13 chapters | 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. 10 Topology and networks. 4) Applications of complex numbers: The stunning graphics of Mandelbrot and Julia Sets are generated by complex numbers. I will now look at some discordant notes and see how they compare with the chords I have already looked at. 19) Natural logarithms of complex numbers. The mathematical nature of the notes in traditional harmony suggests that the sound waves are more pleasing to our brain because of the way the notes fit together. lanchester s combat model ia maths sl 7 exploring an alternative method of calculating the volume of a star The approximate ratio for this chord shows that the ratio is not as precise, This evidence would suggest that notes which are traditionally considered to be in harmony are mathematically neater than those that are not in harmony. Friendly numbers, Solitary numbers, perfect numbers:Investigate what changes the condition of numbers, Force: Calculating the intensity of a climbers fall based upon their distance above where they last clamped in. We can use a matrix representation of complex numbers to test whether Eulers identity still holds. 14 Advice from an IB Examiner on topics you should avoid. Lack of explaination and a lost opportuinity for reflection on how reflection fits with conjecture). Find out more! Updated: 01/07/2022 Table of Contents. 7. A mathematical model is commonly written as an equation. 1. Part 1 Firstly, I will find the Maximum point of the trajectory of the ball. How can we use computers to gain a deeper understanding of sequences? They have data and different comparisons that may be great for you. In your development, you may investigate the correlation between different topics or ideas within Mathematics SL and HL or your AI SL. If you want some personalized help, kindly reach out to us at esquirewritings@gmail.com. Examples of Mathematical Modeling Tales from the Crypt Matthew D. Johnston,1,3,*Carina M. Edwards,1,3,Walter F. Bodmer,2Philip K. Maini,1,4and S. Jonathan Chapman3 Matthew D. Johnston 1Centre for Mathematical Biology; Mathematical Institute; University of Oxford; Oxford, UK If any points are chosen at random in a square what is the expected distance between them? Solving math word problems. 1) The Van Eck Sequence The Van Eck Sequence is a sequence that we still dont fully understand we can use programing to help! As a member, you'll also get unlimited access to over 84,000 Monty Hall problem: How does Bayesian probability work in this real-life example, and can you add a layer of complexity to it? 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. Math models can also be used to learn about a system, visualize data, or understand the origins of the system. Using the relation obtained in 2, solve for z'(2). 12) Towers of Hanoi puzzle This famous puzzle requires logic and patience. 5) Diophantine equations: These are polynomials which have integer solutions. In the same time b* (1/a +D) cars cross over the crossing. 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. 11) Understanding the fourth dimension: How we can use mathematics to imagine (and test for) extra dimensions. So for instance you decided to correlate 2 things. 45) The Mordell Equation. 2 0 obj 1) Modular arithmetic This technique is used throughout Number Theory. Youve likely spent weeks relaxing and thinking about anything other than school! They may also tell you that this one will work for you and this one wont sew and sure that you take their advice into consideration. 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? Only choose a complex topic if you can explain it in simple terms such that it is easily understandable to your peers. If you had done the calculations and the mathematics earlier then you would have realized that these two variables do not have a relationship and then you can pick other different variables and select the ones that have a good relationship and which you can build a discussion on. Subscribe and get the latest IB guides, notes,news, tips and product updates. For example, Mod 3 means the remainder when dividing by 3. May 2022. Nonetheless, if you feel like you want to search for your topics, an excellent place to start would be the IB Mathematics textbook. Fermats Last Theorem is one of the most famous such equations. Can we find a function that plots a square? According to student reviews, IB Maths is a struggle for many students working towards getting their diplomas. The mathematical nature of the notes in traditional harmony suggests that the sound waves are more pleasing to our brain because of the way the notes fit together. . 11) Projectile Motion Investigation II. Did your learning affect your life in any way, or how might it affect the lives of others? This is a nice geometry puzzle solved using a variety of methods. For this reason, this theory does not only apply to sound coming to electronic instruments but every kind of instrument. This can help you avoid so very many problems. 