Transcript for:
IB Maths IA Guide

hi everyone i'm ashley um in case you haven't been here before then um i graduated from the ib four years ago and since then i have been tutoring people in the ib and on this channel then i make videos about the ib with just some tips that helped me um achieve the marks that i did um and also just talk a little bit about my experience studying medicine at the moment so obviously today we're going to be chatting about the maths ia and a step-by-step guide to getting a seven so in this video we're going to be talking about what actually is the mass ia how does it differ from other maths assessments um breaking down the marking criteria so really trying to interpret them and therefore create a checklist of things that you need to include in your maths ia to score in those higher spans uh and then finally steps of actually writing a math ia so how to select a topic how to plan your ia how to actually go about writing it and then finally at the end i have annotated my own ia in terms of the marking criteria that i'm addressing in each section and i know that there are a lot of example maths is online that you can just google but i thought that me sitting down and going through it with all of you and actually explaining why i included the things that i did and what marking criteria i was trying to hit with each of the particular paragraphs and components that i included might be a little bit more helpful than just seeing this random blank really long ia that feels kind of um unattainable like it's just you can't really see the structure from that so hopefully from reading through sort of my example and talking through my thoughts um during it then it can kind of give you a sense of how you might be able to translate um some of those same reflections and structures to your own uh investigation so before we start all of that um i just wanted to start this video with a little bit of a pause um to say that the maths ia is very challenging i think for a lot of people in the ib math to begin with is challenging is a challenging subject for a lot of people um i know it was for me i've mentioned in my previous video about ib maths that it was my the subject that i struggled the most with and i think with the ia especially then a lot of people before doing the ib they've never done something like the ia before so those two things combined are kind of a recipe for struggle and difficulties so i suppose i know that a lot of people will probably come across this video when they're googling for help because they're having trouble with their ia and i just wanted to kind of offer a bit of empathy and commiseration in the fact that i know that i shared a lot of stress tears when i was completing my ia and the fact that it is a really difficult process but just because you're having difficulties with your i ia doesn't mean that it's going to turn out terribly or that you're not going to do well or that you're not going to get the marks that you need i would say most people have a difficult time with the massa particularly and so don't feel like if you're struggling with it that it's somehow a reflection on your ability to complete it or your maths ability overall nothing like that a lot of this i'm going to be kind of speaking from a student's perspective so because i graduated four years ago i graduated on the old syllabus before there was aa and ai but the course that i did is basically the equivalent of maths aasl now so that's kind of the context that i'm speaking from um for the marking criteria component i am going to be bringing in a little bit of my experience from tutoring math students um but especially towards the end when i'm talking about the process of completing the maths ia i'm most mostly just going to be speaking subjectively from my own experience of the trials and tribulations of the massa some of the mistakes that i made that hopefully you can avoid um and yeah overall just kind of view this hopefully um as you know almost like i'm an older student at your school and i've completed the ia and i just want to pass on a little bit of the knowledge that i've gained along the way in the hopes that it might be able to help you through the journey a little bit more i've also i'm doing this in a little bit of a different format than usual because i think that it's going to be quite a long video considering that i've i wanted to include everything in one video um so that you know anytime you have a question about the maths ia there's something in this video that you can use to address it so i hope that you can kind of come back here as a resource um but because of that um i hope that you know you'll kind of settle down get somewhere cozy grab a cup of tea so that we can just kind of have a well one-way chat about the maths ia um rather than it being i hope you don't view this as kind of like a stressful video look at like the immense amount of work that i have to do we'll look at this like crazy massage that like she presented at the end like hopefully we can just kind of talk through how the like what the math diet is and hopefully you can take away some kind of helpful points for when you do your own mass ia which i'm sure will be amazing as well so here we go what is the maths ia so the math ia for those who are maybe a bit newer to the ib then ia stands for internal assessment which all the internal assessments mean that they are assessments which are marked by your teachers but then those marks are moderated by the ib markers so the maths i a specifically it accounts for 20 of your final math grade but other 80 comes from the final exams and although it is called the math ia it's also sometimes called the maths exploration so which i think is kind of a good term to summarize what it actually is so in order to explain what actually is the mass ia then i thought a good way to do it would be just to contrast it with the context that most of us have for maths which is maths exams or maths homework questions so for maths homework questions if we set the scene you don't choose the question you just open up your textbook there's a question there you answer it or you open up your exam paper you don't get to choose your questions it would be amazing if you did but you don't get to choose the question in contrast with the maths ia you do get to choose your questions you get to choose your topic any random topic you want some economics theory something about mountains i don't know any random topic and try to find questions about that topic that interests you you know why how does the slope of the mountain affect the speed of skiers going down it or how does the i don't know the height of the plant or the maybe the surface area of the leaf of a plant influence its height or something like i i don't know these are just random uh topics that i'm coming up with but with basically the thing is that you almost take on the role of the creator of a test where you're the one who's choosing the questions that you're going to ask yourself so that's great because it gives you a lot of freedom and you don't have to answer questions that you don't want to answer that you think are going to be too difficult that are going to be out of your scope but also obviously it's a bit tricky because it means that now you actually have to figure out what questions there are to ask but the idea is that you find an area that you're interested in and you figure out what questions are kind of interesting about that and you try to use maths to answer those questions so the other big difference between the maths ia and maths exams is that in maths exams there's one correct answer and there are there's one or only a few acceptable methods to answer that question or to get to that answer so if you look at the marking criteria for a maths exam then you'll see that there are a few marks allotted for specific uh points in the working or in your working that they're looking to see and then one mark at the end for attaining the correct answer so because of this setup it means that you don't have to justify anything that you're doing within the exam they know that this question is on a specific thing like they know for example that it's an independent probability question so if they see you put down the independent probability formula they're not going to be shocked and they don't need any justification as to why you did that they're just like oh it's an independent probability question so they put down the independent probability formula okay tick that's one mark you know whereas in the maths ia because everyone is answering different questions and there are multiple different methods which you could use to answer the same question then it means that you have to actually justify why you're doing what you're doing because there isn't a template model of working out that you're supposed to be following you have to explain oh i've decided to use an independent probability because this is what an independent probability is and i can see that that applies to this situation because and because that is the case then i'm going to use this formula which can be applied to independent probabilities so you know there's a lot more i suppose explanation and reflection that's required in the maths ia because you have to think why am i actually doing what i'm doing that's going to be a recurring theme throughout this video why am i doing what i'm doing next um last two sort of concepts is the fact that the maths exam obviously you have a limited amount of time and so there's sort of a limited depth that you can get into a topic within a single question um whereas in the maths ia the ib suggests that you spend around 30 hours on your maths ia so that amounts to many many pages of working and a lot of time doing math so it means that you can really get in deep to a topic and you have the ability to sort of have all of your results build on one another as you go through these multiple pages of working and justification and then the other the final point is that for maths exam questions obviously you only have limited tools available to you whereas with the maths ia everything is fair game you can in fact you're encouraged to google and research different types of maths different methods different um you obviously have to do a lot of research about the topic that you're going to be talking about to make sure that you're getting that correct but you know like you can research aspects of maths which are about the same difficulty as the course but you know maybe they haven't been specifically covered and if they're going to help you in your investigation then you're encouraged to use the internet to research the answers or research how to use those new methods um you can also use excel often we're working with quite large numbers or you know quite a few numbers in our math ias because they're longer than you know your typical exam question so a lot of people find excel helpful um and then yeah sometimes it involves photos and sometimes you're gathering your own data so you need equipment to gather that in order to yeah get the data that you're going to be analyzing your in your ia so that's kind of an overview of the maths ia and i hope that you're seeing a little bit at the moment some of the parallels between the maths ia and some of the other ias that you have either done or will do particularly the science ias so the whole purpose of a science ia is to find some question in the world that you would be interested in investigating and using the scientific method to try and find the answer to that question in the same way the maths ia asks you to look at the world try to find a question that you're interested in answering and use maths as a tool to try to answer that