extended essay ideas math

Mathematics Extended Essay Topics for IB

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• Writing Metier

Ever felt the exhilaration that comes with cracking a complex math problem? That’s the sheer beauty of mathematics – it’s a world where numbers dance, patterns emerge, and solutions await the keen observer. Felt that? Hah?

Now, imagine channeling that same enthusiasm and zest into your Math Extended essay. It might sound like a challenge, but isn’t that what we thrive on? With the right Math EE topic, you can showcase your mathematical prowess and leave an indelible mark on your IB evaluators following the general criteria. 

To help you with that, I’ve curated a list of Math extended essay ideas that span the spectrum from the accessible to the intricate. 

So, let’s begin.

IB Math extended essay ideas

These aren’t just topics; they’re gateways to exploration, understanding, and innovation. 

Ready to get started?

Easy-to-approach topics

For those looking for a gentler introduction to the Math Extended essay, below is a list of 10 engaging and manageable IB Math EE topic ideas, each with a research question and a brief description on how to approach it:

Patterns in Pascal’s Triangle

Research Question: 

How do patterns emerge in Pascal’s Triangle?

Description: 

Begin with the construction of Pascal’s Triangle, then delve into the exploration of its patterns, such as triangular numbers and the Fibonacci sequence.

Mathematics of Voting Systems

How do different voting systems weigh individual votes mathematically?

Introduce various voting systems, then analyze the mathematical principles behind each, discussing fairness and potential biases.

Geometry in Art

Research Question:  

How is geometry used to create visual appeal in art?

Explore various art pieces, highlighting the geometric principles employed, and discuss their impact on aesthetics.

The Math Behind Baking

How do ratios in baking recipes affect the final product?

Investigate the importance of maintaining specific ratios in baking recipes and experiment with variations to observe changes in outcomes.

Probability in Card Games

How does understanding probability enhance success in card games like Poker?

Delve into the rules of Poker and then analyze various hands and scenarios using probability principles.

Symmetry in Nature

How is symmetry exhibited in natural formations?

Explore the concept of symmetry mathematically and then identify and analyze its presence in various natural formations like leaves, flowers, and animals.

Mathematics of Music

How do mathematical patterns influence musical scales and rhythms?

Investigate the structure of musical scales, rhythms, and time signatures, highlighting the underlying mathematical patterns.

Simple Interest vs. Compound Interest

How do simple and compound interest methods impact savings over time?

Define both interest methods and then use mathematical modeling to compare their effects on savings over various periods.

The Golden Ratio in Architecture

How is the Golden Ratio applied in iconic architectural designs?

Introduce the concept of the Golden Ratio and then analyze its application in various famous architectural structures.

Mathematics of Juggling

How do mathematical patterns and sequences dictate juggling techniques?

Explore basic juggling techniques and patterns, analyzing the mathematical sequences that jugglers use to maintain rhythm and control.

Each of these topic ideas and RQs is approachable yet offers ample scope for exploration and analysis within the realm of mathematics.

Intermediate topics

For those seeking a bit more challenge without diving into the deep end, the topics below offer a balanced blend of complexity and accessibility.

Here’s a list of 10 average-difficulty IB Math Extended essay topics, each with a research question and a brief description of how to approach it:

Game Theory in Economics

How does game theory provide insights into competitive market behaviors?

Introduce game theory principles and use business world case studies to show strategic decision-making influenced by game theory.

Fractals and Nature

How do fractal patterns manifest in natural phenomena?

Description:  

Delve into the mathematical concept of fractals and explore their appearance in various natural settings, such as coastlines, mountains, and plants.

Mathematics of Population Growth Models

How do mathematical models accurately predict population growth in urban areas?

Introduce population growth models and use real urban area data to validate these models, discussing influencing factors.

Cryptography and Internet Security

How do modern cryptographic techniques ensure data security on the internet?

Explore the evolution of cryptography, focusing on modern techniques, and discuss their role in ensuring data security in online transactions.

Mathematical Modeling of Epidemics

How can mathematical models predict the spread of infectious diseases?

Introduce basic epidemiological models and analyze their effectiveness in predicting disease spread using real-world data.

Topology and Coffee Cups

How does topology explain the mathematical similarity between a coffee cup and a donut?

Dive into the basics of topology and use it to explain the often-cited comparison between coffee cups and donuts, emphasizing the concept of homeomorphism.

Chaos Theory and Weather Forecasting

How does chaos theory impact the accuracy of long-term weather forecasts?

Introduce chaos theory, then delve into its application in meteorology, discussing the challenges and limitations in predicting weather.

Mathematics Behind Neural Networks

How do mathematical algorithms drive the functioning of neural networks in artificial intelligence?

Explore the structure of neural networks and delve into the mathematical algorithms that enable their learning and functioning.

Optimization Problems in Logistics

How can mathematical optimization improve efficiency in supply chain logistics?

Investigate real-world logistics challenges and demonstrate how mathematical optimization techniques can offer solutions.

Number Theory in Modern Cryptography

How does advanced number theory underpin modern cryptographic techniques?

Delve into number theory concepts and their application in modern cryptographic methods, emphasizing their role in ensuring data security.

These topics and research questions offer a balanced blend of complexity and accessibility, making them suitable for students seeking a moderate challenge in their Math Extended essay.

Advanced topics (with potential for higher rewards)

For the brave hearts ready to dive deep, these topics are challenging but can yield impressive results when tackled effectively.

The list of 10 challenging IB Math Extended essay ideas, each with a research question and a brief description:

Navier–Stokes Existence and Smoothness

What are the mathematical implications of the unsolved Navier–Stokes existence and smoothness problem in fluid dynamics?

Delve deep into the Navier–Stokes equations, exploring their significance in fluid dynamics and the challenges surrounding their unsolved problems.

Riemann Hypothesis and Prime Numbers

How does the Riemann Hypothesis relate to the distribution of prime numbers?

Investigate the Riemann Hypothesis, its historical context, and its profound implications for the distribution of prime numbers.

Quantum Cryptography and Key Distribution

How does quantum cryptography enhance security in key distribution?

Explore the principles of quantum mechanics applied to cryptography, focusing on the advantages and challenges of quantum key distribution.

Elliptic Curves and Cryptography

How do elliptic curves underpin modern cryptographic techniques?

Dive into the mathematics of elliptic curves and their pivotal role in modern cryptographic algorithms.

Four Color Theorem and Graph Theory

How does the Four Color Theorem demonstrate the complexities of graph coloring?

Investigate the history and proof of the Four Color Theorem, discussing its implications and challenges in graph theory.

Complex Analysis in Quantum Mechanics

How does complex analysis influence the mathematical foundations of quantum mechanics?

Delve into the principles of complex analysis and explore their applications and significance in quantum mechanics.

Twin Prime Conjecture

What are the implications and challenges of the Twin Prime Conjecture in number theory?

Investigate the Twin Prime Conjecture, its history, and its significance in the realm of number theory.

Knot Theory and DNA Replication

How does knot theory provide insights into the process of DNA replication?

Explore the mathematical intricacies of knot theory and its applications in understanding the complexities of DNA replication.

Ergodic Theory and Thermodynamics

How does ergodic theory connect with the principles of statistical thermodynamics?

Dive deep into ergodic theory, exploring its foundational concepts and its connections to statistical thermodynamics.

Langlands Program and Number Theory

What is the Langlands Program, and how does it seek to unify different areas of mathematics?

Investigate the Langlands Program, its objectives, and its profound implications in unifying disparate areas of mathematics, particularly number theory.

These topics are undoubtedly challenging but can yield impressive results when tackled effectively. They offer a deep dive into complex mathematical concepts and theories, making them ideal for students aiming for the highest grades in their Math Extended essay.

Get extended essay help

Before continuing to the next block, I suggest our Math EE writing or editing services . Our company has been working with numerous IB students and helped them write custom IB extended essays.

Join a team of happy IB students who have followed the IB extended essay rubric and criteria and gained better results with Writing Metier and our Math assignments help !

Overused Math EE topics (proceed with caution)

While these topics are popular, they’ve been explored extensively. If you choose one, ensure you bring a fresh perspective:

• The Fibonacci Sequence in Nature.
• Pi and its Mysteries.
• The Monty Hall Problem.
• The Birthday Paradox.
• Exploring Pascal’s Triangle.
• The Mathematics of the Pyramids.
• The Tower of Hanoi Problem.
• Benford’s Law.
• The Four Color Theorem.
• The Mathematics of the Rubik’s Cube.

Keep in mind that selecting such a topic will require hard work to find a new custom angle of research and sometimes might not lead to higher grades .

In Conclusion

Alright, IB champs, that wraps up our curated selection of Math EE topics, each with its unique flavor and challenge. The topic is just the starting point. The real magic happens when you infuse it with your insights, analysis, and unique perspective. 

Mathematics isn’t just about numbers; it’s about stories and trips within the confines of equations and graphs. As you gear up to tackle your Extended essay, keep that passion alive, keep questioning, and most importantly, enjoy the process. 

Don’t forget to reserve extra space because it may take time to write an extended essay . And if you’re ever in doubt, remember that Writing Metier is here to guide you through every step of the process.

Free topic suggestions

Vasy kafidoff.

Vasyl Kafidoff is a co-founder and CEO at WritingMetier. He is interested in education and how modern technology makes it more accessible. He wants to bring awareness about new learning possibilities as an educational specialist. When Vasy is not working, he’s found behind a drum kit.

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Extended Essay Writers

How to Write a Math Extended Essay? A Comprehensive Guide

Luke MacQuoid

Ah, the Math extended essay! It’s an excellent opportunity for students in the IB program to showcase their knack for numbers. From my experience, crafting an impactful essay requires mathematical talent and a solid understanding of what makes a paper genuinely resonate.

Throughout this article, you’ll find gems on selecting Math extended essay topics , how to structure your essay, and even some common pitfalls to avoid. So, let’s jump right in, shall we?

What is a Math Extended Essay?

You may be pondering, “What is a Math extended essay?” According to the IB criteria, this piece is a 4,000-word research document that prompts students to research a mathematical topic of interest thoroughly. It’s not just an ordinary research paper; think of it as your gateway to mastering a subject you’re genuinely passionate about. Trust me, from my experience, it’s a pivotal component of your academic growth.

Let’s clarify further. Math extended essay isn’t just a routine school assignment you might complete on a typical day. Instead, it’s a comprehensive exploration of a distinct topic within Mathematics. But remember, it’s not all about numbers or equations. It’s about showcasing your ability to reason, analyze, and communicate your findings in writing.

Here are all the critical elements of a top-notch Math extended essay :

• Clear Thesis . A strong paper begins with a defined proposition or statement set for investigation.
• Thorough Research . Look into reputable sources, journals, and academic papers. Absorb as much relevant information as possible.
• Logical Flow . Your essay should transition smoothly from one topic to the next, ensuring readers can follow your train of thought easily.
• In-depth Analysis . Beyond stating facts, analyze them critically and draw your conclusions.
• Personal Touch . Reflect on your genuine interest and connection with the topic.
• Effective Expression . Aim for clarity in your writing, ensuring readers can quickly grasp your points.
• Ethical Standards . Properly cite all your sources and avoid any form of plagiarism.
• Reflection . Share insights on your learning process, the challenges faced, and the strategies you employed to address them.

So, you might wonder, “Why take on such a demanding task?” Here’s the thing: based on what I’ve learned and observed, the Math extended essay plays a significant role in the IB program. It’s essential for obtaining your IB diploma and can significantly enhance your college application. More importantly, it’s an opportunity to challenge yourself academically, fostering intellectual growth.

Committing to this task and seeing it through will be a significant academic accomplishment. Best of luck!

Getting Started with Your Math Extended Essay

The inception of any great essay starts with topic selection and understanding the guidelines, naturally.

Topic Selection

Choosing the right topic is the first milestone. Think about the Mathematical areas that captivate your interest. Whether it’s the logic of algebra, the complexity of calculus, or any other field, there’s a vast Mathematical universe to explore. While broad subjects might seem tempting, concentrating on specific IB Math extended essay topics is often more effective. Your issue should be clear-cut and straightforward and uphold strong academic integrity in line with IB standards.

Understanding Guidelines

After settling on a topic, it’s essential to acquaint yourself with the IB’s precise expectations . From my experience, grasping these guidelines is foundational to the essay’s success:

• The IB has detailed guidelines regarding the structure and layout of extended essays. Ensure you’re well-versed in font choice, spacing, and the like.
• While the IB often leans towards MLA or APA citation styles, be sure to check the style preferred by your institution. Accurate citations aren’t just about avoiding plagiarism; they lend authenticity to your work.
• IB evaluates your extended essay based on distinct criteria, such as clarity, depth of knowledge, presentation, and personal connection to the topic. Familiarizing yourself with these parameters can guide your research and writing trajectory.
• The extended essay process in the IB program includes consultations with a designated supervisor. These sessions are golden opportunities to glean insights and refine your approach.

In essence, the proper groundwork ensures a smoother path ahead. With a compelling topic and a robust grasp of the IB guidelines, you’re primed to craft a stellar Math extended essay. Embrace the process and aim for excellence!

Math Extended Essay: Research and Planning

Research is the backbone of your essay! Adequate preparation is necessary for a subject as complex and layered as Math.

Behind every successful essay is a bedrock of meticulous research and detailed planning. Given the intricate nature of Mathematics, gathering your tools and strategies is paramount before plunging into the writing phase. First, seek out robust platforms that offer a plethora of verified information :

• Online Databases . Websites like JSTOR , Google Scholar , and MathSciNet host a rich collection of articles, papers, and journals dedicated to Mathematics.
• Academic Journals . Publications such as the “American Journal of Mathematics” or the “European Journal of Mathematics” provide peer-reviewed papers on many topics.
• University Libraries . Many universities offer access to their digital libraries, which can be goldmines for in-depth research.
• Professors and Mentors . Never underestimate the power of a conversation. Sometimes, discussing your topic with experts can lead to new insights and perspectives.

