How to Structure & Format Your Maths IA
- March 23, 2023
Table of Contents
- 1 Introduction:
- 2.1 Introduction:
- 2.2 Bad Introduction:
- 2.3 Good Introduction:
- 2.4 Mathematical Background:
- 2.5 Exploration:
- 2.6 Conclusion:
- 2.7 Good Conclusion:
- 2.8 References:
Mathematical exploration is an important part of the International Baccalaureate (IB) program, and writing a math Internal Assessment (IA) is a key requirement for students seeking to earn an IB diploma. The IA provides an opportunity for students to delve deeper into a mathematical concept of their choice, and to demonstrate their understanding and application of mathematical concepts and techniques . Math IA examples can serve as valuable references when embarking on your IA journey.
Mathematics Analysis and Approaches (Math AA) is one of the two courses offered by the IB for Mathematics. Math AA focuses on developing students’ mathematical knowledge and skills in pure mathematics, including algebra, calculus, geometry, and trigonometry. Mathematics Applications and Interpretation (Math AI) is the other course that focuses on applying mathematics to real-world contexts, including statistics, probability, and modeling.
Both Math AA and Math AI require students to complete an IA by the end of the course and the IA is an extremely important part of a student’s math grade. However, writing a successful math IA requires more than just a solid grasp of mathematical concepts ; it also requires careful planning and structure. In this blog post, we’ll explore the key elements that make up a strong math IA structure, including the introduction, mathematical background, exploration, and conclusion. We’ll discuss the purpose and content of each section, and provide tips and strategies for crafting a clear and effective IA. Whether you’re just getting started on your math IA, or are looking to refine and improve your existing work, this blog post will provide valuable insights and guidance to help you succeed.
Structure of the Math IA:
The IA for both Math AA and AI follows a similar structure. Students are required to select a topic from one of the four areas of study: Algebra, Functions and Equations, Circular Functions and Trigonometry, and Calculus. The IA should be approximately 12-20 pages long, excluding appendices, and must contain the following components:
In this section, you should introduce the topic you have chosen and explain why it is important or interesting. You should also include a clear statement of the aim and objectives of your IA . A well-crafted introduction, like in the following maths IA examples , can engage your readers and set the stage for your exploration:
In this math IA, I will explore the topic of calculus. Calculus is a branch of mathematics that deals with rates of change and slopes of curves. I will look at some calculus concepts such as derivatives and integrals and try to explain them in simple terms. This will help readers understand the basics of calculus.
Why it’s bad:
This introduction is too broad and does not provide a clear focus for the IA. It is also not engaging and doesn’t grab the reader’s attention.
Have you ever wondered how the trajectory of a soccer ball is calculated after it’s been kicked? What about the math behind predicting the weather or designing roller coasters? All of these scenarios involve the application of calculus, a branch of mathematics that allows us to understand the behavior of curves and rates of change. In this IA, I will explore the concepts of calculus through real-world examples, demonstrating how it can be used to solve complex problems and enhance our understanding of the world around us.
Why it’s good:
This introduction sets up the IA by engaging the reader with real-world scenarios and providing a clear focus on exploring calculus. It also hints at the importance and relevance of the topic, making the reader interested to learn more.
Mathematical Background :
This section should include a brief overview of the mathematical concepts and techniques that you will be using in your IA. It is important to show a deep understanding of mathematical theory and to provide clear explanations of any equations or formulas you will be using. You can find that in most Math IA examples or sample IAs often begin with a solid mathematical foundation:
Bad Mathematical Background:
- The background is too general and does not provide specific information on the mathematical concepts that will be used in the IA.
- It does not indicate the level of mathematical knowledge that is required to understand the IA.
- It does not provide any context or motivation for why these mathematical concepts are important.
Good Mathematical Background:
- The background provides specific information on the mathematical concepts that will be used in the IA.
- It indicates the level of mathematical knowledge that is required to understand the IA.
- It provides context and motivation for why these mathematical concepts are important.
- It is written in clear and concise language that is easy to understand.
- It may include references or additional resources that readers can use to refresh their knowledge of the relevant mathematical concepts.
This is the most substantial section of your IA and should demonstrate your ability to use mathematical tools to solve a real-world problem. You should explain the methodology used to investigate the problem and provide clear evidence of your calculations and reasoning. It is important to show your work clearly, including any graphs or diagrams you create look at some of t hese math ia exploration examples
Bad Exploration Section:
- The exploration is too simplistic and does not demonstrate a deep understanding of the mathematical concepts being discussed.
- The methodology used to explore the mathematical concepts is not clearly described, making it difficult for readers to follow the logic of the argument.
- There is no data or evidence provided to support the conclusions drawn in the exploration.
- The exploration does not connect the mathematical concepts to any real-world applications or examples.
Good Exploration Section:
- The exploration demonstrates a deep understanding of the mathematical concepts being discussed, and provides a clear explanation of how these concepts are being applied.
- The methodology used to explore the mathematical concepts is clearly described, making it easy for readers to follow the logic of the argument.
- The exploration is supported by data or evidence, which helps to strengthen the argument being made.
- The exploration connects the mathematical concepts to real-world applications or examples, which helps to provide context and motivation for why these concepts are important.
- The exploration may include diagrams, graphs, or other visual aids to help illustrate the mathematical concepts being discussed.
- The exploration may include examples of how the mathematical concepts have been used in previous research, or how they can be applied to solve real-world problems.
In this section, you should summarize your findings and explain how they relate to the original aim and objectives of your IA. You should also reflect on any limitations of your investigation and suggest potential areas for further research . A poorly-crafted conclusion, like in the following math IA conclusion examples , can leave a bad impression:
In conclusion, we have explored the concepts of calculus and shown how they can be applied to solve problems. We have seen that calculus is a powerful tool for understanding rates of change and curves, and can be used to model a wide range of phenomena. We hope that this IA has given you a better understanding of calculus and its applications.
This conclusion is too general and does not summarize the specific findings of the IA. It also does not provide any insights or recommendations for further research or applications.
In conclusion, we have demonstrated how linear regression can be used to model real-world data and make predictions. Our analysis has shown that this technique can be used to effectively model and predict various phenomena, from the price of stocks to the spread of infectious diseases. However, there are still many areas where linear regression can be improved, such as accounting for nonlinear relationships or dealing with outliers. Future research in this area could explore these issues and develop new techniques for improving the accuracy and reliability of linear regression models.
