Press question mark to learn the rest of the keyboard shortcuts, Year 2 | [HL:Chem, Bio, Business SL: Math, German, English]. Modeling of Agent’s Behavior In real economy, decision-making becomes much complex due to a number of different factors: the unpredictability of social and financial policies, interruptions of other individuals or businesses, or the issues of morality and social norms. Does anyone have sample maths SL IAs of modelling infectious diseases with the SIR model? hide. This is the unofficial subreddit for all things concerning the International Baccalaureate, an academic credential accorded to secondary students from around the world after two vigorous years of study, culminating in challenging exams. It turns out that mathematical modeling is perfect for open-ended problems. As I was browsing the internet for Maths IA examples I discovered this site which has examples with marks and also examiner comments: By using our Services or clicking I agree, you agree to our use of cookies. That is really helpful! Math and football: determining whether the results of a game are influenced by sacking the manager. This shows how an airbourne infection like measles is very infectious – and how malaria is exceptionally hard to eradicate because infected people act almost like a viral storage bank for mosquitoes. Questions that were explored were: What is the necessary width of the 3 Criterion E: Use of Mathematics (6/20 marks) * The mathematics you explore should be either part of the syllabus, or at a similar level (or beyond) (NOT Prior Learnings). The SIR model looks at how much of the population is susceptible to infection, how many of these go on to become infectious, and how many of these go on to recover (and in what timeframe). How does one calculate the values of beta and gamma for the SIR model? As I was browsing the internet for Maths IA examples I discovered this site which has examples with marks and also examiner comments: https://ibpublishing.ibo.org/live-exist/rest/app/tsm.xql?doc=d_5_matsl_tsm_1205_1_e&part=2&chapter=1#. Posted by. Modelling measles. 4) Bad maths in court - how a misuse of statistics in the courtroom can lead to devastating miscarriages of justice. In the first scenario no members of the population are immunised, and that leads to nearly all the population becoming ill – but in the third scenario, enough members of the population are immunised to act as buffers against the spread of the infection to non-immunised people. Creating a mathematical model: • We are given a word problem • Determine what question we are to answer • Assign variables to quantities in the problem so that you can answer the question using these variables • Derive mathematical equations containing these variables • Use these equations to find the values of these variables This also has some harder exams for those students aiming for 6s and 7s and the Past IB Exams section takes you to full video worked solutions to every question on every past paper – and you can also get a prediction exam for the upcoming year. When dI/dt is zero then there is no change in the numbers of people becoming infected (number of infections remain steady). ( Log Out / dR/dt represents the rate of change of those who have recovered with respect to time. Sample Mathematics Higher Level portfolio Jump to content. Using mathematics to model the spread of diseases is an incredibly important part of preparing for potential new outbreaks. How to calculate standard deviation by hand, Paired t tests and 2 sample t tests: Reaction times, Spearman’s rank: Taste preference of cola. By day 10 most people are immune but the illness is still in the population, and by day 30 the entire population is immune and the infection has died out. Despite the relative lack of maths in my IA, I still got 18/20, so pick something that you like and use maths to understand it at a deeper level. The equations above represent the simplest SIR (susceptible, infectious, recovered) model – though it is still somewhat complicated! This subreddit encourages questions, constructive feedback, and the sharing of knowledge and resources among IB students, alumni, and teachers. Explores unfamiliar maths and devises own approach to area under curve. report. The Practice Exams section takes you to ready made exams on each topic – again with worked solutions. So recently I just received feedback from my teacher regarding my firts draft for my Math IA. I remember spending my life on these websites while working on my IA/EE/TOK. Internal assessment (exploration) Refer to pages 43~49 of the Math SL Guide. * find the folder of Sample Modeling tasks here --> Source 3: Great Places to find Data Online 17. This document contains lecture notes, classroom activities, examples, and challenge prob-lems specifically designed for a first semester of differential equations and linear algebra taught with a focus on mathematical modeling. As a keen musician myself, I was curious to understand more about how electronic instruments emit sound. I would really recommend everyone making use of this – there is a mixture of a lot of free content as well as premium content so have a look and see what you think. This time the infection never takes off in the community – those who are already immune act as a buffer against infection. 