Remember, the depth and breadth of your research directly influence the strength of your arguments. Always verify the authenticity of your sources; a well-researched essay stands tall among its peers.

Timeline for Writing Math Extended Essay

Managing time is a lifesaver in the whirlwind of IB coursework, deadlines, and extracurriculars. Crafting a detailed timeline ensures you stay on track and prevents last-minute scrambles.

• Exploration . Dedicate the initial phase to exploring potential topics, understanding guidelines, and preliminary reading.
• Intensive Research . This phase involves deep diving into your chosen topic, gathering data, and organizing your findings.
• Drafting . Begin with an initial draft. Lay down your arguments, flesh out your thoughts, and structure your content.
• Review and Refinement . Revisit your draft, make necessary revisions, and incorporate feedback from peers or mentors.
• Finalization . Proofread, ensure adherence to guidelines, and prepare for submission.

Breaking down your process into manageable chunks alleviates stress and enhances the quality of your work.

Need help with your IB extended essay?

From research and analysis to structuring and editing, our skilled mentors will be by your side, helping you craft an exceptional extended essay that not only meets the wordcount and stringent IB criteria but also reflects your passion for selected IB group .

To wrap it up, remember that while the task might seem daunting, meticulous research and detailed planning are your allies. Harness them wisely; your Math extended essay will meet and exceed expectations. Happy researching!

Structuring Your Math Extended Essay

Organization is key, folks! How you structure your essay could make or break your grade.

Introduction

Your introduction should present the issue you’re investigating, why it matters, and how you plan to tackle it. This part is the roadmap of your essay; it sets the tone for the reader.

In this section, present your research, arguments, and findings. Dabble in some theory, show your equations or models, and remember to analyze their relevance. As you go, remember to build a logical flow. Use transition words to guide your reader through your discussion.

It is where you tie all your findings together. A well-crafted conclusion leaves a lasting impression, briefly highlighting your significant discoveries and their implications.

Math Extended Essay: Common Mistakes to Avoid

When creating an essay of the caliber expected for the IB program, the devil is often in the details. Many students have sailed through the bulk of their paper writing only to stumble near the finish line due to seemingly minor oversights. Awareness of these pitfalls is essential, especially in an undertaking as significant as the Math extended essay.

A common trap that students often fall into is vagueness. One might use ambiguous phrases or general statements to sound sophisticated or cover a wide range of ideas. Instead of making broad claims, focus on your main idea and flesh it out with detail and precision. 

Another critical area that cannot be overemphasized is plagiarism. While it’s tempting to borrow a perfectly phrased sentence or a well-structured argument, doing so without proper attribution is academically dishonest and can jeopardize your entire essay. When in doubt, always give credit where credit is due.

Another often overlooked aspect is the flow and structure of the essay. Transitioning smoothly from one point to the next, ensuring that each segment of your paper leads seamlessly into the next, can make a difference in your work’s overall quality and readability.

Review and Revision in Math Extended Essay

One of the most powerful tools in this phase is peer review. While you’ve been deeply engrossed in your essay and every argument, equation, and citation, there’s immense value in having another set of eyes scan your work. It doesn’t necessarily mean someone who’s an expert in your topic but can provide a fresh perspective. They can identify areas that might be unclear to a new reader.

Following peer review, there’s the intricate task of editing and proofreading. While these terms are often used interchangeably, they serve distinct purposes. Editing is all about refining the content. Proofreading, on the other hand, is about the nitty-gritty. It ensures that your grammar is spot-on and that there are no misplaced punctuations.

In all of this, reflection is a vital element often overlooked. Taking a step back, setting your essay aside for a day or two, and returning to it with renewed vigor is immensely beneficial. With a fresh mindset, you might find new angles to consider or realize there are redundant points that can be removed.

To Sum It Up

Writing a Math extended essay can be challenging but also incredibly rewarding. So, according to general IB criteria and years of personal experience, the time and effort you invest in this project will be well worth it. Good luck, young scholars!

Luke MacQuoid has extensive experience teaching English as a foreign language in Japan, having worked with students of all ages for over 12 years. Currently, he is teaching at the tertiary level. Luke holds a BA from the University of Sussex and an MA in TESOL from Lancaster University, both located in England. As well to his work as an IB Examiner and Master Tutor, Luke also enjoys sharing his experiences and insights with others through writing articles for various websites, including extendedessaywriters.com blog

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International Baccalaureate (IB)

IB students around the globe fear writing the Extended Essay, but it doesn't have to be a source of stress! In this article, I'll get you excited about writing your Extended Essay and provide you with the resources you need to get an A on it.

If you're reading this article, I'm going to assume you're an IB student getting ready to write your Extended Essay. If you're looking at this as a potential future IB student, I recommend reading our introductory IB articles first, including our guide to what the IB program is and our full coverage of the IB curriculum .

IB Extended Essay: Why Should You Trust My Advice?

I myself am a recipient of an IB Diploma, and I happened to receive an A on my IB Extended Essay. Don't believe me? The proof is in the IBO pudding:

If you're confused by what this report means, EE is short for Extended Essay , and English A1 is the subject that my Extended Essay topic coordinated with. In layman's terms, my IB Diploma was graded in May 2010, I wrote my Extended Essay in the English A1 category, and I received an A grade on it.

What Is the Extended Essay in the IB Diploma Programme?

The IB Extended Essay, or EE , is a mini-thesis you write under the supervision of an IB advisor (an IB teacher at your school), which counts toward your IB Diploma (learn more about the major IB Diploma requirements in our guide) . I will explain exactly how the EE affects your Diploma later in this article.

For the Extended Essay, you will choose a research question as a topic, conduct the research independently, then write an essay on your findings . The essay itself is a long one—although there's a cap of 4,000 words, most successful essays get very close to this limit.

Keep in mind that the IB requires this essay to be a "formal piece of academic writing," meaning you'll have to do outside research and cite additional sources.

The IB Extended Essay must include the following:

• A title page
• Contents page
• Introduction
• Body of the essay
• References and bibliography

Additionally, your research topic must fall into one of the six approved DP categories , or IB subject groups, which are as follows:

• Group 1: Studies in Language and Literature
• Group 2: Language Acquisition
• Group 3: Individuals and Societies
• Group 4: Sciences
• Group 5: Mathematics
• Group 6: The Arts

Once you figure out your category and have identified a potential research topic, it's time to pick your advisor, who is normally an IB teacher at your school (though you can also find one online ). This person will help direct your research, and they'll conduct the reflection sessions you'll have to do as part of your Extended Essay.

As of 2018, the IB requires a "reflection process" as part of your EE supervision process. To fulfill this requirement, you have to meet at least three times with your supervisor in what the IB calls "reflection sessions." These meetings are not only mandatory but are also part of the formal assessment of the EE and your research methods.

According to the IB, the purpose of these meetings is to "provide an opportunity for students to reflect on their engagement with the research process." Basically, these meetings give your supervisor the opportunity to offer feedback, push you to think differently, and encourage you to evaluate your research process.

The final reflection session is called the viva voce, and it's a short 10- to 15-minute interview between you and your advisor. This happens at the very end of the EE process, and it's designed to help your advisor write their report, which factors into your EE grade.

Here are the topics covered in your viva voce :

• A check on plagiarism and malpractice
• Your reflection on your project's successes and difficulties
• Your reflection on what you've learned during the EE process

Your completed Extended Essay, along with your supervisor's report, will then be sent to the IB to be graded. We'll cover the assessment criteria in just a moment.

We'll help you learn how to have those "lightbulb" moments...even on test day!  

What Should You Write About in Your IB Extended Essay?

You can technically write about anything, so long as it falls within one of the approved categories listed above.

It's best to choose a topic that matches one of the IB courses , (such as Theatre, Film, Spanish, French, Math, Biology, etc.), which shouldn't be difficult because there are so many class subjects.

Here is a range of sample topics with the attached extended essay:

• Biology: The Effect of Age and Gender on the Photoreceptor Cells in the Human Retina
• Chemistry: How Does Reflux Time Affect the Yield and Purity of Ethyl Aminobenzoate (Benzocaine), and How Effective is Recrystallisation as a Purification Technique for This Compound?
• English: An Exploration of Jane Austen's Use of the Outdoors in Emma
• Geography: The Effect of Location on the Educational Attainment of Indigenous Secondary Students in Queensland, Australia
• Math: Alhazen's Billiard Problem
• Visual Arts: Can Luc Tuymans Be Classified as a Political Painter?

You can see from how varied the topics are that you have a lot of freedom when it comes to picking a topic . So how do you pick when the options are limitless?

How to Write a Stellar IB Extended Essay: 6 Essential Tips

Below are six key tips to keep in mind as you work on your Extended Essay for the IB DP. Follow these and you're sure to get an A!

#1: Write About Something You Enjoy

You can't expect to write a compelling essay if you're not a fan of the topic on which you're writing. For example, I just love British theatre and ended up writing my Extended Essay on a revolution in post-WWII British theatre. (Yes, I'm definitely a #TheatreNerd.)

I really encourage anyone who pursues an IB Diploma to take the Extended Essay seriously. I was fortunate enough to receive a full-tuition merit scholarship to USC's School of Dramatic Arts program. In my interview for the scholarship, I spoke passionately about my Extended Essay; thus, I genuinely think my Extended Essay helped me get my scholarship.

But how do you find a topic you're passionate about? Start by thinking about which classes you enjoy the most and why . Do you like math classes because you like to solve problems? Or do you enjoy English because you like to analyze literary texts?

Keep in mind that there's no right or wrong answer when it comes to choosing your Extended Essay topic. You're not more likely to get high marks because you're writing about science, just like you're not doomed to failure because you've chosen to tackle the social sciences. The quality of what you produce—not the field you choose to research within—will determine your grade.

Once you've figured out your category, you should brainstorm more specific topics by putting pen to paper . What was your favorite chapter you learned in that class? Was it astrophysics or mechanics? What did you like about that specific chapter? Is there something you want to learn more about? I recommend spending a few hours on this type of brainstorming.

One last note: if you're truly stumped on what to research, pick a topic that will help you in your future major or career . That way you can use your Extended Essay as a talking point in your college essays (and it will prepare you for your studies to come too!).

#2: Select a Topic That Is Neither Too Broad nor Too Narrow

There's a fine line between broad and narrow. You need to write about something specific, but not so specific that you can't write 4,000 words on it.

You can't write about WWII because that would be a book's worth of material. You also don't want to write about what type of soup prisoners of war received behind enemy lines, because you probably won’t be able to come up with 4,000 words of material about it. However, you could possibly write about how the conditions in German POW camps—and the rations provided—were directly affected by the Nazis' successes and failures on the front, including the use of captured factories and prison labor in Eastern Europe to increase production. WWII military history might be a little overdone, but you get my point.

If you're really stuck trying to pinpoint a not-too-broad-or-too-narrow topic, I suggest trying to brainstorm a topic that uses a comparison. Once you begin looking through the list of sample essays below, you'll notice that many use comparisons to formulate their main arguments.

I also used a comparison in my EE, contrasting Harold Pinter's Party Time with John Osborne's Look Back in Anger in order to show a transition in British theatre. Topics with comparisons of two to three plays, books, and so on tend to be the sweet spot. You can analyze each item and then compare them with one another after doing some in-depth analysis of each individually. The ways these items compare and contrast will end up forming the thesis of your essay!

When choosing a comparative topic, the key is that the comparison should be significant. I compared two plays to illustrate the transition in British theatre, but you could compare the ways different regional dialects affect people's job prospects or how different temperatures may or may not affect the mating patterns of lightning bugs. The point here is that comparisons not only help you limit your topic, but they also help you build your argument.

Comparisons are not the only way to get a grade-A EE, though. If after brainstorming, you pick a non-comparison-based topic and are still unsure whether your topic is too broad or narrow, spend about 30 minutes doing some basic research and see how much material is out there.

If there are more than 1,000 books, articles, or documentaries out there on that exact topic, it may be too broad. But if there are only two books that have any connection to your topic, it may be too narrow. If you're still unsure, ask your advisor—it's what they're there for! Speaking of advisors...

Don't get stuck with a narrow topic!

#3: Choose an Advisor Who Is Familiar With Your Topic

If you're not certain of who you would like to be your advisor, create a list of your top three choices. Next, write down the pros and cons of each possibility (I know this sounds tedious, but it really helps!).

For example, Mr. Green is my favorite teacher and we get along really well, but he teaches English. For my EE, I want to conduct an experiment that compares the efficiency of American electric cars with foreign electric cars.

I had Ms. White a year ago. She teaches physics and enjoyed having me in her class. Unlike Mr. Green, Ms. White could help me design my experiment.

Based on my topic and what I need from my advisor, Ms. White would be a better fit for me than would Mr. Green (even though I like him a lot).

The moral of my story is this: do not just ask your favorite teacher to be your advisor . They might be a hindrance to you if they teach another subject. For example, I would not recommend asking your biology teacher to guide you in writing an English literature-based EE.

There can, of course, be exceptions to this rule. If you have a teacher who's passionate and knowledgeable about your topic (as my English teacher was about my theatre topic), you could ask that instructor. Consider all your options before you do this. There was no theatre teacher at my high school, so I couldn't find a theatre-specific advisor, but I chose the next best thing.

Before you approach a teacher to serve as your advisor, check with your high school to see what requirements they have for this process. Some IB high schools require your IB Extended Essay advisor to sign an Agreement Form , for instance.