This conclusion provides a clear summary of the main findings of the IA, and suggests potential avenues for further research and development. It also highlights the relevance and importance of the topic, and indicates that there is still much to be learned and discovered in this field.
It is important to include a list of all sources that you have used in your IA. This includes any textbooks, articles, websites, or other resources that you have consulted. You should also provide clear citations within your IA to show where you have used information from these sources.
Here are a few pointers on how to format your IA well:
- Title Page: The title page should include the title of your IA, your name, your candidate number, the date, and the word count.
- Page Numbers: All pages of your IA should be numbered, including the title page and appendices.
- Font and Size: Use a clear, legible font such as Times New Roman or Arial in size 12. Use a larger font for headings and subheadings.
- Line Spacing: Use double line spacing throughout your IA, except in tables, equations, and diagrams.
- Appendices: Any additional material, such as raw data, should be included in appendices at the end of your IA. Make sure to refer to these appendices in the main body of your IA.
- Graphs and Diagrams: All graphs and diagrams should be labeled clearly and should have appropriate titles and axes. Use colors and shapes to distinguish between different data points or lines. Make sure that the labels and titles are legible and that the scales are appropriate for the data being presented.
- Equations: All equations should be presented clearly, with variables and constants clearly labeled. Use appropriate notation and make sure that equations are properly formatted, with fractions, exponents, and other mathematical symbols clearly presented.
- Tables: All tables should be labeled clearly and should have appropriate column headings. Make sure that the tables are presented in a logical order and that any units of measurement are clearly indicated.
- Language: Use clear and concise language throughout your IA. Avoid using jargon or technical terms unless they are necessary. Make sure that your writing is grammatically correct and that you use appropriate punctuation.
- Proofreading: Finally, make sure that you proofread your IA carefully before submitting it. Check for spelling and grammar errors, and make sure that all of your equations, graphs, and tables are properly labeled and formatted. It can be helpful to have someone else read through your IA to check for errors or inconsistencies.
Here are a few additional tips to help you write a successful IB Math AA and AI IA:
- Choose a topic that you are interested in: You will be spending a lot of time on your IA, so it is important to choose a topic that you find engaging and challenging. This will help you stay motivated and focused throughout the process.
- Use a variety of sources: In order to demonstrate a deep understanding of the mathematical concepts and techniques used in your IA, it is important to use a variety of sources and to cite them properly. This demonstrates that you have researched your topic thoroughly and are able to apply the knowledge you have gained from a range of different sources. Textbooks and academic journals can provide a strong foundation for your research, as they often present complex mathematical concepts in a clear and concise manner. Reputable websites, such as those associated with educational institutions or professional organizations, can also provide useful information and insights.
- Show your working: it is important to not only arrive at the correct answer to a problem but also to show the steps you took to reach that answer. This process is referred to as “showing your work.” By including all of your calculations, graphs, and diagrams in your solution, you are demonstrating your thought process and reasoning. Additionally, including visual aids such as graphs and diagrams can make your solution more clear and effective. They can help to illustrate complex mathematical concepts and make them easier to understand. It is important to label all of your graphs and diagrams and to include a caption or explanation that describes their significance. This will help your audience understand the context of your work and the purpose of your visual aids.
- Use real-world examples: The IA is an opportunity to apply your mathematical knowledge and skills to real-world problems. Whenever possible, use examples that are relevant to your own life or that demonstrate the practical applications of the mathematical concepts you are studying. By selecting examples that are relevant and meaningful to you, you can not only create a more engaging project but also deepen your understanding of the mathematical concepts you are studying. The IA provides an opportunity to demonstrate the practical applications of mathematics and showcase the importance of this field in solving real-world problems.
- Seek feedback: Don’t be afraid to ask your teacher or classmates for feedback on your IA. They may be able to provide helpful suggestions for improving your work or catching any errors that you may have missed. It is important to approach feedback with an open mind and a willingness to make changes to your work. Be receptive to constructive criticism and take the time to carefully consider any suggestions or comments that are made. Use this feedback to refine your ideas, improve your analysis, and make your IA more effective overall.
In conclusion, the structure of your IB Math AI and AA IA is crucial to the success of your project. Your IA should be well-organized, clearly written, and contain all necessary components, such as an introduction, background information, data collection and analysis, and a conclusion. By following the guidelines provided by the IB, selecting an appropriate topic, and using effective mathematical tools, you can create a compelling IA that showcases your skills and knowledge in mathematics. Remember to plan ahead, manage your time effectively, and seek help if needed. With these tips in mind, you can excel in your IB Math IA and AA IA and achieve your academic goals.
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How to Structure and Format Your Math IA
How to Structure Your Math IA Format
Are you getting ready to present your Math IA? In this article, we’re breaking down the best way to format yours in a way that promotes independent thinking and personal engagement. By following this guide, you’ll be able to score highly in your mathematics course.
Understanding What Math IA is All About
Students are required to investigate an area of mathematics and then present it as a written body of work.
Based on this, it is clear that the student needs to know the appropriate mathematical language and relevant key terms to engage in the topic.
While there are different perspectives when it comes to formatting your maths IA, we recommend the steps outlined below.
By following this tried and tested structure for your math IA, each student will be able to present their findings consistently and optimally
Personal connection and engagement with the subject matter are key. Familiarise yourself with the steps below, and then dive into your chosen topic. Utilising technology can be helpful in conducting a thorough exploration of the topic.
The use of mathematics to prove and explain concepts is applicable to various contexts. This assessment is a great way for students to expand their knowledge and learn valuable skills.
Your assessment needs to define the concept and aim of the work. This will help to keep your data analysis focused. These ideas need to be conveyed in your writing. This is an area of maths that is not strictly bound to the number!
The examiner will be looking at the quality of the idea and the body of work in relation to the assessment criteria.
How to Structure and Format Maths IA
According to student reviews, IB Maths is a struggle for many students working towards getting their diplomas. Apart from the dreaded mathematics exam , you’re also expected to write up the exploration of a topic.
You can think of the IA as a written mathematical presentation that will impact your final grade.
Many IB students find it hard to study mathematical concepts. This process can help you reflect on new relevant logic that you may not have known previously.
So, where do you even begin your IA? Start with the IA format!
Math IA Structure: What is the Internal Assessment?
The internal assessment is an individual evaluation that focuses on subject-related work.