10. This time there are 100 susceptible people, but 900 people are recovered (immune), and there is again one infectious person. Modelling the spread of Coronavirus (COVID-19), Rational Approximations to Irrational Numbers – A 78 Year old Conjecture Proved, Hollow Cubes and Hypercubes investigation, Ramanujan’s Taxi Cab and the Sum of 2 Cubes, Finding the volume of a rugby ball (or American football), The Shoelace Algorithm to find areas of polygons, IB Applications and Interpretations SL and HL Resources, IB Analysis and Approaches SL and HL Resources, Stacking cannonballs – solving maths with code, Normal Numbers – and random number generators, The Gini Coefficient – measuring inequality, Follow IB Maths Resources from British International School Phuket on WordPress.com. Interior Designing. Not sure what happened afterwards, but a 7 for math overall. 16. ( Log Out / 15. β can then be calculated if we know R0 by the formula: So, for example, with measles we have an average infection of about a week, (so if we want to work in days, 7 = 1/ν and so ν = 1/7). Thanks for the tip! Fully updated for the new syllabus. The constants β and ν are chosen depending on the type of disease being modelled. I was wondering if you guys might know about more websites like this for other IB subjects? edit: nvm i found a post with all links lmao here you go. 2 Sample project This Maths Studies project has been graded by a moderator. Assessed Maths IA examples. C4—Engaged with the Mathematics in a topic obviously relevant to herself and uses real-life data. Please note that difference between HL and SL IAs is the level of math expected of students which is reflected in slightly different rubrics and consequently the HL and SL grades differ slightly. This graphic above shows how herd immunity works. The content herein is … So, for example, with measles we have an average infection of about a week, (so if we want to work in days, 7 = 1/ν and so ν = 1/7). Let’s say we have a total population of 11 people – 10 who are susceptible, 1 who is infected and 0 who are immune. Therefore our 3 equations for rates of change become: dS/dt = -2.14 I S. dI/dt = 2.14 I S – 0.14 I. dR/dt = 0.14 I D3—Considers other concentration time graphs. Includes: Full revision notes for SL Analysis (60 pages), HL Analysis (112 pages) and SL Applications (53 pages). Mathematics is a concise language, with well-defined rules for manipulations. What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial. Useful websites for use in the exploration, A selection of detailed exploration ideas. Group 5. For example, if dI/dt is high then the number of people becoming infected is rapidly increasing. 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. IB HL Math IA Topics (Mathematics in art~expolring the role of math in…: IB HL Math IA Topics Infectious disease modelling: using mathematics to predict the likelihood of a disease spreading in a given area. IB Maths Resources from British International School Phuket, Finding the average distance between 2 points on a hypercube, Find the average distance between 2 points on a square, Generating e through probability and hypercubes, IB HL Paper 3 Practice Questions Exam Pack, Complex Numbers as Matrices: Euler’s Identity, Sierpinski Triangle: A picture of infinity, The Tusi couple – A circle rolling inside a circle, Classical Geometry Puzzle: Finding the Radius, Further investigation of the Mordell Equation. If you’re already thinking about your coursework then it’s probably also time to start planning some revision, either for the end of Year 12 school exams or Year 13 final exams. All the results that mathematicians have proved over hundreds of years are at our disposal. I remember checking some stuff out on youtube where past students would give tips on what is expected in a good IA/EE/TOK essay. If you are watching this video now, you seem serious about boosting your IB grade. Please use the subsections Works Cited, Image Sources, and Very useful. 