Make sure that you ask your IB coordinator whether there is any required paperwork to fill out. If your school needs a specific form signed, bring it with you when you ask your teacher to be your EE advisor.

#4: Pick an Advisor Who Will Push You to Be Your Best

Some teachers might just take on students because they have to and aren't very passionate about reading drafts, only giving you minimal feedback. Choose a teacher who will take the time to read several drafts of your essay and give you extensive notes. I would not have gotten my A without being pushed to make my Extended Essay draft better.

Ask a teacher that you have experience with through class or an extracurricular activity. Do not ask a teacher that you have absolutely no connection to. If a teacher already knows you, that means they already know your strengths and weaknesses, so they know what to look for, where you need to improve, and how to encourage your best work.

Also, don't forget that your supervisor's assessment is part of your overall EE score . If you're meeting with someone who pushes you to do better—and you actually take their advice—they'll have more impressive things to say about you than a supervisor who doesn't know you well and isn't heavily involved in your research process.

Be aware that the IB only allows advisors to make suggestions and give constructive criticism. Your teacher cannot actually help you write your EE. The IB recommends that the supervisor spends approximately two to three hours in total with the candidate discussing the EE.

#5: Make Sure Your Essay Has a Clear Structure and Flow

The IB likes structure. Your EE needs a clear introduction (which should be one to two double-spaced pages), research question/focus (i.e., what you're investigating), a body, and a conclusion (about one double-spaced page). An essay with unclear organization will be graded poorly.

The body of your EE should make up the bulk of the essay. It should be about eight to 18 pages long (again, depending on your topic). Your body can be split into multiple parts. For example, if you were doing a comparison, you might have one third of your body as Novel A Analysis, another third as Novel B Analysis, and the final third as your comparison of Novels A and B.

If you're conducting an experiment or analyzing data, such as in this EE , your EE body should have a clear structure that aligns with the scientific method ; you should state the research question, discuss your method, present the data, analyze the data, explain any uncertainties, and draw a conclusion and/or evaluate the success of the experiment.

#6: Start Writing Sooner Rather Than Later!

You will not be able to crank out a 4,000-word essay in just a week and get an A on it. You'll be reading many, many articles (and, depending on your topic, possibly books and plays as well!). As such, it's imperative that you start your research as soon as possible.

Each school has a slightly different deadline for the Extended Essay. Some schools want them as soon as November of your senior year; others will take them as late as February. Your school will tell you what your deadline is. If they haven't mentioned it by February of your junior year, ask your IB coordinator about it.

Some high schools will provide you with a timeline of when you need to come up with a topic, when you need to meet with your advisor, and when certain drafts are due. Not all schools do this. Ask your IB coordinator if you are unsure whether you are on a specific timeline.

Below is my recommended EE timeline. While it's earlier than most schools, it'll save you a ton of heartache (trust me, I remember how hard this process was!):

• January/February of Junior Year: Come up with your final research topic (or at least your top three options).
• February of Junior Year: Approach a teacher about being your EE advisor. If they decline, keep asking others until you find one. See my notes above on how to pick an EE advisor.
• April/May of Junior Year: Submit an outline of your EE and a bibliography of potential research sources (I recommend at least seven to 10) to your EE advisor. Meet with your EE advisor to discuss your outline.
• Summer Between Junior and Senior Year: Complete your first full draft over the summer between your junior and senior year. I know, I know—no one wants to work during the summer, but trust me—this will save you so much stress come fall when you are busy with college applications and other internal assessments for your IB classes. You will want to have this first full draft done because you will want to complete a couple of draft cycles as you likely won't be able to get everything you want to say into 4,000 articulate words on the first attempt. Try to get this first draft into the best possible shape so you don't have to work on too many revisions during the school year on top of your homework, college applications, and extracurriculars.
• August/September of Senior Year: Turn in your first draft of your EE to your advisor and receive feedback. Work on incorporating their feedback into your essay. If they have a lot of suggestions for improvement, ask if they will read one more draft before the final draft.
• September/October of Senior Year: Submit the second draft of your EE to your advisor (if necessary) and look at their feedback. Work on creating the best possible final draft.
• November-February of Senior Year: Schedule your viva voce. Submit two copies of your final draft to your school to be sent off to the IB. You likely will not get your grade until after you graduate.

Remember that in the middle of these milestones, you'll need to schedule two other reflection sessions with your advisor . (Your teachers will actually take notes on these sessions on a form like this one , which then gets submitted to the IB.)

I recommend doing them when you get feedback on your drafts, but these meetings will ultimately be up to your supervisor. Just don't forget to do them!

The early bird DOES get the worm!

How Is the IB Extended Essay Graded?

Extended Essays are graded by examiners appointed by the IB on a scale of 0 to 34 . You'll be graded on five criteria, each with its own set of points. You can learn more about how EE scoring works by reading the IB guide to extended essays .

• Criterion A: Focus and Method (6 points maximum)
• Criterion B: Knowledge and Understanding (6 points maximum)
• Criterion C: Critical Thinking (12 points maximum)
• Criterion D: Presentation (4 points maximum)
• Criterion E: Engagement (6 points maximum)

How well you do on each of these criteria will determine the final letter grade you get for your EE. You must earn at least a D to be eligible to receive your IB Diploma.

Although each criterion has a point value, the IB explicitly states that graders are not converting point totals into grades; instead, they're using qualitative grade descriptors to determine the final grade of your Extended Essay . Grade descriptors are on pages 102-103 of this document .

Here's a rough estimate of how these different point values translate to letter grades based on previous scoring methods for the EE. This is just an estimate —you should read and understand the grade descriptors so you know exactly what the scorers are looking for.

Here is the breakdown of EE scores (from the May 2021 bulletin):

How Does the Extended Essay Grade Affect Your IB Diploma?

The Extended Essay grade is combined with your TOK (Theory of Knowledge) grade to determine how many points you get toward your IB Diploma.

To learn about Theory of Knowledge or how many points you need to receive an IB Diploma, read our complete guide to the IB program and our guide to the IB Diploma requirements .

This diagram shows how the two scores are combined to determine how many points you receive for your IB diploma (3 being the most, 0 being the least). In order to get your IB Diploma, you have to earn 24 points across both categories (the TOK and EE). The highest score anyone can earn is 45 points.

Let's say you get an A on your EE and a B on TOK. You will get 3 points toward your Diploma. As of 2014, a student who scores an E on either the extended essay or TOK essay will not be eligible to receive an IB Diploma .

Prior to the class of 2010, a Diploma candidate could receive a failing grade in either the Extended Essay or Theory of Knowledge and still be awarded a Diploma, but this is no longer true.

Figuring out how you're assessed can be a little tricky. Luckily, the IB breaks everything down here in this document . (The assessment information begins on page 219.)

40+ Sample Extended Essays for the IB Diploma Programme

In case you want a little more guidance on how to get an A on your EE, here are over 40 excellent (grade A) sample extended essays for your reading pleasure. Essays are grouped by IB subject.

• Business Management 1
• Chemistry 1
• Chemistry 2
• Chemistry 3
• Chemistry 4
• Chemistry 5
• Chemistry 6
• Chemistry 7
• Computer Science 1
• Economics 1
• Design Technology 1
• Design Technology 2
• Environmental Systems and Societies 1
• Geography 1
• Geography 2
• Geography 3
• Geography 4
• Geography 5
• Geography 6
• Literature and Performance 1
• Mathematics 1
• Mathematics 2
• Mathematics 3
• Mathematics 4
• Mathematics 5
• Philosophy 1
• Philosophy 2
• Philosophy 3
• Philosophy 4
• Philosophy 5
• Psychology 1
• Psychology 2
• Psychology 3
• Psychology 4
• Psychology 5
• Social and Cultural Anthropology 1
• Social and Cultural Anthropology 2
• Social and Cultural Anthropology 3
• Sports, Exercise and Health Science 1
• Sports, Exercise and Health Science 2
• Visual Arts 1
• Visual Arts 2
• Visual Arts 3
• Visual Arts 4
• Visual Arts 5
• World Religion 1
• World Religion 2
• World Religion 3

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12 Strong Topic Ideas For A Math Extended Essay

Writing a math extended essay can be quite a challenge unless you are using an IB extended essay writing service . You have many factors to consider such as following the right format, choosing the best approach for your study, and defending your thesis (if required). So choosing an engaging topic that pertains to today’s issues is a crucial first step when you are in the planning stages.

Obviously, mathematics are your primary interest or else you wouldn’t have this assignment, to begin with due to not being enrolled in a course that goes above and beyond Algebra 102 or Geometry 104. (Even if you’re forced to endure a statistics course, you would have some interest in mathematical data or at least possess an awareness of working with numbers in your chosen field.) So one bit of advice on selecting a topic for your extended essay topics is to combine your intrigue with math with a problem, scenario or specific career domain (e.g.: medical, technology, sociology, business, etc.) that will not only hold your attention but also relate to current trends or events.

So here some suggestions for fascinating math essay topics to get you started:

In the area of education, some possible themes are:

• Possible correlation between district-level standardized test scores or GPA’s and performance on the SAT
• Prevalence of stress and coping skills of secondary university-bound students (Think ratios and statistics)
• Effectiveness of literacy programs (school or community-wide) towards improving reading skills (You can probably narrow down to an age range or grade level(s))

For the medical field, the possibilities are endless. Consider these three suggestions:

• Possible direct correlation between usage of “antibacterial” products, like hand sanitizer for instance and the rise of the “Super Bug.”
• The odds of another pandemic, similar to the 1918 worldwide influenza outbreak, occurring
• The impact of advertising on childhood obesity (Again, think ratios, statistics, and probability)

In the realm of computer technology, you can look into any one of these subjects:

• Best formula and combinations for SEO
• The use of prime numbers and modular arithmetic to maintain privacy with RSA Public Key Cryptography
• Correlation between the use of electronic pay services (Skrill for example) and users’ professions.

Of course, there are a variety of areas to explore within the content of math itself and its applications. Some possibilities include the following:

• Study of alternatives to Euclidean geometry and their applications
• Close study of Sophie Germain’s Theorem
• Real life dilemmas that can be solved with strategies of complex number problem-solving

As you can see, there are many different subjects to explore when writing about mathematical concepts and how they relate to the real world. You can dive more into the content area of science and hypothesize the route(s) of a comet that could impact the earth. Concerning sociological and psychological studies, you can look into various statistical investigations of human behavior. Another rather amusing numerical investigation could involve a study of probability in gambling venues or about other types of gaming, like Fantasy Football. (Be careful with your finances, though.)

However, some tips to remember as you examine these topics is to choose the “sub-area” that interests you the most (unless it’s all about the math), as you will devote a lot of time to this project; make sure you have a clear and measurable hypothesis; and clarify any questions on format with your instructor. With these recommendations and a lot of calculating, you will compose the perfect paper.

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• Paper about the chemistry of water

IB Math EE - Propel Your Mind To A 34/34

Unlock the secrets to acing your IB Math EE with a guaranteed 34/34 score! Propel your mind to success and make the most of your potential. 💯

Table of content

Extended essay & what is it❓, ib math ee vs math ia 🥊 , wth is an ib math extended essay 🌋, a brief about ib math ee 🩲, sexy pointers you can't-miss 🤤, 4 ways to find the right math ee topic ⭕, formulate your research question 🔎, planning your research & essay 📖, structuring your essay 🏗️, ib math ee reflection, what to do 🪞, ib math ee criteria 🧮, ib math ee examples 🛹.

It's time we address the elephant in the room.

IB Mathematics Extended Essay.

There, we said it.

If you've taken up IB Math EE, we're here to tell you that it isn't over, contrary to what you might have heard.

Researching, planning, and finally writing a good IB Math EE is no walk in the park, but rest assured that you'll feel different once you've gone through this valuable document.

Nail IB presents the only comprehensive guide you need to nail your IB Math EE.

Let's keep it accurate.

IB Math EE is a rigorous, independent, academic research essay that calls for,

• a keen interest in Mathematics,
• strong mathematical aptitude & reasoning,
• a focused and disciplined approach, and most importantly,
• essential tips, techniques, and quality guidance.

When one opts for IB Math EE, one should ensure a strong passion for Mathematics and a solid mathematical foundation. Not to mention being willing to devote their time and effort to this self-directed research.

Disclaimer -  If you have second thoughts, you should reconsider and re-evaluate your choice because it's no use aiming in the dark.

There needs to be more!

Invaluable tips and techniques are the last missing piece of the IB Math EE puzzle.

Given the panic and stigma around Math Extended Essay, what students need, is not some more panic; instead, expert guidance to keep them pumped to write their EE papers with skill, precision, and utmost zeal. And so, true to our word, we're here to help you.

Say it out loud for me - I got this!

Before diving any further, we are thrilled to share our premium IB Math resources. Check out the  IB Math AI SL  bundle and the  IB Math AI HL  bundle, including everything from comprehensive, up-to-date video lecture courses by Adam Nazha to curated IB Resource Libraries. All your IB DP Math queries are now answered!

While you're at it, check out our  IB Math AA SL  repository, where Patrick Jones (yep, you got that right, our very own  PatrickJMT  - the best Mathematics instructor in the world) will guide you with a brilliant video lecture course he has created to help you nail your concepts and exams alike! Happy learning!

Returning to our one-stop guide for all things IB Math EE, let us see what this article will cover.

• Extended Essay & What is it ❓
• IB Math EE Vs Math IA  🥊
• WTH Is An IB Math Extended Essay?  🌋
• A Brief About IB Math EE ?  🩲
• Sexy Pointers You Can't Miss  🤤
• 4 Ways To Find The Right Math EE topic  ⭕
• Formulate Your Research Question  🔎
• Planning Your Research and Essay  📖
• Structuring Your Essay  🏗️
• Writing Your Essay Writing Your Reflection  🪞
• IB Math EE Criteria  🧮
• IB Math EE Examples  🛹

First things first, let’s briefly discuss what an Extended Essay is.