Alongside the criteria, samples of the student’s work (oral performances, portfolios, lab reports, and essays) are also submitted to the IB for the final grade.
It should show personal engagement with the topic at hand. In this case, it is about the investigation of and correlation between mathematical concepts.
Breakdown of the Math IA Assessment : Appropriate Mathematical Language
Let’s take a look at the criteria for your Math IA. Knowing how you’re being graded will make it much easier to make sure you’re ticking all the boxes.
Presentation (4 marks)
The first criterion is about the presentation, with the aim of assessing the general organization and coherence of your IA.
Although students tend to focus on the complexity of math that their exploration demonstrates, a full 4 points are rewarded for the clarity of your explanations and structure.
In order to score in the top range here, make sure your IA is clearly structured. We’ve shared the optimal format in the next section.
Mathematical Communication (4 marks)
The second criterion looks largely at the mathematical language you have used, such as:
Ensure that these three components are accurate and consistent throughout your IA.
Terms like “plug in” or “put in” should be replaced with mathematically sophisticated words like “substitute.”
Personal Engagement (3 marks)
To achieve the top marks for personal engagement, your engagement must be truly authentic and drive the exploration forward.
It needs to be independent and unique. It should display a degree of creativity in that you present mathematical ideas in your own way and explore the topic from various different perspectives.
This involves making predictions about things you may be interested in, and then finding ways to manipulate the problem, formula, or question to encompass those areas.
Reflection (3 marks)
The IB needs us to do more than just show what we’ve done.
During the reflective stage, connect the results with the initial aims. By doing this, you can determine findings throughout the process.
It is about evaluating the research to pick up on all evidence that goes beyond what a typical mathematical test would.
The IB is all about learning, so be sure to show the marker your growth throughout the IA.
Use of mathematics (6 marks)
This section looks at the quality of the maths and how relevant it is to the exploration.
The IB is measuring relevancy by checking that you only included maths that is directly intended to answer the research question.
It is also worth noting that the maths produced should be at a similar level to the math you cover in your syllabus. This doesn’t mean that you’re confined to only looking into topics that are covered on your syllabus, but it should be of the same rigour!
How to Format these Sections
Like almost all of your internal assessments, your Maths IA has to begin with a super clear introduction that sets the context and aim of the whole exploration.
It is a great place to show your ‘personal engagement’ with the topic you’ve chosen for your IA.
Be sure to account for your interest in the top, its relevance in your life, your prior knowledge about it, what you wish to achieve, and how you’ll arrive at an answer.
You may also include any personalised problem statements and explain how you aim to achieve a solid investigation on the topic.
The body of your IA exploration should focus on the particular topic you have chosen to investigate and the relevant mathematical material that will address the intended aim of the work.
A pivotal point to consider is the level and clarity of the mathematics you use – the IB rewards a lot of marks for the use and communication of Mathematics, so keep this in mind when you start writing your Maths IA up!
For more info on how to write the exploration, check out our complete Math IA Guide .
Math IA investigation:
As with all assessments, you also need to include a solid conclusion that summarises the research and work you’ve done.
What conclusions did you reach, and did you succeed in exploring the aim that you set out at the beginning of the Math IA!
Importantly, make sure to also discuss some of the challenges in your IA and what you would/could explore with more time and more words.
Finally, zoom out and think about the further implications of your study.
Did your learning affect your life in any way, or how might it affect the lives of others? How has your involvement allowed you to reflect on different mathematics topics?
There is no specific word count for your Math IA, but the IB advises that the exploration should be around 12-20 pages long.
Fonts and Spacing for Your Math IA:
There are no specific requirements on which font you should use, but going with Arial or Times New Roman is generally recommended, with double line spacing and font size of 12.
You may present your work in a word processing software (like Microsoft Word or Pages), or it can be handwritten.
Diagrams and Graphs:
You should include relevant graphs, tables, and diagrams.
Do not simply place these simply as appendices at the end of the essay – they should be fully and clearly labelled to ensure that the examiner knows what you’ve included and why.
It forms an essential part of your research and shows that you fully understand the examples you have included in your analysis.
Bibliography and Citations:
Your report should include a full bibliography with all sources at the end of the report.
In addition to a bibliography at the end, you must acknowledge all direct quotes that you use throughout your essay.
Topic Ideas for SL and HL mathematics
There are many ideas you can explore for the assessment, including graph theory, surface area, geometry, calculus equations, statistics, linear regression, modelling statistics, the SIR model, etc.
It helps to understood the marking criteria before deciding on your topic to ensure you use premium content in your work that can help you score highly.
In your development, you may investigate the correlation between different topics or ideas within Mathematics SL and HL or your AI SL.
Whatever you choose, remember that you will create a new exploration of complex ideas. It’s wise to form your own opinions based on substantive evidence.
Mathematical Concepts Conclusion: The IB Structure
So there we have it, a well organized exploration of the idea and IB layout of your Mathematics IA !
We hope this will give you the push you need to realise your potential and understand complex and unfamiliar mathematics. As with all mathematics, personal involvement by means of practising is best if you want to score highly in your HL syllabus.
Lanterna Resources and Opportunities for Math IA
If you need a bit more of a boost, we’ve got free resources for IB students that you might find helpful! For more personal engagement, feel free to reach out to your instructor or tutor.
Lanterna also offers the following to support students:
- Revision Courses : These offer a helping hand when it matters the most to boost your grades! Look out for these during the Winter and Easter breaks before the final exam.
- Summer Courses : When you are about to start your first or final year of the IB, the summer presents the perfect opportunity to get ahead.
- Online Private Tuition : One-on-one support from the comfort of your own home, whenever and wherever you need it.
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How To Write Your Mathematics Internal Assessment
Mathematics Internal Assessment (IA) is a crucial component of the IB Diploma Programme. It is a student-led exploration that enables the learner to delve deeper into a mathematical concept or problem of their interest. The Math IA is a 12-20 page report that showcases the student’s ability to conduct independent research, analyze data, apply mathematical concepts, and present their findings in a clear and coherent manner.
These are the reasons why the IA is invaluable:
1.Holistic assessment: The IA gives an opportunity to students to showcase their research skills, and is a more holistic assessment of their mathematical abilities.
2.Developement of critical skills: Problem-solving, logical reasoning, data analysis, and communication are crucial for academic and professional settings.
3.Application of Mathematics in real-world contexts: This allows students to have a more relatable experience with the abstract Mathematical knowledge they have gleaned in their coursework.
