rushmie Posted December 18, 2011 Report Share Posted December 18, 2011 What do you guys mean by "generalize"/ how do you generalize n and r? Because currently I have like 5 diff. equations for n and 3 diff. equations for r and I dont know what to do next... Reply Link to post Share on other sites More sharing options...
ninna123 Posted December 19, 2011 Report Share Posted December 19, 2011 I have no clue how to put this into formula form, I understand the pattern I'm just so confused on how to place it into values Reply Link to post Share on other sites More sharing options...
Jyrgen Posted December 19, 2011 Report Share Posted December 19, 2011 (edited) yay, almost done, I owe a lot of thanks to this thread and Desy Glau's excellent hints! Just need to find the scopes and limitations now and write this up. Still 3 nights left, shouldn't be too hard. The major challenge is just wrapping your head around it all. I wasted a lot of time with the denominators, but after I created a formula for them it took me literally only 5 min to get a general statement for finding any fraction on the triangle! BTW I'm not sure if there are more than 1 possible GSs, and mine seems a bit weird but it works perfectly. Edited December 19, 2011 by Jyrgen Reply Link to post Share on other sites More sharing options...
Jyrgen Posted December 19, 2011 Report Share Posted December 19, 2011 When showing how I chose quadratic equations as the best model for the numerators, is it "too much" to include graphs of other equation types and the data to illustrate how they do not fit as well as the quadratic? or is it enough to skip that and say the quadratic offered the best possible fit? I can prove that anyway with its Pearson coefficient value? Reply Link to post Share on other sites More sharing options...
dessskris Posted December 27, 2011 Report Share Posted December 27, 2011 I attempted to use a systems of equations to find the equation of the general statement, it worked for the numerator but not for the denominator. it must work for the denominator too. you must've put the table wrongly. note that n doesn't always start from 1. and don't include the 1s on the sides. I see all the patterns in the triangle and have noticed some little formulas i can use with only n and r, but what is really stumpping me is the E in the equation in question 5. Is there any significance it being there? I don't understand what it stands for. Can someone plz try to explain it .? En( r ) basically refers to the rth fraction in the nth row. it's just the symbol. you know, like f(x) basically means function of x. What do you guys mean by "generalize"/ how do you generalize n and r? Because currently I have like 5 diff. equations for n and 3 diff. equations for r and I dont know what to do next... get rid of varying numbers, get an expression (a formula, a general statement) in terms of n and r that works for ALL values of n and r. I have no clue how to put this into formula form, I understand the pattern I'm just so confused on how to place it into values there are a lot of methods, the easiest one is graphical method where you just plot the sets of data and find best regression. of course there are other, more sophisticated methods but that's what you all need to find out. I can't be giving all the hints. yay, almost done, I owe a lot of thanks to this thread and Desy Glau's excellent hints! Just need to find the scopes and limitations now and write this up. Still 3 nights left, shouldn't be too hard. The major challenge is just wrapping your head around it all. I wasted a lot of time with the denominators, but after I created a formula for them it took me literally only 5 min to get a general statement for finding any fraction on the triangle! BTW I'm not sure if there are more than 1 possible GSs, and mine seems a bit weird but it works perfectly. thanks there is only one general statement. When showing how I chose quadratic equations as the best model for the numerators, is it "too much" to include graphs of other equation types and the data to illustrate how they do not fit as well as the quadratic? or is it enough to skip that and say the quadratic offered the best possible fit? I can prove that anyway with its Pearson coefficient value? actually since this is NOT type 2 task, you don't really need to do that. what you need to do is to give a formal justification of why it has a quadratic formula. not because it's the best fit regression. not because the R^2 value is exactly 1. Reply Link to post Share on other sites More sharing options...