As the IB defines it, the Extended Essay is a  4000-word in-depth  study, part of the IB Diploma Programme core mandatory for all students.

A  500-word  reflection component-inclusive of 3 reflections - is submitted with the academic writing.

This, of course, is done under the supervision of your IB advisor. The critical thing to note is that you can choose to write an Extended Essay on any subject offered by the IB in your session, though it is highly recommended you settle on a topic you are studying as a part of your IB curriculum.

The purpose of an Extended Essay is to motivate students to conduct formal research on a subject area of interest, independently work on the chosen research question and gain guidance from their respective IB mentors every step of the way.

The IB highlights the significance of the Extended Essay:

• Hands-on learning for undergraduate research
• An opportunity for students to research an area of interest relating to one of the 6 DP subjects opted for by the student.

The skills the Extended Essay aims to develop in students are:

• Coming up with a relevant Research Question
• Personally engaging with a topic of exploration
• A coherent communication of ideas
• Strong Argument building

For better understanding, go through  this document on Extended Essays   by the IB. It will make things more transparent.

Students often confuse their Internal Assessments with Extended Essays, which is a grave mistake. Gaining clarity on both these components of the IB DP core is essential. Let us understand the significant difference between the two.

• While Internal Assessments require students to investigate and explore an idea, Extended Essays are more formal. Students need to perform primary and secondary research on a research question they choose based on a diverse topic about the subject. Since EE is an independently researched essay, your mentor may only be able to give you some of the answers you wanted, unlike the IA.
• Students must write one Extended Essay on a subject of their choice for their IB Diploma Programme, but I must be prepared for all the topics.
• Internal Assessments are graded internally by the subject instructor and then moderated externally. Extended Essays are marked externally by examiners appointed by the IB. Your grade on your Extended Essay is combined with your Theory of Knowledge Essay/Exhibition score to assign you your overall score/points.

Word of caution:  Do not choose the same investigation topic/research question for your Internal Assessment and the Extended Essay.

For a much better breakdown of the EE document, you must go through our article on the  IB Extended Essay . It contains an IB EE checklist you must attend to and a detailed overview of the structure and planning of the EE.

Now that we’ve got our basics to, let’s get down to business. The fear around IB Math Extended Essay makes the most confident students hesitate and doubt their choices. But we aren’t here to scare you. The myth about the horrors of the IB Math EE isn’t all false; it’s a caution. Because unless you’re prepared with ammunition, strategy, and the will to put in the effort, there’s a slim chance you can survive the Math Extended Essay battle.

If you’ve opted for Math Extended Essay, we assume you have a strong passion for Mathematics. When the going gets tough while working on one’s Extended Essay-which, which is usually the case-your only hope at the end of the tunnel is your drive for the subject you’ve chosen. Being a rigorous subject for writing one’s Extended Essay, Mathematics can be incredibly demanding. So unless you want to play it risky, we suggest you reassess your liking for Mathematics. Once you know for sure, that’s when it begins. Lots of research. Since it is an independently written document, you want to be doing your homework well.

We will further break down the IB Math Extended Essay, from planning to execution, so that you can organize your thoughts and make appropriate decisions.

The Math Extended Essay is an in-depth research document covering any topic with a mathematical focus, i.e., not limited to the mathematics theory (shouldn’t be entirely descriptive). IB has divided Math Extended Essays into six categories:

• the applicability of mathematics to solve both real and abstract problems
• The beauty of mathematics examples includes geometry or fractal theory.
• the application of mathematics in the proving of theorems, for example, number theory
• the history of mathematics: the origin and subsequent development of a branch of mathematics over some time, measured in tens, hundreds, or thousands of years
• the effect of technology on mathematics
• in creating links between different branches of mathematics,
• Or in bringing about a new branch of mathematics or causing a particular unit to flourish.

Your Math EE topic should be an extension of your IB Maths syllabus or the practical application of the knowledge you’ve gained in class.

Before moving on to the planning and structure of the Math Extended Essay, here are some pointers you absolutely cannot afford to miss:

• Attempting a Math EE requires a decent amount of hard work. While conducting preliminary research, ensure you land on a topic you can personally engage with and are familiar with. Going for a complicated subject, you can’t comprehend and interpret futile.
• The mathematical work you put in will have to meet a certain level of sophistication, so avoid going for a topic that gives rise to a trivial research question. Your research question shouldn’t be too generic or broad on similar lines. Ensure you can sufficiently narrow down your area of investigation.
• Another thing to remember is that the topic you finally choose should have a good research foundation and room for a novel contribution.
• Incorporate Primary and Secondary research wherever appropriate.
• Proper Referencing should be done for the essay.
• For Reflection, emphasize the Planning, Research, and Writing Processes.

Spitball ideas -  You begin here. Write down any interesting ideas you can come up with. This is your brainstorming session.

Do your Research -  You could not, would not want to meddle with this step, let alone skip it. Research. Read reports, articles, and documentation. Keep jotting important points down simultaneously. The study will and must go on throughout your search for the right math EE topic.

Approach professors/professionals/experts -  Contact concerned lecturers, professors, and industry professionals. They can provide you with invaluable insights. It would be best if you also discussed ideas with your mentor.

Point to Note -  Your goal should be to find a topic you understand and contribute to. It is always recommended to refer to your Math syllabus; something there inspires you to get the ball rolling!

Your essay will be structured as a document answering the Research Question you’re working on. It should be focused, clear and arguable. You will build your essay around your Research Question; hence pay close attention to it.

All you will include in your essay must be mentioned in your Research Question. This means the focused area you will be exploring and the methods you will use to achieve a plausible outcome.

Honing your Research Question is a continuous process. If it appears relatively easy or complex, please rephrase it. Good Research Questions may start with: “How can we model…”, “To what extent…” etc.

Collect Primary and Secondary data and incorporate it wherever appropriate.

Primary sources for Math research include 

• Data-gathering
• Visualization
• Abstraction
• Conjecturing

A few sources to gather Secondary data include Google Scholar, textbooks, databases such as JSTOR, etc. For your essay, know your aims and devise a step-by-step plan to answer your research question while maintaining a mathematical focus.

• Though you can approach your essay in whichever way you like, there should be a consistent logical structure.
• The work done in your essay should develop to answer your research question.
• Subheadings will provide your work with much-needed coherence and viability.
• Describe your way of thinking
• Write definitions and Conjectures.
• Use symbols, theorems, graphs, and diagrams
• Justify your conclusions.
• Visual aids such as graphs and diagrams should be included in the body, while tables and computer programs should be mentioned in the footnotes or the appendix.
• Data must be analyzed appropriately using relevant techniques, correctly reasoned arguments, and adequate methodology to achieve a result.
• Provide the necessary explanation and commentary for all your work.
• Throughout the writing, you may need to re-evaluate the method, approach, and structure to fit the word count adequately.

Once you’re finished writing, you will have to reassess everything from scratch- the equations, the theory, etc., to ensure the coherence of your essay.

• The three reflections should highlight how the process of writing your essay changed in due course of work and what you’ve learned from it.
• The Reflection should emphasize the planning, research, and writing process.
• You should discuss your choices, the re-evaluations you had to make, the limitations of your work, and how you overcame them, if at all.
• The three reflections are written at the beginning, mid, and towards the end of your essay and should have a word limit of approximately 150, 150, and 200, respectively.

Extended Essays are assessed externally by IB-appointed examiners and are marked on a scale of 0 to 34. The score obtained by a student corresponds to a particular band. The bands are:

A -  refers to work of an excellent standard (Level 6)

B -  refers to the creation of a good standard (Level 6)

C -  refers to work of a satisfactory standard (Level-12)

D -  refers to the product of a mediocre standard (Level 4)

E -  refers to the design of an elementary average (Level 6)

Anything below D will be considered a failing grade, and the student will not be awarded the IB diploma.  As we said, your EE is not a component you can mess up.

The Extended Essay Rubric includes the following Assessment Criteria:

Criterion A -   Focus and Method (Covers the topic, research question, and methodology)

Criterion B -  Knowledge and Understanding (Covers context, subject-specific terminology, and concepts)

Criterion C -  Critical Thinking (Covers research, analysis, discussion, and evaluation)

Criterion D -  Presentation (Covers structure, layout)

Criterion E -  Engagement (Covers reflection on planning and progress)

Now that we’ve discovered and learned about the process of writing a Math EE, here are a couple of ideas to give you an idea about how your Math EE questions should be framed:

Topic -  Archimedes’ calculation of areas

Research Question -  What is the legacy of Archimedes’ calculations of circular and parabolic areas in today’s integration methods?

Topic -  Approximation of irrational numbers by rational numbers

Research Question -  How well can π, e, √2, and other irrationals be approximated by rational numbers?

Topic -   The geometry of navigation

Research Question -  What was the role of mathematics and geometry in navigation when we relied on the stars? Does it still play a part now we have manufactured satellites?

You should also check out this  sample band, A Math EE, published by the IB . This will give you an honest insight into making a band-A essay. Also, go through  band B, C, and D extended essays  to understand the loopholes to avoid.

And that’s a wrap!

We hope this comprehensive IB Math EE guide answers your queries regarding the EE. We also suggest you go through  this IB Extended Essay guide  to clarify the Extended Essay component of your IB DP curriculum. You should also try Nail IB’s Extended Essay guide; check it out  here !

At Nail IB, we’re committed to delivering A-quality guidance so that your IB DP journey is smooth and successful. You can explore  our take-test  series here and access   premium guides  here.

Happy learning!

IB Resources you will love!

Nan + free ib flashcards, -1 + free ia samples, nan + ib videos by experts, -1 + ib sample practice questions, ib resources for nan + subjects.

How to Choose an EE Topic (Mathematics)

The Extended Essay is undoubtedly one of the most feared components of the IB program. A 4,000 word research paper can, in fact, seem daunting to those who have only written 500-1000 word essays. Therefore, students should choose a topic that they can not only find sources for, but are also passionate about it.

Mathematics Extended Essays are rare — of the 87,519 Extended Essays submitted in the 2020 May Examination Session only 2,454 were done over Mathematics (2.8%) ( IB Statistical Bulletin 2020 ). Despite the rarity, I chose to write a Mathematics EE because maths is something that fascinates me. To many students, Mathematics EEs sound scary and barely consider writing one. There were many people that told me I was insane and that it was impossible. In the end, I put in the work to make it happen. 

I chose to write my paper on Game Theory and my research question was: “To what extent does Game Theory play a role in Modern Warfare?” 

I found this topic not unlike the way students writing History EEs find their own specific topics. Just as history has countless events in which one can write about, Mathematics is similar with its various branches. I chose a branch that interested me (Game Theory) and used it to solve a real-world problem (Modern Warfare). My economics teacher actually suggested this idea.  They said that, while Game Theory is primarily used in economics, it has numerous applications to maths when discussed alongside warfare. This qualified my essay as a Category 1 Mathematics Extended Essay, which is a paper that discusses “the applicability of mathematics to solve both real and abstract problems” (p. 96, IB Extended Essay Guide ). 

Writing the essay is where, I admit, it got challenging. During the process I had no peers to help me as only a few others had chosen a Mathematics EE, but none of their topics related to mine. Fortunately, my mentor was extremely helpful and I was able to find several books at my local university that were very useful.

Mathematics Extended Essays are bizarre in many ways as things such as word count, varied sentence structure, and high vocabulary do not matter. However, it should be noted that effective communication is key even if that’s done through mathematical expressions. Despite these challenges, I strongly believe that Mathematics EEs are doable, and more people would do them if there was not such a negative stigma about them. I encourage all future IB sessions to consider doing one as the feeling when you have finished is unlike any other. The pride and satisfaction I felt knowing that I took the path less travelled and still found success is something that I hope all future IB students will experience.

You may also like…

• Our Extended Essay series
• Tiffany’s tips for Mathematics HL

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IB Math EE: The Complete Guide for IB Students in 2023

by  Antony W

February 20, 2023

While it’s one of the most dreaded subjects in the IB program, the IB Math EE can be such an interesting area to explore if you love new challenges and can work with numbers.

In this guide, we’ll cover everything you need to know about IB Mathematics EE and even give you some tips to help you score top marks – if not a 34 in the IB program .

IB Math EE is a subject with its own level of difficulty. It requires in-depth research, prior planning, and writing a comprehensive extended essay in a way that aligns with the set guidelines.

If you read this guide carefully and implement the advice we give, we’re confident that you’ll score the grades that you desire for the assignment.

Before we get to anything else, it’s important that you have an interest in Math, a focused approach, and a mathematical aptitude and reasoning. Collectively, these characteristics will help you do well in the subject. 

What’s IB Math Extended Essay?

The Math Extended Essay is a comprehensive research paper on any topic with a mathematical emphasis, including but not limited to mathematics theory. The IB groups math Extended Essays into six categories:

• The applicability of mathematics to solve both real and abstract problems
• The beauty of mathematics, examples include: geometry or fractal theory
• The application of mathematics in the proving of theorems, for example, number theory
• The history of mathematics: the origin and subsequent development of a branch of mathematics over some time, measured in tens, hundreds, or thousands of years
• The effect of technology on mathematics
• In creating links between different branches of mathematics,
• Or in bringing about a new branch of mathematics or causing a particular branch to flourish.

What IB is trying to communicate is quite simple.

If anything, the Math Extended Essay can be either an extension of the Math syllabus or an application of the practical knowledge you gained in your classroom.

IB Math EE vs IB Math IA

One of the most common mistakes that IB students make is to assume that Math EE and Math IA mean the same thing.