4.Development of research and analytical skills that can be used in the university and research environments.
5.A solid IA serves as a good indication to universities that a student is well-prepared to undertake independent study or research. Writing a Math IA can be daunting, but with proper planning and execution, it can be a rewarding experience that helps you understand the beauty and power of mathematics.
In this guide, we will discuss how to organize your Mathematics IA.
IA Cover Page
It should have the following elements: A)Title: The title of the Math IA should be clear, concise, and reflective of the exploration’s focus. It should give the reader an idea of what the IA is about.
B) IB Candidate Number: This is your unique identification number provided by the International Baccalaureate organization. It typically consists of three letters followed by three digits (e.g., ABC123). The candidate number helps identify your work during assessment and ensures anonymity.
C) Session: Indicate the examination session during which the IA was submitted. For example, it could be “May 2023” or “November 2023,” depending on the IB exam session.
D) Page Count: 12-20 Pages in length with double spacing. The page length per subsection is not set, but one can imagine it should correspond to the marking rubric.
E) Course and Level: Specify whether the Math IA is for Standard Level (SL) or Higher Level (HL) Mathematics. This is crucial as the level of sophistication and depth of mathematical exploration may vary between SL and HL.
F) Date of Submission: Include the date when you submitted the Math IA. This helps track the timeline of your work.
G) School Name and Code: Mention the name of your school and the school code. This information helps identify the institution where the IA was completed.
H) Candidate Name: Include your full name on the cover page. This ensures that your IA is properly identified and credited to you.
I) Abstract (Optional): Some schools may require an abstract to be included on the cover page. An abstract is a concise summary of the IA, typically consisting of 100-150 words. It should provide an overview of the research question, the methods used, and the main findings.
J) Declaration of Authenticity (If Required): Some schools or examiners may ask you to sign a declaration of authenticity on the cover page, stating that the work is entirely your own and has not been plagiarized or copied from other sources.
IA Important Rubric Requirements
(A) Mathematical Presentation (0-4) In order to get the full 4 marks for this criterion, there must be a coherent structure, accompanied with clear explanations. A general guideline for this is to break the IA into:
Section 1: Introduction
Introduction – Why, what, then how.
Why? Your IA introduction should include a rationale for why you have chosen your topic for your Mathematical Exploration (the name of this IA). You should find some personal way to engage with your chosen topic to satisfy this requirement. Choose a topic you’re genuinely interested in, state said interest explicitly and use your own personal examples where possible.
What? This is where you define the objective for your IA, and state what you want to achieve with this aim. Picking a topic – specifically an aim – should be considered carefully and in conjunction with your tutor/teacher to ensure there is sufficient depth to your topic (as this depends on whether you’re taking SL or HL Math). Make your aim explicitly – this is important.
Some examples of previous IA topics are listed below (these are basic topics and not finalised research questions) and in the appendix. However, remember that there ought to be some personal engagement within the topic-choosing process: “Why planes travel a curved route and not a seemingly direct route” “Does the stock market’s returns warrant its variance?” “Projectile motion” “L’Hôptal’s rule and evaluating limits” “Image rotations using rotational matrices”
How? You must outline how your exploration topic relates to your specific curriculum, how you’ve completed the exploration, and provide any necessary background information – your classmates should be able to understand your IA if they were to read it.
Then how: This means your plan of action. The level of difficulty must be appropriate for the your level (SL or HL).
Section 2 (Body): Theory & Calculation
Theory Provide only the relevant theory needed to reach a conclusion/understanding of your aim. If there is a particular method (in mathematics, there are often numerous ways to reach the same answer) that you’ve used you should explain the method and why you’ve used this method.
Calculation For this section you must include all formulae and assumptions (i.e., the actual numbers) used to make your calculations and the mathematical steps that you took to reach your aim. Note assumptions’ pertinence if someone wants to repeat your exploration. After going through your mathematical work you must explain how they relate to your exploration topic. Depending on the type of exploration in which you are partaking you should use appropriate graphs, tables, x-y-z planes, or other methods of presenting your results. See below.
As can be seen from the figures above, figures are labelled appropriately. Calculations come with brief explanations and connect the earlier theory with the specific scenario in your exploration.
Note that the theory section should include not only the explanation of relevant theories but also the related background information. Likewise, ensure that the calculation section is comprehensive and includes all necessary formulas and mathematical steps.
Section 3: Reflection, Conclusion, and Bibliography of Mathematical Exploration
Conclusion Your conclusion is a continuation of section 1 and 2. You are answering your aim from your introduction (section 1) with the theory and calculations in from section 2. This should be done in a clear, concise, and coherent manner. Not only should you explain the results and implications of your calculations, but you ought to relate this to the aim raised in your introduction. You may also include much of the reflection in your conclusion if you prefer a more integrated approach. Note the IB says the following regarding where the reflection should be placed: “Substantial evidence means that the critical reflection is present throughout the exploration. If it appears at the end of the exploration it must be of high quality and demonstrate how it developed the exploration in order to achieve a level 3.” This implies a preference for integration but it does not mean you are excluding yourself from a level 3/3 grade for the reflection rubric.
Reflection Your reflection should occur throughout your IA; however, you may also include a separate section depending on the layout of your IA. Here’s what you should do:
- Consider limitations and extensions of your conclusion.
- Similarly consider strengths and weaknesses.
- Relate the mathematics within the exploration to your personal knowledge (or personal engagement).
- Raise future research questions.
- The IB states your reflection must be “crucial, deciding or deeply insightful. It will often develop the exploration by addressing the mathematical results and their impact on the student’s understanding of the topic.”
Bibliography A detailed bibliography is required so you must keep all sources which you utilise throughout your IA process. You should include a thorough bibliography to support your introduction, background, theory, and perhaps calculations. Types of relevant sources include online databases, your school textbook, or specific theories found both online and physically.
- This rubric assess the student’s ability to organize his research and findings in a coherent manner. The fluency of the mathematical language used is assessed via the following ways:Notation
- Symbols (choose universally accepted ones)
- Terminology (All key terms and variables must be defined appropriately when first introduced)
A unique part of this IA is the personal engagement. This rubric assess a student’s ability to make the Mathematics his/her own – Infusing creativity in the exploration of ideas from multiple angles. The student must develop his or her own independent understanding of the topic he/she is exploring. For example, you could write in the first person why you have decided to pursue your interest in Fourier series. You could link it with your interest in understanding heat conduction. You discuss the challenges you encountered during your research, discuss how you felt, and emphasize the mathematical concepts you have learned during the investigative process.
