mm-1005 === Subject: Re: A*X +B*Y+C*Z=0 solutions by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBHMLmR09364; >Well, what about X,Y, Z relative prime as solutions? >george Okay, so X, Y, and Z are coprime (that is, we have gcd(X,Y,Z) = 1). Take gcd(X,Y) = k. Then, Euclids algorithm allows us to find integers a and b such that a*X + b*Y = k. Then, observe that for any number C, a*X + b*Y + C = k + C. Since C is arbitrary, let C = -k. Then a*X + b*Y + C = 0. Now multiply both sides of the above equation by Z, so that a*Z*X + b*Z*Y + C*Z = 0. If we let A = a*Z, B = b*Z, then we have the desired result: A*X + B*Y + C*Z = 0. Hows that? Joseph A. === Subject: Re: A*X +B*Y+C*Z=0 solutions by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBIDPPn13895; Hi Joseph, I Apreciate that you take time to do calculations.Every good mathematician likes calculations no matter what elementary they are. Well my points are these: 1) .I said Any A,B,C integers.What about A,B relative primes case Or A,B,C relative prime case ,are not they part of Any? 2) About yours choosen case:Does Euclid algorithm gives the solution X and Y for any a and b IN NO MORE THAN 15(FIFTEEN ) ARITHMETHICAL OPERATIONS ? 3).This is not about your case.It is just a reminder:X,Y,Z are relative prime. That how it is. this problem a easy or hard one? >>Well, what about X,Y, Z relative prime as solutions? >>george >Okay, so X, Y, and Z are coprime (that is, we have gcd(X,Y,Z) = 1). >Take gcd(X,Y) = k. Then, Euclids algorithm allows us to find >integers a and b such that >a*X + b*Y = k. >Then, observe that for any number C, >a*X + b*Y + C = k + C. >Since C is arbitrary, let C = -k. Then >a*X + b*Y + C = 0. >Now multiply both sides of the above equation by Z, so that >a*Z*X + b*Z*Y + C*Z = 0. >If we let A = a*Z, B = b*Z, then we have the desired result: >A*X + B*Y + C*Z = 0. >Hows that? >Joseph A. === Subject: Re: Reverse Hash Function >I want to ask: Is it possible to build a reverse hash function h() so that >h(h(B)) is equal to B? An analogy: there is a cosine function and an inverse cosine function. Is it true that cos( arccos(x) ) = x? Yes. Is it true that arccos( cos(t) ) = t? Not necessarily. That should start you thinking. What might be the characteristics of your hash function and reverse hash function? -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ Dont move, or Ill fill you full of [... pause ...] little yellow bolts of light. -- Farscape, first episode === Subject: Re: Reverse Hash Function by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBHMLme09360; >I met a problem, and I dont have experience to solve it. Thus, please give >me a help. >My question is: >I have a hash function: h(). >I have a plain text: A >So I can get a hash value B = h(A) >Suppose that I have a reverse hash function: h() >Then I can get a fade plain text A= h(B), probably A is not equal to A, >but it doesnt matter! >I want to ask: Is it possible to build a reverse hash function h() so that >h(h(B)) is equal to B? >I do appreciate if you could answer me or send me a hint. >Merry Christmas! >P. L. Let D be the domain and R be the range of the hash function h; that is, h:D->R. The hash function must be defined so that for some plain text A, the value of h(A) is unique (i.e. h(A1) = h(A2) iff A1 = A2 for all points A1 & A2 in D). Furthermore, for every element B in the range R, there must exist some point A in D such that h(A) = B. Then, we can have an inverse hash function h with domain R and range D; that is, h:R->D with the property that for all points B in R, h(h(B)) = B. >Then I can get a fade plain text A= h(B), probably A is not equal to A, >but it doesnt matter! It does matter. You see for the inverse function to be properly defined, h(B) = A if h(A) = B for B in R and A in D. If you have more specific questions, Ill be glad to address them. Hope that helps. Joseph A. === Subject: Re: help! Bonus! >> How many 3-digit numbers consist only of odd digits? >I make it 250, including negative integers. Interesting philosophical question: is -157 a three-digit number? -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ Dont move, or Ill fill you full of [... pause ...] little yellow bolts of light. -- Farscape, first episode === Subject: Re: help! Bonus! >> How many 3-digit numbers consist only of odd digits? >I make it 250, including negative integers. > Interesting philosophical question: is -157 a three-digit number? Yes, and so are -15.7 1/57 etc === Subject: Re: help! Bonus! > How many 3-digit numbers consist only of odd digits? >>I make it 250, including negative integers. >> Interesting philosophical question: is -157 a three-digit number? >Yes, and so are >-15.7 1/57 etc Once those are accepted, there is no longer any single answer to the OPs homework problem. Not that theres anything wrong with that! :-) -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ Dont move, or Ill fill you full of [... pause ...] little yellow bolts of light. -- Farscape, first episode === Subject: Re: help! Bonus! >> How many 3-digit numbers consist only of odd digits? >I make it 250, including negative integers. > Interesting philosophical question: is -157 a three-digit number? > Yes, and so are > -15.7 1/57 etc Since you opened the box, what about 2*2*2? === Subject: Re: help! Bonus! >Since you opened the box, what about 2*2*2? Oh nooooo!! Pandora is escaping....... --Lynn === Subject: Re: help! Bonus! <0N3EQcNEmLLRmDqiyMSMnfKZhYgp@4ax.comSince you opened the box, what about 2*2*2? > Oh nooooo!! Pandora is escaping....... Oh you naughty snip, you stop the sheriff who would have caught her by her slip ups that 2 and 2 and 2 arent ever odd digits. === Subject: Re: help! Bonus! >Since you opened the box, what about 2*2*2? > Oh nooooo!! Pandora is escaping....... > Oh you naughty snip, you stop the sheriff > who would have caught her by her slip ups > that 2 and 2 and 2 arent ever odd digits. My bad. Forgot the origianl problem. How about 5*5*5 then? === Subject: Re: help! Bonus! <0N3EQcNEmLLRmDqiyMSMnfKZhYgp@4ax.com >Since you opened the box, what about 2*2*2? Oh nooooo!! Pandora is escaping....... Oh you naughty snip, you stop the sheriff > who would have caught her by her slip ups > that 2 and 2 and 2 arent ever odd digits. > My bad. Forgot the origianl problem. > How about 5*5*5 then? Its not a three odd digit number, its a one odd digit number. ;-) === Subject: Re: help! Bonus! How many 3-digit numbers consist only of odd digits? >I make it 250, including negative integers. > Interesting philosophical question: is -157 a three-digit number? Double the fun, is 11.1 a three digit number? For to ignore this point is much big blunder. ;-) Im so sorry you little speck to give you the digit would be undue respect like the negative smidgit who too is uncircumspect. === Subject: Re: need the answer to a riddle >imagine folding a large piece of paper in half. If you continue > this >process 50 times how many layers will you have? what is the rule > for >the number of layers compared to the number folds? >>lets see >>0 folds = 1 layer = 2^0 >>1 fold = 2 layers = 2^1 >>2 folds = 4 layers = 2^2 >>3 folds = 8 layers = 2^3 >>... >>n folds = 2^n layers >>BTW Try folding a piece of paper more than 7 times in this way. It >>becomes too thick to fold any more. > and the number of creases in n folds is > 2^n - 1. > i love this sort of stuff =) > Joseph A Similarly: How many moves does it take to solve the Tower of Hanoi with N disks? --Dan === Subject: Re: Vector problem by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBIDPQP13899; Having tried a similar exercise using the same method, Im stuck again: A force R= (5i +12j). R is the resultant of two forces P and Q. The line of action of P is parallel to the vector (i + 2j) and the line of action of Q is parallel to the vector (i + 3j). Determine the forces P and Q , expressing each in terms of i and j. ---- Well...obviously P+Q=R An earlier part of the exercise asked me to calculate the magnitude of R (13N) and the angle between the line of action of R and the i to the nearest degree (67.bc) I started by assuming that P and Q were parallel, but I guess that is not what the question says. I guess that I have to relate the vectors to the magnitudes and dont know where to start...! Any help appreciated. Jo >> Im afraid I still cant see it. Sorry... >> I must add the 2 forces (3i + xi) + 4j + yj) = R >Right. So R = (x + 3)i + (y + 4)j >> and this is parallel to i + 2j >Actually, in your original problem I believe it >had to be parallel to (i - 2j), which is what >Ill use. >> By being parallel the angles and direction will obviously be the same. >Correct. Being parallel means the direction of the vectors >must be the same but their magnitudes need not be. So >what operation changes the magnitude of a vector but leaves >its direction unchanged? >Multiplication by a scalar. >So c(i - 2j) is parallel to (i - 2j). >Therefore > (x + 3)i + (y + 4)j = c(i - 2j) >which gives you > x + 3 = c > y + 4 = -2c >Just eliminate c to get a relation between x and y > y + 4 = -2(x + 3) > y + 4 = -2x - 6 > y = -2x - 10 >Lets check a value. For x=0, y=-10, and > (3, 4) + (0, -10) = (3, -6) >which is indeed parallel to (1, -2). >And yes, this means there are an infinity of (x, y) pairs that give a >resultant parallel to (1, -2). Do you see why? If not, draw the >vector (3, 4). Then draw the line which contains all vectors parallel >to (1, -2). It should be clear that there are an infinity of vectors >you can draw from the head (3, 4) that touch the line defined by (1, -2). >a) Find, the nearest degree, the acute angle between the line of >action of R and the vector i. >As you stated above, parallel means directions are the same. >So that means R is in the same direction as (1, -2). Which >means that the angle between R and (1, 0) is the same as the >angle between (1, -2) and (1, 0). So compute that angle. >-- >Rich Carreiro rlcarr@animato.arlington.ma.us === Subject: Re: Vector problem > Having tried a similar exercise using the same method, Im stuck > again: > A force R= (5i +12j). R is the resultant of two forces P and Q. The > line of action of P is parallel to the vector (i + 2j) and the line of > action of Q is parallel to the vector (i + 3j). > Determine the forces P and Q , expressing each in terms of i and j. > ---- For scalars u and v, to be determined, u(1+2j) + v(i + 3j) = (5i + 12j) So u + v = 5 and 2 u + 3 v = 12 === Subject: Re: Vector problem > Having tried a similar exercise using the same method, Im stuck > again: > A force R= (5i +12j). R is the resultant of two forces P and Q. The > line of action of P is parallel to the vector (i + 2j) and the line of > action of Q is parallel to the vector (i + 3j). > Determine the forces P and Q , expressing each in terms of i and j. > Well...obviously P+Q=R Yes. Start with the definition of parallel. As in the last post, if vector A is parallel to vector B, that means that A = cB where c is a scalar. So that means you know that P = p(i + 2j) and Q = q(i + 3j) where p and q are scalars. Now use P+Q=R to determine p and q, and from that, P and Q. -- Rich Carreiro rlcarr@animato.arlington.ma.us === Subject: looking for problems by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBIDPP313863; >Given any integers A , B , C find x,y ,z such that: > A*x+B*y +C*z=o using no more than 15(fifteen) arithmetical >operations! x,y,z relative prime,A,B,C relative prime too so we can get away the rivial cases.OK? george ghiata === Subject: Pells eq. algorythms by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBIDPPI13873; Is anybody can tell me how many elementary algorythms to find the solutions to the Pells eq. are out there? Name them if you please george === Subject: Advanced help for students in doing assignments (New Year discount is provided) I am a scientist, providing advanced help for undergrad, postgrad, distance education and adult students in doing assignments, theses, projects, dissertations, etc. I can do your assignment instead of you for a fee, but take into account, that submission solution provided by me as your own is your responsibility. SEND YOUR ORDER NOW! Subjects available: -mathematics -physics -electrical engineering -computer science -communications -systems analysis -business & management -international business -HR & PR management -other (inquire your specific subject) Please visit my web site: http://www.megaone.com/expert2005/consultant.htm for more info and rates. You may submit your assignment text online by filling in a feedback form. CONTACT: contact me *only* from my web site (above). === Subject: Calculus by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBIMH5F25023; Explain why it may be wise in a Calculus class to have the relationship of the circumference and area of a circle be a primary example of the derivative/integral relationship. === Subject: Re: Calculus >Explain why it may be wise in a Calculus class to have the >relationship of the circumference and area of a circle be a primary >example of the derivative/integral relationship. Others mileage may vary, but for myself, I might point it out when teaching differentials. I think that showing the students how a change of 1 in the radius gives approximately 2*pi*r change in area by examining the circular strip that is added gives insight into why the rate of change of area is the circumference. Im not sure I would use it as a primary example though, whatever that means. --Lynn === Subject: Re: Calculus >Explain why it may be wise in a Calculus class to have the >relationship of the circumference and area of a circle be a primary >example of the derivative/integral relationship. Determining the relationship using Calculus techniques illustrates the meaningfulness of these techniques; they are relationships which the student has previously studied and with which he has become acquainted. G C === Subject: Re: Need sources on how and why math manipulatives are good. Peter, I have also read various works by Marilyn Burns, and I believe her to be the leading researcher/practitioner with the utilization of math manipulatives among her contemporaries. It is with great enthusiasm that I reply to your posting, I only wish that it were more recent. I myself have a great love for math manipulatives, and am not yet even a teacher. Throughout my training, however, I have been lucky enough to find cooperating teachers who share a love for math manipulatives the way I do. As you can imagine, I have had many fulfilling experiences in the classroom with the use of MMs because of this shared respect. I believe that it is not only necessary to use MMs during the math block, but to also allow for overall availability throughout the entire schoolday. You would be surprised at how often students incorporate MMs into various other school study ventures (even in play/freetime). By making MMs ubiquitous, you will ultimately foster mathematic understanding among your students that you never thought possible. I have seen it myself, firsthand...and I strongly advocate for the use of MMs. They not only show students physical representations of math concepts, but also allow for mathematical creativity and discovery that may not be possible through instruction itself. Every child is different, and discovers and understands concepts his/her own way. By incorporating MMs into your classroom, you will allow students the opportunity for discovery on their own...which I believe to be the most important part of education all together. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Rhetorical Property Hey guys! Just returned from the math convention in St. Louis by Dr. Rita Bussing. Shes pretty much a GENIUS! Anyway, I learned a new math trick that could help you and any student struggling with the basic skills of math. I was introduced to rhetorical property by Dr. Bussing. It goes like this: Objective: To delete the double negatives of semi-intergral equation. First, look at your variables in the equation and solve for them. {Ex. 2xî-(4aa + Pi) .85 (x + 7)} Next, subtract every nuber by zero. Now, your problem must be simplified. Move all of your variables behind the addition sign and add the word or between each variable. Get the reciprocal of each number, deleting the variable. Your answer could be 1/3 or 45/9 What did I tell you guys, its a synch!!!!! -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Number Recognition To Leslie: Ive read your e-mail about number recognition Maybe my nummolt program will be useful to you: It converts a number in base 10 blocks You can find the program at my page http://www.nummolt.org The download page is http://www.geocities.com/nummolt/nummolt/numdown.htm Maurici Carb.97 Jordi http://www.nummolt.org Spain >I am doing a short research paper on how to teach number recognition. >I tutored a third grade student who was unable to look at the number >22, for example, and tell me what that number was. He could create >numbers using base ten blocks, but he could not look at any number and >tell me what that number was. When I research online, it tells me how >to teach a toddler number recognition, but that is not appropriate for >this situation. Could someone please give me some resources to help >with this paper. I greatly appreciate it. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Moderator Away and Unavailable Dec. 12-19 Hello Newsgroup Participants, The moderator will be away and unable to perform moderator they will be queued and I will review them upon my return. Your messages will not be lost. They will simply be waiting until I get back at which time I will review and post them. However, during this time while I am away, no new messages will be posted to the newsgroup, since I will not be available to approve and post messages. k12.ed.math moderator kem-moderator@k12groups.org http://www.thinkspot.net/k12math/ === Subject: Re: technology in the classroom Im doing some research on incorporating technology into Math lessons. I am a student at the University of Wisconsin Madison, preparing to become an elementary school teacher, and Ive had some great experiences incorporating technology into math. In fact, it is a requirment within the School of Education, in order to fulfill the standards needed to graduate. My experience thus far has involved the use of spreadsheets, and an online math manipulatives program. When teaching my students about the fundamentals of graphing, I incorporated the use of spreadsheets as an integral part of the unit. Not only did it show them how useful a spreadsheet program can be (knowledge that every student should know regardless), but also connected real-world information/data to various kinds of graphs. I believe that it helped students gain a stronger grasp on the concept behind graphs, and also the methods used in which to create them. As for math manipulatives online, I must say that it was my favorite. Im sure you are familiar with math manipulatives such as pattern blocks and the like...but the online version allowed students to make 3-D models that wouldve been impossible without the use of a computer. The program allowed students to turn the object around in any direction...look inside of the object...etc. Students were absolutely enthralled by the program, and ultimately learned a lot. My personal opinion regarding the incorporation of technology into math, and other subjects, is absolutely necessary...especially in todays world. I believe that children need something that they can relate themselves, and seeing that we are now surrounded by technology...it only makes sense, no? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Technology in the classroom I must respectfully disagree with your opinions regarding the use of computers in a classroom setting. I believe that in this day and age, computers and other technologies are pertinent to a childs educational literature based upon research that has found not only that technology is an educational aid/enhancer in todays schools, but also a must in that the children of tomorrow will be ill-prepared if not exposed to the effective ways in which technology can (and should) be utilized. Granted, traditional methods of teaching (without the use of computers) will continue to produce excellent results...and I understand that it is difficult to break the mold that has been set in place for so very long, yet there is an ultimate necessity for changing with the times. If children are experiencing computers only within the confines of their households, which usually fosters nothing more that gameplay and nonsensical internet browsing, many will never be enlightened as to the true potential that can be utilized by using a computer. Thus, I believe that it is so very important to teach students how to use computers correctly (internet searches, word processing, spreadsheets, etc.) so that they will be prepared for a world that hasnt even started to discover itself technologically. The advances that will ensue within the next 10-20 years will be tremendous. The human race is in the middle of an age of discovery that continues to accelerate...faster and faster...almost to the point, now, that we cant even see or feel it. Scary? Yes!! But in order to prepare our children for this inevitable future, we must incorporate technology as often as possible within Americas (and the worlds...) schools. We must!! -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry - Proving trigonometric identities How do you prove the following identity: cosA * cotA + sinA = cscA -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Help Can someone please solve this problem- 2,236,000-17,740Y=3,500,000 -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: dont understand algebra >can you explain basic algebra to me ,i can,t catch on to it i have big probelm with understanting ALGEBRA so CAN YOU HELP -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: combinations concept I am doing a short research paper on how to teach combinations. Here in Malaysia, we teach permutation and combination to students in Form 5 ( age of 17-18 ). Students always have problems with this topic. I wonder if students in other countries facing this problem? How teachers teach this topic effectively? Students always feel frustrated when they fail to get the correct answers. I would like to investigate if CAI can help by using the elaborative feedbacks to give extra explanation. Could someone please give me some comments how to teach this topic effectively? I greatly appreciate it. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Limit n^(1/n) = ? when n approaches +infinite limit n^(1/n) = ? when n approaches +infinite The answer is 1. How come? I think it for a long time. I cannot solve it. Can someone help me or give me a hint? I really want to know the solution. Dan -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Numb3rs Has anyone heard anything about this new show on CBS called Numb3rs? Ive seen a couple of commercials for it (starts in January) and it looks pretty cool--like they use numbers and patterns to solve crimes. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Algebra I in 2 yrs > Is there any research out there as to the value or effectiveness of > teaching a conventional algebra I course over a two year period? Im not sure about research but there are curriculum developers (Glencoe for one) who have guidelines for teaching their Algebra I courses in two years. I teach an Algebra 1A/1B type class that takes two years to complete. The idea behind it is to have the time to provide the background knowledge that might be missing prior to teaching the new concept. I have the luxury of extra time to re-teach fractions, percents, decimals, positive and negative numbers, etc. As anecdotal evidence our program has been very effective at catching kids up. Bernadette -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: e Jerry Beeler (jerrybeeler@att.net) queried: : Eulers number: All too often I see something like this : : Ôe has the value of approximately 2.718 and often appears in : physics and math and we call log(base e)n as ln(n). : : Im teaching a GT Algebra II next term and would like to go a : little further than that. But ... this is Algebra II, though GT level, : I can find only very complicated calculus oriented derivations for e, : and not real examples. : : Can anyone give me (1) a non calculus oriented derivation or : explaination for e, and (2) an example or two of where it often : appears in physics and math. In the British Columbia high school curriculum, we are mandated to introduce Ôe, but how much students are to understand is rather vague. Given a formula like: y=326e^(5.6x) and a value for Ôy, they should be able to solve for Ôx. (Presumably using the LN() function rather than by knowing the value of Ôe.) Our department has been debating how to introduce Ôe and how much detail to attempt. My preferred approach follows: Review compound interest, noting that shorter compounding intervals lead to higher earnings. Have students calculate the returns for an investment with interest compounded annually, monthly, daily, hourly, minutely. (Any further and there is too much round off error for accuracy.) This doesnt work as well with current interest rates as it did back when we had double digit interest. In any case, the students should note that there are diminishing returns as the compounding interval decreases towards zero. Next I give the students a table of returns for a specific investment compounded minutely for a variety of interest rates (specified as decimals rather than percents - 0.05 rather than 5%). They are to make a graph from the table (which goes up to ridiculus interest rates, like 5.00 - 500%), and find a mathematical model (a formula) to match that graph. With guidence, the students realize the function is exponential with a base of about 2.718... Now I point out that THIS exponential base is actually built-in to their calculators: e^x along with its matching logarithm: Ln(x). So they have two logaritms in their calculators to choose from, either base 10 or base e, and either can be used to solve most exponent and logarithm problems. We finish by doing some other examples of continuously compounded interest, and then I mention that they will see this number in a variety of other contexts later on - its not just for banking. This example of continuously compounded interest is the only naturally occuring high school example of Ôe I can think of. Using a base of Ôe for other exponential functions doesnt really make much sense without calculus or at least talking about a continuously compounded growth rate. In high school, if you want radioactive decay, it makes much more sense to find the half life and use a base of (1/2). For population growth, find the actual annual percentage growth rate Ôr and use a base of (1+r/100). Without the necessity of calculating derivatives or working from differential equations, a base of Ôe is entirely unmotivated for these examples. The famous equation related five of the most important numbers in mathematics: e^(i*pi) + 1 = 0 is beautiful, but meaningless to most high school students who havent even studied imaginary numbers, but less the machinery of calculus needed to justify this equation. Robert |)|/| || Burnaby South Secondary School || |orewood@olc.ubc.ca || Beautiful British Columbia Mathematics & Computer Science || (Canada) -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: e === << Subject: e Message-id: Eulers number: All too often I see something like this : Ôe has the value of approximately 2.718 and often appears in physics and math and we call log(base e)n as ln(n). Can anyone give me (1) a non calculus oriented derivation or explanation for e, and (2) an example or two of where it often appears in physics and math. >> The curve formed by a cable hanging from two points under its own weight can only be described using e. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Sine and Cosine >> In the equation y=(a)sin b(x+c) what does the C do to the graph? > Shifts it left and right. > Bill -- As Bill said this is correct, and it is called the acrophase of the function. As a digression are these two functions equivalent: y1=cos(x+0) and y2=sin(x+(PI/2)) (the sine-function is a cosine-function with an acrophase of 3.1415.../2 Ronny Mandal === Subject: Re: need the answer to a riddle >> imagine folding a large piece of paper in half. If you continue >> this >> process 50 times how many layers will you have? what is the rule >> for >> the number of layers compared to the number folds? > lets see > 0 folds = 1 layer = 2^0 > 1 fold = 2 layers = 2^1 > 2 folds = 4 layers = 2^2 > 3 folds = 8 layers = 2^3 > ... > n folds = 2^n layers > BTW Try folding a piece of paper more than 7 times in this way. It > becomes too thick to fold any more. > T >> and the number of creases in n folds is >> 2^n - 1. >> i love this sort of stuff =) >> Joseph A > Similarly: > How many moves does it take to solve the Tower of Hanoi with N disks? > Since you opened the box, what about 2*2*2? Oh nooooo!! Pandora is escaping....... Oh you naughty snip, you stop the sheriff > who would have caught her by her slip ups > that 2 and 2 and 2 arent ever odd digits. > My bad. Forgot the origianl problem. > How about 5*5*5 then? > Its not a three odd digit number, its a one odd digit number. ;-) Darnit, how about 1+2+3 then? I know, I know, thats an even number. === Subject: Re: looking for problems by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBJLiIi02880; Hi Todd, I am not beating the bush around as a you do not express your opinions in mathematical termslike :you are wrong and here is why.Or, are you frustated because you can figured it out? Then say it:I gave up;I am not able do it and enlighten me. Not to imply that is something wrong with me just because you can get to the end of it.Yes, a,b,c ,Y,x are natural numbers. george ghiata >>I mean : >>Change Y^2=A*x^2+1 into a PytagoriansTriangle formula:a^2+b^2=c^2 >>That will show where the mathematical origins of pells eq.are coming >>from:well back to 500.b.c. >Yes, why dont you tell enlighten us and tell us how you do that? >Bear in mind that a, b, c, Y, x are supposed to be integers in >these Diophantine problems. >Lets hear it. Stop beating around the bush. >Todd Trimble === Subject: Re: H Linear systems of eq.solutions by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBJLiIA02904; Forget about this problem.somthing wrong about this one >As i said there is a method to find in no more that 15 arithmetical >operation such that >A*X+B*Y+Z*C=0 where A,B,C are relative prime integers and X,Y,Z are >coprimes too. >Therfore we can resolve any Homogeneous linear system of as many >number of given integers a,b,c,d e..........n and unknowns >x,y,z,u,v............