After 3 years of being with our beloved teacher Mr. Kichan, it is sad to see someone I look up to leave our school. Though i wish him all the best for his future, we couldn’t finish our ib journey together. Sir if you are reading this (pretty sure you will) I hope your future ahead of you will be bright but you should come back when we graduate ok?? 🙂
Mr. Bean
looking back at my journey with our beloved teacher Mr. Kichan, i can’t seem to find the very first assignment i had with him (since it’s a test he decided to give the day i came back to school :’) ). So instead i decided to find the first assignment I had in JC1 “Initial thought: “Are you Mr. Bean?” “
So after looking back at this assignment, I realised “damn i was lazy at writing”. everyone was writing paragraphs after paragraphs and here i am with:
after almost a whole year of JC1, i think my brain is still wired poorly because if i were asked this question, i would probably say something similar. However, if i’m really forced to re-answer this question differently i would say something along the lines of:
Mr. Bean is the very embodiment of the DON’Ts of IB or any occupation. Instead of putting so much effort on cheating or strategising, why not redirect the effort to actually studying :’)
Memorable lessons
So this is the part where the most memorable lessons are placed. Unfortunately, i don’t rlly have any memorable lessons except for two lessons we had in sec 4. In secondary 4, we learnt vectors and statistics. I chose these two topics specifically because, how could i forget them! Statistics was that one lesson i remember because, i don’t remember anything. We had an assignment in Environmental Science which needed statistical results such as standard deviation, p-values and f-ratios. I didn’t understand what any of these were and my teacher asked, “didn’t you study this in maths or physics?” All i could do was smile. sorry kichan :p
Vector was that one lesson that was along the end of the year. For some reason, Mr. Kichan asked us to come to school and we did vectors for the whole day. FOR. A. WHOLE. WEEK. I don’t know how he managed to get the other teachers to give up their classes, but he did. suffice to say my brain was done with maths for several weeks.
Memorable memories
For most of my lower secondary years, i’ve heard stories of this “Hottie K” from my older brother. My brother was notorious for his naughty behaviour and his C Average in Maths but for some reason, around the time when this “Hottie K” came to SIS, he suddenly became an A* average student. My brother wouldn’t stop talking about this amazing teacher. To my surprise, Mr. Kichan came to babysit my class one day. I was excited to see who this amazing teacher is but for more than half the class, all he was doing was sitting in the desk silently working. After the second half of the class, a group of students in the back started laughing and Mr. Kichan blew up mad. My first impression of Mr. Kichan was that he was a serious teacher that shouldn’t be made mad. I didn’t understand why my brother’s grades shot up and his interest in this teacher was so high as he wasn’t a serious studying student. However, when i reached secondary 3, he did a 180 flip and his personality from what i remembered was sooo different. Though we had small interactions before, this is what made me :O and understand why my brother likes him so much.
Another memorable memory is an event called SISMO (for more details please see my blog 🙂 thx). This event caused my brain cells to commit suicide. Even though it was not the best thing to go through, it was still an achievement and i am proud of myself and my friends that we went through all that. Especially Kichan who helped out with the public relation. :’)
Ancol was another fun memory. I was kidnapped from my friend’s home to be taken across the city. We went on a 10min boat ride, got lost in the highway and finished off eating cow brain in a padang restaurant. Even though it was a short day, i wish we could go out all together again before you leave :).
Thank you Sir for not only helping me enjoy my school life but for improving my brothers school life and all my classmates. Though it was a short 3 years, it was still a fun 3 years. We may not know what the future has in store for us but i’m sure it will be a good future for you :). Do come visit once in a while for us to meet and catch up again. Mathletes for life.
“there is always a chance for failure and a chance for success but there won’t be a chance if you don’t try”
Pre workshop
SISMO is a math olympiad held and organised by SIS KG. Us mathletes decided that after several years of trying out math olympiads, we can start our own math olympiad. My senior was the first batch of SISMO organisers and since it was a success, we decided to continue their work and hold the second year (but first for online) SISMO.
As the Director of Curriculum (DoC) I, along with my other fellow DoC, was tasked to create the heart and soul of SISMO, the paper. Honestly when my beloved teacher, Mr. Kichan, assigned this role to me I was hesitant as everyone knows they remember a math olympiad mainly through the paper. If it was a bad paper, they will not return. This placed a lot of pressure on me and i was close to rejecting the role. However, I thought to myself, it would be cool if i can make a paper that would be remembered by many people. I also know that i would never succeed if i never try so i thought that I would give it a shot. And i did. (Unfortunately this is all done online so theres not much pictures. Pls bear with it 😦 )
For my male viewers out there who went through school surely can relate to group projects with that one very hard working girl in your grade. She will make you work really hard even when you don’t want to :(. Unfortunately part of the DoC is that hard working girl and my winter holiday disappeared because of that but hey, at least all the questions were done when we came back to school.
My experience as a DoC is pretty dull as all i did was think of a question and write it down on the google docs. Thats pretty much all the three of us did until the start of school. However, the challenging part of being a DoC is that after you finished making the questions, you have to compile the paper.