Use of Mathematics
This rubric assesses how well a student uses the Mathematics in the exploration. Simplicity is encouraged, and the level of difficulty should be pegged at the level of the course. The Mathematics must be precise, and exhibiting a clear logical structure. Note the difference between receiving a 6/6 for the use of mathematics rubric for HL/SL according to the IB:
SL – “Relevant mathematics commensurate with the level of the course is used. The mathematics explored is correct. Thorough knowledge and understanding are demonstrated.”
HL – “Relevant mathematics commensurate with the level of the course is used. The mathematics explored is precise and demonstrates sophistication and rigour. Thorough knowledge and understanding are demonstrated.”
In both cases you should use mathematics of a similar level to what you are studying in your respective studies. However, in HL, the mathematics that is explored must be precise and shows sophistication and rigour. Students must show the mastery and use of complex concepts, be able to see the Mathematical problem from various viewpoints, and see the ways to link different areas of Mathematics.
E.g., use of mathematics carries a weighting of up to 6/20 while reflection carries a weighting of up to 3/20. Hence, you should expect to spend more pages on calculations than your reflection.
Topics to spur interest (note these topics are not developed but are included to stimulate your own more developed aims):
In conclusion, a well-structured layout is crucial for a successful Math IA, including an introduction, main body, analysis, and conclusion. Meeting the rubric requirements is also essential for a high grade, which includes criteria such as presentation, communication, and reflection. By following these guidelines, you can write an engaging and informative Math IA.
If in doubt, reach out to experienced tutors at Quintessential Education for extra help and guidance. Start your journey towards academic success today!
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Maths Internal Assessment: Advice & Tips
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For your Mathematics Internal Assessment, you have to complete a Mathematical Exploration on a topic of your choice. Whilst sometimes feared by students, this is a chance for you to explore an area of mathematics that interests you! It is a piece of written work that is graded out of 20 marks in total and contributes to 20% of your total grade. Here we look at the structure of the assessment, how to choose a topic, how to lay out your assignment and what to include.
Structure and how to choose a topic
The Maths IA forms 20% of your overall grade for Maths studies, SL and HL. The IBO recommend that it is 6-12 pages in length and includes maths that is commensurate with the level of difficulty of the course. This can be partly formed by maths studied within the IB maths syllabus, but it is also recommended that you look elsewhere for inspiration.
You could look at the optional modules (available at HL) that you do not study for potential starting points and build from here. Alternatively, think about an area which interests you where maths could be applied. Personally, I chose to investigate the bottle flip for my Maths IA as this became well known whilst we were preparing our IA ideas. Choosing something personal will allow you to score highly on the personal engagement criteria, which we will talk more about below.
A good way to structure your internal assignment would be the following:
- Introduction – Consider the background to your topic and where there is an opportunity for mathematical exploration
- Rationale – Why did you chose your topic (linking this to the introduction)
- Aim – What you would like to achieve from your exploration. Make sure these are clear and focused aims and show evidence supporting your personal engagement
- Main body – Where the maths comes in. Look at different perspectives on the problem and discuss their respective merits and outcomes
- Conclusion – What did you learn, what were your limitations and what areas are there for further exploration and application of your research?
Whilst this is a good way of approaching the assessment, the IBO state that this is definitely not the only way. If you think there is a better way do use it as this may allow you to show personal engagement and score highly.
The IA marking criteria are split into 5 categories, which we break down below:
Communication (4 marks)
The way you communicate in the Internal Assessment needs to be coherent, well organised, concise and complete. Conciseness has been emphasised as the IBO have recognised that some IAs have been too long and this has detracted from the quality of students’ work. To reiterate, 6-12 pages of concise and rigorous critical thinking is a good guide regarding how much to write.
In addition, the IBO have recommended that all graphs, tables and diagrams should be embedded in your main body (not as appendices). This will help the examiner read through your work clearly and so will improve your chances of scoring a better mark. Similarly, citing when and where other people’s ideas are used throughout your essay is key, as well as having a bibliography at the end. This will ensure you steer clear of plagiarism by highlighting to the examiner which work is your own – which will also improve your chances of scoring highlight in personal engagement.
Mathematical presentation (3 marks)
Firstly, the IBO recommend that you define key terms where required. Definitions, which can be found in textbooks or journal articles (please remember to reference!), will help the examiner follow your exploration and shows that you understand the topic. Similarly, ensure that you are using appropriate mathematical language such as notation, symbols and terminology. Try not to be too complex in the language you use as, if used wrongly, this may show a lack of understanding and drag both your mathematical presentation and communication marks down. However, please do use mathematical language where necessary. Define it, and explain clearly what it is referring to in your exploration.
Furthermore, try to make your work look visually pleasing by using multiple methods of presentation. These may be formulae, diagrams, tables, charts, graphs or models, and should be used to demonstrate your understanding of the topic. Please type out your own equations and draw your own graphs (for example, use Desmos and print screen, limiting any branding that is visible) and ensure all graphs have axes labels and headings. Finally, and most importantly, ensure all graphs have a purpose! This will demonstrate an ability to critically highlight the key elements of your exploration in a concise and coherent manner.
Personal engagement (4 marks)
Often the trickiest of the 5 criteria to score highly in, personal engagement requires you to demonstrate your connection with the topic. There are a number of things you can do that will improve your mark in this criterion:
- Speak in first person – This will show that you are the one who undertook and researched this project and that you value it
- Present the exploration in your own style – Differentiating yourself from other students in this way will show you have not just followed a template approach
- Talk about the challenges you faced – Doing so will improve your marks in the personal engagement and reflection criteria
- Discuss how you felt (surprised, frustrated) as your investigation progressed – Again, this shows your personal connection with your exploration
- Highlight the mathematical concepts you have learned – How has this exploration developed your mathematical ability?
Why Pi matters
Reflection (3 marks)
Proving yourself wrong or getting a result you were not expecting is not necessarily a bad thing as it will offer you a chance to reflect and score highly on this criterion. Try to recognise what caused the result that you were not expecting and, as importantly, how this could be fixed. Also reflect on the successes of your exploration – Did you succeed in proving something, obtaining an optimum result or modelling a difficult concept? Discussing both the strengths and the weaknesses of your work here will help you to score highly.