51) Complex numbers as matrices Eulers identity. ie 6 is a perfect number because 1 + 2 + 3 = 6. << /ProcSet [ /PDF /Text ] /ColorSpace << /Cs1 7 0 R >> /Font << /TT1 8 0 R 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? Request this IA to be marked. 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. ), Continued fractions- Use of continued fractions as representations of real numbers.. These waves look very similar to the major chord waves, as only one note has changed; the C# has gone down by a semitone. You may present your work in a word processing software (like Microsoft Word or Pages), or it can be handwritten. Why does the twin paradox work? 1) The Monkey and the Hunter How to Shoot a Monkey Using Newtonian mathematics to decide where to aim when shooting a monkey in a tree. These are some of the best Math IA Topics. 23) Perfect Numbers: Perfect numbers are the sum of their factors (apart from the last factor). During the reflective stage, connect the results with the initial aims. Maths can be used to both make these codes and break them. Start with the IA format! While there are different perspectives when it comes to formatting your maths IA, we recommend the steps outlined below. 7) Patterns in Pascals triangle: There are a large number of patterns to discover including the Fibonacci sequence. Example 3: A small town is quickly growing, and the mayor is worried. (B. How strange things happen when we start to manipulate divergent series. 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. Equation 2: y=sin(587.33/440x), Equation 1: y=sinx
Pythagorean triples: Can you find patterns in what numbers form a pythagorean triple? Putting it all together gives: {eq}v_f = v_i + at {/eq} -> {eq}v_f = 0 + 80*10 {/eq}. Mathematical modeling numerically describes the world. succeed. Pages 15. 32) Soap Bubbles, Wormholes and Catenoids. 8) Finding prime numbers: The search for prime numbers and the twin prime conjecture are some of the most important problems in mathematics. ~gv;pg9;{eF4"_=}GiRpfg)ZS-7q-25+0Zj9Ga!Q
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Q`;|':OO/Vk!&rgXC`ERY). Maths - SL. 49) Rational approximations to irrational numbers. endobj To model this problem, we need the following tools. It should show personal engagement with the topic at hand. Linear regressions: Run linear regressions using OLS to predict and estimate the effect of one variable on another. 22) The Folium of Descartes. 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For more info on how to write the exploration, check out our completeMath IA Guide. What is the next best alternative if this is not viable? Financial Mathematics Equations & Problems | What is Financial Mathematics? 12) Projectile Motion III: Varying gravity. 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. Youll have to plot a lot of curves. 4 0 obj There are many different uses for mathematical models such as understanding relationships or making predictions about the future, and there are many different types of mathematical models that can be used depending on the needs of the scientist. % Familiarise yourself with the steps below, and then dive into your chosen topic. IA Review. 2) Gravity, orbits and escape velocity Escape velocity is the speed required to break free from a bodys gravitational pull. These are questions that every scientist, mathematician, businessman, and economist will eventually ask, and to answer them requires a mathematical model of the system. If you find yourself struggling with anything from finding a topic to writing your evaluation, here are the answers to 5 of the most frequently asked questions about the econ IAs, answered by expert IB graduates. What would projectile motion look like on different planets? 14, Advice from an IB Examiner on topics you should avoid. 10) Is Intergalactic space travel possible? Topics include Algebra and Number (proof), Geometry, Calculus, Statistics and Probability, Physics, and links with other subjects. 41) Arithmetic number puzzle It could be interesting to do an exploration where you solve number problems like this one. Physical Models Overview & Examples | Scale & Life-Size Models, Using Nonlinear Functions in Real Life Situations. 30) Can you solve Oxford Universitys Interview Question?. There is a $1 million prize for solving the Riemann Hypothesis and $250,000 available for anyone who discovers a new, really big prime number. This will help to keep your data analysis focused. When it comes to this type of article, youll find that it may be filled with [], At the beginning of the school year, it can feel extra challenging to get motivated. I'll add the moderated mark sometime. 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. 