question so both of them are trying to get you to use your own initiative to find something that you're interested in looking at and investigating about the world and they're both trying to get you to use the tools of their respective subjects as a means of investigating the subject or investigating the topic or yeah investigating the topic that you're looking to investigate in your ia so i think that was helpful for me to kind of think about the mindset of the markers and also similar my science teacher always used to tell me don't worry about the day when you're doing your experiment because it doesn't matter if you get bad results bad results or like results that don't match your hypothesis in some ways that's even better because it gives you so much to reflect on in your discussion and i would say the same thing for your maths ia obviously if you can't even get started with your maths then that doesn't give you much to reflect on but if you're having difficulties and challenges and things that you're not understanding and you need to change your method halfway through then that's amazing for your maths ia because that's all builds into the reflection and the justification of what you're doing to say oh i tried this approach but it didn't work so then i shifted to this you know so that's kind of a similarity as well between the mafia and the science ias is that the markers are far more concerned with your thinking how you're justifying the things that you're doing as opposed to being concerned with you getting the correct answer or one specific answer that they're looking for so that's an overview of the maths ia so now we're going to have a little look at the marking criteria so this is where it gets quite um dense so i mean i would encourage you if you have the marking criteria with you to whip it out otherwise i'll have it on the screen so that's fine um but i think it's important before you kind of jump into the maths ia but also any ia this is a good um i suppose exercise is to almost summarize the marking criteria and figure out from what they're saying there the checklist of things that you have to include in your ia in order to sort of tick off and make it undeniable to the marker that you've satisfied those marking criteria so i'm going to go through each of these marking criteria one by one and consider just that thing what's the checklist of things i need to do to satisfy this criteria and how and where in my ia will will i include this so it's one thing to know what to do but it's another thing to actually know where that fits within the broad scheme of your ia so that's what we're going to do so starting out with criterion a communication so there's four marks allotted to this criterion the first adjective so on the left-hand side here i have sort of summarized the key terms or the key words from the marking criteria which is normally written out in full sentences but these are just the key terms and then on the right here i have kind of the interpretation of what they mean by these words and this is based on my own perspective but also what my um teacher told us when we were doing the ia and she was kind of explaining to us what the ia was and how to achieve these marking criteria so first up we have coherently and logically developed and what this basically means is that one section in your ia has to lead to the next one so when i'm thinking about the ia i tend to think of it as almost the story of how you got from asking your initial question and choosing your initial topic all the way to achieving the aim of your investigation and answering that overarching question which you've set yourself so it should be this almost linear narrative of all of your reflections all of your strategies all of the work that you did along this journey of the investigation so because of that it should naturally flow in terms of the fact that if you've changed strategy or if you're suddenly tr including some new working or you're including some new context then that should all link logically in terms of how it came to you when you were doing the maths investigation so normally it would if you're introducing like a new concept it would be because some previous approach or some previous concept was insufficient to answer the question or you were having some trouble with that method so then you would say oh i was having trouble with this method that like you know for x y and z reason therefore i changed approach to this so it's okay to sort of acknowledge almost like the talk essay you can acknowledge the changes and the shifts in your thinking and approaches as you're going through in order to create this smooth transition between everything that's happening there should also be a smooth transition between the different types of uh presentation of information in your ia so a smooth transition between your written out paragraphs your mathematical notation such as you know just formula and numbers and things like that um and also the other presentations so tables graphs all of that kind of stuff um i can't tell you how many ias i've read and marked which they just they're going along i'm reading their paragraph i'm like okay yep this makes sense and then all of a sudden there's this random table in the middle of the page or there's this random graph and i'm like what is this graph i have no idea what your what this is referring to so um please for the sake of your markers it obviously makes sense to you because it's your ia but you should always reference the figure number of your tables and your graphs in your paragraph so say you know i then you know i then uh carried out this formula insert formula here the results of which can be found in figure two that just makes it so much that's the kind of coherence that they're talking about here in the fact that i can see where everything that you've written down fits into your broader investigation having a random unlabeled table that isn't referenced back to the paragraph is not very coherent um so that's kind of one aspect to it also when it comes to your introduction then there are kind of just two structural things that you have to include in your introduction in order to make it logically developed so um first you start out with your rationale of like why you chose the topic that you chose so there you're going to insert a little bit of your personal engagement why was this topic personally engaging for you why is it an interesting topic in general for the world and then you're going to talk about your aim so within this topic what is the overarching question that you want to answer so that's coherent coherent and logically developed and then we have well organized so there's going to be an introduction that's this one here you're going to have a conclusion at the end and then in between you're going to have a body you don't have to have a heading that says body but that's just like the bulk of your essay in between so that's just like you should have headings for introduction and conclusion and then in the body i would suggest headings which outline the kind of steps that you're doing in your process at each stage you'll kind of see them um when i go show my ia at the end i think you can get like an example of how you might use those headings next concise pretty self-explanatory don't include information that isn't directly relevant or if there's if there are things that you can put into your appendices because they're very lengthy then put them into your appendices so the kind of the deal with appendices is that your ia should be able to be understood on its own without the appendices but if you have sort of extra information that you can or want to include then you can put that in your appendices so often you'll put like the full working out or the full um sort of results in your appendices but you'll put a sample equation or a summarized table of the results in your actual ia obviously this all depends on how much data you're processing and how much space you have in your ia um but that's kind of the deal with appendices so if there's anything that you want anything in your sort of like paragraphs that you want understood by the marker you can't just say oh like i did this c appendix one if it's something that's critical to their understanding of your method then you have to put that in your actual ia but if it's something that you know is not maybe it's like the intermediate step in between this step and like the next thing that you're going to do then you can put it in the appendix because it's not critical to them understanding your method have a little drink yes so that's the appendices um so that can help with being concise if you need it and then complete so this just means that you have properly explained all of the steps that you've done so you've not just sort of jumped from one thing and then all of a sudden have all of these new numbers and you haven't explained how you've gotten there and then also how you have met how all of your steps have met the ia's aim so that overarching question that you were trying to answer at the beginning is your ia complete in the sense that everything that you've included in the ia is working towards answering that overarching question so that is the communication criterion a oh i also have y here because this is like a little running theme of why are you doing the things that you're doing you're doing them in order to answer your ia's aim so everything should come with a justification of i am doing this why because i want to meet my ia's aim which is insert here so criterion a now we have criterion b which is mathematical presentation and there are three marks awarded for this criterion the first is for appropriate mathematical language so this includes a couple of things firstly using correct notation and terminology so basically don't call something that's not a normal distribution a normal distribution if it's not an independent probability don't call it an independent probability so basically using those technical terms correctly is what they're talking about here and same with notation just like you know using like function notation correctly or using like sine or cos or something like writing that out correctly is basically what they're saying um always define your variables so appropriate mathematical language means that every time you introduce a new variable you have to say what that variable represents so again this is like a very common thing i even had it in my ias at first before i got feedback from my teacher where i just had like random x's and y's which i just introduced because that was the formula without explaining oh the x is this thing in my you know investigation and the why is this thing in my investigation so you need to define what your variables actually mean otherwise it's super confusing to read um and then finally oh yes when you're if you're typing your ia up in word then you have to whenever you're typing out um numbers or like working then you have to use the insert equation uh function on word you can't just type it out with your keyboard like two and then x written like a normal x you have to use that insert function tool so that you get like two and then like the mathematical x that's just a case for everything it's a formatting thing it looks very nice when you do it but it is a bit of a pain so just keep that in mind so then also you have to define key terms so in addition to not using terms like normal distribution standard deviation independent independent probabilities in addition to using them correctly you also have to define them each time you use them so you'll see this in my ia later if you're working with a normal distribution you have to give a definition and say a normal distribution is