas or structure.

Avoid having to rewrite, restructure, and force additional concepts into the paper, all which may interrupt the fluidity of the investigation.

Additionally, Cite All Sources!

We at InertiaLearning recommend creating a detailed outline with an annotated bibliography.

Step 3: Structure and Writing

Below, we have defined the basic components of the internal and in the order that they should be tackled. This should not be confused with the criterion.

Introduction

Writing an adept and effective introduction is the key to every successful mathematical investigation.

Within this section, you want to introduce the reader to your aim, exploration in general, and how you use mathematical concepts in order to explore your exploration.

It might also assist the fluidity to include a hypothesis or overview.

Remember that this is the beginning of your ‘communication’ to the reader.

The reader MUST understand what you are planning to do within the exploration.

Finally, ensure to define all your variables, assumptions, and key terms.

We advise you to have a noticeable topic sentence saying: “In this mathematical exploration I will be investigating [blank] through the use of [mathematical concept]”.

Analysis

The Analysis part of your Internal is arguably the most important part of the whole paper.

Unfortunately, it is also the most difficult part to describe in a guide.

In this section, you are supposed to represent your thoughts, ideas, and most importantly, your ways to get to the solution.

This means that this is going to be the most difficult part of your paper.

Writing using math can be very difficult.

At InertiaLearning, we advise that you write the quantity of math within the investigation and allow the commentary and analysis to flow around the mathematical superstructure.

Also, this way, the math can be reviewed and checked multiple times, to root out mistakes.

Remember that ALL your answers and ways of achieving these answers must be correct and understandable.

You need to SHOW the reader what you are doing.

With analysis comes interpretation, the method by which you can maximize points for Criterion C and D.

It also shows that you have an in-depth understanding of the topic and thus can dive deeper into the subject.

Essentially, provide a great deal of detail within the commentary of the paper, explaining every step, and all of your process along the way.

Conclusion

The end of your paper has been reached.

Be proud of yourself.

All this hard work is now being summarized, reflected on, and evaluated.

The Conclusion is used to talk about at least 3 limitations and the scope of your exploration.

This is the place in which you write about what you have learned and other possible related extension problems/questions that arose while doing your paper.

Step 4: Review

Reviewing your paper will be one of the most rewarding and difficult challenges in this process.

We can guarantee you that if you don’t review your paper or let it be reviewed by friends/family/teacher it will give you a bad feeling and it will not transform all your potential onto the paper.

In order to help you we have compiled this detailed checklist.

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