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. Login. Taylor series- this is especially a good option if you are taking calculus. 8) Change in a persons BMI over time There are lots of examples of BMI stats investigations online see if you can think of an interesting twist. 2) Solving maths problems using computers computers are really useful in solving mathematical problems. 18) Hyperbolic geometry how we can map the infinite hyperbolic plane onto the unit circle, and how this inspired the art of Escher. Statistical Modeling Purpose & Types | What is Statistical Modeling? 6) Continued fractions: These are fractions which continue to infinity. To achieve the top marks for personal engagement, your engagement must be truly authentic and drive the exploration forward. 15 Closing. 43) Narcissistic Numbers what makes a number narcissistic and how can we find them all? Find out! Or is it better to switch? 36) Can we prove that 1 + 2 + 3 + 4 . Mathematical modeling is used by scientists, mathematicians, businessmen, and economists. 13 40 Mathematics Internal Assessment Ideas. coursework papers, [url=https://tenormin.site/]tenormin 25 mg tablet[/url], Your email address will not be published. Computer modeling has become a popular method for quantitively understanding real-world problems, and chemical formulas, which succinctly describe chemical reactions, have been around for centuries. endobj Its a really useful tool that allows you to compare different variables. 10 0 obj The great Indian mathematician Ramanujan discovered some amazing examples of these. The Risk of Insurance: An investigation into asymmetric information and how being unsure about the future state of the world may lead us to be risk-averse, Gabriels Horn: This figure has an infinite surface area but a finite volume, can you p. Voting Systems: What voting system ensures that the largest amount of people get the official that they would prefer? Simona received her PhD in Applied Mathematics in 2010 and is a college professor teaching undergraduate mathematics courses. 4, 40 Mathematics Internal Assessment Ideas. It is therefore more complicated than the difference of means test. In this blog post well go through our top 3 tips for getting motivated again! In some geometries triangles add up to more than 180 degrees, in others less than 180 degrees. 50) Square triangular numbers. Required fields are marked *. I decided to use Middle A, I altered the wavelengths, or frequencies, of the graphs by changing the coefficient of x. 16 Math IA Ideas The planets follow a surprising pattern when measuring their distances. 4. 16) Graphing polygons investigation. It is clear then, that there is a difference in the mathematical relationship of notes within chords in harmony and discordant chords. This is an area of maths that is not strictly bound to the number! Finally, zoom out and think about the further implications of your study. Bookmark Download. She has 20 years of experience teaching collegiate mathematics at various institutions. Physicists can also use computer modeling to make predictions about what particles are expected to be produced. Exemplars. Mathematical models are used in nearly every field of mathematics, but what is model in math? 5) Stacking cannon balls: An investigation into the patterns formed from stacking canon balls in different ways. Group Homomorphisms: Definitions & Sample Calculations, Teaching Reasoning in Math: Types & Methods, Applying Systems of Linear Equations to Breakeven Point: Steps & Example. 8 Calculus/analysis and functions. The twin prime conjecture states that there are infinitely many consecutive primes ( eg. 21) Projective geometry the development of geometric proofs based on points at infinity. 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. It covers what mathematical modeling is as well as different types of models in math. In order to get the most accurate graph, I used the original frequencies of the other notes3. Before taking action, she wants to know what the town's population will be in one year, in three years, and in four years. This is a nice way to link some maths history with studying an interesting function. Whatever you choose, remember that you will create a new exploration of complex ideas. << /Length 11 0 R /N 1 /Alternate /DeviceGray /Filter /FlateDecode >> 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. 17) Chinese remainder theorem. Essential knowledge for future astronauts. This is where you try and find out the relationship between two variables. Students are encouraged to take a different take through this assignment, a different angle on the mathematical practice. These datasets can easily be found on Gapminder. This graph looks very similar to the major graph, but the actual values, shown in the The following table, are slightly different. 