Part of our job as a DoC is that we have to teach our junior mathletes the ways of math olympiad. Every week we prepare a short paper for them to do. This is also a chance for us DoC to learn the platform we’re going to be using, Ylearn (since we DoC are going to be marking). We would go through past papers in WMI to compile a short 6 question paper for the junior mathletes and after every session, we would have to explain the problems we assigned. This means i can only choose the questions i am capable of doing which is the limiting factor for this exercise. It also doesn’t help that i can only pick those from WMI making the questions I can choose limited. Though i try not to use used questions from previous trials, there may be a day where I do.
some of the practice papers we made
Post workshop
We held a total of 3 zoom session with the participants. A workshop, technical meeting and the actual SISMO day. The workshop is a day where we teach some of the curriculum to the participants such as Vietta’s formula or Heron’s formula. As part of the DoC, it was my job to lead and run the Intermediate/Advanced workshop along with my brother, Raynald. He was in charge of most of the workshop as he was to be a featured guest and i am to support him but when the workshop was about to end, he suddenly, had urgent business to attend to and i had to take over. The problem is I didn’t expect to fully take over the meeting so i didn’t prepare much material and when discussing the switch, My brother didn’t mute. That was embarrassing ._.
Even without much preparation material, I still managed to pull it off and the workshop went smoothly (aside from that previous blunder). With that i hoped the students learnt something new to take to the SISMO day.
The week after the workshop, was the technical meeting. This is where we discuss the rules and regulation for the actual SISMO day. You’d think as a DoC i would just sit there and look pretty but the committee decided it would be a good idea to make the DoC to read the Indonesian part of the script. I don’t mind reading the Indonesian part of the script but I don’t take pride in my formal Indo speaking skills. I take pride in my informal Indo speaking skills. Whats more is that my partner who reads the english part of the script printed her part before we finished editing the script. Though it’s not her fault :p. Problem is i cannot translate on the fly just like that since if i just read the script the english part and Indo part will be different. I just pray that the participants didn’t notice the weird choices of words.
Finally the week after the technical meeting was the actual SISMO day. I was once again in charge of the Indonesian translation part of the script but thankfully this time, the english and Indo part is the same. Oddly enough, even though we held a very detailed technical meeting and gave out a very detailed handbook that the whole committee worked on for WEEKS, some of the participants still doesn’t follow our simple instructions of angling the camera or having two devices for SISMO. We unfortunately had to disqualify them. Funny thing is one of the disqualified participant kept complaining that he didn’t know about the rules when he joined the technical meeting AND have been bothering the coordinators with a lot questions.
After the open ended paper, I had to mark all the junior papers. It was very painful having to juggle monitor the ylearn platform and marking at the same time. Luckily i had help from the other members of the committee so the marking process went smoothly.
After all the results are out, we moved on to the lightning round. As the DoC of the Junior category, I was tasked to run and host the lightning round. The introduction and explanation went so smoothly i was wondering whether they get it or not but i knew they understood what i meant since they managed to answer all the questions in less than a minute. They answered so fast some of the committee members didn’t even finished reading the question when the participant answered. Not only that, the Junior lightning round was finished even before Intermediate or Advanced even started their questioning.
photo with participants
Meetings
Though this section is not in chronological order with the other 2 sections, this category still needed to be its own section as theres quite a story to tell.
Our meeting are actually really painful :’). If we are lucky we would be done before 12 midnight and if not it would be AM when we are done. These long and painful hours are the reason why SISMO takes up most of my time ywy.
It’s in these meetings that we get our job distribution. Though my official title is DoC, I feel like i could pass off as chairperson assistant. We DoC were tasked with not only the papers but also with script editing with the coordinators, translating for the Indonesian part of the script and assisting the director of logistics with the platform issues. Though we DoC handles a lot of little parts of the other departments, we still had to handle the DoC part of our jobs. I’m just glad we only had to help out with small miscellaneous work. This means everyone is doing their main jobs well enough that the event can run smoothly. After all when you are part of a team you gotta help each other out right? :p
IB Learner Profile
Reflective: After having our mistakes pointed out by my heads about the paper, i reflected on what i did wrong in order to come up with a solution and fix my mistakes.
Courageous: Even though I was hesitant to take up the job that was given to me in the beginning, i built up some courage to take up the offer and become one of the DoC.
Communicators: One of the many joys of working in a group is that we get to communicate all the needs and issues we have with each other. Especially with my fellow DoC.
Caring: We as DoC knows that most of the people who joins SISMO are those who have not joined SISMO before as we advertise ourselves as an introductory math olympiad. We DoC stay caring and decided to make this SISMO easier even though the dark side of our personality wants to make it harder.
Thinkers: We DoC spent our whole winter holiday just thinking about SISMO questions to add to the final paper.
Thanks for reading my blog. I hope my fellow readers will want to join SISMO next year 😉
So here I am back again in my E-journals but this time as an IB student instead of an IGCSE one. As a new IB student, I realise how different the curriculum is compared to IGCSE especially in maths. Now as a Math Analysis and Approaches Higher Level (MAAHL) student, we spend less time solving problems and more time analysing it and making essays out of it. In fact, I can safely call it a third language I took because of the word count I write in each essay.