(n1) >The number of calculations is very small as you can figure out from >the begining of this message! Matrixes? Oh,No! forget about them in >this case >george ghiata === Subject: need a ruler? go to my free online/onscreen ruler project by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBJLiIc02919; Did you ever need an online ruler while you were sitting in front of your computer? ænow you can come to this page and use this website to measure things. http://home.earthlink.net/~moon8500/davidmoon.html === Subject: Re: Rabbitting vectors by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBJLiJB02995; >Two rabbits, Alfred and Bertha, are running in a field. The field is a >horizontal plane and O is a fixed point on the field from which all >position vectors are measured. The perpendicular vectors i and j are >unit vectors in the plane. At time t = 0 Alfred is at the point O and >Bertha is at the point with position vector 4j m. Alfred runs with >constant velocity towards the point with postion vector (4i + 3j) m, >and Bertha runs also with constant velocity, towards the point with >position vector (8i + 7j) m . Alfreds speed is 10 m/s, and Berthas >speed is 2sqrt 73 m/s. >The first question asks to find Alfreds velocity, giving the answer >in vector form. >Im at a loss! >I wonder if the mention of Ôunit vectors is important. >If Alfreds speed is 10 m/s its velocity must be the same amount but >with a direction. So the hipotenuse of the triangle formed by the >vectors is 10, which means that the sides squared must add up to 100. >But how do I find those sides? ------------------------------------------------------------- -------- The direction of this vector v(A) is the same as the direction of the position vector r(P) = (4i + 3j) m. In other words, v(A) = c * r(P) = c*(4i + 3j) m where c is a (positive) constant with dimmension [/sec]. |v(A)| = c * sqrt(4^2 + 3^2) = c * 5m = 10 m/sec c = 2 /sec v(A) = (8i + 6j) m/sec === Subject: Re: Rabbitting vectors by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBJLiEJ02695; Still struggling...The position vector is (3i + 4j)away from the origin. That means that the hipotenuse of the triangle should be 5. The fact that Alfreds speed is 10 m/s (the hipotenuse of a different triangle regarding velocity), suggests that there must be a connection, as 10/5 = 2 as the answer to the problem is 2 * (3i + 4j) = (6i + 8j) If I am correct, I still do not understand the connection. Help... Jo >Two rabbits, Alfred and Bertha, are running in a field. The field is a >horizontal plane and O is a fixed point on the field from which all >position vectors are measured. The perpendicular vectors i and j are >unit vectors in the plane. At time t = 0 Alfred is at the point O and >Bertha is at the point with position vector 4j m. Alfred runs with >constant velocity towards the point with postion vector (4i + 3j) m, >and Bertha runs also with constant velocity, towards the point with >position vector (8i + 7j) m . Alfreds speed is 10 m/s, and Berthas >speed is 2sqrt 73 m/s. >The first question asks to find Alfreds velocity, giving the answer >in vector form. >Im at a loss! >I wonder if the mention of Ôunit vectors is important. >If Alfreds speed is 10 m/s its velocity must be the same amount but >with a direction. So the hipotenuse of the triangle formed by the >vectors is 10, which means that the sides squared must add up to 100. >But how do I find those sides? >Knowing from the answer that one side is 6, I wonder if the area under >the graph (4*3)/2 has anything to do with it... >Help appreciated. === Subject: Re: Everything is ok by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBJLiHm02848; What you talk about? Give us more details and names. george >The set of equations given before had been solved for 2 years. === Subject: Re: Everything is ok by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBJLiFs02763; >The set of equations given before had been solved for 2 years. I like eating baked ziti. Seriously though, what are you talking about? === Subject: Re: Pells eq. algorythms by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBJLiGG02782; Hi Todd, Well, I apreciate very much your answer. I observed the diference in the notation : I used A and you use D I think this is coming from the the books we studied. Did you ever tried or see the cyclic method used in India back in 800 A.D to find the solutions? Did you wonder If Archimedes had a method to solve the eq. when in theCatlle story- problem he get us to resolve a Pells equation at the end of calculations? Did you ever wonder what was Fermats method to resolve it? Well , I know,in this Age we are conditioned to be very pragmatic, learn to use a method well and be able to Aply it.So less and less we dont have time to wonder or find diferent ways to resolve a problem. I think you are very nice for writing down for me the use of continuu fractions in this case ,but I was looking beyond this when I put the question.I mean,I wanted to hear some original coming from Wondering. Yes, You gave me the case D=61.In one day,two,three days from now I can show to you my algorythm which I call Fermats algorythm.Well ,this algorythm is much simple than what your preference(my opinion).This algorythm shows how Fermat used it to proof his staments about representations of different primes too. In another words it opens a Window in the Hystorie of past methods Remember, Euler was a master of Algorithms and he fail to find one for Pellequation Some Professors know about this method because I PUT IT OUT ,I have shown it to them in writting.But you have to show to me that you look a little bit in the Hyistory of mathematics.Take a course If you did not or studied it by yourself. It is fascinated and insight inspiring.That if you like mathematics . george_ghiata dec 18-04 >>Is anybody can tell me how many elementary algorythms to find the >>solutions to the >>Pells eq. are out there? Name them if you please >>george >I dont know about how many, but one I find pleasing uses >the continued fraction expansion of D^{1/2} where D is the >parameter in the Pell equation x^2 - Dy^2 = +/-1. We assume >that D is square-free. >The solutions (x, y) of this equation may be identified with >the group of multiplicative units x + yD^{1/2} in the ring >Z[D^{1/2}] (the inverse being of course x - yD^{1/2}). This >group is a discrete subgroup of the union of two hyperbolas >x^2 - Dy^2 = +/-1, and therefore has rank at most 1 [in fact >the rank is exactly 1, but never mind that]; the only roots >of unity are +/-1, so that is the torsion subgroup, and >therefore the group of units is isomorphic to Z_2 or Z x Z_2. >That is, the solutions to the Pell equation are of the form > (-1)^p (a + bD^{1/2})^n (n in Z; p = 0 or 1) >where a + bD^{1/2} is a generator of the torsionfree summand, >and it remains to compute this generator. We remark that >if D = 3 mod 4, then x^2 - Dy^2 = -1 has no solution; >otherwise the generator will satisfy this equation, and its >square will be the generator of the subgroup lying in the >hyperbola x^2 - Dy^2 = 1. >The algorithm for producing a generator rests on a very simple >principle: let r = D^(1/2); then > r = (ar + c)/(br + d) >for integers a, b, c, d iff a = d and c = br^2 = bD. Hence >a^2 - Db^2 will be the determinant of the matrix > |a c| > | | > |b d| >and so we are interested in characterizing such matrices whose >determinant is +/-1. For any such matrix, we can apply the >Euclidean algorithm to resolve (ar + c)/(br + d) as a continued >fraction of the form > a_0 + 1/(a_1+ 1/(a_2+ ... + 1/((r+a_n)...)) >and thus the generating element will arise out of a minimal >equation of the form > r = a_0 + 1/a_1+ 1/a_2+ ... + 1/(r+a_n). >This makes it natural to examine the continued fraction expansion >of r. >Perhaps this is best explained by example. Take D = 7, >r = 7^(1/2), and compute: > r = 2 + (r-2)/1 > 1/(r-2) = (r+2)/3 = 1 + (r-1)/3 > 3/(r-1) = (r+1)/2 = 1 + (r-1)/2 > 2/(r-1) = (r+1)/3 = 1 + (r-2)/3 > 3/(r-2) = (r+2)/1 = 2 + r. >Hence r = 2 + 1/1+ 1/1+ 1/1+ 1/(2+r), and this unwinds to say > r = (8r + 21)/(3r + 8) >so that (a, b) = (8, 3) generates solutions to x^2 - 7y^2 = +/-1. >Notice that > 8/3 = lim_(x -> oo) (8x + 21)/(3x + 8) >so the generator (a, b) has quotient a/b obtained by replacing >r by oo in 2 + 1/1+ 1/1+ 1/1+ 1/(2+r) [chop off the last term: >2 + 1/1+ 1/1+ 1/1 = 8/3]. >If the chop-off involves evenly many terms, then the determinant >of the matrix is +1; otherwise the determinant is -1 and the >generator sits on the hyperbola x^2 - Dy^2 = -1 (so wed have >to square that generator to get the generator of the solutions >to x^2 - Dy^2 = 1). >As an exercise, use this method to compute the smallest nontrivial >solution to x^2 - 61y^2 = 1. Answer: > (a, b) = (1766319049, 226153980) >Todd Trimble === Subject: Re: At what age are children taught these terms? I know that the terms are taught in pre-algebra which is a 6th and 7th grade mathe class. (So the children would be about 10-12 years old). Whether they are mentioned any time before that is questionable. I dont remember being taught those term in elementary anyway, but thats probably because I really didnt pay much attention. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: At what age are children taught these terms? > When I sat down to read about young children > learning math, I first cast my mind back to what > I could immediately remember of that age. The three > words commutative, associative, and distributive > popped up in my head, although I couldnt state > what they meant. I dont recall the age I was > taught them, For elementary-school children, these vocabulary words are less important than developing their computational abilities. They need lots of unselfconscious practice. IMO, too much emphasis on strange words, attached to operations too soon, tend to inhibit carefree work. Im not an elementary-school mathematics expert and dont know what too soon would be. Later on when their vocabularies become richer, students may connect the words with their roots, etc. Commutative is from the Latin mutare, to change; the numbers switch positions, back and forth, commute, mutate. In associative properties, only the parentheses move. There is only one Distributive Property. (The others have two incarnations.) Multiplication distributes over addition. > Are children still taught the terms for these properties, or just the > properties? The text Im reading doesnt specifically say to use the > words, and actually translates the definition into kids language, and > gives examples like clothespins clamped onto a coathanger, which one > whirls 180 degrees to show there is still the same amount. > Does anyone have any special techniques for making these words more > likely to be retained by children? Again, in my experience, its not important for elementary school children to learn these words. But Google is your friend. For example, http://home.earthlink.net/~djbach/basic.html#anchor904011 -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: At what age are children taught these terms? > For elementary-school children, these vocabulary words > are less important than developing their computational abilities. > They need lots of unselfconscious practice. IMO, too much > emphasis on strange words, attached to operations too soon, > tend to inhibit carefree work. I agree. I was taught too soon. > Later on when their vocabularies become richer, students may > connect the words with their roots, etc. > Commutative is from the Latin mutare, to change; the numbers > switch positions, back and forth, commute, mutate. My family was big on etymology, and I even have a book on the Greek and Latin roots of scientific words. Im also sure sprout will be all over the word mutant by the time hes ready for commutative, and its root will be a good way to remember it. > http://home.earthlink.net/~djbach/basic.html#anchor904011 Ahhh, yet another bookmark. I guess I wasnt even asking the biological age, but whether one introduces the term with the rules or not, or if children are expected to know the word when the rules are taught (more strict than a mere introduction). blacksalt -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: new secondary mathematics forum A new forum for discussing secondary and elementary mathematics - for students to discuss what they need help in learning and for teachers to discuss the subjects : http://secmathshare.proboards38.com -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: new secondary mathematics forum This secmathshare site is having technical difficulties right now at ProBoards; currently, the Website Not Responding message comes up. LATER, check if interested at http://secmathshare.proboards38.com Algebryonic -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: new secondary mathematics forum >This secmathshare site is having technical difficulties right now at >ProBoards; >currently, the Website Not Responding message comes up. >LATER, check if interested at http://secmathshare.proboards38.com >Algebryonic Someone mentioned a readability problem. The site is back in operation and is readable. The background is black. Categories are written in white, the boards are labeled in orange, the descriptions of the boards are in white. Algebryonic -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: new secondary mathematics forum Why another forum. This one works just fine? What is the purpose of this forum. Honestly! Financial gain? Just wondering -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: new secondary mathematics forum sternitj@uwplatt.edu wonders why: >Why another forum. This one works just fine? >What is the purpose of this forum. Honestly! Financial gain? >Just wondering This k12.ed.math forum works just fine. What it does not do is place messages into categories on specific boards within the category. Also, once you read a message on the newsgroup, it is gone from your program unless you choose to keep it; then it only remains for a limited time according to how long you choose to keep posts. The categories and named boards permit a way to assist in finding a particular topic or thread. On the newsgroup, the subjects are not categorized. The administrator can put in new categories or new boards according to the trends that occur on the message board forum. ? financial gain from a message board? This is unimaginable. Certainly none for the account holder. Algebryonic -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Research study involving Math Anxiety and Computer Phobia! Hello Educator I am writing to interest you in a research study that is being conducted at the University of Massachusetts Amherst School of research study involves mathematics teachers and other educators who help educate our society. It hopes to provide the participants with some new information and additional understanding about the math anxiety and computer phobia that students (and adults) may experience in and out of the classroom when they are faced with learning or doing mathematics or computer work. If you are interested in participating or want additional information, please send an email to research@davdawn.com Paul OLeary, M.Ed. Primary Researcher Dr. Howard A. Peelle, Chairperson and Research Advisor -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Do you teach this subtraction algorithm? I think that this would be a great subtraction algorithm for those whose attention wanders, because it is a digit extraction algorithm. Example: 1776 -1492 ----- By inspection, the answer is three figures. 1776 -1492 ----- Hundreds digit: 7 minus 4 is 3, but since 76<92, write one less, that is, 2. 1776 -1492 ----- 2 Tens digit: 7 minus 9... we are working mod 10, so make this 7+1=8. As 6 is not less than 2, leave this 8 unchanged. 1776 -1492 ----- 28 Units digit: 6 minus 2 is 4. Result: 284. I like this method because if your attention wanders, it matters little, as each digit is calculated independently of all others. Charming, huh? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Do you teach this subtraction algorithm? I sometimes use that type of subtraction when Im trying to figure out the answer in my head. I dont know why; Ive never been taught it. Im not a teacher though, so I havent taught anyone esle this either. I think its kind of stupid actually (and too confusing for children to learn). -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Trigonometry - Proving trigonometric identities If I have a question: Simplify: tan x cos x ---------- + ------------- 1 - tan x sin x - cos x If I am required to simplify and not prove as I dont know the answer to this equation, is there a standard way to commence simplifying the equation and is there a difined time to stop? Each part of the equation, tan x, cos x, 1 - tan x all can be changed which ones do you change and when do you stop. You can continually change and rearrange and then change again your new answer. I have trouble knowing where to stop if I dont have a defined identity to prove. Hopefully you will be able to understand what I mean! Jason -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry - Proving trigonometric identities >If I have a question: >Simplify: > tan x cos x >---------- + ------------- >1 - tan x sin x - cos x Havent done it but suggest trying common denominator determination and use other (known) identities or relationships. You also may want to use meaning for tangent(x). -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry - Proving trigonometric identities >If I have a question: >Simplify: > tan x cos x >---------- + ------------- >1 - tan x sin x - cos x >If I am required to simplify and not prove as I dont know the answer >to this equation, is there a standard way to commence simplifying the >equation and is there a difined time to stop? Each part of the >equation, tan x, cos x, 1 - tan x all can be changed which ones do you >change and when do you stop. You can continually change and rearrange >and then change again your new answer. I have trouble knowing where to >stop if I dont have a defined identity to prove. >Hopefully you will be able to understand what I mean! Interesting question. With trig expressions such as these, a useful general approach is to put everything in terms of sin and cos. In this particular case, I think a goal is to combine the two terms into one, with a common denominator. See what happens. Be sure to check whether your instructor (or book) has any particular conventions about preferred form for simplification. bob -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry - Proving trigonometric identities Jason, The short answer is that, since these are problems in a textbook, they probably have a pretty short final answer that should be easily recognizable, or -- the answer is in the back of the book. Ill put