this before you start talking about it so that's very different from like say a maths exam and then you have to explain how that definition applies in the context of your ia so say okay a normal distribution is this thing in this thing these are the characteristics of a normal distribution and here that here is how those characteristics are present in the context of my investigation or you know this is what standard deviation is this is what standard deviation means in the context of my specific investigation so you always have to context give the kind of dictionary definition and then give the contextualized definition and then the final point for this marking criteria is multiple forms of expression that's mathematical expression where appropriate so this includes things like using different formulas diagrams tables charts models like all of these different ways to communicate your mathematical exploration um if you're using tables or charts or diagrams and you have to correctly label them with titles at the top so figure one and then with a descriptive title and then also with access titles if you have a graph um but it should be noted here that full marks can be achieved with only one form of representation if it's appropriate so the big thing about these different multiple forms of expression is that you have to choose the form of expression which is appropriate for the type of information that you're trying to express so i can't think of an example right now but um let's say like the difference between a line graph versus a histogram they're working with they're sort of appropriate for different contexts so you have to look at the data that you have and think what's the most appropriate way for me to present this and does this visual representation actually add anything to my communication or would it be easier for me just to explain my findings in words that's kind of what they mean by appropriate like is this the most appropriate visual representation of your findings so that's present mathematical presentation so criterion b then we have criterion c which is personal engagement um and i think this is the one which gets made fun of most by people but i think it is actually pretty important so obviously the part which gets made fun of that like oh i have to show my personal engagement is this first part here so engage with the exploration specifically have your aim address a personal interest and this is addressed in your rationale so these are just easy marks have some personal story have some personal connection with the ia topic hopefully if it's a topic that you're curious about there's a reason why you're curious about it so you'll just naturally have this personal engagement so it's or personal interest so there's you know just remember to include that in your ia um but that's only one component of personal engagement the part that a lot of people don't remember is that there's this part as well which is the fact that they're assessing for personal engagement based on whether you've made your ia your own so this means thinking independently and creatively so this could come out in your topic in your aim or in the methods that you're using so just the fact that you've kind of chosen a kind of interesting uh perspective on a topic or you're kind of you can tell by the way that you're justifying the things that you're doing that it's you who came up with this method to answer these questions and it's you who is interested in asking these questions to begin with um similarly presenting mathematical ideas in your own way if you've explained the concepts if they can tell that you've explained the concepts in your own words that's why it's so important to give the like the dictionary definition and then give like the definition of things in context of your ia and then also when you're justifying what you're doing again show that you actually understand what you're doing by the the fact that they can tell that you've written this in your own words and that you've created your own visual representation so you've created your own graphs based on this and you're able to explain and unpack those graphs um also like for my ia then i collected the numbers that i was actually using within the ia um and so that also showed personal engagement um because to summarize i did it on bowling so i like bowled a whole bunch of games and i collected my scores and i was analyzing my scores within my ia um and so that obviously shows personal engagement because it's kind of creative like i needed to go out and i needed to play all of these games myself and obviously it's mine so there's like that personal attachment to it so if you're collecting your own data then that's also quite a good way to show your personal engagement with the topic because it's not just like some random numbers that you found online it's like your own thing that you've created um and then yes the big note about personal engagement and the reason why i think it shouldn't be overlooked as a marketing criteria or think like oh that's just easy marks to get is the fact that there has to be evidence of your personal engagement in your actual ia so it's not enough for your personal engagement to be obvious to your teacher obviously through talking with your teacher they're going to understand that you've come up with these ideas and that you're interested in it because of this this miss but your personal engagement has to come through in your ia itself so to this external moderator who's never met you who doesn't know you who doesn't know your interests and doesn't realize the like cool quirky ways that you figured out to like solve the issues in your maths ia so that's why you have to really kind of make it obvious throughout that like oh i thought about this i considered these ideas however i realized that no instead i needed to do this and like then i approached it in this way so kind of make it clear when you have i suppose had this almost creative or independent thinking where you've needed to address some sort of issue or you've almost preemptively recognized an issue and therefore designed your massa in a particular way needs to be in your ia you can't just chat about it with your teacher and be like ah personally engaged because even though your teacher is marking it then the external moderator is moderating those marks so that's personal engagement full marks and then criterion d reflection and criterion d and i'll just look forward criterion e is use of mathematics you'll see that there's some overlap there in that if you reflect effectively you're also going to be demonstrating your use of mathematics and your understanding of mathematics so just go back to reflection reflection boils down to two major questions again why why did you do what you did so in a lot of maths ias that i read then people will just chuck in formulas and be like oh i was like looking at this and this was my aim and the data and all of a sudden we have a you know a sequences and series formula and i'm like why are we using sql why did you choose sequences in series as your method what are the variables here i don't understand what's going on so you need to kind of before you do anything have a little justification to be like you know i was thinking about this issue and i saw that sequences in series would be the best way to approach it because you know based on this website that i've read then i predict that there's going to be you know an arithmetic sequence and therefore i'm going to use sequences in series you know whatever the the method is so you need to justify what everything that you have written down you need to have some sort of justification as to why you're trying to do that um also what did you learn from it so this isn't just like i learned to love maths or i learned that you know probability isn't that hard no it's more like what did you learn based on the implications of your results looking at how you used maths and what you were able to produce through it how does that change your conception of this topic how does it change your conception of that overarching question that you were like asking at the beginning have you has it challenged your thinking in any way that's kind of the two major questions so i've broken down just some like smaller ones that you can ask yourself throughout so again explain what you want how what you're doing links to the isa and that's why you did what you did discuss the strengths and limitations of the approaches that you used again why are you doing it because it's a strong approach hopefully compare different mathematical approaches to explain why you chose the one that you did so it's okay to say like i considered this other approach however it wouldn't be appropriate for x y and z reason um how did you decide based on preceding steps or findings what to do next so kind of as you're going through the investigation did your i suppose anticipated approach or what you were planning on doing change at all based on the fact based on some of the findings that you got initially in like the initial steps of your investigation uh what are the implications of your results in your chosen context so that was what i was talking about before like how does the um how do the results that you found impact your the context that you set up in your introduction and you know how does that change your perspective on the world and what should we do as a result of your results or your findings and then comment on what you've learned same as what we were talking about before um note yes reflection throughout is required for the top marks so in comparison to a science ia where you kind of have the big discussion at the end where you know initially you're just objectively presenting everything and then it's at the end when you're like i'm a terrible scientist i made all of these mistakes this is why my results are terrible all of that sort of stuff you kind of leave it all to the end in the math ia then you want to incorporate that throughout your um exploration to say you know like i chose to do this step i understand that there are these limitations associated that with that because i am working with this type of data for example however i chose to proceed because you know of this other reason so kind of acknowledge the limitations of what you're doing throughout and continue to reflect on why you're doing what you're doing basically answer all of these questions as you're doing things again it's kind of showing your reflections and almost your mental journey throughout the ia um and i put a little notebook here because um i think it's quite a good idea to keep either a physical notebook or just a word document which has these kinds of reflections i'll show you later how i like annotated my um documents with these reflections um in order to keep track of them because it's really easy to forget these later and you'd be surprised at how easy it is to forget why you did what you did like you'll open the document the next day and be like what are these numbers what was i doing i don't understand any of these formulas and then you'll be like on a mad goose chase through your documents to try and connect the dots of like why where these random numbers came from so always as you're doing things and it'll help you so much when you're writing your ia later if you even just write out in like super colloquial terms why you're doing what you're doing you can translate that into formal late formal language later but just having that like explanation of where your head was at when you were doing those particular things helps so much when you're writing the actual ia so that's criterion d and now criterion e is the use of mathematics so it has three aspects to it firstly the