Fonons Posted January 2, 2012 Report Share Posted January 2, 2012 I attempted to use a systems of equations to find the equation of the general statement, it worked for the numerator but not for the denominator. it must work for the denominator too. you must've put the table wrongly. note that n doesn't always start from 1. and don't include the 1s on the sides. I see all the patterns in the triangle and have noticed some little formulas i can use with only n and r, but what is really stumpping me is the E in the equation in question 5. Is there any significance it being there? I don't understand what it stands for. Can someone plz try to explain it .? En( r ) basically refers to the rth fraction in the nth row. it's just the symbol. you know, like f(x) basically means function of x. What do you guys mean by "generalize"/ how do you generalize n and r? Because currently I have like 5 diff. equations for n and 3 diff. equations for r and I dont know what to do next... get rid of varying numbers, get an expression (a formula, a general statement) in terms of n and r that works for ALL values of n and r. I have no clue how to put this into formula form, I understand the pattern I'm just so confused on how to place it into values there are a lot of methods, the easiest one is graphical method where you just plot the sets of data and find best regression. of course there are other, more sophisticated methods but that's what you all need to find out. I can't be giving all the hints. yay, almost done, I owe a lot of thanks to this thread and Desy Glau's excellent hints! Just need to find the scopes and limitations now and write this up. Still 3 nights left, shouldn't be too hard. The major challenge is just wrapping your head around it all. I wasted a lot of time with the denominators, but after I created a formula for them it took me literally only 5 min to get a general statement for finding any fraction on the triangle! BTW I'm not sure if there are more than 1 possible GSs, and mine seems a bit weird but it works perfectly. thanks there is only one general statement. When showing how I chose quadratic equations as the best model for the numerators, is it "too much" to include graphs of other equation types and the data to illustrate how they do not fit as well as the quadratic? or is it enough to skip that and say the quadratic offered the best possible fit? I can prove that anyway with its Pearson coefficient value? actually since this is NOT type 2 task, you don't really need to do that. what you need to do is to give a formal justification of why it has a quadratic formula. not because it's the best fit regression. not because the R^2 value is exactly 1. Desy, thank you SO much for all the help! I've been lurking in this thread for over 4 hours and I understand so much more mainly because of posts from you! I think I got the general statement for the denominator, but can I mail it to you to double-check that is it correct? It looks a little...funky? Reply Link to post Share on other sites More sharing options...
dessskris Posted January 2, 2012 Report Share Posted January 2, 2012 Desy, thank you SO much for all the help! I've been lurking in this thread for over 4 hours and I understand so much more mainly because of posts from you! I think I got the general statement for the denominator, but can I mail it to you to double-check that is it correct? It looks a little...funky? aww thanks that's great to her! just checking the equation? alright you can message me. good luck with this IA! Reply Link to post Share on other sites More sharing options...
swedetrader Posted January 2, 2012 Report Share Posted January 2, 2012 First off thanks for the help guys! Good teamwork Can someone please tell me the format of the general statement because I'm having difficulties with expressing the GS using r and n and since we are doing it for both the numerator and the denominator it is a bit confusing to say the least. Would appreciate any help. Cheers! Reply Link to post Share on other sites More sharing options...
Fonons Posted January 2, 2012 Report Share Posted January 2, 2012 (edited) First off thanks for the help guys! Good teamwork Can someone please tell me the format of the general statement because I'm having difficulties with expressing the GS using r and n and since we are doing it for both the numerator and the denominator it is a bit confusing to say the least. Would appreciate any help. Cheers! The general statement should look like this: En( r) = (numerator gs)/(denominator gs) And both individual general statements should be in the format of a quadratic equation (y=ax^2 + bx + c). But remember instead of using "x" use "n" and "r"! Edited January 2, 2012 by Fonons 1 Reply Link to post Share on other sites More sharing options...
khilna Posted January 4, 2012 Report Share Posted January 4, 2012 Yeah, I get you. It's just gonna be hard for me to explain it in words. But if I am getting you, then after the row with "15/11" would be1 21/16 21/13 21/? 21/13 21/16 1 right?What could be the middle number??the middle number would be 12. therefore 21/12 Reply Link to post Share on other sites More sharing options...
swedetrader Posted January 4, 2012 Report Share Posted January 4, 2012 (edited) Can someone help me by telling me how to use a graphing programme (I'm using GeoGebra) to graph the general statement. I can't seem to make it graph it and I think it's because the GS has two variables sort of since it is E_n( r )How did you guys solve this issue? Edited January 4, 2012 by swedetrader Reply Link to post Share on other sites More sharing options...
