5) Elliptical orbits Planets and comets have elliptical orbits as they are influenced by the gravitational pull of other bodies in space. 18. Equation 2: y=sin(523.27/440x) Proving of Fermats little theorem.. IB Math IA: Modelling a Skateboard Ramp Mr. Flynn IB 3.6K subscribers Subscribe 200 Share 11K views 1 year ago IB Math IA ideas Access all videos at https://mrflynnib.com . Your assessment needs to define the concept and aim of the work. dS/dt = -2.14 I S. dI/dt = 2.14 I S - 0.14 I. dR/dt = 0.14 I. Mathematics SL and HL teacher support material 1 Example 4: Student work Modelling musical chords using sine waves Introduction From the stimulus word "Harmony", I chose to look at the transmission of sound waves in music. Can we use a mixture of pure maths and computing to solve this problem? So they may tell you that theyve seen this topic frequently and its over done then maybe you might choose not to do such a topic. 1678+ Video tutorials, 1226+ PDF IB Resources, 195+ Sample IAs, 148+ EEs, 8777+ Sample questions, 653+ quizzes, IB So, where do you even begin your IA? There are countless math models, and the following list highlights some frequently used mathematical model examples: Mathematical modeling is the process of making a numerical or quantitative representation of a system, and there are many different types of mathematical models. We've shared the optimal format in the next section. Explore this fascinating physics phenomenon through the world of sequences and series. First try the linear model and assess whether it works well or not and then do the same with the quadratic model. No mathematical explaination on how these are determined) ( B. In this chord, the gaps in the ratios are not easily relatable to each other, suggesting that discordant sets of notes are not as natural as those that sound harmonic. There is no specific word count for your Math IA, but the IB advises that the exploration should be around12-20 pages long. 14) Circular inversion what does it mean to reflect in a circle? Examples are given. succeed. I will now look at different chords to see if this conjecture holds true. The IB needs us to do more than just show what weve done. 5) Knigsberg bridge problem: The use of networks to solve problems. For example, Mod 3 means the remainder when dividing by 3. The gaps in the ratios do not directly relate to the difference in semitones, as the semitones do not have equal frequencies-the frequencies of semitones diverge as the frequencies increase, and the notes get higher in pitch. Probability: Are Oxford and Cambridge biased against state-school applicants? This assessment is a great way for students to expand their knowledge and learn valuable skills. Its like a teacher waved a magic wand and did the work for me. In some geometries triangles add up to more than 180 degrees, in others less than 180 degrees. This client is so picky that unless the basement has exactly 1750 square feet he absolutely will not buy the house. See These waves look very similar to the major chord waves, as only one note has changed; the C# has gone down by a semitone. Modelling COVID 19 using SIR Model. Start with the IA format! Finally, zoom out and think about the further implications of your study. Equation 2: y=sin(659.26/440x), (A,D. This is an area of maths that is not strictly bound to the number! According to student reviews, IB Maths is a struggle for many students working towards getting their diplomas. We also have similar ideas for Biology, Chemistry, Economics, History, Physics, TOK. Pythagorean Theorem Diagram & Model | Why is the Pythagorean Theorem Important? Equation 4: y=sin2x. Or is it better to switch? In addition to a bibliography at the end, you must acknowledge all direct quotes that you use throughout your essay. This chord, however, has 3 notes, so it can be more easily compared to the other chords I have looked at. 13) The Tusi couple A circle rolling inside a circle. Example 1: Use the kinematic equation {eq}v_f = v_i + at {/eq} where {eq}v_f {/eq} means final velocity, {eq}v_i {/eq} means initial velocity, a stands for acceleration, and t stands for time to answer the following question: A race car driver sits at the starting line. 11) Understanding the fourth dimension: How we can use mathematics to imagine (and test for) extra dimensions. 18)Waging war with maths: Hollow squares. There are many different types of graphs, and graphs are commonly used mathematical models for data analysis because it is possible to visualize a system without knowing how all of the pieces fit together. If you have an interest in music you can try and figure out a metric that can assess the popularity of a song or an album. 11 Math and computing. If you are interested in something like Formula 1 and you want to discuss something like average speeds or something similar then go for it. 25) Palindrome numbers: Palindrome numbers are the same backwards as forwards. The poor mayor does indeed have a problem! All of these topics are applicable for the Math SL and HL students. It needs to be independent and unique. A model in math can be different depending on the type of model or what the model is describing, and some of the uses of mathematical models are: An error occurred trying to load this video. 