some remarks amid your questions, below. > If I have a question: > Simplify: > tan x cos x > ---------- + ------------- > 1 - tan x sin x - cos x > If I am required to simplify and not prove as I dont know the answer > to this equation, is there a standard way to >commence simplifying *** Here are a few suggestions, some or all (or maybe none) of which may work. *** Some problems may require more than just one of the following: *** Simplify using the techniques of simplifying rational expressions (fraction-like expressions which have non-integer things in the numerator and the denominator). *** Convert using various versions of the Pythagorean Identity (sin^2 +cos^2, 1 + tan^2, etc.) *** And, always worth a try: Convert all the trig functions into sines and cosines. *** And, since it is a book problem, have hope that the simplified answer that you get is obviously the intended one. >the > equation and is there a difined time to stop? Each part of the > equation, tan x, cos x, 1 - tan x all can be changed which ones do you > change and when do you stop. You can continually change and rearrange > and then change again your new answer. *** I guess this is time for the Rule of Holes: If youre in one, stop digging! *** Seriously, though, if one method seems to lead nowhere -or worse-, stop and try another method. *** How long to try? For a couple of minutes, maybe a little longer. You can always return to spend more time on any particular method. > I have trouble knowing where to > stop if I dont have a defined identity to prove. *** The specific problem that you stated has an especially simple answer. When you find it, youll know its time to stop. :) > Hopefully you will be able to understand what I mean! > Jason -- Delete the second o to email me. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry - Proving trigonometric identities > Simplify: > tan x cos x > ---------- + ------------- > 1 - tan x sin x - cos x cos(x) tan x cos x = ------ * ---------- + ------------- cos(x) 1 - tan x sin x - cos x sin x cos x = ------------- + ------------- cos(x) - sin(x) sin x - cos x (-1)sin x cos x = ------------- + ------------- sin(x) - cos(x) sin x - cos x cos(x) - sin(x) = --------------- = -1 sin(x) - cos(x) -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry - Proving trigonometric identities > If I have a question: > Simplify: > tan x cos x > ---------- + ------------- > 1 - tan x sin x - cos x > If I am required to simplify and not prove as I dont know the answer > to this equation, is there a standard way to commence simplifying the > equation and is there a difined time to stop? Each part of the > equation, tan x, cos x, 1 - tan x all can be changed which ones do you > change and when do you stop. You can continually change and rearrange > and then change again your new answer. I have trouble knowing where to > stop if I dont have a defined identity to prove. > Hopefully you will be able to understand what I mean! > Jason Yep, figuring out what simplify means is not always simple. I tried an experiment, with a TI graphing calcualtor, I put the expression in with 9 for x. Found it came to -1 for 9 degrees or 9 radians. Can you show this is true for all x? My usual start would be to get rid of tan x. Look at the denominator of the first term: 1 - tan x = 1 - sin x /cos x. Make that a fraction: 1- tan x = (cos x - sin x) / cos x. So your denom. of the first term (after that cos x goes to the numerator) is the negative of the denom. of the second term. Looks like things can be combined. Good luck. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry - Proving trigonometric identities Since the term tan(x) is used, then there is a restriction x is not equal to K Pi where K is an element of Z ; for the term cos(x) / [ sin(x) - cos (x) ] ; divide numerator and denominator by cos(x) ; and you should be able to continue from here. > If I have a question: > Simplify: > tan x cos x > ---------- + ------------- > 1 - tan x sin x - cos x > If I am required to simplify and not prove as I dont know the answer > to this equation, is there a standard way to commence simplifying the > equation and is there a difined time to stop? Each part of the > equation, tan x, cos x, 1 - tan x all can be changed which ones do you > change and when do you stop. You can continually change and rearrange > and then change again your new answer. I have trouble knowing where to > stop if I dont have a defined identity to prove. > Hopefully you will be able to understand what I mean! > Jason -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry - Proving trigonometric identities try converting all expressions to sinx, cosx, simplify you should end up with -1 > If I have a question: > Simplify: > tan x cos x > ---------- + ------------- > 1 - tan x sin x - cos x > If I am required to simplify and not prove as I dont know the answer > to this equation, is there a standard way to commence simplifying the > equation and is there a difined time to stop? Each part of the > equation, tan x, cos x, 1 - tan x all can be changed which ones do you > change and when do you stop. You can continually change and rearrange > and then change again your new answer. I have trouble knowing where to > stop if I dont have a defined identity to prove. > Hopefully you will be able to understand what I mean! > Jason -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry - Proving trigonometric identities > If I have a question: > Simplify: > tan x cos x > ---------- + ------------- > 1 - tan x sin x - cos x > If I am required to simplify and not prove as I dont know the answer > to this equation, is there a standard way to commence simplifying the > equation and is there a difined time to stop? Each part of the > equation, tan x, cos x, 1 - tan x all can be changed which ones do you > change and when do you stop. You can continually change and rearrange > and then change again your new answer. I have trouble knowing where to > stop if I dont have a defined identity to prove. > Hopefully you will be able to understand what I mean! Start by changing all the tan x to sin x/cos x then use the fact that y/y = 1 to get a common denominator. Remember that a/b ad e/f ------- = -------- and ------- = e/g c/d bc g/f --Jeff -- It is only those who have neither fired a shot nor heard the shrieks and groans of the wounded who cry aloud for blood, more vengeance, more desolation. War is hell. --William Tecumseh Sherman Egotism is the anesthetic that dulls the pain of stupidity. --Frank William Leahy -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: At what age are children taught these terms? Im not sure exactly what you are talking about, but I think using the appropriate vocabulary with children, along with words that they know now will broaden their vocabulary and they will learn to use the correct terms. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: At what age are children taught these terms? > Im not sure exactly what you are talking about, but I think using the > appropriate vocabulary with children, along with words that they know > now will broaden their vocabulary and they will learn to use the > correct terms. The question is at what age. I count things out for baby, and he counts out chew sticks for the dog, won-too-twee with a pause, fo-fi, and I might point at them, going the other way, count them out for him, but Im not ready to spring a four syllable word on him. blacksalt -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: At what age are children taught these terms? >> Im not sure exactly what you are talking about, but I think using the >> appropriate vocabulary with children, along with words that they know >> now will broaden their vocabulary and they will learn to use the >> correct terms. > The question is at what age. I count things out for baby, and he > counts out chew sticks for the dog, won-too-twee with a pause, > fo-fi, and I might point at them, going the other way, count them out > for him, but Im not ready to spring a four syllable word on him. > blacksalt My 6th graders copy of Saxon 76 discusses the commutative property of multiplication. I honestly cant remember if Saxon discussed any of the commutative, associative, or distributive proerties in my sont previous grades, and I dont have those texts anymore. If they did, I can only guess that it would have been at least 4th grade, perhaps 5th. So I guess my best answer is somewhere between 4th and 6th grades (U.S.) which normally corresponds to 10-12 years of age. The concepts behind the words are, of course, addressed to some degree or another at a much younger age. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Lesson Plan ALGEBRA LESSON PLAN Overview: This lesson applies the strategies for solving multiplication equations to equations with a fraction as the coefficient of the variable. Objectives: Students will learn how to use multiplication by reciprocals, to solve multiplication equations in which the coefficient of the variable is a fraction. California Content Standards: 1.2 Students add, subtract, multiply, and divide, rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. 2.0 Students calculate, and solve problems involving addition, subtraction, multiplication, and division. 3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations. Warm-Up Activity: Ask students what the word reciprocal means. (If the product of two numbers is 1, then each factor is the reciprocal of the other). Ask students to identify the reciprocals of the following numbers: 1/4, 3/5, 7/8 and 1/n Encourage students to describe what they know about the product of these numbers and their reciprocals (the product equals 1). Direct instructions for all students: Write the first example , 1/4h = 6 on the overhead projector. Ask students how they can change the coefficient of h from 1/4 to 1. Lead students to conclude that multiplying the left side of the equation by 4 will give h a coefficient of 1. Remind students that to keep the equation true, they will need to multiply the right side of the equation by 4/1 as well. Solve the example, showing each of the steps indicated. 