What MAAHL is Like
One of the first thing we studied in MAAHL was Lev Vygotsky’s Social Learning Theory. Though it was more like we discussed the theory and less of studying, I still learnt something new and interesting so I guess I could give it the benefit of the doubt and talk about it. This is basically what i wrote –>
Though this may seem like an eyesore that is too long to read, I am sad to say I was one of the lazier kids that wrote less words compared to others but knowing this is simply a wake up call to make me be less lazy on my research. The tl; dr of Lev Vygotsky’s Social Learning Theory it that humans are social creatures. We live, work and especially study together therefore we have to train our communication skills to get to know the people around us, just like how IB want us to approach learning. This is why being lonely hurts (lonely≠alone).
Toolkits
A new thing we started doing in MAAHL was toolkits. Mr. Kichan told us it was a practice for IA (which is something like making a thesis and is a BIG chunk of our final grade). Though we did a little bit of toolkits when we were IGCSE for practice when we are in IB, I still feel like I under performed in my very first (and currently) only toolkit.
This is the first ever toolkit I ever made in IB MAAHL which is about a pattern of green and white squares and we had to predict the future patterns.
The sheer amount of mistakes I made is crazy and that is still the introduction. I can already feel the disappointment from my teacher as I read his comments on all the things I need to fix. Though I know this will help me moving forward especially when I need to do my IA. For me personally, it was difficult as I was never good in languages and now that IA is a must, I should get used to incorporating languages in maths which will be a pain but it could be an interesting change. I’ll have to see in the future.
Investigations
MAAHL not only have me learning about how to write an essay in maths (cough* toolkit cough*) but it also got my classmates and I thinking about math questions it self. Our teacher Mr. Kichan really enjoy making us discover math topics and new concepts. One of the ways he does this is by giving us “Investigations” to do. In these investigations, he would give odd situations where we have to think deeply about the solutions. Usually, the solutions to the investigation isn’t what you would expect. Most investigations that were given would seem easy at first but when you actually try to do it you realise it is difficult or when you thought you got the answer correct, you realise it was far from the expected answer. Some memorable investigations are:
Similarly to the toolkit above, this investigation is to find a pattern and predict future stages of the fractal. We have to find our how many green and white triangles there will be as well as the length and area of each triangle. Through this investigation, we train our ability to notice patterns and make conjectures.
Since this is the first investigation I did back IGCSE. If you read my previous blogs, you would remember this problem but the difference between then and now is that our teacher, Mr. Kichan allowed us to only answer the questions as if it is a math problem back then but now that we are in IB, when we answer this these questions it should be in an IA format. This IA format is the previously mentioned toolkit so I cannot just reuse my answers from the previous year to say “I’m done sir” as soon as he gave the problem.
If you notice the pink highlights is similar to the highlight my teacher used in the toolkit, you would be correct as this question is from the toolkit. However, this section isn’t about the toolkit but about the investigations itself. As we can see, the question illustrates a fractal. As the stages of the sequence gets larger, the area of green triangles slowly decreases and change into white. The task is to predict the future patterns using logic and patterns.
This investigation was done in an hour. I know you might be thinking while reading this, “an hour?? Whats the big deal?? That’s a lot of time right?” NO IT’S NOT! A typical math exam is around 1 hour 30 minutes and this may or may not take longer. Yes I know the number of questions is less than an exam and yess we did not answer it as if it is an IA but the amount of thinking that goes into this is astronomical.
You might be wondering, “Why would your teacher do this?” That my dear reader is a funny story. When we were given an investigation to do as a homework, most of us didn’t see a final question that said “try me” in the end as we thought our teacher only wants us to do the investigation. However, when one of the only student who saw it (good eye my dear classmate) and was confused, our beloved teacher called for a class discussion. Since nobody else done it, he was furious and because of that as punishment he gave us this very special investigation.
Though we didn’t finish it all, we managed to do a lot of work and submit it in time before he gets even more pissed. To summarise this investigation, we have to find out what a radian is by doing some experiments with circles and eventually uncover all the secrets of radians.
The video investigation is all about the sound of mathematics where we learn about how sound and maths are related through trigonometry. Our teacher gave us our senior’s video presentation and we all immediately had a bad feeling. By doing this investigation, I learned the importance of communication in a group project as we lacked that in our project. We also experienced issues as stated in the limitations but we did overcome them. All in all doing this investigation made me open my eyes to the possibility that math connects every filed of knowledge.
Since this is my first video investigation. Have a watch, enjoy and hope you understand. (my voice sound really bad here soo don’t mind it) 🙂
Feel free to try it out any of the investigations yourself and if you try to search the answers online, you will see how far you are from these answers. 🙂
Discussion Forum
Another part in MAAHL IB our teacher incorporated is the discussion forums. We would be given a topic and then we would research about it. We would then post our research in a platform and read other people’s research. After reading other’s research, we would comment on them while reading other comments. This is where the discussion comes in.
