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Mathematics Portfolio Tips and Queries


dessskris

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why do you want to use "we"? sounds like you had some secret friends who helped you do the portfolio.

maybe it's just your Ms.Word. try using another computer. I use the Ms.Word equation feature but I've heard of this MathType software that works the same way.

example of a general statement:

Y=6x^2-5

where x€Z, x=/=0, Y€Z

please read the Maths IA tips thread because everything is there (many people have contributed really really helpful tips) and if you have any query you can post them there too.

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  • 4 weeks later...
  • 1 month later...

Can someone elaborate about the criteria for "effective use of technology?" It would help if someone could give an example of how a calculator or graphing program was utilized more than simply plotting a function.

Using your GDC, using a GDC on your computer and taking a screenshot, using Excel, using Autograph, using GeoGebra, etc...

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Can someone elaborate about the criteria for "effective use of technology?" It would help if someone could give an example of how a calculator or graphing program was utilized more than simply plotting a function.

most common examples:

using technology to validate/prove your general statement

using technology to generate graphs

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using technology to generate graphs

I thought the rubric said the technology had to be used in a more effective manner than just making a graph.

depends on what the graph is for. if the graph is not being asked but you use a graph to prove the general statement, then it's useful in the development of the IA.

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  • 1 month later...

• A good portfolio should be 16-28 pages long

Is this including tables, graphs and diagrams?

EDIT: Also, if I'm doing one thing more than once, e.g. if I have 5 sets of data and I plot 5 graphs for them, do I show them all? and if I explain them, is it OK if I use the same format but change the values each time?

Edited by brofessional
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A good portfolio should be 16-28 pages long

Is this including tables, graphs and diagrams?

EDIT: Also, if I'm doing one thing more than once, e.g. if I have 5 sets of data and I plot 5 graphs for them, do I show them all? and if I explain them, is it OK if I use the same format but change the values each time?

lol of course that includes tables, graphs, diagrams, etc! XD

yes show ALL your graphs, but you don't need to repeat the explanation. you can just say that you're using the same method as previous, but you still have to show the graph and regression if you're using that.

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Also, should I make sure that I've appreciated the use of technology, e.g. a little paragraph talking about how the answer could not have been found without it, etc...?

What I did is when I introduced a value, expression, etc. generated through technology, I wrote something like "Using a TI-84 Plus GDC, a general statement was generated through [insert method on the calculator here]" or "Using the graphing software [insert name of graphing software], the following graph was generated. This graph represents [something] vs. [other something]". As an extension, you could also find an alternative method of generating the general statement without technology.

Here are my general tips:

I did quite well on my portfolio (well, the type I that I did last month, I've yet to do the type II). One of the aspects of my porfolio that my teacher really liked is my research (which I, of course, properly cited). I used concepts that were not directly taught in class, such as quadratic regression. Don't rely solely on material learned in class, do research on concepts relavent to the portfolio. Remember to cite each outside source you consulted.

My teacher also liked my proper use of mathematical terms. Look up what irrational, real, rational, complex, natural, whole, integers, etc. constitute if you do not know. Learn the difference between an equation and an expression. Also, don't write "plug it in" or "cancels out", instead, write "substitute" or "reduces".

Avoid trial and error to find your general statements. A few of my classmates did this, and I don't think they did so well on their porfolios. Instead try a system of equations, matrices, quadratic regression, or any other method that can be clearly shown and discussed to find general statements.

Although this isn't an English paper, do your best to spell correctly and use proper grammar/punctuation. I would recommend using elements of the MLA (or APA if that's what you normally use) format in your paper to make it easy to read, for example having your last name/page number in the top right hand corner and using MLA/APA style works cited page. Have someone else read it over before submitting it (friend, parent, sibling, etc.) to make sure that it is clear and coherent. If they have no idea what you are talking about, neither will your teacher or an IB marker, should yours be sent.