So before we discuss the Math EE any further, let’ make sure you understand the difference between an EE and an IA.

Extended Essays are more rigorous and formal. They require you to conduct primary and secondary research on a research question that you pick based on the subject you have chosen to study.

Because the EE is a self-researched essay, unlike the IA, your mentor may not be able to provide you with all of the answers you require.

An Internal Assessment, on the other hand, requires you to explore and investigate an idea, but it’s less formal than an Extended Essay. 

For their IB Diploma Program, students must write one Extended Essay on a subject of their choice. However, they will have to write an IA for all their subjects.

The subject teacher grades internal assessments, which are subsequently moderated externally. Examiners appointed by the IB mark Extended Essays externally. Your overall score/points are determined by adding your Extended Essay grade to your Theory of Knowledge Essay/Exhibition grade.

Tips to Help You Get a 7 in IB Math

The following tips will help you to revise well for your IB Math AA or IB Math AI and place you in the position where you’re likely to score a 7:

1. Break a Big Topic into Smaller Topics

Break down a broad Math topic and categorize it into smaller themes before you begin your revision. It’s important to do this to figure out where new knowledge fits into the wider picture.

We understand that breaking down a subject into smaller topic is a little out of the ordinary for math revision because many students tend to leap right into practice almost immediately.

However, splitting a huge subject into smaller and easily manageable sections makes it easy for you to filter each inquiry type and fit the information into your pre-existing mental models.

So get a blank piece of paper, and create a bullet list of all the themes, sub-topics and question types you wish to practice.

2. Read, Analyze, and Understand the Subject Guideline

IB is quite detailed, and all of the questions tested in the examinations are in the guide's curriculum. Read the content, as doing so will direct your learning and show you every type of question you might encounter.

Make a list of all the questions that you’re likely to do in the upcoming examinations by going over each unit's sub-topics that IB could evaluate you, along with examples.

Because the approach provides a personalized checklist of questions the IB can ask, this strategy will lead you through the whole revision process.

Final Thoughts

In May 2021, IB made significant changes to its mathematics subject by dividing it into IB Math AA and IB Math AI . F

rom the time the changes took effect, IB students have the option to choose between the two subject segments depending on their strength and background in Math as well as their future goals.

While the changes give you some kind of flexibility, it does bring with it new challenges to tackle.

And if you don’t know how to get your head around the subject, it can be too complex to handle.

As people who’ve done Math AA and Math AI for as long as we can remember, we know there are those who love to work with numbers and those who label themselves as “not Math people”.

Regardless of where your stand is, the tips we’ve shared in this guide should help you do well in your Math EE.

Get IB Math Help

IB Math assignments can be quite challenging to handle, but you don’t always have to fret because we’re here to help.

Our IB writers have years of experience and knowledge in everything IB, so we can help you get your assignment in Math done within the shortest time possible.

Whether you need your paper in the next 7 days or you have a deadline shorter than that, Click Here to Place Order .

About the author 

Antony W is a professional writer and coach at Help for Assessment. He spends countless hours every day researching and writing great content filled with expert advice on how to write engaging essays, research papers, and assignments.

Math Extended Essay Topics. Let's Make Yours Stand Out!

Table of contents.

Introduction – What is an IB Math Extended Essay?

An extended essay (EE) is a research paper of up to 4,000 words for the International Baccalaureate (IB) program. It is an independent study done by the student in a chosen subject, and it is a requirement for all IB diploma students. An IB Math EE is an individual project done by a student that explores a mathematical concept, question or problem. Students are asked to explain their understanding of the concept and develop their own argument(s) surrounding it.

Before you start your EE, it is important to understand exactly what the assignment entails. First and foremost, you should understand how the IB Math EE relates to the general subject of mathematics. The EE should be focused around a specific question or hypothesis related to mathematics. The aim of the essay is to explore this particular topic, conduct research and analysis, and draw conclusions based on the evidence provided.

The essay should also demonstrate the student’s in-depth knowledge of mathematical concepts, and the ability to apply that knowledge in a rigorous academic setting. It provides an opportunity for students to showcase their skills and hone their expertise in mathematics. Lastly, it is a great way for students to practice their research and independent study skills.

IB Maths Extended Essay Process – Step-by-Step Guide

Writing an International Baccalaureate (IB) Maths extended essay can be a challenging, yet rewarding experience. Many students often find the process to be daunting, but with the right plan of action and understanding, you can make it through with ease.

The first step in the process is to determine the essay topic and type of essay you will be writing . Make sure the topic you choose is relevant to IB Maths and that you can back up any claims you make. Once you have chosen your essay topic , you will need to create an outline or plan of action for yourself. This includes setting individual deadlines and goals for yourself in order to stay on track.

Next, you will need to begin researching and gathering resources for your essay. This is the time where you will look for books, articles, and other materials to support your thesis statement. Be sure to take precise notes and cite your sources as you go to avoid plagiarism.

Find someone to act as your supervisor, who can help guide you through the extended essay process. Your supervisor should be available to answer any questions, provide feedback, and help you stay focused on the task at hand. It is important to establish a good relationship with your supervisor in order to ensure timely and effective communication.

Beforehand, it’s important to familiarize yourself with the assessment criteria and rubric for the extended essay . This will give you a clearer understanding of what is expected from you and how you will be evaluated. Having this knowledge will allow you to create a better structure for your essay that meets the required standards.

Now, you are ready to start writing your essay. Use the plan you created for yourself along with the research you gathered to construct the body of your essay. As you write, be sure to reference all sources correctly, double check for grammar and spelling errors and keep your essay on track. Once you have finished, you are all done.

By following this step-by-step guide and understanding each part of the IB Maths extended essay process, you will make the process easier and less intimidating. Keep in mind the key points discussed throughout the guide and make it a priority to respect deadlines and be organized throughout.

Choosing a Good Extended Essay Topic

When it comes to the IB Maths Extended Essay , one of the most important steps is choosing a good topic. A good topic should be interesting and challenging, but not too complex for you to handle. It should also relate directly to IB Maths, so you can use your knowledge to write the essay.

Here are some criteria to consider when selecting an appropriate topic:

• Does the topic have relevance to your field of study?
• Is the topic researchable and easy to access resources?
• Will the data you need be available?
• Is the scope of the topic manageable?
• Is the topic interesting enough to keep you motivated to finish it?

Some examples of good topics for an IB Maths Extended Essay include:

• The Impact of Advanced Mathematics on Financial Markets
• The Benefits of Using Probability In Business Decisions
• The Use of Calculus in Medicine
• The Role of Algebra in Cryptography
• The History of Numbers

Exploring a few topics before settling on one will give you a better understanding of what kind of topic will work best for your essay. Consider your interests and the resources you have access to, and choose a topic that you will be passionate about. Once you’ve selected a topic, you can begin researching and preparing for the essay!

Preparing the Extended Essay – Resources, Planning and Researching

Once you have chosen your topic for your Maths Extended Essay, the next step is to prepare for it. This involves compiling a list of resources that you will need in order to carry out research and complete the essay. These could include books, research papers, articles and any other material that is relevant to your topic.

You will then need to plan how you want to go about researching and writing your essay. This planning process should involve breaking down the process into manageable steps, such as researching the topic, planning how to structure the essay, writing the first draft and then editing and proofreading. By breaking down the process into smaller chunks, it can be easier to manage and track your progress.

The next step is to carry out the research which your EE will require. Depending on your topic, this could involve looking through textbooks, reading articles and papers, interviewing people or conducting other experiments or surveys. It’s important in the research stage to keep track of where you found each piece of information so that you can cite it correctly later on.

Finally, when you have finished researching and written your first draft, you can start the process of refining and editing the EE. This involves making sure that everything is presented correctly and that all grammar, spelling and punctuation are perfect. Once you are happy with the essay, you can submit it for evaluation.

Supervisors & The Roles They Play

The supervisor plays a crucial role when it comes to your IB Maths Extended Essay. It’s important to find a supervisor who is knowledgeable and experienced in the field of mathematics, as they will help guide you through the process of researching and writing the essay.

Your supervisor should be able to provide you with guidance and advice, as well as setting you deadlines for completing your essay. Depending on the type of Extended Essay you are writing, your supervisor may also have the opportunity to read drafts of the essay and provide feedback along the way, helping to ensure the EE meets all of the assessment criteria.

A supervisor will also typically be responsible for giving the final grade for the Extended Essay, which means that it is essential to develop a good working relationship with them. This can be achieved by attending meetings regularly and using the resources available from your supervisor to ensure you’re making steady progress.

In any event, it is important to remember that your supervisor is there to help you throughout the writing of the EE. They can offer a wealth of knowledge, experience and support so make sure to take advantage of the opportunity.

Evaluation – Possible assessment criteria & EE rubrics

Once you have completed your extended essay for math, it is important to evaluate your work based on the assessment criteria. This means checking how well your essay aligns with the criteria set out by the International Baccalaureate (IB). Different aspects of the essay will be marked separately and then combined to generate a final score.

Here are some of the criteria that you might need to consider for your math extended essay:

• Clarity: Is the essay easy to read and understand? Are there any points that could be interpreted differently?
• Research and Analysis: Has enough research been undertaken in order to support the discussion? Does the analysis of this research accurately reflect the original source?
• Approach: Is the essay structured correctly? Has the argument been logically built, using appropriate evidence?

The IB provides several rubrics which can help you to evaluate your own essay. These rubrics are designed to show you what the IB is looking for when they mark your work. Make sure you familiarise yourself with the rubrics before you submit your essay so that you know what to expect from the evaluation process.

It’s important to be aware of the evaluation criteria for your maths extended essay, as it will help you to understand why certain sections of your essay may score higher or lower than others. This in turn will help you to improve your writing and ensure that you submit the best possible essay.

Example topics to get started – Highlighting five example topics related to IB Maths

When starting your IB Maths extended essay, it can be daunting to think of a suitable topic. To help you get started, here are five example topics you may want to consider:

• Exploring the Relationship Between Fibonacci Numbers and the Golden Ratio – Investigate how the Fibonacci sequence relates to the golden ratio and its applications in mathematics.
• Analysis of Different Methods Used to Solve Quadratic Equations – Analyze different methods of solving quadratic equations and discuss their advantages and disadvantages.
• Explaining the Fundamental Theorems of Algebra – Study the theorems of algebra and explain their importance in mathematical theory.
• A Study on the Mechanics of Number Theory – Analyze the various concepts and principles of number theory and describe its applications.
• Understanding the Geometry of Non-Euclidean Geometry – Examine the different principles of non-Euclidean geometry, including hyperbolic geometry.

These are just five examples to get you started – there are endless other possibilities for topics in IB Maths. Remember to choose a topic that you find interesting and make sure it is relevant to your course of study.

Presenting Essential Content

Having chosen a topic for your IB Maths Extended Essay, it is time to begin writing. Having an outline of what you are going to discuss in each section and thinking about the themes you will focus on can help to guide and structure your essay.

When it comes to presenting the core information that needs to be included, this is where brainstorming and researching helps to create the ‘meat’ of the essay.

Think carefully about which topics could be explored in each section, as well as looking at any suggested themes or topics that examiners may look for. You can create a draft outline of each section if this helps.

You may want to consider the following when planning the content of your essay:

• The aim of the essay
• What evidence will be provided to support your arguments
• Any potential counter-arguments and how to rebut them with evidence
• How to develop a balanced discussion, using comparison and contrast
• Key theories and concepts that need to be discussed
• Insightful quotes from reliable sources
• Any numerical information or data that can be used to support arguments

It is always a good idea when creating your essay to refer back to the main research question or aim of the assignment to ensure that you remain focused.

By doing this, you can be sure that you have included all the essential content needed to answer the research question properly, as well as demonstrating your understanding of the topic.

Referencing correctly

Correct referencing is very important when it comes to writing an IB Maths Extended Essay. It’s how you show the examiner where you’ve got your research from, and how you demonstrate the ideas that you’re presenting in your essay are backed up with evidence.

When it comes to referencing, there are a few main types: in-text citations (where references are mentioned within the body of the essay), endnote citations (where references are included in an endnotes section), and bibliographies (where sources are listed alphabetically at the end of the essay).

In-text citations and endnote citations should include the author’s name, the year of publication, the title of the document, and the page number (if possible) of the reference you are citing. Bibliographies should list the title, author’s name, publication date and URL of any webpages cited. It’s also important to make sure that you’re consistent with the style of referencing – for example, if you’ve used Harvard referencing for one source, make sure you use it for all sources.

It’s also worth noting that some examiners prefer that referencing isn’t done inline – in other words, each reference should be listed in an endnote or bibliographic section at the end of the essay. If you’re unsure of which style to use, it’s best to check with your supervisor – they will be able to give you more advice on the specifics.

In summary, when including references and citations in your IB Maths Extended Essay, make sure they are accurate and consistent. Remember to include all relevant information such as author, year of publication, title and page number (if applicable), and make sure that you are consistent with the referencing style used. Your supervisor will be able to provide more advice on the specifics.

Editing & Proofreading Tips

Writing an extended essay on an IB Maths topic can be a challenging task – especially when it comes to the editing and proofreading stage. The whole process involves careful attention to several areas of the essay, which can make all the difference when it comes to achieving a high grade.

Here are a few tips to help you prepare your essay for submission:

• Start Early: Make sure to give yourself plenty of time to go through each part of the essay and make the necessary revisions.
• Check Your Sources: Check to ensure that all the sources you used are accurate and up-to-date.
• Check Grammar and Spelling: One of the most important aspects of editing is making sure that your grammar and spelling are correct. Use a spell checker before submitting your essay.
• Check for Clarity: Read your essay through from start to finish to check for clarity of thought and make sure everything ties together in the conclusion.
• Get a Second Opinion: Consider getting someone else to read your essay and give their opinion on it. This can help to spot any errors or points that need improvement.