This is a simple discussion forum as it was our first discussion (don’t worry its not graded, at least I don’t think it is). The video was about Mr. Bean cheating on an exam and we are supposed to give our thoughts and opinions on the matter. As we can see my other classmates and my teacher do agree with my point.
Question of the Blog
So part of the blog is to talk about this question. This question talks about a ferris wheel in what I’m guessing a theme park. We have to calculate the volume of the pod for the people to ride in (for whatever reason they want to find out). If we ignore all the useless information, the useful information tells us that the pod’s vertical cross section is a circle making the radius constant. This means b=c=3m (since diameter is the length of two radius combined) and a=4m. Knowing this, we can come up with the equation:
So now we found the volume of the pod yay… (Why can’t math solves their own problems?? I have my own problems to deal with you know… YwY)
Real Life Applications
In MAAHL, I always wonder why do we need to learn these topics. Imaginary numbers are imaginary, they aren’t real right? So why do we have to study them?? It turns out where the field of study involves calculations using sine or cosine waves, imaginary number will be used. An example of this is in electronics where the current is measure sin a sine wave as it fluctuates from positive to negative. The usage of imaginary numbers help in the calculations of imaginary currents and therefore save the people working on these electronics from some electric shocks.
Studying algebra in school has also always been confusing as we can never understood why we need to solve for x. I always thought this to myself while studying algebra when i was a lot younger: “x is just x. Why do we need to solve for it?” It turns out when I eventually take physics, I use algebra A LOT. Trying to find the unknown is quite literally what algebra is so physicians need to use algebra to do their calculations such as how to decrease the force to an acceptable level in a car crash. Without algebra, the airbags in our cars may not be very effective.
One last thing I studied in MAAHL is trigonometry and geometry (I know they are two different topics but they are related so let me livee). This topic has a very obvious real life application. It’s a no brainer that you need both geometry and trigonometry in architecture. Finding out how much area is needed to be covered or the length of a side in a triangle shaped room or something along those lines. You may also use trigonometry and geometry to avoid scammers especially when trying to buy land. They may very well be trying to make the land seem bigger than it actually is.
International mindedness
We as humans are curious creatures. We humans are also typically lazy. This is why we create numbers. Numbers are a way to help keep order in our lives. The thing with humans is if it will make our lives easier, we will learn about it. This is also true with numbers. Fractions was invented by the ancient Egyptians ass a method to represent parts of a whole number while irrational numbers was created by the ancient Greeks as a way to say numbers that can’t be placed in a ratio of other numbers. Imaginary numbers is no different. In the 16th century, a mathematician by the name Rafael Bombelli tried expanding the quadratic formula to solve for cubic formulas. The formula he studied is created by Ferro-Tartaglia-Cardano as is as followed:
The problem is he realise that he would almost always result in a square root of a negative number and as he knows (and most secondary students know) there isn’t a squared number that would result in a negative number as positive squared and negative squared will result in a positive number. This issue was eventually dubbed the Cardano’s problem. Though Bombelli struck a wall, like most mathematicians, he didn’t give up (obviously. Otherwise we wouldn’t be here right now). He eventually found a solution to the issue and that is to:
Since there is no square root of negative numbers yet, Bombelli simply thought “then we’ll make a new number.” This is the birth of imaginary numbers. Though when he proposed this to other mathematician, they were shocked (like the ancient Greece with their irrational numbers) but this invention solved the problem by putting the answers in terms of √(-1) and so now we have a new class of numbers.
IB LearnerProfile
Open-mindedness: As a new MAAHL student, the difference between IGCSE and IB is astonishing. This helps train my open-mindedness since everything I study in MAAHL is something mind blowing.
Communicators: I’m not the only one in this boat. Others are experiencing the same thing I am as they are also new to IB. To make life in MAAHL easy, communicating with my fellow peers helps.
Reflective: Now that I am in IB, I tend to reflect on what I studied in IGCSE. I recall now that most of what I learnt in IGCSE needs to be thrown out the window such as “there is no square root of a negative number”
Thinkers: The different toolkits and investigation trains my thinking in this field. There is always a catch to the answer and there is always a hidden answer to the question. This makes me have to think deeply on the question to get full marks from it.
Inquirers: Having an older brother who also been through IB, I get to hear about the different topics that I have yet to learn. This makes me curious about said topics and made me read about them in advanced. I guess it also helps my open-mindedness and reflective capabilities as what I learnt made me throw the studies I did in IGCSE out the window. AGAIN.
On the 23 of March, we started studying from home due to the COVID-19 pandemic. The government issued the order “work from home” making schools and businesses closed down. To run our distant learning, we used a video conference application called zoom. We also used google classroom to distribute the projects and assignments the teacher wants to assign to us however working from home allows our parents to watch how we students work. As students, most of us procrastinate on our work which is a problem as now parents are complaining to the school that our workload is too little making the student’s, who actually do not procrastinate, life harder as now when they try to finish one work 2 more assignments start piling up. This also affects the students who procrastinate as when they want to work last minute, they have to do more. Most of our teachers would give like one big assignment to do that may take the whole week to do but i try to not procrastinate and i think its unfair that the parents think we don’t have enough work because just doing one of the assignment may take me a whole day to do.