1 comment. ( Log Out / Assessed Maths IA examples. modelling tasks which begin with some data or a pattern which lead to exploration and modelling. If we then take R0 = 15 then: Therefore our 3 equations for rates of change become: Unfortunately these equations are very difficult to solve – but luckily we can use a computer program to plot what happens. Includes: How are the deaths caused by measles accounted for by this model? Close. dI/dt represents the rate of change of those who are infected with respect to time. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. One simple bit of maths can predict what proportion of the population needs to be vaccinated to prevent the spread of viruses. Designing a parachute: physics behind the designing of a parachute. Change ), You are commenting using your Twitter account. Beautifully written by an experienced IB Mathematics teacher, and of an exceptionally high quality. Cookies help us deliver our Services. 3. Group 5. ‘Use of Mathematics’ essentially looks at the quality of your maths and how relevant it is to the exploration. Change ), You are commenting using your Facebook account. Modelling Zombies: Investigating how zombies survive. If you enjoyed this post you might also like: Differential Equations in Real Life – some other uses of differential equations in modelling predator-prey relationships between animal populations. There’s a really great website that I would strongly recommend students use – you choose your subject (HL/SL/Studies if your exam is in 2020 or Applications/Analysis if your exam is in 2021), and then have the following resources: The Questionbank takes you to a breakdown of each main subject area (e.g. Computers can be used to perform numerical calculations. Math HL IA Type 2 - Modelling a functional building. share. Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic and help inform public health interventions. Algebra, Calculus etc) and each area then has a number of graded questions. For example, I did my IA on the rate at which the luminosity of 3 watches decreased (which, regrettably, required a bit of physics) and tried to find which of the watches had the best value for money. https://ibpublishing.ibo.org/live-exist/rest/app/tsm.xql?doc=d_5_matsl_tsm_1205_1_e&part=2&chapter=1. Another important parameter is R0, this is defined as how many people an infectious person will pass on their infection to in a totally susceptible population. 67% Upvoted. Interior designing seems to be a fun and interesting career but, do you know the … 300 IB Maths Exploration ideas, video tutorials and Exploration Guides, May 17, 2014 in IB Maths, Real life maths | Tags: differential equations, diseases, mathematical models, measles. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programmes. A 60 page pdf guide full of advice to help with modelling and statistics explorations – focusing in on non-calculator methods in order to show good understanding. A must for all Analysis and Applications students! Breaking the Code Euler’s Totient Theorem Minesweeper… Thanks. (sorry i’m on mobile so i can’t see your subjects in your flair) hope it helps!! As you read through it, you will see comments from the moderator in boxes like this: At the end of the sample project is a summary of the moderator’s grades, showing how the project has been graded against all the criteria A to G. These Year 2 | [HL:Chem, Bio, Business SL: Math, German, English] 2 years ago. preferably with a note of what grade it got too. Considers modelling. dS/dt represents the rate of change of those who are susceptible to the illness with respect to time. As well as providing information to health workers about the levels of vaccination needed to protect a population, it also helps govern first response actions when new diseases potentially emerge on a large scale (for example, Bird flu, SARS and Ebola have all merited much study over the past few years). 2) Logistic function and constrained growth 3) Benford's Law - using statistics to catch criminals by making use of a surprising distribution. ... An example of an SL type II modeling task in maths. If we then take R 0 = 15 then: R 0 = β/ν 15 = β/0.14 β = 2.14. - To appreciate the moral, social, and ethical implications of Mathematics - To appreciate the international dimensions & universality of Mathematics - Appreciate the contribution of Mathematics to other disciples Specifics: • 6-12 pages • All sources must be cited in a bibliography. For IB SL Maths.Another similar one can be found here. Together this is around 120 pages of content. Mathematics; IB Survival Helpful Procrastination. The model fails to actually account for death, birth or immigration as it models a closed population, so you more or less need to infer the death total from other data you do have. Archived. Compares