Use black text for the equations/expression, but if you want to show that you are multiplying the equation by a conjugate, common denominator, etc. to change the appearance of the expression or work toward solving the equation, use red (or another colour, red would be best I think) to show this so that it is not mistaken for being part of the equation/expression.

More often then not, there are alternative methods to finding the general statements. If you are aiming to get a high mark in the class or just want to do the best you possibly can, try to find and explain a different method to find the general statement.

I don't think it's possible to be too specific. Granted, you don't have to explain every little detail, but be really specific about which number you're subsititing into which equations and why. Show the substitution on your paper. Discuss what that result means. Don't say, "that didn't work", when if you get an undefined value. Why do you think that equation is undefined?

In the scope and limitations, really push the boundaries of the general statement. Some of my classmates said, "Yeah, that would only take one page". No, it won't. Try negative numbers, try pi, try square root 2, try 3/2, try ln 4, try -35/4, anything you can think of. Even if it "does not work", you can discuss why those results were acheived. At the same time, you may find that the general statement does indeed work for irrational numbers. Don't just substitute a bunch of random numbers and record the results, consider each result. Why didn't it produce desirable results? Could there possibly be a pattern? If your general statement has 2 or more variables to consider, create 2 sections/headings, one called "limitations of the a value" and the other "limitations of the b value" or however would work best for the portfolio you're doing.

Edited by opus92fan
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I have a question about the use of technology in our portfolios. I see that the mark scheme states that "student makes full and resourceful use of a calculator or calculator in a manner that significantly enhances the development of the task".

What is the difference between 'enhancing' a task and 'SIGNIFICANTLY enhancing' a task?

use technology to find your general statement, or to prove it.

Also, should I make sure that I've appreciated the use of technology, e.g. a little paragraph talking about how the answer could not have been found without it, etc...?

no. that is called bull****.

I have another question...

Is it correct to assume that because my general statement works for certain rows (I'm doing Lacsap's Fractions) that it will for other rows too? E.g. can I write "We can assume that..."?

Thanks in advance for any help :)

isn't that why you come up with general statements? you generalise, to generate a function that works for all values of n and r!! to validate your GS, you just need to show it works for some values of n and r that you've already generated, and use it to generate more fractions of further values of n and r and show it's correct.

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  • 4 weeks later...

Just a question;

Is it okay if, when creating a function to model data points, our model doesn't fit exactly? Because, to be honest, my model only goes through one point...it's pretty bad. Should I start over, or use this model as the first step in an investigation, and be like "Oh, well that didn't work, so let's try ____"?

Edited by hehe_lalalala
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Yeah, it's OK if your model doesn't fit all your data points. It's not supposed to; it's a model, not an exact fit. However, you model should fit your points pretty closely; your model should be a close a fit as you can get and one that you are able to model mathematically! You can show different models in your investigation and evaluate which one works best but don't go overboard with it.

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Just a question;

Is it okay if, when creating a function to model data points, our model doesn't fit exactly? Because, to be honest, my model only goes through one point...it's pretty bad. Should I start over, or use this model as the first step in an investigation, and be like "Oh, well that didn't work, so let's try ____"?

I can't believe you! you need to use at the very least two points to model your function and your model must then pass through these two. if it doesn't, you must have made a calculation mistake. re-check your work.

I can't tell you whether it'll be fine since idk how good it looks like on the data, but obviously a better fitting function will make the examiner happier and show that you're "smarter"

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Just a question;

Is it okay if, when creating a function to model data points, our model doesn't fit exactly? Because, to be honest, my model only goes through one point...it's pretty bad. Should I start over, or use this model as the first step in an investigation, and be like "Oh, well that didn't work, so let's try ____"?

I can't believe you! you need to use at the very least two points to model your function and your model must then pass through these two. if it doesn't, you must have made a calculation mistake. re-check your work.

I can't tell you whether it'll be fine since idk how good it looks like on the data, but obviously a better fitting function will make the examiner happier and show that you're "smarter"

I did use the points...but I guess it was just a calculation error. I don't get why it's not passing through, ugh. Let me try again..

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