The main problem being that my internet connection is occasionally very weak, this makes it hard to learn and sometimes can’t make the deadlines. Especially during the first few days of the new education system they implemented I was outside breaking the rules in Bali for a week making me unable to keep up with the lessons during those few days. Not only do i miss the lessons, there is the risk of catching the virus outside as Bali doesn’t really seem to care that there is a pandemic. They still go out and circle the cities and still interacting with people. It’s as if they are not scared of getting sick. But there are benefits to studying from home. I get to sleep longer than usual, waking up 5 minutes before the start of class which is a benefit since working till late at night causes me to lack sleep.
My school made its very own math olympiad (sismo) and i got the privilege of joining the first ever sismo. As my brother is the leader of the sismo committee (even though he didn’t do much) i got the special treatment of being nagged to study for sismo. I am a teacher in a community service where we teach the children of the security and the cleaners math and english and with my brother inviting them to participate in sismo, i got to be taught by my brother as he teach the other children. (even though he was repeating what i already knew).
When the day started, we re-registered for the olympiad and took our participant tag, we then waited for the event to begin. We started of with a game of 24 where we place 4 cards of playing cards and we mix and match the order of operation to achieve a value of 24. we played in a group of 3 or 4 and those who win a best of 3, we are allowed to take a random cash prize from a red packet with a prize of either 5,000Rp, 10,000Rp, 20,000Rp or 100,000Rp. I won with a score of 2-0-0-0 and win a 20k cash prize 🥳🥳🥳. This money help payed for my lunch. But after the games, the test was beginning.
First round was the multiple choice question. Which went surprisingly well. My brother mentioned the olympiad was made easier because for some people it is their first olympiad, so as someone with experience with math olympiad i feel as if i have an advantage. Most of the questions i did felt like a breeze but i know from past knowledge that if it was easy for me, for my other opponents is also easy.
After the first round ends, the open ended round began. Honestly i was worried i would under perform in this paper. But after one look at the paper and realising i could do 5 of the 10 questions in the paper. I felt confident in at least making silver. Hopefully.
With the new confidence from the test (and the money earned), i could eat in peace with my friends while waiting for the results. a good thing about sismo is that results don’t take months or a year to release as they have less participants then other bigger olympiads. They finish marking everything within a day and have the results out by the same day. But whats interesting about sismo is that just because you don’t score the highest doesn’t mean u can’t win. They have the lightning round or what others would call it the buzzer round. Where the top 3 participants would go off head to head and answer questions where time is ticking on our faces. the winner of the lightning round gets the platinum award and a 1 million Indonesian rupiah cash prize and to my surprise, I got the second spot and is allowed to participate in the lightning round. :O
The lightning round (as the name suggest) requires speed and precision. But from what i previously notice from the advanced round, if you answered already and made a mistake, you can still answer again. So i guess i kinda took advantage of that. The questions themselves aren’t necessarily hard but the time pressure puts a heavy load on the pen. Every stroke takes an enormous amount of effort but most of the answer was simply just “1”. Even though i guessed most of the answers, i got one question right and it wasn’t through guessing even though the answer was 1 (i can assure you dear readers it wasn’t a guess). Even if i got 1 question right, an unfortunate event happened that my opponent got 2 questions correct (but i think one was doodling idk 🤷♀). But in his defence, he is an intelligent person and have my respect even though he beat me. 😦
Even though i was one position off of platinum, its the valuable experience that i bring home that will last a lifetime. I think it’s an incredible addition to the lightning round as it gives the opportunity to two other people too and the audience may get a cash prize for getting the correct answer if the contestants can’t get the answer. Overall a great experience that we bring back and cherish forever. Plus second place is not bad for the first and last sismo I will join as next year i shall be the commitee.
with “love” to our additional math teacher
ib learner profile:
open minded: i came to the room with the open mind expecting the questions to be something out of the world and part of the unsolved math questions but it turned out alright.
Thinkers: i had to really think of a solution. An unthought of method that is both accurate and fast that i can use to answer the lightning round quickly.
“Its the journey you go through that will be remembered more. The destination comes second.”
Activity 1
In our math class, we learned to use a website called desmos. This is a graphing website that will form the graph of the function we select. In order to master our desmos skills, our teacher has copy pasted a runway to the blank cartesian plane. We are tasked to make a line symbolizing the route a plane would take to land.
Source: Desmos.com
This is the the cartesian plane with the run way with the goal of making a linear equation that will land in the middle of the runway to ensure the safety of the passengers. Mixing and matching the numbers with a lot of trial and error to ensure the line is directly in the middle of the runway. Eventually the perfect equation is found and the passenger all live happily ever after. The heart is to show the love for our passengers to ensure their safety.
Activity 2:
pictures of triangles were given and we are asked to find the perimeter and the area for each of the “triangle”.