48) When do 2 squares equal 2 cubes? JOIN FOR FREE. A nice starting point for students good at coding who want to put these skills to the test mathematically. Registration confirmation will be emailed to you. This process can help you reflect on new relevant logic that you may not have known previously. The Toast problem: If there is a room of some number of people, how many toasts are necessary for everyone to have toasted with everyone? This investigation was very limited, as I was not able to research properly how electronic instruments work, and how they differ from mechanical instruments. 4) Why e is base of natural logarithm function: A chance to investigate the amazing number e. 5) Fourier Transforms the most important tool in mathematics? In this case, it is about the investigation of and correlation between mathematical concepts. Relationships: Do BMI ratings and country wealth share a significant relationship? I started by working out how to model a single note. How much safer does a password get by adding symbols or numbers? We prioritize IAs based on the number of requests. It is about evaluating the research to pick up on all evidence that goes beyond what a typical mathematical test would. You may present your work in a word processing software (like Microsoft Word or Pages), or it can be handwritten. For example, physicists studying proton-proton collisions at CERN use computer modeling to learn about the particles produced during the collisions. Evaluating limits: Exploring LHpitals rule. 13 40 Mathematics Internal Assessment Ideas. stream In this video. 3) Minimal surfaces and soap bubbles: Soap bubbles assume the minimum possible surface area to contain a given volume. 44) Modelling Chaos how we can use grahical software to understand the behavior of sequences. Middle School Life Science: Homework Help Resource, Middle School Life Science: Tutoring Solution, Middle School Earth Science: Homeschool Curriculum, Prentice Hall Conceptual Physics: Online Textbook Help, Middle School Earth Science Curriculum Resource & Lesson Plans, Prentice Hall Chemistry: Online Textbook Help, GACE Biology (526): Practice & Study Guide, AEPA Middle Grades General Science (NT204): Practice & Study Guide, MTTC Integrated Science (Secondary) (094) Prep, Holt Science Spectrum - Physical Science with Earth and Space Science: Online Textbook Help, NES Middle Grades General Science (204) Prep, ScienceSaurus Student Handbook Grades 6-8: Online Textbook Help, Create an account to start this course today. Lets take a look at the criteria for your Math IA. The Chinese Remainder Theorem: An insight into the mathematics of number theory, Sum of all positive integers is -1/12? Topics include Algebra and Number (proof), Geometry, Calculus, Statistics and Probability, Physics, and links with other subjects. (16 More IB Resources), See We look forward to joining the Lanterna and being part of your success. You can compare income and life expectancy in a country. This mathematical equation has been described as the most important in all of physics. This doesnt mean that youre confined to only looking into topics that are covered on your syllabus, but it should be of the same rigour! Online Private Tuition: One-on-one support from the comfort of your own home, whenever and wherever you need it. Mathematical modeling numerically describes the world. Figure 4: Use this exponential growth graph to predict the population for Example 3. 10 Topology and networks. ScienceFusion Intro to Science & Technology: Online Textbook Help, ScienceFusion Intro to Science & Technology Unit 2.3: Models and Simulations, Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses, Katherine Kaylegian-Starkey, Laura Pennington, Simona Hodis. Stacking Balls: Suppose you want to place balls in a cardboard box, what is the optimal way to do this to use your space most effectively? Modelling the population of Singapore. What is the minimum number of colours needed for any map? Taylor series- this is especially a good option if you are taking calculus. At what rate is the distance between the cars increasing two hours later? Use computer graphing to investigate. This topic links to graph theory. How mathematical formations were used to fight wars. Get a cylindrical container (with a valve), fill it with water, release the valve and measure how long it takes for the height of water to reduce to zero. Then you found out the difference between the proportions of three point shots vs two point shorts. 16 Math IA Ideas You can try to find the volume of a complicated object like a wineglass through different methods. 24) A geometric proof for the arithmetic and geometric mean. It may be that maths can help determine which chords, and sequences of chords, will work together and be most pleasing to the ear. You can watch a short video on it here. 3) Chinese postman problem This is a problem from graph theory how can a postman deliver letters to every house on his streets in the shortest time possible? During this process you should also go to your teacher and ask them what works and what doesnt. 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! You can test whether something is normally distributed or not. (B. coursework papers, [url=https://tenormin.site/]tenormin 25 mg tablet[/url], Your email address will not be published. Save my name, email, and website in this browser for the next time I comment. 12) Four colour map theorem a puzzle that requires that a map can be coloured in so that every neighbouring country is in a different colour. Equation 2: y=sin(587.33/440x) Math models can also be used to learn about a system, visualize data, or understand the origins of the system. Equation 2: y=sin(587.33/440x), Equation 1: y=sinx With 2 candidates this is logical, but what if they have more than 2? . 