# IA (HL) Portfolio Type II -- Modelling a Functional Building

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Hi. We got our first IA tasks in math HL last week, which is "Modelling a functional building" and I have a couple of questions about it. Since i have never done it before and our school isn't very experienced in IB yet, i figured i'd ask for help in here..

1) Is there a maximum word limit for the task and if yes, what is it? I have about 3000 words already and I think I have barely covered half the task.

I'm explaining everything quite thoroughly but I think all I write is quite relevant and without it it would be to superficial or hard to understand.

2) How much do you need to show your calculations? Do you need to show steb-by-step how you substitute, deduce and simplify everything? So far I have shown most of my calculations

3) If I were to create a table, do I need to show all the calculations of how I got the data in the table? It usually involves doing the same kind of calculations over and over many times. Is it correct to just write the results in the table? (E.g. when creating the table about the volumes, volume ratios and surface areas of the structure at different heights)

4) The third point in the assignment has "use technology to investigate how changes to the height of the structure affect the dimensions of the largest possible cuboid." Could you assume, what kind of technology do they expect I use. I have figured out a way how to show the effects algebraically with calculations but I don't know about the technology. Is is considered sufficient use of technology if I compare different heights and their cuboid dimensions in a table and plot some graphs on them?

5) It is probably useful in this task to also include 3D graphs of the structure. Can you suggest any good programs that would do this kind of job?

6) Do you know if there are any sample modelling works up on the internet? that would help me a lot in getting the format and everything. I tried google but without much success.

Sorry for so many questions.. I would really appreciate it if you could answer at least some of them shortly because it is due already on monday. also maths is the most important subject for me. So thanks a lot in advance:)

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As far as I know there's quite a lot of leniency when it comes to Mathematics tasks... and also remember your teacher marks them, and only the best three and worst three (or something similar, depending on the size of your class) actually get sent away and moderated. Your teacher is thus your best resource, apart from the actual criteria...

1. No word limit. When I did my modelling task in Math SL, I wrote like 5 pages and had only three models. My 1800 word portfolio was dwarfed by that of some of my classmates (30+ pages sometimes) but I got full marks, before moderation. So my suggestion would be to be concise and effective if you can: it saves your teacher the marking.

2. I think you need to show most of your calculations, or if you make big jumps state the principle used, but it doesn't have to be exhaustive, that is, don't waste time or words or ink. This is more important in certain types of portfolios, like a logarithmic one; if you're modelling you could just use a table and show the calculation for one row or something. Or if you have a sine function indicate how you find a certain answer, but I don't think its necessary to actually show every single number.

3. As I said above, not for every one. I suggest having a title for the table, and then at the heading of each column below the title (or row, depending on how you structure it) you show the general formula, like Volume would be the title and then beneath it, V = s3, where s is the side of a cube.

4. Yep, technology could mean use of excel. For example, if you say that you used a certain formula in excel, and type that formula in below the heading, and that you extended it for the data (what I did for the Matrix multiplications lab, because it would have taken so bloody long otherwise) then that counts.

5. The 3D graph thing is tricky. If you are doing cuboids and stuff you might be able to somehow apply barcharts in MS word to that, but otherwise I wouldn't worry to much about it. IBO doesn't expect you to take things to far - I think the emphasis on technology is so insofar as it will speed up your work, not slow it down.

6. I would upload mine but it's being moderated as we speak, I think, but I'll give you the general structure: Introduction, with some background info on the topic at hand and where it applies in real life, the data (we had to model to fit a certain set of data so I wrote it down again for reference), then the three models, with a graph, an indication of how I built the function, and an evaluation of the limitations of each model as applied to real life, and finally a conclusion and overall evaluation. I also referenced literary data on the actual extrapolated data and compared it with my models, although this may not apply to your topic so much. But on the whole I'd say the structure is not clear-cut like an IB Science lab or something, the tasks are designed to give you freedom and multiple methods of approach, and in a way the criteria are more similar to the English ones than the Chemistry of Physics ones: less absolute requirements.

Just a word of general advice: do it on time and do it well and you'll be fine. If you're really worried ask your teacher to take a look at it beforehand (can't hurt to try) and see if he has a few general comments or words of advice.

Good luck!

Note - I realized just now you're doing Math HL, whereas I did SL and am doing HL next year (weird system). So the stuff on length might not apply perfectly, probably they require you to write a little more, but from what I've seen of other people in my school, the HL tasks are also significantly harder and simply need more space to answer completely.

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Thanks a lot, Aron. That made me feel a bit more confident . Another question came to my mind. What kind of register is it best to use in the portfolio? Should I use pronouns like "by substituting this we get..." and "I will consider this variable..." or is it more appropriate to use passive voice like "from this formula it can be deduced..."?? So far I think I've used like a mixture of both.. And does anyone know for certain if there is a word limit in HL portfolios? Thanks.

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I'm doing an IA on building an office building with a curved roof. I went through the steps with four different models, 2 parabolic ones and 2 semi-circular ones. I don't really know how I can structure more conclusion...does anyone have any suggestions?

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Well, don't forget that conclusion is the summary of all your work. I haven't done this assignment, but type II assignments are very similar in nature. Go through your work and summarize what have you shown or proven. And then, do not forget to analyze all weaknesses and limitations, this is crucial. For example, if you model a function for a given range of data, does your model function work with data out of the given range?