But there is a situation that we cannot ignore. Although the first triangle is given by the question to be an equilateral triangle, the other triangles aren’t mentioned to be equilateral there fore we have to make several assumptions to answer the question.
Ideal conditions (all triangles are equilateral and equidistant from the vertex of the triangle evenly in the middle of the triangle)
If all the triangles are equilateral while being equidistant from the vertex, we can accurately find the perimeter and the area. Since it is revealed that the side of the main triangle is 81, simply multiplying that by three would get us the perimeter. But what about the second figure? If the triangle is equilateral and centralized, we can say that the smaller triangle is 1/3 of the original length. Being an equilateral triangle makes it easy as all we have to do is multiply by 12, after doing the same thing over and over again, I realized that the number of sides is always multiplying by 4 as each side of the triangle adds 2 new sides making 4 sides per original 1. For the area, the next orientation is simply adding triangles to the previous orientation. The first triangle is simply the multiplication of the two side by half and the sine of the angle between the two sides. The two sides are 81cm with the angle of 60 degrees. The additional triangles are with a length of 1/3 of the previous length with a constant angle of 60 degrees. Simply add all the triangles together (there are 4 times more triangles per iteration as it has before). And vóila the area is found.
Non-ideal conditions (non-equilateral triangle or off-centered triangles)
To find the perimeter and area of the iteration, there isn’t a way to accurately measure unless we have the lengths and angle but if it wasn’t specified then we can’t really accurately find the perimeter or area. Simply add all the sides for the perimeter and as for the area get the initial triangle and add all the smaller triangles together to get the total area.
Since the side of the new triangles “sprout” out new triangles it’s essentially splitting one line to make four more lines. This means the number of lines multiply by 4 every new iteration.
Activity 3
We were given a triangle. This triangle is then split into three and for every stage the green triangles are further divided by three and the pattern continue. The question is asking if the initial triangle have a side of one find the other sides. But we have a problem. Similar to the previous question the question never specified the length of the smaller triangles. Or if the sides of the triangle are equal or not. So in order to find the length or area, we need to know the specifics.
Ideal conditions (equilateral triangle with all sides equal)
If the triangle is equilateral and is divided by two, the next pattern will be half the length of the previous pattern. The length is consistently divided by two since all the sides are equal, all the sides stay consistent. For the area, every pattern will divide the triangle by 4 (even though the picture says three its a typo error). If all the triangles have equal area and length, the triangle is divided by four. If we tabulate the results, we can predict the next pattern with the equation of 3^n for the number of triangles, (1/2)^n for the length of each triangle, (1/4)^n for the area of each triangle.
Unideal circumstances
If the triangles isn’t equilateral, we can’t calculate the specific length as each length is different and thus each angle and area is different making tabulating them a nightmare. So without the specific length and angle, it’s difficult.
So we learn that answering questions like these is a pain as we have to make all those assumptions and answer accordingly otherwise we cannot get the specific answer we need.
Reflection
Reflective. As I write this ejournal I reflected on myself as this may be my last ejournal. I wanted to make this ejournal special and spend time and effort to this and to do that i need to reflect on myself and to recall past
Communicator. Having to communicate with my jc 1 mentor and to communicate with my friends and with their help we solve the problem.
Inquirer. I was curious and used that curiosity and find other ways to solve the problem at hand
Unforgettable moments
I remembered the time when all my classmates went to Bali and i was left all alone in Jakarta with some of my friends. At least i got extra week of holiday
citations
Wathall, J., Harcet, J., Harrison, R., Heinrichs, L. and Torres-Skoumal, M.(2019). Education Bookshelf Mathematics Analysis and Approaches Higher Level. [online] Bookshelf.oxfordsecondary.co.uk. Available at: https://bookshelf.oxfordsecondary.co.uk/contents/428/index.html [Accessed 30 Oct 2019]
“Transformation is to change you to the better version of yourself without changing the things that makes you, you.”
Transformation:
There are many different types of transformation but this blog only will only focus on: translation, reflection, rotation and enlargement.
To transform a shape is not changing the fundamentals of the shape that makes it a shape. For example when transforming a triangle, the end result will stay a triangle and not a quadrilateral.
Translation:
To translate a shape is to shift a shape. The orientation and size does not change but the position of the shape does change. Usually a (x,y) coordinate is given to tell us how many points we shift our shape. The x value is the left-right movement of the shape (positive means going right while negative means going left). While the y value is up-down movement (positive means going up while negative is going down).
Key words: translated by (x,y).
Reflection:
Reflecting an object is like looking at a mirror. The image always seem to appear behind the mirror. Reflection is the same. In reflection, theres a “mirror line” which is used to reflect your shape. The orientation of the shape will be flipped depending on the orientation of the mirror line. The distance between shape and mirror line must be equal to the distance between reflected shape and the mirror line.
The triangle’s orientation was flipped horizontally because of the orientation of the mirror line.