Doing all of the above will ensure your essay is well polished and ready for submission. Taking these steps will also help you to become a better writer and ensure that you receive the best possible grade for your efforts.

The completion of an International Baccalaureate Math Extended Essay (EE) is a challenging task that requires a great deal of research, preparation and dedication. In this guide, we have discussed the process from start to finish, as well as some tips and tricks to make it easier. We began by introducing what an EE entails in the context of IB Maths, then progressed through the process step by step. This included topics such as choosing an appropriate EE topic, preparing the essay, and getting it assessed correctly.

We discussed some example topics to get you started on your own EE, and important elements such as structuring the essay and presenting essential content. Referencing correctly was also highlighted so you can be sure your essay is academically sound. Finally, we rounded off with some proofreading tips to ensure your work is error free.

To conclude, it is worth mentioning that the EE process can be daunting. But with the guidance presented within this guide, you should be able to complete a top-notch EE with ease. Good luck!

Including Reference Links and External Sources

Having access to helpful resources is a key part of putting together an excellent extended essay. There is usually a wealth of relevant material available, covering a range of topics related to IB Math. It’s important to reference these sources correctly, so that you can demonstrate the breadth and depth of your research.

Here are some useful tips for collecting appropriate sources and referencing them correctly:

• Collect Appropriate Sources – Use a range of academic sources such as books, journal articles, websites, and other types of documents. Don’t forget to check out online databases for extra research material.
• Use Reliable Sources – Ensure that the sources you use are reliable and up-to-date. Try to use recent published sources where possible.
• Cite Accurately – When citing the sources you use, be sure to include the author’s name, year of publication, and the page number (if relevant).
• Avoid Plagiarism – As mentioned above, it’s important to cite any sources you use. Plagiarism should be avoided at all costs as it can result in a loss of points.

By following these tips, you can ensure that your extended essay makes good use of external sources, and that you cite and reference them correctly. Taking the time to look through a range of materials will also help you to form a well-informed opinion, which is essential for a successful paper.

FAQs about IB Math Extended Essay Topics

• Q: What is an IB Mathematics Extended Essay? A: An IB Mathematics Extended Essay (EE) is an in-depth, project-based essay, which requires a student to explore a topic and present their findings. The Extended Essay should be related to and reflect the knowledge of Mathematics learned in the IB program.
• Q: How difficult is a Mathematics EE? A: Writing an EE is no small task. It requires considerable commitment and hard work as well as dedication to the research, writing and presentation process. However, with adequate preparation, guidance, and support, a student will be able to create a successful extended essay.
• Q: What steps are involved in the process of creating a Mathematics EE? A: The process of crafting a Mathematics EE involves the following steps: selecting a topic, conducting the research, gathering evidence, writing an outline and the draft, proofreading and editing, planning for submission.
• Q: How does one select a suitable topic for a Mathematics EE? A: When selecting a topic for a Mathematics EE, students should consider their interests, display their mathematical knowledge, and choose something that can be researched thoroughly. Additionally, they may find it helpful to review example topics and assess their suitability and feasibility.
• Q: Who is responsible for supervising the Mathematics EE? A: An experienced teacher should provide supervision throughout the EE process and guide the student in proper methodology, accuracy in content, format and presentation of the completed essay.
• Q: How are Mathematics EEs evaluated? A: A Mathematics EE is generally evaluated on the student’s ability to demonstrate relevant content and thorough research, as well as their mastery of the subject, attention to detail and accuracy, originality and creativity.
• Q: What structure is typically used when writing a Mathematics EE? A: A MathematicsEE typically has a conventional structure, which includes the introduction, body and conclusion. In the body, the research problem and approach, main focus and findings should be addressed.
• Q: What type of information is needed to include in a Mathematics EE? A: Mathematical EEs should include mathematical terms and formulas, clear explanations of processes, correct notation and symbols, as well as authentic research.
• Q: What tips can help a student prepare for the EE submission? A: A student can edit and proofread their EE to ensure that all sections are accurate, concise and organized. They should double check all numbers, formulas, citations and references. Moreover, they may want to get feedback from their supervisor and peers.
• Q: How can external sources help a student create a successful EE? A: External sources may provide up-to-date information regarding formatting, research methods, mathematical tools, etc., which a student can use to expand their knowledge and create a comprehensive EE.

Valerie Green

Valerie Green is a dedicated educator who spends her time helping high school and college students succeed. She writes articles and guides for various online education projects, providing students with the tools they need to excel in their studies. Friendly and approachable, she is committed to making a difference in the lives of students.

What’s the Ideal Number of Sources for Your IB EE?

What’s the ideal number of sources for my EE? The answer, nuanced and subject-specific, depends on striking the perfect balance between breadth and depth of research. As a seasoned IB writer, I’ve seen how this balance varies across disciplines — a History EE might thrive on many sources to construct a well-rounded argument, while a Math EE might depend on a few texts for its foundational theory.

How Much Does It Cost to Order a Custom Extended Essay Online?

When tackling the International Baccalaureate program, students often wonder about the cost of ordering a custom extended essay online. As an experienced IB writer, I can tell you that several factors influence this cost. These include the essay’s length, its complexity, the urgency of your deadline, and the writer’s expertise.

Pros and Pitfalls of Using Internet-Sourced EE Topics

In the ever-evolving landscape of academic research, the Internet has emerged as a significant resource for students undertaking the challenging task of the IB Extended Essay (EE). As an experienced IB writer, I’ve observed the transformative impact of Internet-sourced EE topics. This article aims to highlight both the benefits and challenges of this modern approach to research.

How Can You Ensure Originality in Your IB Extended Essay?

Ensuring originality in your IB extended essay is a crucial step in distinguishing your work in the world of academic research. As an experienced IB essayist, I’m here to guide you in creating an essay that not only meets academic standards, but also showcases your unique intellectual contributions. Originality in the IB extended essay is about bringing your personal insights and perspectives to every aspect of your work, from the choice of topic to the final argument.

What’s Your Secret Writing Weapon in EE? Annotated Bibliographies!

Imagine having a map that guides you through the labyrinth of research and enriches your understanding and appreciation of the topic. That’s what an annotated bibliography does. It allows you to keep track of your sources, critically evaluate their content, and reflect on their relevance to your research question. This process deepens your engagement with the topic, providing a clearer direction for your argument and analysis.

Differences Between Primary and Secondary Sources in EE Research

In the fascinating world of Extended Essay (EE) research within the International Baccalaureate (IB) program, understanding the nuanced differences between primary and secondary sources is crucial. As a seasoned IB writer, I’ve learned through experience that the ability to distinguish and effectively use these two types of sources can significantly enhance the depth and credibility of your research.

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Extended Essay: Group 5: Mathematics

• General Timeline
• Group 1: English Language and Literature
• Group 2: Language Acquisition
• Group 3: Individuals and Societies
• Group 4: Sciences
• Group 5: Mathematics
• Group 6: The Arts
• Interdisciplinary essays
• Brainstorming
• Pre-Writing
• Research Techniques
• The Research Question
• Paraphrasing, Summarising and Quotations
• Writing an EE Introduction
• Writing the main body of your EE
• Writing your EE Conclusion
• Six sub-categories for WSEE
• IB Interdisciplinary EE Assessment Guide
• Sources: Finding, Organising and Evaluating Them
• Conducting Interviews and Surveys
• Citing and Referencing
• Check-in Sessions
• First Formal Reflection
• Second Formal Reflection
• Final Reflection (Viva Voce)
• Researcher's Reflection Space (RRS) Examples
• Information for Supervisors
• How is the EE Graded?
• EE Online Resources
• Stavanger Public Library
• Exemplar Essays
• Extended Essay Presentations
• ISS High School Academic Honesty Policy

Mathematics

An extended essay (EE) in mathematics is intended for students who are writing on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Essays in this group are divided into six categories:

• the applicability of mathematics to solve both real and abstract problems
• the beauty of mathematics—eg geometry or fractal theory
• the elegance of mathematics in the proving of theorems—eg number theory
• the history of mathematics: the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds or thousands of years
• the effect of technology on mathematics:
• in forging links between different branches of mathematics,
• or in bringing about a new branch of mathematics, or causing a particular branch to flourish.

These are just some of the many different ways that mathematics can be enjoyable or useful, or, as in many cases, both.

For an Introduction in a Mathematics EE look HERE . 

Choice of topic

The EE may be written on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Students may choose mathematical topics from fields such as engineering, the sciences or the social sciences, as well as from mathematics itself.

Statistical analyses of experimental results taken from other subject areas are also acceptable, provided that they focus on the modeling process and discuss the limitations of the results; such essays should not include extensive non-mathematical detail.

A topic selected from the history of mathematics may also be appropriate, provided that a clear line of mathematical development is demonstrated. Concentration on the lives of, or personal rivalries between, mathematicians would be irrelevant and would not score highly on the assessment criteria.

It should be noted that the assessment criteria give credit for the nature of the investigation and for the extent that reasoned arguments are applied to an appropriate research question.

Students should avoid choosing a topic that gives rise to a trivial research question or one that is not sufficiently focused to allow appropriate treatment within the requirements of the EE.

Students will normally be expected either to extend their knowledge beyond that encountered in the Diploma Programme mathematics course they are studying or to apply techniques used in their mathematics course to modeling in an appropriately chosen topic.

However, it is very important to remember that it is an essay that is being written, not a research paper for a journal of advanced mathematics, and no result, however impressive, should be quoted without evidence of the student’s real understanding of it.

Example and Treatment of Topic

Examples of topics

These examples are just for guidance. Students must ensure their choice of topic is focused (left-hand column) rather than broad (right-hand column

Treatment of the topic

Whatever the title of the EE, students must apply good mathematical practice that is relevant to the

chosen topic, including:

• data analysed using appropriate techniques

• arguments correctly reasoned

• situations modeled using correct methodology

• problems clearly stated and techniques at the correct level of sophistication applied to their solution.

Research methods

Students must be advised that mathematical research is a long-term and open-ended exploration of a set of related mathematical problems that are based on personal observations. 

The answers to these problems connect to and build upon each other over time.

Students’ research should be guided by analysis of primary and secondary sources.

A primary source for research in mathematics involves:

• data-gathering

• visualization

• abstraction

• conjecturing

• proof.

A secondary source of research refers to a comprehensive review of scholarly work, including books, journal articles or essays in an edited collection.

A literature review for mathematics might not be as extensive as in other subjects, but students are expected to demonstrate their knowledge and understanding of the mathematics they are using in the context of the broader discipline, for example how the mathematics they are using has been applied before, or in a different area to the one they are investigating.

Writing the essay

Throughout the EE students should communicate mathematically:

• describing their way of thinking

• writing definitions and conjectures

• using symbols, theorems, graphs and diagrams

• justifying their conclusions.

There must be sufficient explanation and commentary throughout the essay to ensure that the reader does not lose sight of its purpose in a mass of mathematical symbols, formulae and analysis.

The unique disciplines of mathematics must be respected throughout. Relevant graphs and diagrams are often important and should be incorporated in the body of the essay, not relegated to an appendix.

However, lengthy printouts, tables of results and computer programs should not be allowed to interrupt the development of the essay, and should appear separately as footnotes or in an appendix. Proofs of key results may be included, but proofs of standard results should be either omitted or, if they illustrate an important point, included in an appendix.

Examples of topics, research questions and suggested approaches

Once students have identified their topic and written their research question, they can decide how to

research their answer. They may find it helpful to write a statement outlining their broad approach. These

examples are for guidance only.

An important note on “double-dipping”

Students must ensure that their EE does not duplicate other work they are submitting for the Diploma Programme. For example, students are not permitted to repeat any of the mathematics in their IA in their EE, or vice versa.

The mathematics EE and internal assessment

An EE in mathematics is not an extension of the internal assessment (IA) task. Students must ensure that they understand the differences between the two.

• The EE is a more substantial piece of work that requires formal research
• The IA is an exploration of an idea in mathematics.

It is not appropriate for a student to choose the same topic for an EE as the IA. There would be too much danger of duplication and it must therefore be discouraged.

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IB Extended Essay Ideas

What’s covered:, what is the ib extended essay, extended essay examples, how is the ee scored, how does the extended essay affect my admission chances.

The International Baccalaureate Diploma Programme (IBDP or IB) is a rigorous high school program considered to be equivalent to the AP system, if not harder. Along with coursework and examinations in this two-year long program, there are expectations to write an in-depth essay on one subject of your selection, called the Extended Essay (EE). The following article is about the EE and presents ideas for topics to write about. 

The EE is an essay required to gain the IBDP and pass the course. It’s not like any regular essay, as it gives the student a chance to write a college-level research paper at an earlier point of their lives, giving them useful exposure for their future endeavors in further education. The essay is written in a single subject of your choosing, giving you six options to choose from. The EE is usually done in one of your HL classes, as it could have more scope to produce a more in-depth paper based on the increased amounts of coursework available in HL. 

The essay is expected to be around 4,000 words long, making it not only lengthy to read but time-intensive to produce. This means students must usually figure out which subject they’re writing for early, to give them time to start earlier. The process of planning a draft, along with your appointed EE supervisor, can take up most of your time in the first year of IB (11th grade). It’s common to not start the actual writing until our 2nd year, where you not only have learned enough coursework for the subject, but have also drafted enough to create a well-written essay. 

Choosing a topic for the EE can be difficult, but hopefully the ideas and examples in this article can give you some inspiration to create your own. 

Given there are 6 subject groups in IB, each with numerous options for those groups it would be nearly impossible to suggest examples for each subject, instead we will show examples for popular subjects. These examples can serve as blueprints for crafting your own ideas! 