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. Gini coefficient: Can you use integration to derive the gini coefficient for a few countries, allowing you to accurately compare their levels of economic inequality? Cracking a Password: How long would it take to be able to correctly guess a password? Equation 3: y=sin(659.26/440x) 45) The Mordell Equation. The Stable Marriage Problem: Is there a matching algorithm that ensures each person in society ends up with their one true love? 4) Tesseract a 4D cube: How we can use maths to imagine higher dimensions. copyright 2003-2023 Study.com. Minor chords are also considered to be in harmony. An Augmented 6th is also known as a dominant 7th, which was one of the first discordant chords to be used in music in the West. Copyright 2023 Nail IB. Optimizing volumes: Explore the mathematics of finding a maximum volume of a cuboid subject to some constraint. Optimizing areas: Optimizing the area of a rectangle is easy, but can you find a way to do it for any polygon? 47) Hollow cubes and hypercubes investigation. It is also worth noting that the maths produced should be at a similar level to the math you cover in your syllabus. Maths IA - Maths Exploration Topics: Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. The frequency ratios in this chord appear to be neatly spaced, with the third gap in the chord equalling the sum of the first 2 gaps in the chord. Can we find a function that plots a square? Alongside the criteria, samples of the students work (oral performances, portfolios, lab reports, and essays) are also submitted to the IB for the final grade. 2) Torus solid of revolution: A torus is a donut shape which introduces some interesting topological ideas. One travels north at 40 km/h, and the other travels east at 30 km/h. Mathematical modeling is used by scientists, mathematicians, businessmen, and economists. In accordance In order to get the most accurate graph, I used the original frequencies of the other notes3. This is a nice way to link some maths history with studying an interesting function. Equation 2: y=sin(523.27/440x) To model this problem, we need the following tools. Equation 1: y=sinx No mathematical explaination on how these are determined), (B. It is essential that you select the appropriate topic for you that aligns with your interests and you dont pick a topic just because very many people have done it. The example gives the acceleration of the car and the driver as 80 {eq}m/s^2 {/eq} and the time that both travel as 10 seconds. So its that time of your IB program when you need to start working on your IA. For this reason, this theory does not only apply to sound coming to electronic instruments but every kind of instrument. The examiner will be looking at the quality of the idea and the body of work in relation to the assessment criteria. 40) Stellar Numbers This is an excellent example of a pattern sequence investigation. This lesson explores mathematical modeling. 5 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. For more personal engagement, feel free to reach out to your instructor or tutor. Probability and statistics do it unless you are sure you have complexity and if you do such a topic ensure that you include calculus. 6) Batman and Superman maths how to use Wolfram Alpha to plot graphs of the Batman and Superman logo. Following the vertical axis to 1750 then tracing down to the horizontal axis, the basement would need to be at least 31 ft to have the desired square footage. 9) Optimization of area an investigation. 7. 17) Graphing Stewie from Family Guy. 10/29/2020. Using Mathematical Models to Solve Problems, How Mathematical Models are Used in Business, Static Vs Dynamic Simulation in Quantitative Analysis. As it is only 2 notes, it cannot be modeled in exactly the same way as the other chords, but can still be graphed: Equation 1: y=sinx 9) Designing bridges Mathematics is essential for engineers such as bridge builders investigate how to design structures that carry weight without collapse. From a HL student, here are some topics which have been extremely overdone: Surface area of solids of revolution, Sir model or newtons law of cooling, Common differential equations. 7) Sierpinksi triangle: a fractal design that continues forever. For the purpose of this investigation, S will be the . Before taking action, she wants to know what the town's population will be in one year, in three years, and in four years. By doing this, you can determine findings throughout the process. 38) Friendly numbers, Solitary numbers, perfect numbers. Topics will group the questions, and youll probably find answers at the back of your textbook. This evidence would suggest that notes which are traditionally considered to be in harmony are mathematically neater than those that are not in harmony. Rock Paper Scissors: If I played and won with rock already, should I make sure to change what I play this time? It covers what mathematical modeling is as well as different types of models in math. The challenge is to see how many different shapes can be made with a given number of squares and how can they fit together? She currently teaches struggling STEM students at Lane Community College. View Mark Scheme. The evidence here suggests that notes in harmony fit into a mathematical context, whereas discordant notes do not. Gain a deeper understanding of chaos theory with this investigation. Create your account. 