3) Minimal surfaces and soap bubbles: Soap bubbles assume the minimum possible surface area to contain a given volume. Enrolling in a course lets you earn progress by passing quizzes and exams. The examiner will be looking at the quality of the idea and the body of work in relation to the assessment criteria. Use Figure 4 to help the mayor find out how fast her town is growing. Login. Other examples of math models are the Pythagorean theorem and line graphs. An equation is a mathematical statement that describes one quantity in terms of the other quantities present in the system. Can you find the pattern behind it? This analysis can be done in minutes or hours, but without a computer the same analysis could take decades. We also have similar ideas for Biology, Chemistry, Economics, History, Physics, TOK. One of the reasons that equations and graphs are commonly used mathematical models is because they can easily answer these questions, and Example 3 illustrates how a graph can be used to predict the future. Copyright 2023 Esquire Writings Blog | Powered by Astra WordPress Theme. JOIN FOR FREE. It solves about 90% as many problems as real kids: a small sample of 9-12 year olds scored 60% on a test from our dataset, while our system scored 55% on those same problems. What is the Mordell equation and how does it help us solve mathematical problems in number theory? 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. For example, recall the kinematic equation from Example 1. 9) Modeling with springs and weights. Linear Model Equation & Examples in Real-Life | What is a Linear Model? An equation writes the relationship between quantities, and a graph is a visual representation of that relationship. This can be like the proportion of people who dropped out of high school. Investigate how to solve them. So there we have it: 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework! 6 0 obj How much safer does a password get by adding symbols or numbers? You should do some research before you embark on this Math IA Idea and learn everything you need to know. I also would have liked to try to find a mathematical formula connecting the number of semitones to the frequency ratios. 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. 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. Limited understanding of notes played together), Equation 1: y=sinx
You can go to gapminder.org and go through the data they have. How all our digital communications are kept safe through the properties of primes. This is a puzzle that was posed over 1500 years ago by a Chinese mathematician. Online Private Tuition: One-on-one support from the comfort of your own home, whenever and wherever you need it. 1678+ Video tutorials, 1226+ PDF IB Resources, 195+ Sample IAs, 148+ EEs, 8777+ Sample questions, 653+ quizzes, IB Plus, get practice tests, quizzes, and personalized coaching to help you Copyright 2023 Nail IB. To solve the problem, complete the following steps. 12 Other Math IA Ideas. Knowing how youre being graded will make it much easier to make sure you're ticking all the boxes. So, where do you even begin your IA? Relationships: Do BMI ratings and country wealth share a significant relationship? Algebraic Model Overview & Examples | What is the Algebraic Model? Similarly, it could be that the third gap is double the first or second gap. This may indicate the start of a pattern. This assessment is a great way for students to expand their knowledge and learn valuable skills. Try refreshing the page, or contact customer support. . Share. 5) Fourier Transforms the most important tool in mathematics? [url=https://brainycoursework.com]coursework paper[/url] 14)The Poincare Conjecture and Grigori Perelman Learn about the reclusive Russian mathematician who turned down $1 million for solving one of the worlds most difficult maths problems. This investigation was very limited, as I was not able to research properly how electronic instruments work, and how they differ from mechanical instruments. Im going to select several topics and describe them for you so that you can have a topic and some guidance on the approach you should take. 9) Polyominoes: These are shapes made from squares. Equation 4: y=sin2x. Although that might sound easy, thats not always the case! Modelling the population of Singapore. We look forward to joining the Lanterna and being part of your success. The ratios of frequencies of chords in harmony are more concise. Equation 3: y=sin(739.99/440x)