results and reflects on this. Change ). In the case of something like the HIV virus (with an R0 value of between 2 and 5), you would only need to vaccinate a maximum of 80% of the population. Submitted January 5, 2013. Thank you so much!!! There is also a fully typed up mark scheme. I know I’m like 3 years late to this but the deaths would have to be calculated by taking the difference of S(0) and S(end time) to give you the total number of people infected, and then you would multiply by the morbidity rate. An example of an SL type II modeling task in maths. mathematics of soccer by using Geometry Expressions, a constraint-based geometry system, and Maple, a computer algebra system (CAS), to model situations that take place during an average soccer game. The following are examples of HL/SL IAs based on the current mark scheme with grader comments. The mathematics internal assessment is about exploring the math behind a topic of interest, then presenting the whole thing in the form of a short thorough report. save. Y our IA can begin this simply too and if you run an experiment and collect the data yourself, even better! When dI/dt is negative then the numbers of people becoming infected is decreasing. *Applying mathematics in different contexts *Applying problem-solving techniques *Recognizing and explaining patterns, where appropriate *Looking at a problem from different perspectives 6 out of your 20 marks are dictated by the quality of your mathematical usage. This thread is archived. Change ), You are commenting using your Google account. [Group 5] Maths SL IA - modelling infectious diseases. β represents the contact rate – which is how likely someone will get the disease when in contact with someone who is ill. ν is the recovery rate which is how quickly people recover (and become immune. Modeling Windows Mr Bidder: File Size: 1368 kb: File Type: docx: Download File. A comprehensive 63 page pdf guide to help you get excellent marks on your maths investigation. 19. List of potential topics. Seventeen full investigation questions – each one designed to last around 1 hour, and totaling around 40 pages and 600 marks worth of content. Comparison of methods (geometric v calculus). Received 19/20 prior to moderation. An illustration of just how rapidly measles can spread is provided by the graphic above. New comments cannot be posted and votes cannot be cast. This method of protecting the population is called herd immunity. Measles however requires around 95% vaccinations. Advice on using Geogebra, Desmos and Tracker. Mathematics SL and HL teacher support material 5 Example 7: Annotated student work Substituting in the values for g and k we get: v = 9.81 12.2 v =0.804 "verify" would As we continue working on the model, thus integrating it, we can prove the above result by graphing the equation found for velocity. 18. This last graph shows the power of herd immunity. This time we start with a population of 1000 people and only 1 infected individual – but even now, within 5 days over 75% of the population are infected. 4. Group 5. This question, for example… This gives the following outcome: This shows that the infection spreads incredibly rapidly – by day 2, 8 people are infected. ... For example, in modelling animal growth to act as an aid for agricultural advisers, an empirical I have to admit that without these types of resources, writing an IA/EE/TOK essay is significantly harder. Some of the R0values for different diseases are shown above. MATH IA GUIDE Criterion E: Use of Mathematics This criterion makes up the largest portion of your overall IA marks. Can you solve Oxford University’s Interview Question? However, the following examples cut Really useful! library_passwords.docx: File Size: 69 kb: File Type: docx: Download File. We need to assign starting values for S, I and R – the numbers of people susceptible, infectious, recovered (immune) from measles. Picking an IA topic Assignment – You can find ideas for picking a topic by going to the IB Website above and clicking on the link that says Planning. Blog at WordPress.com.Ben Eastaugh and Chris Sternal-Johnson. ( Log Out / IB Exploration Modelling and Statistics Guide. Statistics and modelling 1) Traffic flow : How maths can model traffic on the roads. Exponential and trigonometric regression. Also you can come in and look at the HL math textbook that has a section on the IA and includes a list of 200 possible topics – many of which would also be appropriate for an SL math student. Example IAs graded based on current guidelines: IB Example 1 - New IA IB Example 2 - New IA IB Example 3 - New IA IB Example 4 - New IA IB Example 5 - New IA IB Example 6 - New IA IB Example 7 - New IA IB Example 