extent to which you use mathematics in the ia and what this is really asking is is this actually a math ia so a lot of times um people in their initial suggestion of topics will come up with things that are actually physics or economics ias with a little bit of maths in them so they're actually more so to do with other subjects in the ib um i wouldn't worry too much about whether you're doing this when you're trying to select a topic just because your teacher will pull you up on it very quickly if you ask like oh is this a good topic they'll be like that's not a mass ia so i wouldn't be too worried about deciphering it yourself but just be kind of aware that that's an issue you want the focus to be using maths to explore these things not just using subjects which use maths as a tool sometimes like economics or chemistry or physics or something else um the math should be relevant and correct so um when they mean when they say relevant then what they're really looking for is math that is used in a is the type of maths used suitable for the way it is used i didn't phrase that very well but like given the context that you're trying to use the maths in is the type of maths that you've used relevant or appropriate kind of like what i was saying if you are trying to calculate a percentage you're not going to randomly use a probability formula or maybe a more realistic example if you're working with let's say conditional probabilities you're not going to use an independent probability formula so that's what they kind of mean by like suitable or even um [Music] let's say if you have a um if you have a a data set which has a lot of outliers you would use the median rather than the mean in most contexts because of those outliers so it would be more suitable to use the median so if you use the mean if you had some justification for it then it would be fine but if you didn't have any justification then it maybe wouldn't be considered suitable so that's what they kind of mean by relevant and then also correct is very interesting because the maths can be correct even if occasional minor errors occur if they don't detract from the flow of mathematics or lead to an unreasonable outcome so unlike in a maths exam where if you make a mistake in your maths then you'll usually get a mark taken off for it in that cya they're not really concerned with like really small algebraic errors or anything like that obviously do your best to not do them but overall they're more concerned with your general methodology your reasoning behind that methodology and whether your outcomes whether you're able to assess personally if the outcomes that you get are reasonable for the context in which you're performing them like does it for like when it whenever you're doing questions and then it's like if you're trying to split up people into a group into groups and then your answer is something like oh you get 1.23 people per group and then you have to say okay well that might be the answer but i'm only going to put one person in each group because i'm not going to cut a person so that i can get 0.23 you know of a person um so that's what it kind of means in terms of like unreasonable outcomes so yeah your maths i'll say this afterwards but demonstrated a thorough knowledge and understanding throughout the work so that basically means that you have to include all of your working you've explained again explained and justified your approach so you can see how this kind of um has a symbiotic relationship with the reflection marking criteria even though only three marks are allotted for reflection then a lot of things that you might think are reflection help to support the marker seeing your use of mathematics um because you've justified everything based on how you reflected and realized that you needed to use this particular method um yeah and so the correct answer is not enough you must show all of the steps you took to attain it so you can't have random numbers coming out of nowhere you have to show all of your steps and what i was going to say is that you have to use i don't know if i put this here but overall the maths that you use has to be commensurate with the course that's kind of a phrase that is thrown around um and i wouldn't be too concerned about it because again your teacher will pull you up pretty quickly if the math that you're using is too simple um for the course and they'll say you know you have to include some more complex maths but if you're using things which you found in your textbook then in general it's going to be commensurate with the course and also you don't have to based on this the math that you use doesn't have to be that complicated um sometimes i know for me i wasn't expecting to use such complicated maths but like later down the line i got myself into a pickle with the ia and so i had to use this formula which wasn't from the course and i had to research it and everything um and so then i had to use some more challenging maths but overall it's not necessary based on these marking criteria to choose the most challenging maths from the um from the course because in the ia what they're really more so assessing assessing is your justification and your understanding of applying maths in context and your ability your creativity to come up with a question and an aim so yeah i suppose that's just to kind of say don't pick a topic that based on the fact that you think it will need really hard maths to um analyze or you know don't purposely make the maths in your ia really hard i always kind of say to my students that the type of maths that you use should be guided by the questions that you're trying to answer so whatever maths is helpful whatever tools whether that's excel whether that's your graphing calculator whether that's you know some other mathematical tool that you have at your disposal whatever helps you answer the questions then that's what you should use so don't sort of purposefully try to manipulate the maths so that it's harder because you won't gain any extra marks for that alone so that's the end of our marking criteria overall and oh yeah the other thing i wanted to say is if we go back up here then we can see that the use of mathematics accounts for six of the marks in the ia overall all of the others account for much more so even if you got very low marks in your use of mathematics if you manage to make your working coherent and logical if you use the correct sort of form like formatting and presentation and you gave all of the definitions of the mathematical terms that you were using if you showed personal interest and also had a kind of interesting approach to it and if you made sure that you reflected on what you were doing throughout then you would still get a really great mark overall even if you got a low mark in the use of mathematics so i think a lot of people get kind of tied up or worried about like i don't know how to answer this mathematical question like i don't know what i'm doing like if this is too hard but even if you're struggling with those things as long as you make sure that you're doing well on sort of the almost like the ribbon on top like the packaging of the maths that you're doing then you can still get a really good mark for your ia so that's just kind of like obviously you're focusing on your mathematics throughout because it's a maths ia but there's all of this other sort of reflection and communication and presentation marks that you can also pick up um that can kind of save you if your maths is getting um a little bit dicey so that's kind of the end of the objective part of this video where i'm just going through like what it is and the marking criteria and all of that so now i'm going to have a bit of a chat of just sort of like my whole process of going through the ia and from start to finish how i figured out my topic all the way to writing the final thing um so we're going to start with selecting your ia topic which i know is a big issue for a lot of people because it's really difficult to just choose a topic like a random topic and figure out which one is good and what's going to make a good ia and all of these things so i kind of have these steps here which is what i did for my maths ia so the first one was to find a topic and the way that i did this is that i kind of used google and a little bit of my imagination in two ways so the first way was to pick a topic from the textbook so let's say sequences in series or probability or statistics or functions or whatever and just put in real life afterwards or applications something like that and then it will come up with a whole bunch of results of how sequins and series are applied in real life and that can give you like a whole bunch of random topics obviously if you're particularly interested in a topic in your textbook this could be a good approach however it's a bit tricky because you'll just get a whole bunch of random subject matter and so it might be harder you'll be sifting through a lot of results before you wind you find one that you have personal engagement with so that's one approach um the other one is just to say to type in mathematics or maths in and then insert topic that you're already interested in here so i put in ballet but like i would just do this you know rapid fire i'd be like maths of food maths of um i don't know buildings maths of dance maths of uh i don't know knitting maths of juggling you know like i would just have all of these things that i was interested in and then i would just put maths of blank and then insert the topic that i was interested in and then that's kind of a really good litmus test to see is there actually any maths behind these topics because sometimes i would type in let's say like maths or food and then there would be like no legit sources that would pop up and i'd be like ah okay this probably there's probably no maths ia to be found under this topic um whereas like you can kind of see there if i put in mathematics of ballet then a kind of official looking pdf comes up with the mathematical modeling of ballet and so that could kind of just as a quick sort of i guess test of whether this is a topic that i should investigate more that would tell me okay well there is at least some mathematics someone somewhere has already looked at mathematics in ballet so there might be something also for me to look out there so the big thing that i see students doing when they're googling for their msia is they'll say like they figure out a topic that they are interested in and then instead of putting like mathematics in ballet they'll just say they'll just type into google like ballet maths ia and that will usually not give you very good results because despite me saying oh there's lots of like maths eyes out there obviously like there's this infinite number of topics and only in comparison a relatively small number of ias available online so chances are you're not going to find an ia on that topic um and i think it just is then disheartening because you're like oh i can't find it like this is a bad topic or whatever um when it's not it's actually good because then it means that it's kind of original um and also even if you did find an ia that was on that topic then it might not really be the angle that you're interested in looking at um like i know for i don't know just for like probability topics just because my ia was on probability so i always think of that then like there's even if someone else my final a like i said was on the probability of bowling even if i found someone else who was doing bowling they might have done like assessed bowling from the perspective of functions or from the perspective of sequences and series or um i don't know some other topic right so even if i found a mathemate that was on