Example EE Topic 1 – Math HL

Example Topic: Practical Applications and Implementations of the Golden Ratio

This irrational number is often represented visually as such: 

This image contains fibonacci vectors, a visual representation of the golden ratio. It’s an interesting concept because it’s a shape/ratio that our brains are seemingly wired to prefer things to take form in, a subconscious level of attraction. Many architects and artists today use this ratio to produce visually appealing works of art, but what other practical applications have risen from this mathematical concept? An EE would be a great way to learn more about this and present it in an interesting manner! 

Example EE Topic 2 – Physics SL

Topic: Build Your Own Radio

This topic requires some fundamental understanding of circuitry and electronics, a big component of physics SL and HL. Building a radio requires thorough understanding of currents, resistances and circuit design aspects that are usually best understood through practical, hands-on learning. 

This project could also demonstrate your knowledge in waves, specifically radio and microwaves required to operate the radio. If documented right throughout the whole process, this could make for not only a very extensive and interesting EE, but fun as well! 

Example EE Topic 3 – English SL/HL

Topic: The Effects Of Shakespearean Literature On Modern English

English EE topics are a bit more difficult than other subjects because it may be the least objective class to write about. That being said, it can also be the most creative EE to write for, with this topic being an ideal example. 

Shakespeare contributed lots to literature and writing, especially in the form of plays and dramas, but how can these be observed in modern day literature? Focus on how forms of comedy from Shakespeare’s plays are implemented in modern comedy, or how some forms of artistic expression from that era could be considered problematic today. 

To make this better suited for HL, try going more in depth about other forms of literature that draw from Shakespearean influence, and more specific implementations of humor, such as slapstick (just an example of many). 

Talk about how literature personally influences you, because this EE is an opportunity to not only present information through research, but to also indulge the reader about yourself and your personality! 

IB scores the EE out of 34 points, with 5 letter grades being assigned as boundaries:

EE and Theory of Knowledge (TOK) are graded together along with CAS, to form the “core” of IB which is worth a total of 3 out of 45 points. The following table details this:

The EE doesn’t have much direct influence on your chances of admission, but learning how to write a great essay through the EE can. The admissions process requires writing a great quality essay to showcase yourself to the office of admissions as best as you can. The EE not only teaches you how to write an informative essay, but a high quality one as well! More factors are also responsible for your chances of admission, and for more info on this check out CollegeVine’s admissions calculator ! This intuitive tool uses your standardized test scores, GPA and more to calculate your chances of admission into a university of your choosing!

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Extended Essay Essentials

• Individuals and Societies
• Interdisciplinary
• Mathematics

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What's in this guide?

What's in this guide.

In this guide, you will find essential documents for writing the EE in 

Essential documents include Subject Specific Guidelines and Sample Essays.

Introduction to the EE in Mathematics

From Mathematics: An Introduction:

An extended essay (EE) in mathematics is intended for students who are writing on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Essays in this group are divided into six categories:

• the applicability of mathematics to solve both real and abstract problems
• the beauty of mathematics in the proving of theorems - e.g., number theory
• the history of mathematics; the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds, or thousands of years
• in forging links between different branches of mathematics,
• or in bringing about a new branch of mathematics, or causing a particular branch to flourish.

For a longer general overview of an arts-related EE, see Mathematics: An Introduction . This document contains information on:

• Topic Selection
• Examples of Topics
• Treatment of the Topic
• Research Methods
• A Framework for the EE in the Mathematics.

Mathematics EE

• Mathematics Subject Specific Guidelines  - A short guide on how to write the Mathematics EE
• Score Reports  - See what students did (and did not do) well in these short reports from the chief examiner.
• Sample Papers  - Read sample EE papers provided by IB and see how they scored
• Mathematics Subject Specific Guidelines
• 2021 Mathematics Score Report
• 2018 Mathematics Score Report
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Guide to the IB Extended Essay in 2024

January 24, 2024

If you’re an International Baccalaureate student getting ready to write your IB Extended Essay, you might be experiencing some very understandable trepidation. But have no fear—we’re here to help you understand what’s required of you, how to plan ahead (IB extended essay topics), and how you’ll be graded (IB extended essay rubric). Keep reading for a good dose of preparation and confidence before you begin the journey. In this article, we’ll cover:

What is the IB Extended Essay?

The ib extended essay—required content, ib extended essay topics.

IB Extended Essay—Sample Essays

IB Extended Essay Tips

Ib extended essay rubric, ib extended essay—more resources.

The IB Extended Essay is a 4,000-word paper that asks you to immerse yourself in research and academic writing. A required part of the IB program, the Extended Essay is a chance to dig deep into a topic that fascinates you.

Although it’s no small task, the IB Extended Essay is an opportunity to gain practical research and writing skills that will come in handy again in college. As you write, you’ll learn how to:

• Identify credible sources
• Formulate a research question and limit your scope of research
• Communicate ideas to an audience
• Develop a well-supported argument

The IB Extended Essay is largely an independent, self-directed project, but don’t worry—the IB program doesn’t throw you into the deep end. You do get to select a mentor (usually a teacher at your school) to help guide you through the process. As you write, you’ll be required to meet with your mentor three times. As part of your final evaluation, your mentor will interview you in a final reflection section called a viva voce . During the viva voce, your mentor will check for plagiarism and malpractice, ask you to reflect on challenges and difficulties, and prompt you to discuss what you’ve learned through the research and writing process. Your mentor will then generate a report that factors into your final grade.

Your final essay must include the following:

• Contents page
• Introduction
• Body of the essay
• References and bibliography

For this essay, it will be up to you to generate a topic; the International Baccalaureate does not provide prompts. However, your essay will need to fit within one of six provided subject areas . You’ll choose from the following list of IB Extended Essay Topics:

• Language and literature
• Language acquisition
• Individuals and societies
• Mathematics

IB Extended Essay Topics (Continued)

At a glance, the subject areas might look limited, but the topics you can choose to write about are actually wide-ranging. The “Individuals and societies” category includes social science topics like economics, history, world religions, and philosophy. And, if you’re leaning toward “Science,” you can choose from classic subjects such as biology, chemistry, and physics, or related topics like environmental systems or health science, among others.

The IB also offers a special “World Studies” option for students interested in researching global issues. This subject would allow you to center your writing on global issues such as migration, global health, cultural exchange, or climate change.

Wondering what an outstanding IB Extended Essay looks like? The International Baccalaureate provides quite a few sample student essays online . Here are five essays that earned A grades.

Language and literature: An exploration of an aspect of the narrative voice in Vladimir Nabokov’s Lolita

Environmental Systems and Societies: The economic impact of the 1995 reintroduction of grey wolves to Yellowstone National Park

Psychology: To what extent do social networking sites (SNS) usage lead to experience of anxiety in adolescents?

Music: Composition techniques in the 1st movement of Johannes Brahms’s Symphony No. 2, Op. 73

Business Management: Corporate Culture at Oracle

1) Pick something you’re passionate about

As you can see from the titles above, the IB Extended Essay is a great place to delve into a niche topic that fascinates you. Since you’ll be spending many months on this essay, you’ll want to pick a topic you genuinely enjoy spending time learning about. It’s also smart to choose something you’ve already learned about in your IB classes so that you have a strong foundation of knowledge to start with. In music class, do you love pondering why music makes us feel a certain way? Maybe an essay about music theory will keep your gears turning. Do you come alive trying to solve seemingly impossible problems in physics class? Now’s your chance to put those equations into action.

Since this essay is all about your academic interests, it’s also a good idea to pick a topic that’s relevant to what you plan to study in college. Selecting a relevant topic will provide you with significant exposure to the field and will also give you something meaningful to talk about in your college admissions essays.

2) Limit your scope

What’s the meaning of life? Why do wars happen? What is time? Some questions are just way too big to answer, and your IB Extended Essay is not a good place to tackle expansive, philosophical questions. Instead, think of this essay as a place to investigate one piece of a big question. If, let’s say, you’re generally interested in what helps women reach positions of leadership in business, this is a good place to examine how one or a few companies approach this issue. Or, if you’re interested in studying what inspires surrealist painters, you’ll want to pick one or a few painters to research, likely all from the same time period. For both these topics, you’d need a whole textbook to tackle the full question, but limiting your scope will make it much easier to write a clear and cohesive 4,000 words.

On the other hand, it’s possible to narrow your focus too much. It would be impossible, for example, to write 4,000 words about a single sentence in a novel. Make sure you talk about scope early and often with your mentor. Together, you can find the perfect Goldilocks scope for your project that’s not too big and not too small.

3) Choose a good mentor

Speaking of mentors, choosing wisely will help you enormously as you embark on your IB Extended Essay. You’ll want to make sure you choose someone with existing knowledge in your research topic. Your English teacher may be able to give you great writing advice, for example, but they won’t be able to guide your research and scope if you’re writing about marine animals or modern dance.

Before you approach a teacher, make sure you have at least one topic idea (or even a few ideas) in mind so that you can make sure they’ll be a good fit to supervise your project. When you meet with them, find out what their mentorship style is like. Make sure they’ll have time to read several drafts of your essays, meet with you a few times, and give you feedback. Some IB schools will require your IB Extended Essay mentor to sign an agreement form too, so make sure you find out what paperwork is required in advance.

4) Get organized, way organized

The IB Extended Essay is not something you can crank out the night before it’s due. The essay is meant to be a substantive, in-depth, thoughtful, and thoroughly researched analysis, and Rome simply isn’t built in a day. This might be the longest paper you’ve written to date, and this project might require more research than you’ve been asked to do before. Timelines vary by school, but you’ll likely spend between eight months and a year working on your IB Extended Essay. So, how will you pull it all off? For these 8-12 months, organization will be your guiding light. We recommend you:

• Get started early. If your essay is due November of your senior year, start generating topic ideas during your junior year right after winter break.
• Create a long-view schedule for yourself. What will you accomplish each month of your process?
• Give yourself deadlines. Once you choose a mentor, suggest 2-3 draft deadline dates so that you will be held accountable throughout the writing process.
• Find a note-taking system that works for you. You’ll be reading many articles and books and it’s hard to keep track of all your sources. Create a document or spreadsheet where you keep track of the sources you’ve found and check them off as you read. As you finish reading a text, type up important quotes and a few notes explaining how it connects to your topic and to your other texts.

5)Write a messy first draft

Writing never comes out perfect the first time, even for New York Times bestselling authors and the most experienced researchers. In your first draft, give yourself permission to get all your thoughts out, no matter how unstructured or rambling they are. Call this your brainstorming draft. When you’re ready to revisit it, see what patterns emerge, what common ideas you can group together, what beginning buds of ideas you can make bloom into full-fledged analysis.

6) Communicate for an audience

When you’re used to producing writing that only your teacher reads, it can be hard to remember to write for an audience. But at the end of the day, writing is communication , and the best writing is clear and thorough communication that anyone could pick up and read. For your IB Extended Essay, you’ll want to remember that many people will be reading your final essay, and not all of them will be experts in the niche topic you choose to study. Ask yourself: how can I explain my research to an audience who doesn’t already agree with my analysis?

To communicate to an audience, you’ll want to:

• Provide lots of general background information on your topic.
• Don’t assume your reader is familiar with your sources. Introduce them as if they’re guest speakers about to walk up to a podium and deliver a lecture.
• After including quotes, facts, and figures, be sure to explain what those sources mean in your own words and how they connect to your bigger-picture argument.
• Don’t assume your arguments are self-evident. In this essay, communicating for an audience means supplying ongoing interpretation and analysis, even if it feels like you’re explaining the obvious. Your reader isn’t on your research journey with you, so your points might not be so obvious to your reader.

Although your IB Extended Essay provides a report that factors into your grade, your essay will also be assessed by external examiners the IB. Per the IB Extended Essay Rubric , essays are graded on a scale from 0 to 34 based on 5 different criteria:

• Criterion A: Focus and Method (6 points maximum)
• Criterion B: Knowledge and Understanding (6 points maximum)
• Criterion C: Critical Thinking (12 points maximum)
• Criterion D: Presentation (4 points maximum)
• Criterion E: Engagement (6 points maximum)

As you can see, Critical Thinking is the most significant rubric category. This means that the IB wants to see you arrive at your own unique analysis of your topic, drawing connections between sources and data, and making well-supported arguments. This means they want a lot of you: your ideas, your interpretations, your thoughts. Make sure you emphasize that in your essay, but of course don’t forget the other categories.

The score a student receives corresponds to a letter grade scale that is slightly different than what we’re accustomed to in the U.S. Here’s the letter grade to numerical score breakdown:

You must earn a D or higher to receive your IB Diploma. To learn more about the different criteria included in the IB Extended Essay Rubric, you can explore the IB’s full guide to the Extended Essay .

We hope you found our look at the IB extended essay rubric and IB extended essay topics to be helpful. Ready to dive into research? You may want to read our 10 Expert Tips for Improving Reading Comprehension before you hit the books.

And if you’re a high school student in the process of mapping out your pathway to college, take a look at a few other useful guides:

• IB vs AP—Which Classes are Best for College Admission?
• How to Earn College Credit in High School
• High School Course Requirements for College Admission
• SAT Score Calculator
• ACT Score Calculator 
• High School Success

Christina Wood

Christina Wood holds a BA in Literature & Writing from UC San Diego, an MFA in Creative Writing from Washington University in St. Louis, and is currently a Doctoral Candidate in English at the University of Georgia, where she teaches creative writing and first-year composition courses. Christina has published fiction and nonfiction in numerous publications, including The Paris Review , McSweeney’s , Granta , Virginia Quarterly Review , The Sewanee Review , Mississippi Review , and Puerto del Sol , among others. Her story “The Astronaut” won the 2018 Shirley Jackson Award for short fiction and received a “Distinguished Stories” mention in the 2019 Best American Short Stories anthology.