Moreover, try to discuss different approaches that you have taken or could have taken and how these may have impacted your results. For example, did you use a simple model to begin with (as I did in my IA), which allowed you to isolate the key equations, and build a more complex structure from here? Evaluating potential approaches from different perspectives will show strong critical analysis.
Furthermore, if you have space you could discuss the implications of your work or areas for further exploration. Do the results you have obtained imply any policy changes or develop our understanding of a topic area? Alternatively, could you apply your research to other fields, or explore further areas within the topic? If so, please try to include these to score highly for reflection.
Use of mathematics (6 marks)
Unlike many people think, you do not have to use mathematics that is way beyond the course level to score highly on this criterion. The IBO recommend that you use maths that is “commensurate with the level of your course”. This may take a syllabus topic, such as calculus, and develop it to go beyond what is covered in the IB course. Alternatively, it may apply this knowledge to a new scenario, as I did using differentiation when modelling the bottle flip. Ensure that, whichever level you choose, your exploration remains at a level where you can include “creativity or (a) personalised problem” to ensure you score highly on the personal engagement criterion as well.
One useful source of topics could be the optional modules that you do not cover as part of your course. If you are a Standard Level mathematician you have free reign to choose one of the Higher Level optional modules for inspiration. For example, a student interested in computer science may choose to explore the use of Dijkstra’s and Kruskal’s algorithms in graph theory. It is important to remember that the IB is more concerned about how you show your knowledge and understanding of the mathematical topic you choose. Sophisticated mathematics may include understanding and use of challenging mathematical concepts, looking at a problem from different perspectives or seeing underlying structures to link different areas of mathematics. The maths need not be complicated, just well explored.
Once you have written your exploration, it is important to proof read it and ensure that there are no grammatical errors and all references use the same structure. Moreover, please make sure that all of the 5 areas listed in the mark scheme have been addressed explicitly. Here is a link to a very useful proof-reading checklist to ensure you have everything included.
Whichever topic you choose to do your Maths IA on, there are 3 important things to remember:
- Be engaged! Show your personal enthusiasm for the topic through writing in first person, using your own style and describing the challenges you faced and how they made you feel.
- Aim to be clear, consistent and concise! Be clear with your use of mathematical terminology by defining it where necessary; be consistent with your layout and referencing style; and be concise when writing your work – longer does not always mean better.
- Have fun! This is your chance to explore an area of maths that is likely to not be covered by the syllabus and interests you. Make the project your own and enjoy the experience as much as you can.
Best of luck!!
If you need any help with your Maths IA or any of your other IB subjects, we offer tuition, talks and consultations about everything IB. Please get in touch if you would like to find out more, please see the relevant links at the top of the page, or check out a similar blog post from the great team over at Lanterna Education on how to structure and format your Maths IA here .
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IB Math IA Guide - Math IA Shenanigans That No One Will Tell Yeh!
Ace Your IB Math IA with our ultimate guide for 2023! Get top marks and ace your IA with ease. Discover proven tips, tricks and strategies to nail your Math IA today!
Table of content
Criterion a - mathematical presentation: (levels- 0, 1, 2, 3, 4), criterion b - mathematical communication: (levels- 0, 1, 2, 3, 4), criterion c - personal engagement: (levels - 0, 1, 2, 3), criterion d - reflection: (levels - 0, 1, 2, 3), criterion e - use of mathematics: (levels - 0, 1, 2, 3, 4, 5, 6), introduction, body of your exploration.
IB Math students will tell you how they’re always on the edge of their seats for some help, but IB Math IA takes that anxiety to an entirely different level. The reality is far from frightening; nonetheless, IB Math IA can be handled well with a unique IB Math IA topic in hand and lots of coffee!
But does that guarantee a dependable 7?
It takes more than just a perfect IB Math IA topic to ace.
How’s that, you’d ask.
From researching several IB Math IA examples to planning the mathematical working of your exploration, your IB Math IA structure will get you into trouble if you don’t give it the time it demands. With all the varied content available in bulk online, the process is bound to become anything but easy.
But worry not!
You are at the right place - The Ultimate Guide to IB Math IA!
This article covers IB Math IA rubrics, process key pointers, the structure of the investigation, and interesting IB Math IA topics that will stimulate your mind and help you begin your exploration!
You should also know about the updated course structure of IB Mathematics. Students are allowed to opt for any one of the following four courses in Math:
- Analysis and Approaches ( AA HL ) - Higher Level
- Analysis and Approaches (AA SL) - Standard Level
- Applications and Interpretation (AI HL) - Higher Level
- Applications and Interpretation (AI SL) - Standard Level
For more information about choosing your course, check out our latest article: Confused about IB Math AA & IB Math AI?
Also, here’s a great surprise for all students!
Patrick Jones , the creator of PatrickJMT Math Videos, acknowledged as the best Math teacher globally with over 1.2 million subscribers on YouTube, has gotten on board with our team at Nail IB! How great is that! He is already working on creating an entire Nail IB video course, and it will prove to be a wholesome guide for you as you tread on your IB Math journey! You should check out his excellent, world-renowned content here !
Before moving any further, we insist you check out our Free IB Resources for IB Mathematics SL and IB Mathematics HL. These are specially assembled for your benefit and will surely assist you on your IB Math journey!
For an absolute hold on IB Math, check out our premium notes designed and curated specially for you, be it IB Mathematics SL or IB Mathematics HL . These bundles are not just limited to messages but offer past year papers and How-to Guides for Extended Essays, Internal Assessments, and more; examples included! You’re in for a smooth ride with these by your side;)
You can also stream our webinar on How to Write an IB Math Internal Assessment in under 30 minutes and hear directly from a recent IB graduate to understand the fundamental pointers and some fantastic hacks to lay the foundation of your IB Math IA. Getting the proper guidance ensures you a 7 in the subject you have feared for too long. Click here to watch it now!
First things first, let’s understand the criteria. Unless we acknowledge the requirements against which our exploration is scored, it’ll be equivalent to a shot in the dark. The conditions, irrespective of whether you opt for SL, HL (AA or AI), are as follows:
Assessment is done on the conciseness, brevity, and clarity/coherence of your investigation. The proper structure must be given to your IA. As per IB guidelines,
a coherent exploration is,
- Logically developed
- Easy to follow and,
- Meets the Aim.