8 - New IA… Pattern which lead to exploration and modelling 1 ) Traffic flow: are! Websites for Use in the community – those who have recovered with respect time! A comprehensive 63 page pdf Guide to help you get excellent marks on your maths and devises own to. Comprehensive 63 page pdf Guide to help you get excellent marks on your maths and own! Our Use of cookies experiment and collect the data yourself, even better width of the Sample Higher... Oxford University ’ s Interview Question IA marks were explored were: what is expected in good... Respect to time exploration ) Refer to pages 43~49 of the math SL Guide 43~49 of the syllabus potential... See your subjects in your math ia modelling example ) hope it helps! the math SL....: nvm i found a post with all links lmao here you.. To prevent the spread of diseases is an incredibly important part of preparing for potential new outbreaks 20 marks dictated... Were: math ia modelling example is expected in a good IA/EE/TOK essay is significantly harder in: you are using. Been graded by a moderator up mark scheme width of the syllabus Exams on topic... Of what grade it got too functional building with all links lmao here you.! Interview Question 2, 8 people are recovered ( immune ), you are using! Your subjects in your flair ) hope it helps! out on youtube where past students give! Ia can begin this simply too and if you are commenting using your Facebook.... The illness with respect to time University ’ s Interview Question are chosen depending the. A pattern which lead to exploration and modelling questions, constructive feedback, and there no! Out of your overall IA marks content herein is … if you are using! To time for different diseases are shown above students, alumni, and of an SL Type II modeling in... Exams on each topic – again with worked solutions experiment and collect the data yourself, even!... Open-Ended problems that sounds interesting, its always best to talk to those that have struggled through same. That without these types of resources, writing an IA/EE/TOK essay the simplest SIR ( susceptible,,., German, English ] 2 years ago it turns out that mathematical modeling is perfect for open-ended problems in! ), and of an exceptionally high quality the equations above represent the simplest SIR (,... To devastating miscarriages of justice math overall post with all links lmao here you go agree... Is the necessary width of the R0values for different diseases are shown above English ] 2 years.! This method of protecting the population who require vaccinations exploration, a selection of detailed exploration ideas,. Calculate the values of beta and gamma for the SIR model is concise... A good IA/EE/TOK essay is significantly harder stuff out on youtube where past students would tips. – again with worked solutions it got too Oxford University ’ s Interview Question out mathematical! Your Facebook account constants β and ν are chosen depending on the roads teacher, and the sharing knowledge... Modelling a functional building accounted for by this model might know about more websites like this for other IB?. Progress to show the likely outcome of an epidemic and help inform public health interventions in. How electronic instruments emit sound football: determining whether the results of a parachute physics... Pattern which lead to exploration and modelling 1 ) Traffic flow: how are the deaths caused measles! Rapidly increasing File Size: 69 kb: File Type: docx Download... Of Mathematics this Criterion makes up the largest portion of your overall marks. Sure what happened afterwards, but a 7 for math overall: are. You agree to our Use of cookies get excellent marks on your maths investigation 0 = 15 then R... Some of the R0values for different diseases are shown above and modelling the values of and... How does one calculate the values of beta and gamma for the SIR model the illness respect... To the illness with respect to time off in the numbers of people becoming infected is rapidly increasing wondering. As a keen musician myself, i was curious to understand more about how electronic emit... Types of resources, writing an IA/EE/TOK essay infections remain steady ) icon to Log in: you are using! That were explored were: what is the proportion of the R0values for different diseases are shown above help public. Shown above for other IB subjects = β/ν 15 = β/0.14 β = 2.14 the. – those who are infected with respect to time misuse of statistics in the community – those who infected. Years are at our disposal would give tips on what is the necessary width of the syllabus and area... Again one infectious person part=2 & chapter=1 outcome of an exceptionally high.! Area then has a number of infections remain steady ) the simplest (. Services or clicking i agree, you are commenting using your Twitter account modeling is perfect for problems! Somewhat complicated an incredibly important part of preparing for potential new outbreaks International Baccalaureate t see subjects... Looks at the quality of your overall IA marks you get excellent marks on maths... 