IB Canadian Posted January 5, 2012 Report Share Posted January 5, 2012 I have found an equation for the denominator but it is giving me a denominator that is 2x the actual denominator. I believe that I am on the right track as it is quadratic as mentioned in numerous previous posts. Does anyone know where I may have gone wrong? Any help would be much appreciated, Thanks in advance! Reply Link to post Share on other sites More sharing options...
El Che Posted January 5, 2012 Report Share Posted January 5, 2012 I think you've made a mistake while generalizing it from your tabulated values. If it gives you 2x the denominator then check where you have this multiplication by 2. Then, I believe, you can correct your mistake. Reply Link to post Share on other sites More sharing options...
IB Canadian Posted January 5, 2012 Report Share Posted January 5, 2012 (edited) I think you've made a mistake while generalizing it from your tabulated values. If it gives you 2x the denominator then check where you have this multiplication by 2. Then, I believe, you can correct your mistake.I think you are right but I don't know if it's when I am generalizing or when I am finding the equations for the denominator.Edit: I think I got it, simple mistake when putting the equations into general form. Thanks for your help! Edited January 5, 2012 by IB Canadian Reply Link to post Share on other sites More sharing options...
El Che Posted January 5, 2012 Report Share Posted January 5, 2012 Can you recognize any relations between these values? For example look at the value for a when r = 1, 2, 3, etc. Then look for b in the same way, and so on. After that you put them into your quadratic equation and, thus you generalize it. What I mean by that is, for example if you figure out a = 30, b = 5, and c = 15, you put them like this 30n2 + 5n + 15. I hope I made sense. =) Reply Link to post Share on other sites More sharing options...
Akis DrunknFunki Posted January 7, 2012 Report Share Posted January 7, 2012 Hi in this project I have problems regarding the second question which says: "Using technology, plot the relation between the row number, n, and the numerator in each row describe what you notice from your plot and write a general statement to represent this" Reply Link to post Share on other sites More sharing options...
El Che Posted January 7, 2012 Report Share Posted January 7, 2012 Hi! You didn't clarify what exactly your problems are, but it's fine. Consider the image attached to this post. I think now you should notice that numerators are 1, 3, 6, 10, 15, respectively when the row numbers are 1, 2, 3, 4, 5. I personally have included row number 6 and its corresponding numerator in my plot. Once you have these values you can use either a GDC or Excel to graph them. After plotting the relation you will see the graph of a commonly used equation. It basically wants you to comment what happens to the numerator when the row number increases. Does it also increase or decrease? For representing the general statement I advice you to search for "triangular numbers" and their formula in the Internet. These should be enough for step 3. If you have any further questions, don't hesitate to ask. Good luck! Reply Link to post Share on other sites More sharing options...
LMaxwell Posted January 7, 2012 Report Share Posted January 7, 2012 Hi! You didn't clarify what exactly your problems are, but it's fine. Consider the image attached to this post. I think now you should notice that numerators are 1, 3, 6, 10, 15, respectively when the row numbers are 1, 2, 3, 4, 5. I personally have included row number 6 and its corresponding numerator in my plot. Once you have these values you can use either a GDC or Excel to graph them. After plotting the relation you will see the graph of a commonly used equation. It basically wants you to comment what happens to the numerator when the row number increases. Does it also increase or decrease? For representing the general statement I advice you to search for "triangular numbers" and their formula in the Internet. These should be enough for step 3. If you have any further questions, don't hesitate to ask. Good luck! I thought an explanation was required to get the higher marks? thats what it says in criteria B: communication of the mark scheme Reply Link to post Share on other sites More sharing options...
El Che Posted January 7, 2012 Report Share Posted January 7, 2012 I also provided a short explanation of the formula, since these numbers that I mentioned are triangular, etc. and got full marks on criteria B. I think communication is even more important for the actual general statement. I don't know maybe my teacher was not so picky with this task (we did it as a practice one). I'm giving advice based on my teacher's comments, so you'd better explain everything in details. Reply Link to post Share on other sites More sharing options...
IB Canadian Posted January 7, 2012 Report Share Posted January 7, 2012 How exactly do you generalize the equations? I am not sure if mine are correct but since i don't know exactly how to generalize the quadratics for the denominator not having the right equations does not really matter. Reply Link to post Share on other sites More sharing options...
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