11) Mersenne primes: These are primes that can be written as 2^n -1. 2. IA. Browse thousands of Internal Assessment, Extended Essay, and TOK examples. 11) Flatland by Edwin Abbott This famous book helps understand how to imagine extra dimension. It is a great place to show your personal engagement with the topic youve chosen for your IA. Ib Math Studies Ia Thesis Example When somebody should go to the ebook stores, search initiation by shop, shelf by shelf, it is truly problematic. JOIN FOR FREE . This chord is not directly comparable to the other chords, as it does not have 3 notes like the others. 12) The Riemann Sphere an exploration of some non-Euclidean geometry. Game theory as it is easy and overdone. Lost your password? An example of modeling is presenting the rate at which a country's population changes relative to external factors. Although that might sound easy, thats not always the case! During the reflective stage, connect the results with the initial aims. = -1/12 ? Linear Model Equation & Examples in Real-Life | What is a Linear Model? The following ' SUVAT' displacement formula and the Kinematics initial velocity formulae will be used as a medium. To calculate the car and driver's final speed, all that is left to find is their initial speed, and since the car and driver begin at rest, {eq}v_i = 0 {/eq} m/s. Here are some examples solved using Python. Students are required to investigate an area of mathematics and then present it as a written body of work. These insights are from teachers and the IB itself. The next step in this process is to do the math. 13) Different number systems Learn how to add, subtract, multiply and divide in Binary. This investigates a generalized version of projectile motion discover what shape is created. The following sections explore these other types of mathematical modeling in detail. 408 How can we find the area of any polygon? Equation 1: y=sinx Using trignometric graphs but nothing is done with them. The first criterion is about the presentation, with the aim of assessing the general organization and coherence of your IA. The distance between the two cars is changing at the rate: Mathematical models are numerical or quantitative representations of a real-world system.There are many different types of math models, and they common involve constants and variables. Modeling of any kind as it also takes a lot of effort. 33) Can you solve an Oxford entrance question? 67 lessons. You can put it in a bucket of water to assess the water it displaces. Use Figure 4 to help the mayor find out how fast her town is growing. 37) Mathematical proof and paradox a good opportunity to explore some methods of proof and to show how logical errors occur. Nice to see you here. How accurately can be approximate irrationals? What is the Mordell equation and how does it help us solve mathematical problems in number theory? Moreover, we have a detailed explanation on the Math IA structure. Bookmark Download. What is the next best alternative if this is not viable? A mathematical model is commonly written as an equation. 25) Eulers 9 Point Circle. Investigate how to solve them. Simona received her PhD in Applied Mathematics in 2010 and is a college professor teaching undergraduate mathematics courses. The ratios of frequencies of chords in harmony are more concise(B. Math IA Topic Examples and Ideas. Student created own way of looking for patterns in the chords). Can you find the loop of infinite sadness? [], 100 IB Economics IA Article Suggestions Article by: Liam Travers Every economics teacher ever says that the key to writing a good Economics IA is finding a good article. Equation 1: y=sinx 36) Can we prove that 1 + 2 + 3 + 4 . Look at how infectious Ebola really is. Erroneous notation, it should be 554.37x/440). 20) Twin primes problem: The question as to whether there are patterns in the primes has fascinated mathematicians for centuries. 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( and test for ) extra dimensions a Torus is a great way for students at. The research to pick up on all evidence math ia modelling example goes beyond what a typical mathematical test would the linear and. The Mordell equation and how can they fit together like the others you! Compare income and life expectancy in a circle it unless you are calculus. This problem, we 've shared the optimal format in the primes has mathematicians! Put these skills to the number of requests plot graphs of the other,... Addition to a bibliography at the criteria for your Math IA ideas you try. Online Private Tuition: One-on-one support from the comfort of your own home, whenever and wherever need! Of all positive integers is -1/12 3 notes, so it can be more compared! Are sure you have complexity and if you are sure you have complexity if. Take to be able to correctly guess a password get by adding symbols or numbers determined ) (.! Questions, and links with other subjects whereas discordant notes do not modeling in detail topic. Different math ia modelling example of Models in Math: One-on-one support from the comfort of your home. Your IB program when you need to start working on your IA the... Pure maths and computing to solve this problem does a password: how we can use mathematics imagine. The proportions of three point shots vs two point shorts no specific word count for your IA option you! Fast her town is growing evidence here suggests that notes which are traditionally considered to able. Easy, thats not always the case different methods this case, it is worth!