bowling then like it might influence my thinking too much and make me start to go down the same track as that person who did the mass ia so i think it's just easier to stick to like you'll get better results if you just stick to googling like general mathematical like mathematics applications or like specific topic applications in real life um rather than trying to base your ia off some other students ia so that's how i kind of chose my topic um i'll show you one of my one of my failed ia topics was on juggling so that's how i found that one so the mathematics of juggling is what i typed into google i found all these results um and then my final i found my same my final ia topic the same way i was like the mathematics in bowling and then i was like i'm kind of interested in doing probability probability in bowling okay is that there okay and then i found some results um so yeah you can do that um so after you find your topic then you want to choose an overarching question that you're trying to answer about that topic so with my ia for example my overarching topic would be bowling and then my overarching question would be like obviously we'll get to this later but i would be like okay i'm interested in doing probability what specific probabilities am i interested in looking at in bowling is it the probability that i win a game is it the probability that i score above a certain score is it the probability of you know like there's an infinite number of questions that you can answer around probability in bowling so you have to kind of pick the one that you're the most interested in and then step three is to create a list of the smaller questions you would need to answer this to you would need to answer to address your aim so if my aim is to figure out the probability of me scoring above a certain score in a game of bowling then i would need to figure out my probability so my little list of smaller questions is what is my probability of getting a strike what's my probability of getting a spare what's my probability of getting you know a nine or a eight or whatever the other scores are it's been a while since i've done my ia um you know and maybe i would want to and then start to think about like other ways that you could expand it so you know if you know my first probability is you know i get above a certain score once maybe like another question that i could ask is what's the probability that i get above that certain score twice you know something like that so you know just kind of start brainstorming these smaller questions that you could ask almost like what are the steps that you would have to take what are the smaller questions that you would have to answer to answer that overarching question and that is kind of your personal engagement of figuring out your approach to answering that big question and then step four is describe theoretically how you would approach answering these questions those smaller questions what calculations would you use what formula formulas would you have to invoke how does it apply to your ia's context and then ask your teacher for feedback based on this so this was kind of how my school went about structuring our ia prep was that we had to submit these ia proposals which were basically this we had to you know basically have a step-by-step guide to our ia already with a structure before we'd even started writing it to kind of say okay these are all of my subheadings with like the smaller questions that i need to answer and then i'm going to use this formula i'm going to use the independent probability formula i'm going to use you know i'm going to create a probability distribution and then i'm going to analyze it i predict that it's going to be a normal distribution so i'm going to be able to analyze it this way you know all of these kinds of things so this is the really critical step because this is going to show you whether this is a viable topic for your ia and what you're looking out for is whether there's enough depth there to be able to base an entire ia off it and also whether the questions that you're answering are kind of logical and again link back to the aim or the overarching question that you're trying to answer so assess that overarching question is that overarching question actually interesting or actually something that you want to answer and then do each of the smaller questions actually link back to it and then finally do you actually have an idea of how you would go about answering those smaller questions because sometimes you ask these questions and you're like i don't even know where i would start with this and even after reflecting on it for a long time you're like i still don't know so maybe don't do an ia topic where you have big blank spaces under these potential questions where you have no idea where to start in terms of the working and that's why i kind of said ask your teacher for feedback based on this because i think this is a good time at least at my school this was like the first round of feedback that we got was on these um proposals so we could get like the green light or not to start ria because it kind of gives your teacher a good overview of like could this potentially work as an ia topic and what are your plans going forward so that's selecting your ia topic and also just want to mention here that you will go through this process with lots of potential ia topics i kind of mentioned that i had like rapid fire googling of like maths of food mass of water maths of all these things all of these things um and in that process you'll reject some um but also your teacher will reject others when you thought you were on the right track so i'll share afterwards about my failed ia um but yeah like oftentimes you'll think like oh this is an amazing topic i'm so excited to do it like this is so great and then you'll share with your teacher and they'll be like no that's not a very good topic try again and you'll be like but i just spent hours researching this and i drafted up this whole proposal and i was so excited about it like what am i supposed to do now um and you just have to kind of let it go like try not to get too attached to any ia topics before your teacher has approved them because um at the time it can really feel like a setback like i just spent like five hours researching this why did they reject my topic but when you think about the 30 hours and often more than 30 hours that you're dedicating to your ia overall then to get a not so great topic rejected at the start is actually going to make your life way easier earlier so your teacher is really doing your kindness if they reject your topic if they don't think that it's suitable um so don't worry it's part of the process most people have been there either rejecting lots of topics themselves or having their teacher reject their topics um so you know above all listen to your teachers feedback and trust their judgment because they have seen a lot more successful and unsuccessful ias than you have um and so they know what the iaib wants and they can kind of see into the future what issues you're going to run in with run into with an ia before you can see that so i would just kind of trust what they say and like it's kind of like this so i'm going to share my unsuitable ia topic and this is one at the time where i was like this is a great topic like this is so amazing like i'm so excited to do this and i shared it to my teacher and she was like that's not a good topic um and at the time i couldn't understand why but now after tutoring for a few years and looking back on it i'm like i'm so glad i didn't do that topic because it just would have been so challenging and hard to make a good ia out of that i was happy that i didn't do it so the main issues with it was that there was insufficient depth so i wouldn't have been able to make enough content out of the ia and there was also no clear aim so i'll just share my proposal with you now so this was my initial proposal um for the mathematics of juggling um so i was into juggling at the time and so i thought oh the maths of juggling that's bit that's a bit fun um and yeah so i talked about like my personal engagement with it and then um when i searched up the maths of juggling like i got all of this cool notation to do with it and it's like the side swap notation or space-time diagrams and there's all this stuff to do with like the gradient of the space-time diagram and like the space between your hands and like the distance here and the height of it and so i thought oh wow this is really great i can um i can think about it from the perspective of like me improving my juggling um and therefore like using these diagrams to analyze how fast you can throw the ball and hence how high you should throw it like basically you know when you're starting to juggle like you learn at first and you're super slow throwing the balls but then eventually you can like speed up um and so like if you need to throw the balls slower then you need to throw them higher because you need to give yourself more time to have the ball in the air so that you can catch it more slowly um so i was like oh i'll figure out how long i want like one beat to be like one like change of the ball change of the ball change of the ball um i'll use the diagram to figure out the speed and i'll sub it into this and i'll you know like do all these things um but the issue was that that only has one answer if i figure out how fast i want one beat to be i find the speed from the space time diagram i sub it into this formula and then i graph a parabola that's probably max like two pages of working out so that's not long enough or deep enough or complex enough for a maths ia and it took me like i probably spent like 10 hours researching and trying to understand these juggling diagrams but it just wasn't going to work as an ia and also the aim overall just doesn't make sense because the whole purpose of juggling is that it's like a performance it's like aesthetic whatever you know it's an art form so analyzing like how high you can throw the ball so that you can juggle properly it doesn't really make sense because what you should really be practicing is to be able to juggle belt better so you have you know like you want to be able to have variety in how high you throw the ball and the different patterns that you throw the ball because that's the whole purpose of juggling is to develop new skills and to be able to juggle in different patterns and in different speeds so you can entertain an audience so overall just the aim didn't make sense like within the context of juggling and then also the questions that i was like these smaller steps or smaller questions that i was asking myself they they wouldn't have provided me with enough uh content for the ia um i've also had these other ideas of like oh i could look at the like sequences and series like there's like something with the notation like oh i could find the nth term and i could view him take myself to make sure that i'm throwing the ball at the correct height to get it to be the correct speed and therefore for it to land at the same point as this theoretical diagram it's not adding anything to the like exploration mathematically like i'm kind of testing something with a video but i'm not adding any further mathematical exploration to my ia by doing that so you can see that that doesn't really add anything um yeah my applications yeah that doesn't matter that yeah it doesn't add anything to the exploration so i hope through sharing my failed proposal at an ia that firstly it makes you feel a little bit better if you have had an ia rejected um because we've all been through it and you know like you you'll find a better topic and you know your teacher will approve that and