Also, a well-organized exploration,
- Includes Introduction
- Describes the Aim of the investigation and
- Has a Conclusion
Assessment is done on the appropriateness of the mathematical terminology, notation, and symbols used to progress the exploration. Marks and notes should be correctly used as are used in IB textbooks. For example, x2 should not be written as x^2.
If used, different mathematical representation tools such as tables, graphs, and diagrams must be relevant to the working and be commented on/explained well. Avoid inconsistent use of Mathematical terminology. Applying ICT Tools(for example- GeoGebra and Desmos ) should be made wisely. For Calculations, Graphic Display Calculators can also be used, but that doesn't outdo math formulas' importance.
Assessment is done on the personal involvement shown. The sure shot way to ensure Engagement is, first and foremost, by going ahead with a topic that interests you (something unique or that affects real-life situations). Personal Engagement is seen throughout the exploration by:
- Independent thinking and creativity showed by the student
- Making the Math Idea your own
- Investigating the idea from varied perspectives
- Exploring different possibilities
Avoid portraying superficial interest. Opportunities for demonstration of personal Engagement should be noticed.
Assessment is done on the evaluation and analysis of the investigation. Mentioning the significance of your exploration results, discussing possible limitations, and justifying why you chose the procedure you did can portray a fair reflection of the IA. Merely explaining your results will get you only a score of 1 out of 3. According to IB guidelines, a review should be meaningful and critical.
A meaningful reflection includes
- Considering limitations in the work
- Comparing different Mathematical Approaches
- Linking to the Aim
- Commenting on the Learning
A critical reflection entails,
- Considering What Next
- Discussing the implications of the results
- Discussing the strengths and weaknesses of the approaches
- Considering different perspectives
Reflection is an analysis of the student's work, seen throughout the exploration, not just the Conclusion.
Assessment is done on the implementation of Mathematics in the IA. It is essential to understand that the Math used should be on par with the course, nothing too simple and nothing you need help understanding. Also, the Mathematics used should be fully understood and engrained by you. Unfamiliar Mathematics, if used, should be explained well by giving personal examples. As per IB guidelines, students are expected to produce work that is,
- Commensurate with the level of the course(should either be part of the syllabus at a similar level or slightly beyond)
- Relevant Mathematics used means Math which supports the development of the exploration towards the completion of its Aim
To score higher levels in Criterion E, it is crucial to understand the meaning of the following terms:
- Precise Mathematics is error-free and uses an appropriate level of accuracy at all times
- Sophistication means the Math should be commensurate with the HL syllabus
- Rigour involves clarity of logic and language when making Mathematical arguments and calculations.
Here is a fully annotated sample IB Math IA, going through which you can gain a lot of insight (Read the annotations properly).
Another example, the Breaking the Code investigation(fully annotated)- is given here for IB Mathematics HL. The IA explores encryption and decryption in the context of Mathematics.
- Going through the report, we see that the document needs more structure in the beginning since the Introduction does not mention the Rationale or Aim. You don't want to be committing such a blunder.
- Moving further, we see that the body encompasses Math, which is well explained, thereby excelling on criterion E when graded on the SL scale. To excel in HL, the math should have been more rigorous than descriptive.
- Toward the end, the report needs to include a Reflection on the results obtained, which doesn't fare well for the IA. Potential implications of the topic need to be included, and the Conclusion seems bland.
Another interesting annotated sample- for IB Mathematics SL- Regularisation of Irregular Verbs: When can I use the words swimming and know correctly? is given for reference here . Understand which key points have been missed and which have been taken care of. The more you go through sample IAs, the better your chances of preparing an investigation that'll be scored well.
Like any other exploration, your IB Math IA expects you to give it a fair shot of effort and interest. If you see it as a burden, it will undoubtedly become one. Equally important is to draw an analogy between the topic of your choice and the math involved. Taking care of these points in general, let's understand all that goes into making one's IB Math IA (a brief outline):
- It can have a personal story attached; mention it in your Introduction. If not, explain how the topic underhand impacts real-world situations and motivates you to land on it. Your passion for the IA idea shows in your work, and you don't want to be doing your investigation just for the sake of it.
- f you're curious about Fibonacci numbers, the Golden ratio , and nature alike, try looking for relationships among them on the Internet. This will entail going through many research papers, publications, and journals and finally settling on mathematical findings and proofs that will help you investigate that particular something you wish to explore. For example, if you want to study how Traffic Jams have math running in the background , research it in detail since Traffic snarls are an imminent pain for us all. Only you will have to pick up parts you think are relevant and understandable to you.
- The cycle of Inquiry, Action, and Reflection in learning is vital. Learning the implication of Plagiarism, Collusion, and Duplication of Work is essential to keep one's IA transparent and impressive.
- Besides citing references in the bibliography section, ensure you include it in the body as a footnote or in the exploration itself. Citing credible sources shows how transparent your work is and helps examiners cross-check for correctness. Acknowledging the author's work is essential to the IA-making process.
With this, let's discuss the Structure/Layout of the Investigation. There are numerous guidelines available all over the Internet. Regarding the IA length, though you should keep 6 -12 pages as the prescribed length, your focus should be on including all that pertains to your idea and ruling out everything that's not. So don't set out with a mindset to refrain from exceeding six pages; set out to include everything you know needs to be. Similarly, it is advised to make sure the Math used is suitable for SL and HL levels.
Without any further adieu, let's highlight what the layout of the IA should look like:
- Sets the background of your exploration and gives an argument for your topic choice. Your Rationale tells why you chose so and so topic.
- This is where you define your investigation's objective and tell what you wish to achieve with this idea.
- Let's say, for instance, you have opted for Math HL; for a simple mathematical investigation that scores six on the Math SL grade scale, you might end up with a mere four on the HL. The difficulty of your opted Math subject should reflect in your Internal Assessment. It would help if you also outlined the areas of mathematics you will cover in your investigation.
- Elaborate on the method you used for the exploration and justify why you chose to proceed with that particular method.
- Use relevant mathematical tools like labelled graphs, charts, etc., for your mathematical work and explain them in the IA context.
- State your results relating them to the Aim of your Internal Assessment. The significance and impact of these results should be highlighted, as well. In addition, briefly tell how the exploration was helpful to you and all you have gained from it. Possibilities of extension should be mentioned. The bibliography is for you to cite the sources used by you in the making of the IA. We suggest you use the Citation Machine for additional guidance in the bibliography.
Now that we're comfortable with the IB Math IA structure let's look at some interesting IB Math IA topics that will get your creative juices flowing and help kickstart your Math IA journey today!