Key words: The shape was reflected at (equation of mirror line)
Rotation:
Rotating an image would change both the position and the orientation of the shape. There is a point called the “centre of rotation” this point will be the pivot for the rotation to occur. The shape will then rotate at a certain angle either clockwise or anti clockwise. Usually a multiple of 90.
We usually use a trace paper to find the rotation. Place a piece of clear plastic over the shape n trace the shape then connect the closest point to the pivot and rotate. When the targeted angle is reached simply retrace the image. Simple right? That is if you you have a trace paper. But if you don’t? There’s another way. Connect all the points from the image to the pivot. Place a protractor in the pivot aligning the 0 degree with the connecting line and measure out the targeted angle. The distance between the shape and pivot os equal to the rotated shape and the pivot.
Key words: rotated by (angle) degrees anti/clockwise at (x,y) (centre of rotation)
Enlargement:
Just as the name implies, the shape would change in shape. Depending on the scale factor, the shape may change size drastically. If the scale factor is greater than 1 then the shape will get bigger but what if the scale factor is a fraction between 0 and 1? Then the shape will diminish. And if its a negative scale factor? The image will get flipped. But how does all this work? A point will be determined as the “centre of enlargement” which will determine where the enlarged shape will be drawn.
Connect all the points of the shape to the centre of enlargement. These are the guidelines we will be using. Find the points where the distance between the line is multiplied by the scale factor. (Ex. If the scale factor is half find the three lines where the distance between them is halved). If the scale factor is negative, then we continue the lines beyond the centre of enlargement.
Irl application:
The knowledge of microscope was based on enlargement. The centre of enlargement was supposed to be the focus point of the microscope and the lens is the scale factor. Armed with the knowledge of enlargement, we can make the microscope.
The steering wheel is designed by the help of rotation. The car is armed with the hardware that makes the wheel rotate 90 degrees clockwise if the steering wheel is also rotated 90 degrees clockwise. With the center of the wheel as the pivot, the car can rotate easily because of this concept.
Cameras are made to receive the light that was reflected from an object. In order for us to see, light needs to be reflected off that object to our eyes but man have made artificial eyes called the camera that pick up on these reflected light and store it in the system.
Matrices:
Think of matrices as placing numbers in excel. A different cell a different number. Matrices are defined by the number of rows ad columns it have. The picture above is a 10 by 10 matrix (row by column). This is known as the order of matrix.
Addition and subtraction:
Matrix can only be added if the order of matrix is the same (ex. (3×2) + (3×2)). To add or subtract a matrix is really simple simply add or subtract the number within each cell.
Multiplication and division of matrices:
This is where it gets tricky. To multiply a matrix, the first matrix’s row must be equal to the second matrix’s column. The inner number must be equal and the outer numbers will tell us the order of matrix that we will be expecting. (Ex(2×3)*(3×4)=(2×4)).
To multiply the matrix, we multiply the row by the column and add up all the products to be placed in the cell.
The zipper method tells us we multiply the top number with the most left number than add that with the middle number’s product and the last number’s product.
To divide a matrix is impossible. There is no division in matrix but there is a reciprocal of a matrix known as inverse matrix. Multiplying a matrix by an inverse matrix is basically the
If we multiply a number by the identity matrix, we will always achieve the original matrix. (A*I=A).
So now we know identity matrix. But what about inverse matrix. First, we need the determinant.
To find the determinant, we multiply across and subtract the two products (as shown above). The determinant will determine whether we have an inverse matrix or not. If the determinant is equal to 0 than we do not have an inverse matrix. This is because the solution to find inverse matrix is:
We take the reciprocal of the determinant and multiply it to the matrix that have been slightly changed. The top left number and the bottom right number will switch its position and the remaining two numbers will be multiplied by -1. (As illustrated above).
Ib learner profile
Inquirers:
I explore the calculator and acquire the ability to use the calculator and solve matrices problems for me. The usage of shift 6 allows us to input matrices and do the question for us.
Reflective:
Writing this ejournal gave me the opportunity to rethink about all the concepts i have learnt, reminding me the journey i went through to learn transformation.
Sets and probability is the second most hated math topic, only losing to calculus. But even if many hate it and seem pretty useless, it have some real life stuff to it.
Probability is the study of chance. Knowing probability can help change your life or save your life. In the casino, knowing the chances of winning could change your whole life. People who spend all their money on the slot machine would know not to if the odds of winning is one in a million whereas playing poker instead brings the winning rate closer to a 50-50 chance. If players are armed wit the logic and the knowledge, the majority of those bankrupt players could have been saved.
Sets is placing points up in groups. This is a form of organization of data where we can see which data overlaps two or three category or if its excluded from all categories. This method of organizing can further help research to exclude data from outside the category to simplify the research or help find probability significantly decreasing the rate of stress.
Even though it seem useless, just having the knowledge of probability could change your life and the use of sets will save your mental state from the enemy known as stress.
D”Facts are stubborn but statistics are more pliable”
-Mark Twain
Statistics is the building block of research as every research needs data collected and the data collected is what we call statistics.
A comparison of math grades and Chinese grades both rounded down to the tens across 9 grades.