you're gonna go forward and it's gonna be great um even better i'm sure like if i had done an eye on this it would have been terrible um but also like i hope you can kind of see some of the mistakes that i made and hopefully not make them yourself so when you're writing out like this plan it looks like i've got like all of this research research yes all of these diagrams yes it's so mathematical but when it comes down to the actual maps i was going to do four steps is all i had that's not enough for an ia so when you write out your steps then think about that think is this enough to fill up an ia and then yeah like really reflect on your aim be like is this relevant to the context that i'm talking about no it's not so yeah trying to make an aim which is actually relevant to the context and the questions like that you want to answer overall so that's my failed ia um so going back to ias now once you've selected your topic you actually have to write your ia um so this is just going to be me kind of talking through how i approached the actual writing process so at this point when i had my actual um uh what's the word proposal for my bowling ia then i had like a very detailed structure um and everything actually i will just stop sharing for a moment and i will open i'll just get that open so i forgot to open this beforehand um so for my juggling one oh sorry for my bowling one after my failed juggling one um then i had a new proposal that was actually acceptable um yes so this was my bowling proposal um so you can see that i have you know specific personal engagement there like i did for juggling um and then i have applications like i did for juggling but you can see i have a much more detailed plan of what i'm going to do and there's actually a lot of content here so probability of winning against a professional bowler i have all of these steps of like how i'm going to create this score how i'm going to collect this data i'm going to collect this data from online i'm going to create histograms to find the probability distributions and i'm going to um like i'm going to i think that they're going to be distributed normally but even if they're not then i'm going to work with the central limit theorem so like i'm already predicting like what issues i could run into with my ia and figuring them out i'm going to find the average and standard deviation i'm then going to use a t-test to work out the probability that i'm going to beat the professional so you can see this is already so much more expensive than my initial um application or proposal um and then i'm going to investigate the probability of winning a competition the probability of me doing a perfect game where i score 300 or an extension i propose a potential extension for my maths i so you'll see when i actually go through my real mass ia that i didn't end up doing all of these i stopped here because this ended up this and this ended up being enough content for my whole ia um but you can see that there was so much more to dig into in terms of this topic compared to the original juggling ia which didn't have much going for it so yes that was like my new proposal so if you're figuring out a topic and your proposal looks something like this and you are already able to anticipate some of the issues you might have and you're you know like having this like really good reasoning as to why you would do the things that you do then like that's probably a pretty good sign that the ia will turn out pretty well and doing all of this planning beforehand is going to make it so much easier when you're writing your ia because you're basically just following instructions and steps from your past self and you just have to go through the motions you're like the robot controlled by your past self whereas if you don't have a plan then you're just kind of like making it up as you go along and it's a bit scary because you don't know what you're going to do next in your ia um so that is i done my proposal so then in terms of actually writing the ia i found that it was really easy to get lost in the maths itself um and so i found that it was the easiest way to kind of keep everything clear in my mind and not get confused about what i was doing was to write each step so the steps that i had in my proposal write them out on a separate document so here i was finding the probability of a frame score probability of explanation spreadsheet blah blah blah blah all of this um and what i found this helped with as well so it kept things separate but also it helped me to finish one section and just move on rather than constantly finessing the first section so i find when everything's in a big document together then i always feel like i want to re-read the first page before i keep going with anything else and that means that the introduction and like the first page gets super good but then all of the other pages are kind of like not so good and like you know you never make much progress that way because you're constantly like re-reading the things you've already done rather than producing new content so i found that separating it out was a good way to kind of approach that writing process also on these individual documents you can kind of see here i'm using the comment section in word to write out those little notes like justifying why i'm doing what i'm doing and this is going to be good for later when you have to explain these things and also when you are talking about challenges and having to reflect on those things later you're going to have these um like this whole history of things you had considered with regards to this particular portion of your maths ia so that's very helpful as well to kind of keep track of those things throughout because again like i said before you're going to forget them later um once you've actually completed the math you're going to be like oh that was easy and then you like you think oh how do i actually figure that out initially i don't know so that's writing that ia and then also on the individual um pages if you're using excel um then at least for me i ended up with these massive excel spreadsheets that were really hard to navigate and initially i gave these titles to the tables that i had in them that i thought were so intuitive but by the time i had like 10 or 12 different massive tables of results then the titles were no longer intuitive because they were all like probability of bowling frame score probability of bowling pin score or something like that and i'm like what's the difference between a pin score and a frame score i don't know past actually confusing so the way that what helped me um was to insert screenshots of my excel spreadsheets into the uh individual documents below the explanations to which they correspond so here is like my explanation of like the different roles and like the different probabilities and then here is the part of my excel spreadsheet where i actually did those calculations so for me obviously in my final written out documents then i didn't include any of these screenshots it was more so just for personal reference to help me kind of navigate those spreadsheets and not get lost in terms of like what am i actually looking at right now so after i had completed those individual documents i had written out drafts which for me is just like code for like this is like the final like compiled document now rather than just sort of like individual steps um so piece by piece i would copy and paste the individual explanations into that central document and that meant that yeah as i was putting them in then i could kind of slowly assess as i was copying and pasting them whether i needed to add like little linking sentences to make them make sense and all flow together as a cohesive document so that's what i did i kind of put the first couple into this first draft and then the next couple into the second draft and then the third and then like you know i slowly built it up until it was all of them and then i got feedback from my teacher on this sixth draft so i just kind of wanted to have this included in here to show that um i think i kind of mentioned something similar in my 45 video but when you're presenting your ia drafts for feedback then you always want to present the very best of what you have to give because if you present a draft with a whole bunch of mistakes that you could fix yourself then your teacher is only going to highlight those most obvious mistakes because they're going to be like oh this i this ia has like lots of issues in it let's just fix like the most glaring ones to begin with um and so you won't get the really valuable feedback because you're only getting feedback on the things that you yourself could have already picked up and you won't know that anything else is wrong like the more complex stuff like structural things or there's an issue with your reflection here or that piece of math isn't quite right like they're also going to be looking at like oh you didn't define any of these variables there's a random graph in the middle of your page it's like what are you doing you know so make sure that you've really finessed your draft to the best of your ability before you give it to your teacher for feedback because for the massa especially i think there's like i got such a valuable feedback even when i thought what i was submitting was like i was like this is the best thing i could ever make it i got heaps of feedback from my teacher to be like change this change that you need to include this here i was like wow there was so much more that i needed to do so definitely do your best before you give it to a teacher so that is the end of like the little explanation of how i went about everything so now this is the final section where i'm just going to be going through my ia which i've annotated in terms of the marking criteria um which will hopefully like i said here give you an idea of like how to structure an ia and also how to incorporate the components of the marking criteria into an ia so let's do that so here is my ia probability in bowling um and also the unannotated version of this was also already on my uh the google drive that i have in the uh description linked in the description of all of my videos but i'll also upload after this my this annotated version and then also the powerpoint that i just went through so this is my massage and you see i've kind of color coded my highlighting in terms of the different marking criteria so um mathematical understanding that's criterion e i don't know why i called it that um communication reflection personal engagement mathematical presentation so um the introduction so i kind of start with this um with my rationale why have i chosen bowling which has to begin with what is bowling so i've kind of contextualized it within the fact that you know for teens a bowling alley is a fun place to relax with friends um they're most most concerned with enjoying the activity than the actual scores however when playing competitively one is constantly tracking one's own scores and those of one's competitors i experienced this when in this when my primary school offered weekly bowling as a specialized sport personal engagement yes um to crawl up the leaderboard i learnt which balls to use how to hold them and the right way to to bowl as i learned i watched my average scores slowly increase as much as bowling is a fun sport for teenagers and families it is also a skillful game played seriously at an international level to win one not only has to improve one's own scores but also outperform the other competitors on the day as explained by the world bowling organization bowling is an easy game to play tough sport to master so again i'm giving context my rationale as to why i'm choosing bowling why is bowling a