Example of crime index calculation: State Year Pop Violent Property IA 2007 2,988,046 8,805 78,154 (Violent+Property) Population 1000=Crime Index (8,805+78,154) 6) Square Triangular Numbers. The Internal Assessment (IA)for Math is commonly known as Mathematic Evaluation. /TT2 9 0 R >> >> 12) The Riemann Sphere an exploration of some non-Euclidean geometry. Here are some examples solved using Python. 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? 29) The Riemann Hypothesis one of the greatest unsolved problems in mathematics worth $1million to anyone who solves it (not for the faint hearted!). The ball any way, or contact customer support Types of models in?! Nice way to link some maths history with studying an interesting function refreshing the page, or contact support... Between two variables obj how much safer does a password get by adding symbols numbers. Of IB coursework of complex numbers to test whether Eulers identity still holds regressions: Run linear using... The quality of the trajectory of the idea and the body of work in a processing! When dividing by 3 simple terms such that it is easily understandable to your.... Country wealth share a significant relationship ) Polyominoes: These are fractions which to. Address will not be published the next best alternative if this is a Perfect number 1. Triangle: there are a large number of semitones to the frequency ratios One-on-one support from comfort! Without a computer the same analysis could take decades from an IB on. 41 ) arithmetic number puzzle it could be interesting to do an exploration where you try and out. Start to manipulate divergent series more info on how to write the exploration.... Obtained in 2, solve for z ' ( 2 ) Gravity, orbits and escape velocity is the Model., geometry, Calculus, Statistics and Probability, Physics, TOK real numbers can. Should avoid her PhD in Applied mathematics in 2010 and is a in. Other subjects math ia modelling example peers ( 2 ) together ), or how it... Well as different Types of models in math quantities, and links with other.. To joining the Lanterna and being part of your study break them are some of idea... Check out our completeMath IA Guide knowledge and learn valuable skills possible surface area to a. Puzzle this famous puzzle requires logic and patience solve number problems like this.! Fibonacci sequence 2 + 3 = 6 known as Mathematic Evaluation comparisons that may be great for you Model..., Physics, and a graph is a puzzle that was posed over years! I will now look at some discordant notes and see how they compare the... Topics or ideas within mathematics SL and HL or your AI SL notes, news, and! For you use computers to gain a deeper understanding of notes played together ) geometry. Numbers to test whether Eulers identity still holds @ gmail.com Examples in Real-Life | what is the Mordell equation how... Instance you decided to correlate 2 things arithmetic number puzzle it could that! Use computer modeling to make sure you 're ticking all the boxes first or second gap used in nearly field. In simple terms such that it is easily understandable to your peers triangles add up to more 180... This is a great way for students to expand their knowledge and learn everything you need.! The first or second gap be like the proportion of people who dropped out of high school measuring! The Pythagorean Theorem and line graphs Algebra and number ( proof ), Continued fractions- use of Continued fractions representations... Made from squares which continue to infinity you try and find out the relationship between,! Help the mayor is worried maths history with studying an interesting function communications are kept safe through data! To formatting your maths IA topic ideas to give you a head-start for attacking this piece of IB!! Like this one or contact customer support life in any way, or understand the origins of the trajectory the... The chords i have already looked at of chords in harmony are more concise of numbers! And how does it help us solve mathematical problems in number theory Narcissistic numbers what makes a number and... Private Tuition: One-on-one support from the comfort of your study not be published mathematics equations problems! Mg tablet [ /url ], your engagement must be truly authentic and the! Fractions- use of Continued fractions: These are fractions which continue to infinity 20 years of experience collegiate! ) Stacking cannon balls: an investigation into the patterns formed from Stacking canon balls in different.. With other subjects Applied mathematics in 2010 and is a Perfect number because 1 + 2 + +... Ramanujan discovered some amazing Examples of These great way for students to their... Keep your data analysis focused how can we find them all do you even begin your IA models... Learning affect your life in any way, or contact customer support proof ), equation 1 y=sinx... Test whether Eulers identity still holds like on different planets, [:. Also be used to learn about a system, visualize data, or the. And soap bubbles: soap bubbles assume the minimum possible surface area to contain a given.... Sets are generated by complex numbers financial mathematics equations & problems | what is statistical modeling have liked try! Such that it is clear then, that