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Math Extended Essay Ideas

By KyleAdams October 14, 2010 in Extended Essay

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I have a few different general topic ideas, I just don't know how to turn those into a condensed RQ. Please give me suggestions if you know of any that would fit with the topic. I kind of just need something to stimulate my brain to start thinking up more ideas.

1) Combinatorics

2) Fractals

3) Golden Ratio

4) Derivatives

If you have any ideas of an RQ I could develop out of those topics please don't hesitate to respond. I am already way behind in my choosing of a topic, because I had originally wanted to do English thinking it would be easiest, but I decided to go with math, something I really enjoy.

I did some thinking about a different topic. I started thinking about doing an EE about the math in music. I think an EE on the math of the Harmonic/Overtone Series would be doable, and I could incorporate trig functions like sine cosine based on the sound waves and show how sound waves turn into overtones and such.

Does this seem like a doable topic? I don't have enough research done to know an exact RQ, but that is the sort of outline of a topic.

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Ohhhh golden ratios! My friends doing that and connecting it with religion.

Ok so I read stuffs about John Cage, Philip Glass, Aleatoric Music, etc. I haven't really found something doable since my first topic turned out to be not so doable, so I am still looking for ones.

http://www.tedbursa.k12.tr/ib/html/maths.html

Well, here are some top scoring extended essays on a schools website that you can use as examples.

There's no problem with doing an extended essay in Maths, just make sure you can do the work though. One of the IB teachers who's been teaching IB for the longest amount of time (Edit: for my school lol) said there was a girl one year who had "faked" some of the math on her extended essay, and therefore got an E on it. So, pick a topic that you know you'll be able to comprehend, so you won't have to be making up formulas at 5AM before school starts lol.

I think there are sufficient topics that could be done for math that relate to music. There is the logarithmic scale, for instance, that the frequency of pitches is based on. It is something like a logarithm with a base of 1/212. I think if I do the harmonic series and overtones then I can possibly do something that relates the graphs of the sine curves that model each of the sounds and then show how they relate to the overtones and such. I don't know for sure, that is just a possibility, I just am at a loss for any other topics. If anyone has any ideas based on any of the possibilities I have presented, then please let me know.

During the summer before IB1, I had a topic that I came up with that I absolutely loved. When I learned there wasn't anywhere to go with it and the topic would be too difficult/long for an extended essay, I decided to choose another, completely different topic. The topics were even in different subjects lol.

I know I don't have to do math, but it's the one subject I really enjoy and that I want to go on with in college most likely. I think this is something I really want to do, even if I don't have a topic yet. I think my indecisiveness is partly the problem, but I just can't tell if something is a good enough topic or not. I think there is enough to do with the harmonic series and overtone series but I am not certain.

Well I am not really sure if I will stick to the music one, but I am now looking at combinatorial game theory, and I also looked through Heinrich Dorrie's 100 Great Problems of Elementary Mathematics. Some of those problems looked interesting so I may see if I can do one of those. What do you think? Some of the better problems I saw in that book were the following:

The problems about finding location based on astronomy.

Steiner's Sphere, Circle, or Ellipse problem.

The Square as an Image of the Quadrilateral.

Berwick's Problem of the Seven Sevens.

Bernoulli-Euler Problem of the Misaddressed Letters.

Euler Problem of Polygon Division.

The Euler Number.

Nicolaus Mercator's Logarithmic Series.

Newton's Sine and Cosine Series.

Fermat-Gauss Impossibility Theorem.

Gauss' Fundamental Theorem of Algebra.

Those are some of the ones I think I could do. Anyone have any comments about them? Also, is it true that the research question has to somehow be applicable to real life? Can it not be solely theoretical or something?

I am now looking at combinatorial game theory, and I also looked through Heinrich Dorrie's 100 Great Problems of Elementary Mathematics. Also, is it true that the research question has to somehow be applicable to real life? Can it not be solely theoretical or something?

The RQ can be something theoretical, BUT it is often said that a theoretical Math EE which is not applicable to real life could only score a B. If you do not mind getting a B, go ahead. Otherwise, just play safe.

I know that finding a good topic is very hard, as I also feel it; but now that you have stuffs (ideas), show them to your MATH TEACHER first. Or probably your EE supervisor if you have already got one. They will then decide which one is good, which one is not good. They should know better than me and so I cannot say which of those problems are good since I do not know what they are all about. A lot of apologies.

A topic (in combinatorics) I found quite interesting but barely knew where to start with it: Since my guess is "Not all solitaire games are solvable" (or are they?), what are the chances that a solitaire game is solvable? This could be extremely hard to do so one might want to look at a simplified version of the game and try extrapolating the results; or maybe play a thousand solitaire games to get an idea of the probability lol.

http://www.tedbursa.k12.tr/ib/PDF/Mathmatics_3.pdf

I think that EE is purely theoretical,and it is on the "50 Excellent Extended Essays" list put out by IB.

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Extended essay

The extended essay is an independent, self-directed piece of research, finishing with a 4,000-word paper.

One component of the International Baccalaureate® (IB) Diploma Programme (DP) core, the extended essay is mandatory for all students.

Read about the extended essay  in greater detail.

You can also read about how the IB sets deadlines for the extended essay , find examples of extended essay titles from previous DP students and learn about the world studies extended essay .

Learn more about the extended essay in a DP workshop for teachers . 

DP subject briefs

Find out about what each subject offers within the Diploma Programme (DP).

Our DP subject briefs—for both standard and higher level—contain information about core requirements, aims and assessment.

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A variety of data — about children’s academic outcomes and about the spread of Covid-19 — has accumulated in the time since. Today, there is broad acknowledgment among many public health and education experts that extended school closures did not significantly stop the spread of Covid, while the academic harms for children have been large and long-lasting.

While poverty and other factors also played a role, remote learning was a key driver of academic declines during the pandemic, research shows — a finding that held true across income levels.

Source: Fahle, Kane, Patterson, Reardon, Staiger and Stuart, “ School District and Community Factors Associated With Learning Loss During the COVID-19 Pandemic .” Score changes are measured from 2019 to 2022. In-person means a district offered traditional in-person learning, even if not all students were in-person.

“There’s fairly good consensus that, in general, as a society, we probably kept kids out of school longer than we should have,” said Dr. Sean O’Leary, a pediatric infectious disease specialist who helped write guidance for the American Academy of Pediatrics, which recommended in June 2020 that schools reopen with safety measures in place.

There were no easy decisions at the time. Officials had to weigh the risks of an emerging virus against the academic and mental health consequences of closing schools. And even schools that reopened quickly, by the fall of 2020, have seen lasting effects.

But as experts plan for the next public health emergency, whatever it may be, a growing body of research shows that pandemic school closures came at a steep cost to students.

The longer schools were closed, the more students fell behind.

At the state level, more time spent in remote or hybrid instruction in the 2020-21 school year was associated with larger drops in test scores, according to a New York Times analysis of school closure data and results from the National Assessment of Educational Progress , an authoritative exam administered to a national sample of fourth- and eighth-grade students.

At the school district level, that finding also holds, according to an analysis of test scores from third through eighth grade in thousands of U.S. districts, led by researchers at Stanford and Harvard. In districts where students spent most of the 2020-21 school year learning remotely, they fell more than half a grade behind in math on average, while in districts that spent most of the year in person they lost just over a third of a grade.

( A separate study of nearly 10,000 schools found similar results.)

Such losses can be hard to overcome, without significant interventions. The most recent test scores, from spring 2023, show that students, overall, are not caught up from their pandemic losses , with larger gaps remaining among students that lost the most ground to begin with. Students in districts that were remote or hybrid the longest — at least 90 percent of the 2020-21 school year — still had almost double the ground to make up compared with students in districts that allowed students back for most of the year.

Some time in person was better than no time.

As districts shifted toward in-person learning as the year went on, students that were offered a hybrid schedule (a few hours or days a week in person, with the rest online) did better, on average, than those in places where school was fully remote, but worse than those in places that had school fully in person.

Students in hybrid or remote learning, 2020-21

80% of students

Some schools return online, as Covid-19 cases surge. Vaccinations start for high-priority groups.

Teachers are eligible for the Covid vaccine in more than half of states.

Most districts end the year in-person or hybrid.

Source: Burbio audit of more than 1,200 school districts representing 47 percent of U.S. K-12 enrollment. Note: Learning mode was defined based on the most in-person option available to students.

Income and family background also made a big difference.

A second factor associated with academic declines during the pandemic was a community’s poverty level. Comparing districts with similar remote learning policies, poorer districts had steeper losses.

But in-person learning still mattered: Looking at districts with similar poverty levels, remote learning was associated with greater declines.

A community’s poverty rate and the length of school closures had a “roughly equal” effect on student outcomes, said Sean F. Reardon, a professor of poverty and inequality in education at Stanford, who led a district-level analysis with Thomas J. Kane, an economist at Harvard.

Score changes are measured from 2019 to 2022. Poorest and richest are the top and bottom 20% of districts by percent of students on free/reduced lunch. Mostly in-person and mostly remote are districts that offered traditional in-person learning for more than 90 percent or less than 10 percent of the 2020-21 year.

But the combination — poverty and remote learning — was particularly harmful. For each week spent remote, students in poor districts experienced steeper losses in math than peers in richer districts.

That is notable, because poor districts were also more likely to stay remote for longer .

Some of the country’s largest poor districts are in Democratic-leaning cities that took a more cautious approach to the virus. Poor areas, and Black and Hispanic communities , also suffered higher Covid death rates, making many families and teachers in those districts hesitant to return.

“We wanted to survive,” said Sarah Carpenter, the executive director of Memphis Lift, a parent advocacy group in Memphis, where schools were closed until spring 2021 .

“But I also think, man, looking back, I wish our kids could have gone back to school much quicker,” she added, citing the academic effects.

Other things were also associated with worse student outcomes, including increased anxiety and depression among adults in children’s lives, and the overall restriction of social activity in a community, according to the Stanford and Harvard research .

Even short closures had long-term consequences for children.

While being in school was on average better for academic outcomes, it wasn’t a guarantee. Some districts that opened early, like those in Cherokee County, Ga., a suburb of Atlanta, and Hanover County, Va., lost significant learning and remain behind.

At the same time, many schools are seeing more anxiety and behavioral outbursts among students. And chronic absenteeism from school has surged across demographic groups .

These are signs, experts say, that even short-term closures, and the pandemic more broadly, had lasting effects on the culture of education.

“There was almost, in the Covid era, a sense of, ‘We give up, we’re just trying to keep body and soul together,’ and I think that was corrosive to the higher expectations of schools,” said Margaret Spellings, an education secretary under President George W. Bush who is now chief executive of the Bipartisan Policy Center.

Closing schools did not appear to significantly slow Covid’s spread.

Perhaps the biggest question that hung over school reopenings: Was it safe?

That was largely unknown in the spring of 2020, when schools first shut down. But several experts said that had changed by the fall of 2020, when there were initial signs that children were less likely to become seriously ill, and growing evidence from Europe and parts of the United States that opening schools, with safety measures, did not lead to significantly more transmission.

“Infectious disease leaders have generally agreed that school closures were not an important strategy in stemming the spread of Covid,” said Dr. Jeanne Noble, who directed the Covid response at the U.C.S.F. Parnassus emergency department.

Politically, though, there remains some disagreement about when, exactly, it was safe to reopen school.

Republican governors who pushed to open schools sooner have claimed credit for their approach, while Democrats and teachers’ unions have emphasized their commitment to safety and their investment in helping students recover.

“I do believe it was the right decision,” said Jerry T. Jordan, president of the Philadelphia Federation of Teachers, which resisted returning to school in person over concerns about the availability of vaccines and poor ventilation in school buildings. Philadelphia schools waited to partially reopen until the spring of 2021 , a decision Mr. Jordan believes saved lives.

“It doesn’t matter what is going on in the building and how much people are learning if people are getting the virus and running the potential of dying,” he said.

Pandemic school closures offer lessons for the future.

Though the next health crisis may have different particulars, with different risk calculations, the consequences of closing schools are now well established, experts say.

In the future, infectious disease experts said, they hoped decisions would be guided more by epidemiological data as it emerged, taking into account the trade-offs.

“Could we have used data to better guide our decision making? Yes,” said Dr. Uzma N. Hasan, division chief of pediatric infectious diseases at RWJBarnabas Health in Livingston, N.J. “Fear should not guide our decision making.”

Source: Fahle, Kane, Patterson, Reardon, Staiger and Stuart, “ School District and Community Factors Associated With Learning Loss During the Covid-19 Pandemic. ”

The study used estimates of learning loss from the Stanford Education Data Archive . For closure lengths, the study averaged district-level estimates of time spent in remote and hybrid learning compiled by the Covid-19 School Data Hub (C.S.D.H.) and American Enterprise Institute (A.E.I.) . The A.E.I. data defines remote status by whether there was an in-person or hybrid option, even if some students chose to remain virtual. In the C.S.D.H. data set, districts are defined as remote if “all or most” students were virtual.

An earlier version of this article misstated a job description of Dr. Jeanne Noble. She directed the Covid response at the U.C.S.F. Parnassus emergency department. She did not direct the Covid response for the University of California, San Francisco health system.

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Sarah Mervosh covers education for The Times, focusing on K-12 schools. More about Sarah Mervosh

Claire Cain Miller writes about gender, families and the future of work for The Upshot. She joined The Times in 2008 and was part of a team that won a Pulitzer Prize in 2018 for public service for reporting on workplace sexual harassment issues. More about Claire Cain Miller

Francesca Paris is a Times reporter working with data and graphics for The Upshot. More about Francesca Paris