significant topic to look at it's because it's not only interesting to me because i play you know i've bowled in the past and i enjoyed it but also because it's this serious international competition and therefore my findings would have relevance to these international athletes reflecting on my first hand experience of improvement through of improvement through training made me consider what chance i not having bowled regularly for many years would now have of winning against a professional bowler this is the aim of my um of my maths ia the central question of what probability what i have now and that's because based on my plan before whether i would be able to beat a professional bowler was kind of the final step i would need to calculate all of these other probabilities my probabilities their probabilities beforehand but the final step and the culminating question that was all for the purpose of answering was would i be able to beat a professional bowler or what's the probability of me being a professional bowler also notice the fact that i'm using the word reflecting on my first hand experience so i'm really drawing attention to the fact that firstly that it's personal engagement because it's first-hand experience but also i'm reflecting reflection reflecting give me those marks for reflection please that's what i'm doing there so the aim of this investigation is to examine the probability of obtaining certain scores depending on one skill level and hence beating an opponent in this case the professional bowler and then this is kind of like what i need to figure out obtaining certain stores depending on skill level in order to figure out this final question this particular aspect was chosen as this investigation's results could be used by aspiring and competing professionals alike to determine their probability of success in a certain competition this could inform not only the competitions they enter but also help with goal setting for training programs so you can see that i'm asking i'm kind of reflecting on why have i chosen this aim in particular why would this be helpful given the context of bowling that i've explained up here so that is my introduction i've given my rationale and i've also presented my aim and i've also done a little bit of reflection sprinkled in so we now have to start the investigation now we can't jump into an investigation about bowling without me first explaining the basics of bowling because you can't just assume that the marker your teacher but also the ib moderator is going to know anything about the topic that you're talking about and so you need to include the research and the information which is going to be necessary for them to understand the maths that you're doing later in your investigation so for me that was uh you know establishing what is ten pin bowling i'm going to be using the term bowling to refer to 10 pin bowling throughout this investigation i explained the scoring system with 10 frames how you get a point knock down how you get extra point bonuses if you get a strike and a spare and all of these things i just explained like the score existing system of bowling because that's necessary to be able to understand my maths later so that is that um then i move on to figuring out the probability of single role scores so you can see for the communication criteria then i'm really like it's logical and coherent because you can see clearly how i'm moving through the structure of my ia i started with my introduction i first i then established the how bowling is scored i then established the probability of single role scores i then do the probability of frame rolls i then do the probability of frame scores and then do the probability of frame scores with scoring bonuses and then eventually we do the probability of game scores and then the skewness of probability distribution and then normalizing the distribution through a transformation and then the probability of winning against a professional bowler so you can see i like built up really logically from individual bowls to individual frames to an individual game to winning against a professional bowler so that's just kind of like an idea when you're thinking about how to use your headings try to think about how you can move from sort of the small compo the smallest components and like the equations which are associated with that and then try like move to bringing the big pieces of your ia together in order to create sort of a logical structure um so for the single role scores um [Music] what is important here i won't go through everything um you can see i've kind of underlined here again i'm using those key terms of i realized on reflection like i was first considering this like so really highlighting the fact that i'm reflecting on this process um here we have an example of the like mathematical presentation probability distributions list the probability that each possible value for a variable occurs so i'm giving just like a textbook definition of probability um again textbook definition on here probabilities are independent when the probability of one events occurrence doesn't affect the probability of another events occurrence and then i've also explained it in the context of bowling here so uh that is kind of that section there so yeah i've kind of just to kind of look at this first section what i'm aiming to do is find the probability of single roll scores i don't just jump to this section here and say well single roll scores are independent probabilities therefore i'm going to use this formula and therefore i'm going to calculate them no instead i started by reflecting and saying well at first i thought that it would be a simple process of taking my game scores and creating a probability distribution however i soon realized that um in the latter part of the exploration where i was calculating the probability of being a professional competitor that would require the probability of extreme scores which were unlikely to be attained in the small experimental sample so therefore i'll skip through a few things here but therefore the investigation will begin by breaking down bowling to its most basic level the individual bowls so i'm like going through well i considered doing it this way however after a bit of reflection i realized that i can't do it that way so therefore i'm going to approach it from the probability of single role scores and then i jump into my actual um working out so um we have things here look i'm introducing my variables there i'm just in brackets um i'm explaining the context of the equations before i introduce them so i'm not just chucking this random equation in and being like oh i'm using independent probabilities here's a you know here's a formula i'm saying i'm introducing it saying the theory the probability of knocking down a certain number of pins in r1 roll one could be calculated using this formula and then i define all of the variables in the formula um here you can kind of see some um what's the word reflection on saying and on accounting for um how the theoretical probability doesn't account for how a player's ability makes the probability of some scores higher than other than others in orders that reflect that the pins often knock down other pins in their vicinity making certain scores more likely than others for these reasons using theoretical independent probabilities would be inappropriate so again i'm kind of that's that kind of weighing up the strengths and limitations of alternate approaches then you know it kind of shows that i took that time to reflect on oh like could i just use the theoretical probabilities and then i was like no i can't and this is why so again just analyzing why you can or cannot do something or why you did do something a particular way you can see here my referencing to a figure so therefore experimental probabilities were used to form a probability distribution figure one and then here figure one with a descriptive title and column headings there so it's all really easily identifiable and my table links in with my paragraphs as well um rather than just like imagine if i just chucked this in here without this title and without this reference here even if i chucked it in with probability distribution of row one i've just come out of this means that there were effectively 11 frames in these four games and then all of a sudden you have a a table saying probability distribution of row one like that doesn't make very much sense so like that's why it's so important to have these figure um titles and then referencing those in your body paragraphs where it's relevant um this also contributes to the marking criteria of having multiple forms of mathematical expression because it's a probability distribution and obviously this is a very succinct way to present that like probability information so you would get marks for being concise there as well so then probability of frame rolls you can see i have another table another probability distribution here so i get another multiple forms of mathematical expression i then have without scoring bonuses um again you can see that i'm using um my brackets here in order to reference the appendix and also notice the fact that i say the um like the probabilities you they were calculated as displayed in figure one so i have some sample calculations here and the full calculations are in appendix one so they don't need to see my calculations for every single frame score in on in order to understand my method so that's why i can put those full calculations in my appendix but i still need to include a table of sample calculations so they can understand what my method was to begin with um moving down here uh this can be helpful as well to include sentences like this like thus frames and score domains affected similarly were addressed together so almost like it's kind of like a meta um discussion of your ia to say like this is how i'm going to be organizing my iaa just so that you're prepared for it and can like follow easily uh you can see i have more like sort of maths things here where i was working out the probability formulas and justifying why they were the case um and here i have some like reflection on one may think that because of the tense frame extra role bonus it would require a different formula however within this domain the only two options are a strike followed by two bowls or a spare blah blah blah blah there was a whole justification for it but again it's like this was my initial assumption however like this is not the case because of these things and that's why i've done it why have you done the things that you've done because of this reflection um again labeling my variables um okay so this was a big issue in my maths ia that i wanted to talk about so i had this issue here where i finished my calculations for the probability of getting any of my um frame scores so like within a bowling frame in 10 pin bowling the maximum score you can get is 10 so that's f10 and then i think this was the i don't remember what this was this part here it's been so long since i've done my ia obviously um oh no sorry sorry this is the the maximum score that you can get within a frame in bowling is 30 and that's by three strikes in a row and then these frames within 10 pin bowling then you have three goes like 10 frames where you're trying to bowl down the pins so like you have 20 bowls overall two for each frame that's what this is talking about so it's kind of like the probability of scoring zero for frame one is 0.0122 so that's what this whole table is um the issue that i found was that probabilities um at least um [Music] probabilities of like events which are what's the word again um [Music] opposite to one another like if one thing occurs the other