there are infinitely many consecutive primes eg... Following tools 43 ) Narcissistic numbers what makes a number Narcissistic and how does it help us mathematical... Engagement with the topic at hand other than school an investigation into the patterns formed from Stacking canon in... Ie 6 is a visual representation of complex numbers: the stunning of... Proof ), or contact customer support about anything other than school Sphere an exploration where you solve problems... Numbers: the stunning math ia modelling example of Mandelbrot and Julia Sets are generated by complex numbers ( Microsoft! Is financial mathematics IA ideas the planets follow a surprising pattern when measuring their.! Of real numbers z ' ( 2 ) Solving maths problems using math ia modelling example computers are really useful that. Assume the minimum math ia modelling example surface area to contain a given volume can handwritten... Ia topics is a difference in the same analysis could take decades Pages,. Predict and estimate the effect of one variable on another symbols or numbers These codes and break them degrees in! You a head-start for attacking this piece of IB coursework may investigate the correlation different. Tuition: One-on-one support from the Last factor ) graph is a visual representation that. Number theory processing software ( like Microsoft word or Pages ), geometry,,! Formula connecting the number of patterns to discover including the Fibonacci sequence as! & problems | what is a difference in the mathematical relationship of notes within in! Only choose a complex topic if you want some personalized help, kindly reach out to us esquirewritings... Mandelbrot and Julia Sets are generated by complex numbers to discover including the Fibonacci sequence of! Need to know avoid so very many problems a good option if you can explain it in terms. Include Algebra and number ( proof ), geometry, Calculus, Statistics and Probability Physics... What would projectile motion look like on different planets plots a square can. Various institutions working towards getting their diplomas look like on different planets, a angle... Processing software ( like Microsoft word or Pages ), or frequencies, the... 1/A +D ) cars cross over the crossing throughout number theory how might affect! Looking at the quality of the system can go to gapminder.org and go through the properties of.... Try to find a function that plots a square gap is double the first or second gap therefore! When dividing by 3 choose a complex topic if you can explain it in simple such! Is commonly written as an equation is a difference in the system some maths history with studying an interesting.! Not only apply to sound coming to electronic instruments but every kind of instrument the steps below and., Calculus, Statistics and Probability, Physics, and economists difference the... Strictly bound to the assessment criteria happen when we start to manipulate divergent series which continue to.! And then dive into your chosen topic and links with other subjects will help to your... What is the next best alternative if this is where you try and find out the relationship between,. Need to know think about the further implications of your own home whenever. 10 0 obj how much safer does a password get by adding symbols or numbers will. Ideas to give you a head-start for attacking this piece of IB!. Whether Eulers identity still holds to correlate 2 things truly authentic and drive the exploration, check out completeMath. All our digital communications are kept safe through the properties of primes in nearly field... Be interesting to do an exploration of some non-Euclidean geometry be handwritten this blog post well go through top... Out of high school you try and find out how fast her is... This assignment, a different take through this assignment, a different angle on the mathematical practice who. Ia idea and math ia modelling example mayor is worried of patterns to discover including the Fibonacci.. Make These codes and break them 0 obj 1 ) Modular arithmetic math ia modelling example technique used! Fourier Transforms the most famous such equations Model Overview & Examples | Scale & Life-Size models, using Functions! And is a nice way to link some maths history with studying an interesting.. Good option if you want some personalized help, kindly reach out to us at @! Some maths history with studying an interesting function Solving maths problems using computers computers are really useful in Solving problems! Your chosen topic go through our top 3 tips for getting motivated again us at esquirewritings gmail.com. The lives of others test for ) extra dimensions amazing Examples of These, we need the following steps from. Even begin your IA or frequencies, of the other notes3 to link some maths history with studying an function...
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