The main point of type II assignments is to understand the limitations of mathematics.

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You probably are already done with this model but if not, I believe there is no word limit for Math Portfolios. Also I think a passive voice would sound much more appropriate, right? By the way, have you or has anyone else found any interesting programs to design 3D figures? I know they are not really important but right now I am doing them on Microsoft Word and I think the presentation would improve a lot with better graphs. Thanks.

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1. I think that a normal IA would have more than 10 pages but I dunno, even Daedalus scored perfectly with 5 pages, so yeah no limit, but I'd say that around 30 pages is the normal one

2. Yup step by step, but dont make it so detailed for example:

2x + 4y = 10

(2x + 4y)/2 = 10/2

x + 2y = 5

x + 2y - x = 5 - x

2y = 5 - x

thats too crazy. just skip lines 2 and 4. but make sure that you write the necessary steps and dont miss the important ones out

3. have you done a phy/chem lab report? I think you might want to give one example for each column, and give the general formula. but if the data&working aint so much, you might want to write down every calculation

4. my (experienced) math teacher said, when they say technology, they refer to the softwares. meaning maybe you use ms.word/excel to construct charts instead of drawing them with hands,scanning it and putting the picture on your report (OMG LMAO). if you have texas instruments, connect it to your laptop and you might want to take screenshots of the calculations instead of typing them in ms.words.. then if you draw functions, equations, geometry stuff, again dont draw with hand and scan, use autograph or any other graphing software (altho I think that autograph has been the best one). since you have a table, plot the data into a graph. they expect it.

5. I think you need to provide. use Autograph. not a freeware, but my school has the installer (and it's cracked) and they do give us, so we just need to copy and install to our laptops unfortunately I have deleted the installer from my USB so later when I have time I will ask for it again and I would upload it to maybe 4shared

6. I dunno hehe

ah and try to use passive register most of the time.

however in the intro you would need to say smthg like

"I will be investigating the relationship between the value of n and the ratio of the areas of the polygons in this report.. blah blah.. in order to show the working and graphs more easily, I will get help from softwares called 'Autograph' and 'TI-nspire'"

rephrase my last sentence haha I forget what I said in my report..and you might need to say smthg like

"firstly, I will be investigating this relationship in a triangle when n=1. blah blah..."

"secondly, I will be investigating this relationship in a triangle when n=2. blah blah..."

"thirdly, I will be investigating this relationship in a triangle when n=3. blah blah..."

(table, plot graph, make conjecture, prove)

"next, I will be investigating this relationship in a square when n=1. blah blah blah blah..."

~

however Im new in IB so I might not be giving good suggestions. but I've been doing a Pre-IA, the segments of a polygon (that counts as a topic test.otherwise I wouldnt have worked really hard.) for a holiday HW. that's all that I know from my teacher&seniors

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Hi karlp and Daedalus,,

I've sent each of you guys an email asking if you could help me with my portfolio task, this very same one. So if you see this post plz check your inbox and tell me if you could help!

Thanks so much!

If anyone else has done this portfolio task before plz send me an email at *************** (ask me through PM)

Id appreciate it a lot.

Thank you guys.

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Edited by Mahuta ♥

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No, this way we can't.

Oh, and do not post in capital letters, extremely annoying.

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is there any formula to finding the maximum volume of the cuboid? and when i plot the graph,is it suppose to be a linear graph?

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.....the type 2 dimensions of the cuboid

Edited by Mahuta ♥
Stop using text speak and ask specific questions. Maha

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Hi Guys! I am doing portfolio work on the same topic! cant do it!!! axxxx..... help please!!! . The building has a rectangular base 150m long and 72m wide. The maximum height should not exceed 75% of its width for stability or be less than half the width for aesthetic purposes. The minimum height of a room in a public building 2.5m.

Create a model for the curved roof structure when the height is 36m. Find the dimension of the cuboid with maximum volume which would fit inside this roof structure

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Hey,

few days ago i was given the portfolio on modelling a building as an architect... i have found the the volume of building using integration , but how am i supposed to go about finding dimensions of the maximum cuboid..

Any help will be appreciated , thanks!

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i can help if ur willing to help me figure out my patterns of lines portfolio

.....

Edited by 2401 Tangents
no text speak

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i would recomend you to use geogebra to model both the building and the cuboid.

For the maximum area of the cuboid, you take the equation for the buildiing(parabola) and differentiate(+also insert 2x(value of the width of the cuboid)) in order to find the maximum.

Kind of hard to explain like this, hope this helps

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i would recomend you to use geogebra to model both the building and the cuboid.

For the maximum area of the cuboid, you take the equation for the buildiing(parabola) and differentiate(+also insert 2x(value of the width of the cuboid)) in order to find the maximum.

Kind of hard to explain like this, hope this helps

Could you please explain further clearly? I can understand until differentiate but i don't understand "+also insert 2x(value of the width of the cuboid"?

I know why you say that but the thing i don't get is where we should insert "2x value"?

Thank you very much

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Please anybody who is doing or has done this help me with this???

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has anybody tried to use the ellipse equation for this ?

and can anyone confirm that the maximum volume is at x=20.7 ( width = 41.4)

And how do you usd technology to investigate how changes to the height of the structure affect the dimensions of the largest cuboid ??

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I've been working on this IA for a few days now...

Did anyone else find that the equation for the volume remains the same (hence, same derivative) for all possible parabolas?

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