thing doesn't occur ah complementary probabilities that's what i'm searching for the word that i was searching for the sum of complementary probabilities is supposed to be one because the probability that an event occurs and the probability that um that an event doesn't occur should be a hundred percent because you've covered both options there however when i added up my probabilities for this table then i got 1.112 and 1.089 so like basically i didn't i didn't satisfy this test that i had set out for myself where i was like oh i'm going to check whether my probabilities are correct because if they're correct then they should all add to one and then they didn't add to one and i was like oh this is very bad very very bad um but after a while i figured out that they were actually ratios that i had calculated like the fact that they didn't all add to one meant that they necessarily weren't probabilities um and so then i figured out they were just um values in the distribution which were like sort of ratios in ratio to one another and so if i divided them all by a certain value then that would get the probability um obviously me explaining it now doesn't make much sense and to this day i'm kind of like i don't know if that was legitimately correct maths this is what i was saying before about that criterion e where like whether your maths is correct they care more about your justification and why you're doing the things that you're doing than whether it's like 100 correct so like i might have made a small error here i'm not totally sure my teacher didn't say anything about it so i don't know but i might have made a small error here but it didn't drastically disrupt the flow of my mathematics and it didn't give me unreasonable outcomes at the end so therefore it would still be considered correct even if i don't know what i'm doing is actually a little bit dodgy so that's this section here so that was like a big issue that i overcame you can see there's a big reflection section here in light blue where i'm saying like i ran into this era i figured this out therefore this is what i did to solve this issue so if you run into any big issues like that like try to keep a log of the things that you're doing and why you thought the way that you did so you can have this kind of big reflection section um then we have the same kind of thing here it's good to signpost the things that you're doing just like at the beginning of this section to kind of say the frame score probabilities we use to find the game score probabilities like to kind of say hey that's what we're doing in this whole section here um [Music] again another form of mathematical expression once i had figured out the game scores then i put them into a probability distribution with the axis labels the figure label appropriate scale all of that jazz more reflections here more definitions of what a standard deviation is what is the significance of a low standard deviation um talking about skewness now because my distribution wasn't perfectly normal that was a big issue i was like oh what am i going to do if my distribution isn't perfectly normal um initially i thought i could use the central limit theorem but then that was not working so then i had to figure out a different way to do it so then i figured out found the skewness formula online and decided to apply that um so anyway that was just me adapting the skewness formula to the context of my investigation and then i normalized the distribution i kind of transformed the x-axis values so that it would become a normal distribution again the math here is not that important because obviously this was something that i spent more than 30 hours on doing but the important concept is the fact that like i'm facing this issue of okay i've mapped the probability of my game scores i am calculating at skewness in order to assess whether it's a normal distribution or not alas i find that it is not a normal distribution therefore like i have this whole section discussing how i'm overcoming this issue reflecting on why i'm approaching it the way that i am approaching it um and then coming up with this new graph um and kind of again interpreting the the graph here like although the distribution visually appears negatively skewed this is simply because of the positioning of the mean of the scale so kind of reflecting to say yeah it looks this way but there's a reason for that um and then finally once i had created my probability distribution then i applied my pro my probabilities to winning against a professional bowler and there was a big issue here in terms of um only having game scores and so i couldn't use the same process that i had used for myself where i had access to both my role scores which i kind of added up to give my game scores whereas online i only had game scores available so i kind of discussed the limitations that that placed on my investigation and like that's kind of a good note like if something isn't available to you or if you're having some issue with processing the data like it's okay to kind of pivot your approach or use an approach which is like less than optimal and just acknowledge like i had to use this approach because something else was happening so for me it's like i had to use this other approach because only the game scores were available ideally i would like to do it the same way that i calculated my probability distribution but is not possible so that was just another big chunk of reflection here so you can see how that reflection is really integrated throughout the ia um and then i use the t-test to figure out the probabilities of me winning over this american player i think mcewen yes an american bowler um so i figure out this probability and the probability of me winning is 0.00064 um and then again that would i calculate i was like oh now that i have this probability i can figure out the number of games it would take me to win which was 1562.5 um so a lot um so then when it comes to your conclusion the um format i would say is first talk about what the main takeaway is from the results that you see so for me it was this exploration has demonstrated how bowling's objective scoring interacts with skill level to determine the likelihood of obtaining certain scores that's me kind of like rephrasing my aim in order to demonstrate i have addressed my aim through this exploration um this principle was demonstrated through the extremes of an amateur and a professional so that shows a little bit of like my creativity or my personal engagement like this idea that i had to really demonstrate this characteristic of bowling through putting me up against the number one bowler in the world at the time um so that's kind of a little bit of personal engagement there to have thought of this question or this approach to answering some questions about the probability of bowling um however the same process could be applied to any proficiency level so i'm also thinking about the applications of my ia to other people that isn't specifically one of the marking criteria for the maths ia in the same way that it is for the um like science ias and other ias um but i think it's still nice to put it in to kind of say well if this is the broader context of bowling then like it could be used in these ways um we have a little bit of reflection here what have i learned i've got a new appreciation for elite bowlers as calculating my minuscule chance of winning against a professional underlined the disparity between our abilities um however again this is like oh i've changed my thinking however these results contradict my gut reaction that it would be impossible for me to beat a world ranked athlete this is a hopeful perspective for aspiring bowlers that if they compete in enough competitions the odds may eventually fall in their favor so how has my understanding of the topic of bowling shifted as a result of using maths to investigate it is really what i'm reflecting on there and then finally i finished my ia with a reflection on the limitations of my approach overall to kind of say well the human aspects reduce the reliability of such mathematical explanations explorations using experimental probabilities one would think that larger samples would provide more accurate values but for bowling the larger the sample the more one has practiced and likely the more one has improved thus earlier scores may not reflect one's current skill level therefore as the sample go grows calculated probabilities become less accurate in representing the present moment um so that was actually a i remember a reflection that i had written down as i was actually bowling over the course like when i was collecting my scores i was like i'm improving a little bit at the beginning and then towards the end i'm like so tired because i've bowled so many games and so then now my scores are terrible at the end and i was kind of reflecting on the fact that oh you know normally if you're thinking about experimental probabilities like flipping a coin the more that you flip the coin the closer those experimental probabilities will align with the theoretical probability but i was like that's so not what's happening with my bowling and so then that was something that i wrote down and then like i saved it for later and then i was able to include it in my final ia so just whenever these little reflections or thoughts come to you just pop them down somewhere and make sure you have them saved away because it really sort of i think takes away a lot of the heavy lifting that you have to do at the end to come up with all of these reflections because instead they've just sort of like popped into your mind there's like questions of like oh that's a little bit weird um as you've gone throughout so you can see as well just here i have like a whole bibliography work from where i was like investigating not only bowling and getting those scores but also like looking up the t-score formula and the skewness formula just because that isn't like part of the i ib course um you have my calculations that i gave the sum the sample calculations for before and then you have like my probability distribution the before dividing through so this is like the one where it was actually ratios and not probabilities um and then i have my probability distribution of game scores so you can see that this would have been way too long to include within my ia but i can just say like i calculated this probability distribution of scores you can see it in this graph here so i have represented it so that the marker can understand what i'm talking about but i don't have to include it as a table form in my ia i can just put that in my appendices um and then yep that was her scores and that was my ia so um that's pretty much everything um i hope that this has been in somewhat somewhat helpful i know it was a little bit rambly because it's a bit less scripted than my usual videos and obviously this wasn't edited i've just done it all in one take um but i hope you've still been able to get something valuable for from it and at the very least you know you can look through the powerpoint that i wrote out and this ia which i'll have uploaded to the google drive um and if there's anything that's still unclear then like feel free to um ask comments ask in the comments below and like i'm sure like other people can also you guys can help each other out um because you guys actually know stuff too and have different perspectives on the mass ia so it's good if it's not just me um answering the questions or giving my perspective like you guys all have something to offer too um so yeah i hope that's kind of cleared up some things about the maths i a and um hopefully you'll stick around for some other iv videos yep okay thanks for watching