- Simulating models to study and forecast weather patterns. (You could come up with a personal account that led you to land on something like this)
- Exploring the different probabilities associated with a game of your choice; for example, Solitaire(if you're a game buff).
- Investigating the Math associated with the Global Positioning System(GPS) and the intricacies of the technology involved.
- Exploring Fermat's little theorem or Goldbach's conjecture (one of the most significant unsolved problems in Mathematics).
- Finding the volume and surface area of an egg, apple, mango or any other real-world object using Calculus's power (Simulation could be used). A good IA on modelling manages to score an easy 15-16 marks out of 20.
- Investigating the structural designs of bridges that prevent collapse under loading.
- Studying complex roots graphically.
- Exploring how guitar frets are arranged in Pythagoras Ratios.
- Comparing which will prove beneficial: lump-sum payment of a lottery prize or fee done in instalments?
- Understanding how ISBN codes and Credit Card Codes can be cracked.
And that's a wrap!
Just like any other IA, IB Mathematics IA needs to be started early so that you don't end up compiling just anything at the last minute!
Give it the time it needs, and it will surely pay off. It might seem heavy, but once you decide to pursue an idea of your liking, there will be no turning back! Keep in mind the essential pointers and win the battle courageously!
Want some A-quality guidance? Look no further; at Nail IB, we have assembled premium content for you to ace your IBs, and you should check out our resources for a smooth IB experience. Click here for top-notch IB resources or to assess how your prep is going! Our exclusive Nail IB course, created by Patrick Jones, will be out soon too, so stay tuned, as there is no way you would want to miss the holy grail every Math IB student wants!!
This article will serve as a solid foundation for your Math IB Internal Assessment.
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Writing A Good IA Introduction
By shotaway , June 9, 2008 in Maths Studies
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Is this for SL, math studies or HL? I did math SL and we didn't need an intro.
[quote name='__inthemaking' post='18112' date='Jun 10 2008, 11:09 AM']Is this for SL, math studies or HL? I did math SL and we didn't need an intro.[/quote] Maths SL. From my understanding it's not something big, but an introduction is required.
Just introduce what u plan on accomplishing in your IA and how u plan on doing it =P
Yeah, it's not something very extensive. I remember I had that IA and I introduced it in a couple of lines and still got a 7. I'd copy and paste what I had but I'm still waiting on my results. Don't stress too much over it.
[quote name='shotaway' post='18118' date='Jun 9 2008, 11:40 PM']Maths SL. From my understanding it's not something big, but an introduction is required.[/quote] Really?! I never did an intro for my maths SL IAs. Is it really a requirement then, because I ended up with a 18/20 overall on my IA and a 7 in math (I took the May 2007 exam) with no intro. All I did was type up all the given data and questions exactly and answer the questions.
Actually ... You don't have to make an intro for a math IA. However, putting the information nicely with a good introduction that explains the planning for the IA will be better, and helps you to get a better score.
I just wrote my internal assessment on matrices. a pretty easy way to introduce your paper is like talking to a 7 year old boy. some kind of; in this paper i will try to find the relationship of a pair of matrices elevated to a serie of numbers ......
- 11 months later...
Best way to do it is to connect the first step to your conclusion at the end so that its clear to the marker that you've made the connection. My teacher said that your IA should read like an essay rather than answering questions, you shouldn't even put the numbers or anything, so it should just flow.
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IB Math SL Internal Assessment: Directions
- Statistical Analysis
Length: 12-20 pages - no word count; logic, precision and clarity count more than length.
- An introduction that states your rationale/purpose for the topic
- Cite any references or direct quotes using MLA format
- State all definitions and explanations of concepts
- Use proper notation, applicable graphs, and mathematical computations
- Personal engagement
- A conclusion that ties up the major ideas, including whether the results are reasonable. What went wrong? Why? Think TOK
- Use the rubric to guide you
Can an examiner clearly identify your topic?
How did you collect your data? What questions did you ask? Did you do a survey? Who answered it? Did you give it personally or over social media?
Do you have well defined processes and well defined parameters?
Step by step explanations.
What are your variables?
What do you need to find to complete your process?
What else do you need to know?
All processes should be in the order that you will complete them. Correlation must be completed before Linear Regression, so it should be described in the introduction before linear regression.
Make sure your pages are numbered and that your work is double spaced. IB prefers Arial font.
1. If creating a graph, make sure everything is labeled
2. Show ALL work, every step
3. Include all equations - use the format from class, do not Google the equations
4. After each process, give a brief explanation to the results of the process and how they connect to your topic
5. Create your model, then use technology to compare
6. Analyze for extrapolating and interpolating data
1. Data should be collected through survey, observation, or research
2. Data should be relevant
3. Data should be sufficient in both quantity and quality: 30-50 for a good model
4. Data should be organized in a form that is appropriate for analysis
5. If you are using a survey, you must include the survey - it can be in the paper or added as an appendix
6. Data taken from another source must be cited and must be raw, unanalyzed data; do not use percentages for Chi Squared
1. Create a meaningful conclusion, bringing back together all of your processes and summarizing the results
2. Explain how each process connects to bring you to the conclusion of either proving or disproving your hypothesis
3. Indicate validity - did the processes you used properly help you get to the conclusion you wanted to achieve? Is there any other process that could have been added or anything you would have done differently?
4. Discuss reliability of your model if using statistics
5. Think of real world applications, do outside factors affect the outcome?
6. Could this project lead you into more research or analysis? How?
7. BE REFLECTIVE!
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IB Math Studies Internal Assessments
IA Introduction Rough Draft
Title- Must be at the top of the page
Font Arial Size 12
Single spacing or greater
Make sure to email a copy to yourself
Introduction must include
(Leave a space)
2) Explanation of why research is important to you
(leave a space)
3) STATEMENT OF TASK- (write the words) statement of what you will be doing in the project and how you will be doing it. This could be 1 or 2 sentences only.
4) Detailed Plan
a. What data will be collected, population, description of the sampling process, if you are conducting the survey, write about it, or if you are conducting an experiment describe the process.
b. How will this data be organized?
c. Write about the 3 math processes that will be used (2 simple, 1 further) Write about the relevancy of each math process. Explain why that math process is critical to your paper.
d. Write a preliminary conclusion. Write about what you think is going to happen. You can refer back to this statement when you do the section on validity.