Using the calculator, we kind find all kind of things such as the mean of both the x variable and y variable. We can also draw a best fit line through the points using the calculator and find the relationship of both points.
Through the calculator, we know that the mean of x variable is 85+5/9 and the y variable is 62+2/9. Its best fit line have an equation of y=-1.4x+182 and the relationship between each other is negatively strong (r=-0.61394)
Statistics is used in real life too. Such as when we have a lot of points from hundreds or thousands of participants competing against each other. Statistics can arrange them easier and rank them from highest to lowest or vice-versa. Or by putting a boundaries in an elimination competition where “below nth place shall all be eliminated” statistics will make it easier to find out who is in which place.
Data gathering:
Credits: Raynald Gozali
Data gathering is a pain if poorly organized thats where statistics comes in. If its organized well, we can draw our best fit line without the use of calculator and keep things organized. With more complicated research and more data, statistics’s part will really shine.
“History repeats itself thats why we need to know our mistakes to prevent repeating them”
“Its better to walk the right way alone than the wrong way with everyone.”
“If u don’t understand his method, find your own method you understand”
Numbers:
the main thing i learnt in numbers is the sequences we did. There we learned three types of sequences arithmetic, quadratic and cubic sequences. Our beloved teacher thought the lesson so well and finish arithmetic sequence in a day and the other two sequence was burned through quickly. The only troubles I personally have is to find the a b c d values of cubic and quadratic sequences but if you cant figure out how to do things your textbook try to drill in you, find other ways to solve your problems. Other problems I personally encountered was finding the nth term and and the sum of all the terms. Which we learned was a specific equation. But again i learnt another method to solve questions relating to sum of terms. We could use sequences when we want to find out like an output of a factory. Lets say the factory makes 3 more products more than what it made yesterday. In this scenario we can predict the number of products it makes at a certain day.
Algebra:
Algebra (to my surprise) is hated by a lot of students as it is portrayed as a hard topic. But we’re forgetting that ever since we were in kindergarten, we done algebra before. It may be a difficult topic to grasp but it is the most useful math topic in the history of math. It is one of the fundamental topic a secondary student need to know as it is the simplest way to solve any problem. This is true especially in physics. Using algebra helps you visualize what you’re supposed to do and can help solve the questions efficiently and effectively. Generally what we learned in algebra is to analyze and understand the the given expression or equation and occasionally graph the possible solutions. Even though algebra is a vast topic, it is necessary for us to solve a lot of different problems.
Mensuration:
The topic of mensuration isint so bad. Its just i dont really see the application of it in real life. Only if you are taking arts or architecture. But aside from the application, the topic itself is really simple. Its only area surface area and volume. But what makes the topic a real challenge is how our teacher overcomplicate the questions making it really challenging but all in al its for preparation for the real exams so we all will come to appreciate his efforts. But the difficulties in this topic is probably the frustum but that’s about it.
Geometry:
In geometry we refreshed a lot of what we learnt in the past. Pretty much everything we did was discussed before in my life only circle theorem is new to me n my classmates (unless they learnt it in the past) the interesting thing about circle theorem is how we have to be observant and notice the circle theorems we can find in the circles. Its a difficult thing to notice something so small but it helps you get a good grade by noticing the small things in life. But the thing i really hate about this chapter is the 3D question. Im really bad with anything 3D so i would struggle here.
Trigonometry:
Trigonometry is the chapter that is almost impossible without the calculator. Though if we don’t take physics or arts, we don’t really need trigonometry anywhere in our lives. But if we do take physics, we would need trigonometry like how to find the distance a car travels in a car accident or if a murder scene that uses something like a wrecking ball as a murder weapon. Our beloved teacher with his beloved teaching methods, drilled the concepts in the most grueling way possible. An Amazing Test. Topics like sine, cosine and tangent were the torture devices that day.
Graphs:
The worst topic to ever be thought in school. The thing about me is my handwriting so divine the teacher never accepts it. Especially since the graphs we get for the test is always the impossible graphs with weird contortions and difficult to draw. Like drawing quartic equations or fractional equations. Also following the standards for igcse is a hassle. The drawing has to be smooth and not sticky or feathery.
Calculus:
The topic that a lot of people hates. Except everyone in my class loves it. I don’t understand why people hates calculus. because it’s actually very useful. Kinda. Though all first derivative do is they tell the gradient of the point in the curve so i don’t find it all that useful. The concept is very simple and is easy to understand in fact it is the topic that holds The highest average in the test. First derivative is only to multiply the coefficient with the exponent and subtract the exponent by one. It isn’t really too hard.
Sets:
Even satan has his nice day where he would torturing and do some good in his life. That’s what our math teacher did. He found some of us having trouble in sets because of the national exams coming up. We did sets in the classroom and we learnt pretty little. We covered the whole topic in two days. I guess satan’s good days don’t really last long. Pretty much the new things we learn is subsets and proper subsets. Yay.
So thats it in sec 3. Of course when you do sec 3 there will be some up and downs but at least from reading this you know what to expect. But the main lesson is appreciate your teacher isn’t from hell. 😀
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