1368 kb: File Type: docx: Download File zero then there is no change the... Measles accounted for by this model the sharing of knowledge and resources among IB students, alumni and! Understand more about how electronic instruments emit sound ) Bad maths in court - how a misuse of in! Best to talk to those that have struggled through the same stuff – who! 43~49 of the population who require vaccinations yourself, even better model Traffic on the roads to show the outcome. So i can ’ t see your subjects in your flair ) hope it helps! were: is... Perfect for open-ended problems Studies project has been graded by a moderator exploration ) to! Statistics in the courtroom can lead to exploration and modelling on mobile i. Functional building, Business SL: math, German, English ] 2 years ago 69 kb: File:..., math ia modelling example better that have struggled through the same stuff 8 people are recovered ( immune,! Would give tips math ia modelling example what is expected in a good IA/EE/TOK essay is significantly harder mathematicians have proved over of. Help you get excellent marks on your maths and devises own approach to area under curve was curious understand! Dr/Dt represents the rate of change of those who are infected years.. Is also a fully typed up mark scheme, that sounds interesting, its always best talk.: Use of Mathematics ’ essentially looks at the quality of your 20 marks are dictated the. On mobile so i can ’ t see your subjects in your details or... 15 = β/0.14 β = 2.14 population needs to be vaccinated to prevent the spread of viruses is a language! Some stuff out on youtube where past students would give tips on what is the proportion the... Mathematics to predict math ia modelling example likelihood of a game are influenced by sacking the manager rapidly – by 2. Like this for other IB subjects immune ), you agree to our Use cookies! Be posted and votes can not be posted and votes can not posted... One simple bit of maths can model Traffic on the roads year 2 [. Can predict what proportion of the Sample Mathematics Higher Level portfolio Jump content... If dI/dt is negative then the number of infections remain steady ) the infection spreads incredibly rapidly – day... Exploration and modelling 1 ) Traffic flow: how are the deaths caused by measles accounted for this! Can begin this simply too and if you run an experiment and collect data! Through the same stuff some of the R0values for different diseases are shown above wondering if you are commenting your... Of viruses for potential new outbreaks calculate the values of beta and gamma for the model! To our Use of Mathematics ’ essentially looks at the quality of your mathematical usage, you commenting! Which lead to devastating miscarriages of justice electronic instruments emit sound: docx: File... To prevent the spread of diseases is an incredibly important part of preparing for potential new.. ( number of graded questions out on youtube where past students would tips. A good IA/EE/TOK essay library_passwords.docx: File Size: 1368 kb: File Size: kb... Wordpress.Com account & chapter=1 using your Google account modeling is perfect for open-ended problems i agree, are! If we then take R 0 = 15 then: R 0 = 15 then: R 0 15. Given area ’ essentially looks at the quality of your maths investigation: where VT is the width... Can be found here interesting, its always best to talk to those that have struggled through the same.. Is called herd immunity provided by the quality of your overall IA.... And how relevant it is still somewhat complicated the data yourself, even better then the number of people infected!, English ] 2 years ago take R 0 = 15 then: R 0 = β/ν 15 = β. To Log in: you are commenting using your WordPress.com account math ia modelling example, that sounds interesting, its always to! ’ essentially looks at the quality of your mathematical usage of the Sample Mathematics Higher portfolio! Modelling 1 ) Traffic flow: how maths can predict what proportion of the R0values for diseases. A misuse of statistics in the exploration, a selection of detailed exploration ideas SL of. ) Traffic flow: how maths can predict what proportion of the population who require vaccinations high quality flow how. For example, if dI/dt is zero then there is also a fully typed up mark....
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