1/4h = 6 (4/1)1/4 [Eth] h = 6/1 (4/1) (4/1)1/4 [Eth] h = 6/1 (4/1) 4/4 h = 24/1 h = 24 Solve the second example showing each of the steps indicated: -2/5x = -20 (-5/2)(-2/5) [Eth] x = -20(-5/2) (10/10) [Eth]x = 100/2 x = 50 Working in small groups: Divide class into small groups. Students will work in pairs by helping each other, developing strategies and sharing the answers (in each pair one student must have good math skills). Group Problem Solving: Have small groups of students consider the following situation. Havermill School needs to increase its students.89 reading and math scores. Currently 1/7 of the school, 30 students, score above average in reading and math. By the end of the year, the school would like 1/5 of its students to score above average. If the school meets its goal, how many students will score above average? (1/7)x = 30 (7/1) [Eth] 1/7 = 30(7/1) (7/7) [Eth] x = 210/2 x = 210 (1/5) [Eth] 210 = 42 Homework assignment attached. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: acceleration I am helping my daughter with her math/science but i am confused myself. given data distance(km), time(s) 0 0 5 10 12 20 20 30 30 40 42 50 56 60 ----------------- question: what is the acceleration between 20s and 30s? answer: isnt it 0.006 km/s^2 ? My daughter insists that it is 0.8 km/s^2 Please help. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration > I am helping my daughter with her math/science but i am > confused myself. > given data > distance(km), time(s) > 0 0 > 5 10 > 12 20 > 20 30 > 30 40 > 42 50 > 56 60 > ----------------- > question: what is the acceleration between 20s and 30s? > answer: isnt it 0.006 km/s^2 ? > My daughter insists that it is 0.8 km/s^2 > Please help. Using the 3-point formula v(t0) = (1/20)[s(t0+10) - s(t0-10)] for the numerical derivative (v being velocity, s -- distance, t -- time) I obtain: v(20) = 0.75 km/s and v(30) = 0.9 km/s which yields an average acceleration of 0.015 km/s^2. The more accurate 5-point formula v(t0) = (1/120)[s(t0-20) - 8s(t0-10) + 8(t0+10) - s(t0+20)] for the numerical derivative gives v(20) = 0.75 km/s and v(30) = 0.89167 km/s, for an average acceleration of 0.01417 km/s^2 I got these formulas from Burden and Faires, Numerical Analysis. It is assumed that the position function has a continuous 3rd derivative. - Brett -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration >I am helping my daughter with her math/science but i am >confused myself. >given data >distance(km), time(s) >0 0 >5 10 >12 20 >20 30 >30 40 >42 50 >56 60 >----------------- >question: what is the acceleration between 20s and 30s? >answer: isnt it 0.006 km/s^2 ? > My daughter insists that it is 0.8 km/s^2 >Please help. As several people have noted, the question is not very clear. That is, it requires some approximations/simplifications. It may be clear enough within the context of the class. It would help if you would post how each of you did this. Then we can comment on whether each approach is reasonable, or whether there is some serious error of logic or calculation. In any case, commenting on your approaches would be much more instructive to the student than just checking answers. bob -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration Originally, there are two preceding questions: 1) what is ave. speed at 20 sec? 2) what is ave. speed at 30 sec? 3) what is acceleration between 20 sec and 30sec? I think the answers to 1), and 2) are 0.6km/sec, 0.666km/sec. please help further. p.s. these questions are for 8th grader. >I am helping my daughter with her math/science but i am >confused myself. >given data >distance(km), time(s) >0 0 >5 10 >12 20 >20 30 >30 40 >42 50 >56 60 >----------------- >question: what is the acceleration between 20s and 30s? >answer: isnt it 0.006 km/s^2 ? > My daughter insists that it is 0.8 km/s^2 >Please help. > As several people have noted, the question is not very clear. That is, > it requires some approximations/simplifications. It may be clear > enough within the context of the class. > It would help if you would post how each of you did this. Then we can > comment on whether each approach is reasonable, or whether there is > some serious error of logic or calculation. In any case, commenting on > your approaches would be much more instructive to the student than > just checking answers. > bob -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration >Originally, there are two preceding questions: >1) what is ave. speed at 20 sec? >2) what is ave. speed at 30 sec? >3) what is acceleration between 20 sec and 30sec? >I think the answers to 1), and 2) are 0.6km/sec, 0.666km/sec. #3 follows from #1 and #2. If we take those answers for 1 and 2, then #3 is the difference of them divided by 10 seconds. That is (0.666-0.6)/10 = 0.0066 km/(sec^2). (This does not agree with either answer you have below.) As to what the answers should be for #1-2, that involves interpreting a poorly written question. I think I see where you get your values. I would have been inclined to calculate the average speed over the preceding interval. But it is a guessing game. Is this from the book? If so, there should be clues about interpreting questions there. If it is from the teacher, I would have hoped that the student in the class would know what the teacher meant. I would also add that if we calculate the average velocities the way you did, then using them to calculate acceleration is now questionable. bob >please help further. >p.s. these questions are for 8th grader. >>I am helping my daughter with her math/science but i am >>confused myself. >>given data >>distance(km), time(s) >>0 0 >>5 10 >>12 20 >>20 30 >>30 40 >>42 50 >>56 60 >>----------------- >>question: what is the acceleration between 20s and 30s? >>answer: isnt it 0.006 km/s^2 ? >> My daughter insists that it is 0.8 km/s^2 >>Please help. >> As several people have noted, the question is not very clear. That is, >> it requires some approximations/simplifications. It may be clear >> enough within the context of the class. >> It would help if you would post how each of you did this. Then we can >> comment on whether each approach is reasonable, or whether there is >> some serious error of logic or calculation. In any case, commenting on >> your approaches would be much more instructive to the student than >> just checking answers. >> bob -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration >I am helping my daughter with her math/science but i am >confused myself. >given data >distance(km), time(s) >0 0 >5 10 >12 20 >20 30 >30 40 >42 50 >56 60 >----------------- >question: what is the acceleration between 20s and 30s? >answer: isnt it 0.006 km/s^2 ? > My daughter insists that it is 0.8 km/s^2 > Originally, there are two preceding questions: > 1) what is ave. speed at 20 sec? > 2) what is ave. speed at 30 sec? > 3) what is acceleration between 20 sec and 30sec? > I think the answers to 1), and 2) are 0.6km/sec, 0.666km/sec. > please help further. > p.s. these questions are for 8th grader. The average speed for the first 20s is 0.6 km/s and the average speed for the first 30s is 0.666... km/s, true. That doesnt really tell us the acceleration between 20s and 30s but it is ok to use: (0.666... - 0.6)/10 or 0.0066666 km/s^2 --Jeff -- It is only those who have neither fired a shot nor heard the shrieks and groans of the wounded who cry aloud for blood, more vengeance, more desolation. War is hell. --William Tecumseh Sherman Egotism is the anesthetic that dulls the pain of stupidity. --Frank William Leahy -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration >>I am helping my daughter with her math/science but i am >>confused myself. >>given data >>distance(km), time(s) >>0 0 >>5 10 >>12 20 >>20 30 >>30 40 >>42 50 >>56 60 >>----------------- >>question: what is the acceleration between 20s and 30s? >>answer: isnt it 0.006 km/s^2 ? >> My daughter insists that it is 0.8 km/s^2 > > Originally, there are two preceding questions: > > 1) what is ave. speed at 20 sec? > > 2) what is ave. speed at 30 sec? > > 3) what is acceleration between 20 sec and 30sec? > > I think the answers to 1), and 2) are 0.6km/sec, 0.666km/sec. > > please help further. > > p.s. these questions are for 8th grader. > The average speed for the first 20s is 0.6 km/s and the > average speed for the first 30s is 0.666... km/s, true. > That doesnt really tell us the acceleration between 20s and 30s > but it is ok to use: (0.666... - 0.6)/10 or 0.0066666 km/s^2 > --Jeff IMHO, it is highly inaccurate to compute average velocities over the interval from starting time to present time (unless the present time is very near the starting time). It is much better to compute velocity from points near the point of interest. In another post, I gave the 3-point formula, which essentially averages (numerically) the average velocities from previous point to current point, and from current point to succesive point. This choice is a good one, and can be rigorously justified, under some differentiability assumptions which almost certainly hold in a physical setting. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration >I am helping my daughter with her math/science but i am >confused myself. given data >distance(km), time(s) >0 0 >5 10 >12 20 >20 30 >30 40 >42 50 >56 60 >----------------- >question: what is the acceleration between 20s and 30s? >answer: isnt it 0.006 km/s^2 ? > My daughter insists that it is 0.8 km/s^2 >> > Originally, there are two preceding questions: >> > 1) what is ave. speed at 20 sec? >> > 2) what is ave. speed at 30 sec? >> > 3) what is acceleration between 20 sec and 30sec? >> > > I think the answers to 1), and 2) are 0.6km/sec, 0.666km/sec. >> > > please help further. >> > > p.s. these questions are for 8th grader. >> The average speed for the first 20s is 0.6 km/s and the >> average speed for the first 30s is 0.666... km/s, true. >> That doesnt really tell us the acceleration between 20s and 30s >> but it is ok to use: (0.666... - 0.6)/10 or 0.0066666 km/s^2 >> --Jeff > IMHO, it is highly inaccurate to compute average velocities over the > interval from starting time to present time (unless the present time is > very near the starting time). It is much better to compute velocity from > points near the point of interest. In another post, I gave the 3-point > formula, which essentially averages (numerically) the average velocities > from previous point to current point, and from current point to > succesive point. This choice is a good one, and can be rigorously > justified, under some differentiability assumptions which almost > certainly hold in a physical setting. IMHO, it is better to treat this piecewise. Each interval can be analyzed separately to determine the ending velocity and the acceleration required to reach that point, the ending velocity for one interval becomes the boundary point for the next. This is similar to using simple equipment to analyze the motion of a car around a race track. During some portions of the path the car is accelerating and during some portions it is decelerating. Averaging over multiple intervals just doesnt give a good picture of what is happening. The formulas to use are simple: P = P0 + (V0 * T) + (1/2)a(T^2) V = V0 + aT Since you know the P0, V0, and T for each interval, you can calculate this on a piecewise basis. Use the first equation to find the acceleration over the interval and use that acceleration to find the ending velocity for the interval. tim -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration >>I am helping my daughter with her math/science but i am >>confused myself. >>given data >>distance(km), time(s) >>0 0 >>5 10 >>12 20 >>20 30 >>30 40 >>42 50 >>56 60 >>----------------- >>question: what is the acceleration between 20s and 30s? >>answer: isnt it 0.006 km/s^2 ? >> My daughter insists that it is 0.8 km/s^2 > Originally, there are two preceding questions: > 1) what is ave. speed at 20 sec? > 2) what is ave. speed at 30 sec? > 3) what is acceleration between 20 sec and 30sec? I think the answers to 1), and 2) are 0.6km/sec, 0.666km/sec. please help further. p.s. these questions are for 8th grader. >The average speed for the first 20s is 0.6 km/s and the >average speed for the first 30s is 0.666... km/s, true. >That doesnt really tell us the acceleration between 20s and 30s >but it is ok to use: (0.666... - 0.6)/10 or 0.0066666 km/s^2 >--Jeff >>IMHO, it is highly inaccurate to compute average velocities over the >>interval from starting time to present time (unless the present time is >>very near the starting time). It is much better to compute velocity from >>points near the point of interest. In another post, I gave the 3-point >>formula, which essentially averages (numerically) the average velocities >>from previous point to current point, and from current point to >>succesive point. This choice is a good one, and can be rigorously >>justified, under some differentiability assumptions which almost >>certainly hold in a physical setting. > IMHO, it is better to treat this piecewise. Each interval can be analyzed > separately to determine the ending velocity and the acceleration required > to reach that point, the ending velocity for one interval becomes the > boundary point for the next. This is similar to using simple equipment to > analyze the motion of a car around a race track. During some portions of > the path the car is accelerating and during some portions it is > decelerating. Averaging over multiple intervals just doesnt give a good > picture of what is happening. The formulas to use are simple: > P = P0 + (V0 * T) + (1/2)a(T^2) > V = V0 + aT > Since you know the P0, V0, and T for each interval, you can calculate this > on a piecewise basis. Use the first equation to find the acceleration over > the interval and use that acceleration to find the ending velocity for the > interval. > tim There are two problems with your analysis: 1) V0 is not known for any interval. Your values are guesses --- educated guesses --- but guesses nonetheless. 2) You are assuming that the acceleration is constant on each interval, which is generally not the case. Your formula for P does not apply for non-constant acceleration. Determining velocities by averaging over multiple intervals is well supported in the literature on numerical analysis. - Brett -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration > Originally, there are two preceding questions: > 1) what is ave. speed at 20 sec? > 2) what is ave. speed at 30 sec? > 3) what is acceleration between 20 sec and 30sec? > I think the answers to 1), and 2) are 0.6km/sec, 0.666km/sec. > please help further. > p.s. these questions are for 8th grader. I dont believe your answers are correct. You must work this as a piece-wise path. The velocity at 20 sec is .4km/sec and at 30 sec is 1.2km/sec. tim >>I am helping my daughter with her math/science but i am >>confused myself. >>given data >>distance(km), time(s) >>0 0 >>5 10 >>12 20 >>20 30 >>30 40 >>42 50 >>56 60 >>----------------- >>question: what is the acceleration between 20s and 30s? >>answer: isnt it 0.006 km/s^2 ? >> My daughter insists that it is 0.8 km/s^2 >>Please help. >> As several people have noted, the question is not very clear. That is, >> it requires some approximations/simplifications. It may be clear >> enough within the context of the class. >> It would help if you would post how each of you did this. Then we can >> comment on whether each approach is reasonable, or whether there is >> some serious error of logic or calculation. In any case, commenting on >> your approaches would be much more instructive to the student than >> just checking answers. >> bob -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration > I am helping my daughter with her math/science but i am > confused myself. > given data > distance(km), time(s) > 0 0 > 5 10 > 12 20 > 20 30 > 30 40 > 42 50 > 56 60 > ----------------- > question: what is the acceleration between 20s and 30s? > answer: isnt it 0.006 km/s^2 ? > My daughter insists that it is 0.8 km/s^2 > Please help. I think this requires a little more rigorous examination than you have gotten so far. Based on my calculations the acceleration should be 0.08km/s^2. The formula for position is P = P0 + [V0 * t] + (1/2)(a)(t^2) where P0 is starting position, V0 is starting velocity, a is acceleration, and t is time 1. First interval P0 = 0 in your problem and I am assuming that so does V0. So, for the first interval we would get P = (1/2)(a)(t^2) Since P = 5 and (t^2) = 100, a = (5/50) = 0.1 km/(sec^2) We also know that V = V0 + at where V0 is starting velocity, a is acceleration, and t is time. Since V0 = 0 (assumption) and a = 0.1 km/(sec^2) V = (.1)(10) = 1 km/sec at the end of the interval 2. Second interval P0 is 5, V0 is 1km/sec, t = 10sec and P = 12 So P = 5 + (1 * 10) + (1/2)a(100) = 12 12 = 5 + 10 + 50a; 12 = 15 + 50a; -3 = 50a; a = (-3/50) = -0.06 km/(sec^2) V = V0 + at ; V = 1 + (-0.06)(10) = 1 - 0.6 = 0.4 km/sec ------------------------- I think Ive done this correctly. I didnt want to do the homework for you but didnt know how else to show it. Ive left the last segment for you to do. If you dont get 0.08km/s^2 let us know and well see what we can see. tim -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration > I am helping my daughter with her math/science but i am > confused myself. > given data > distance(km), time(s) > 0 0 > 5 10 > 12 20 > 20 30 > 30 40 > 42 50 > 56 60 > ----------------- > question: what is the acceleration between 20s and 30s? > answer: isnt it 0.006 km/s^2 ? > My daughter insists that it is 0.8 km/s^2 The question is a very badly posed one. With only discrete points, the velocity and acceleration are unknowable. You need to make some assumptions about how acceleration varies, and there are many reasonable assumptions (stepwise constant acceleration between timepoints, minimal mean-square surge, ...) I plotted the points and they are very close to the curve 0.00881 t^2 + 0.4 t + 0.1184 which would be a constant acceleration of 0.0176 km/sec^2. I also tried fitting a cubic to the data, and got an acceleration of 0.01429 at 20 seconds and 0.01512 at 30 seconds. If I fit just the points for 10,20,30, and 40 with a cubic (a reasonable interpolation technique), I get 0.000166667 t^3 -0.005 t^2 +0.733333 t -2 for an acceleration of 0 at 20 seconds ramping up linearly to 0.005 at 30. If I fit a quadratic for points 10,20,30, I get a constant acceleration of 0.01. If I fit a quadratic for points 20,30,40, I get a constant acceleration of 0.02. Other interpolation assumptions will result in other acceleration estimates. ------------------------------------------------------------ Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus Professor of Biomolecular Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Senior member, IEEE Board of Directors, ISCB (starting Jan 2005) life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration Given the tabular data as distance versus time, the question is asking for the average acceleration over the period of 20 seconds to 30 seconds. Recall that average acceleration is the change in velocity over the time interval. Hence compute the velocity at 20 seconds and 30 seconds, take the difference and divide by the interval, 10 seconds. velocity at 20 seconds = (12-5)/10 = 0.7 km/sec velocity at 30 seconds = (20-12)/10 = 0.8 km/sec acceleration over 20 - 30 second interval = (0.8 - 0.7)/10 = 0.1/10 = 0.01 km/sec*sec Eugene Manista > I am helping my daughter with her math/science but i am > confused myself. > given data > distance(km), time(s) > 0 0 > 5 10 > 12 20 > 20 30 > 30 40 > 42 50 > 56 60 > ----------------- > question: what is the acceleration between 20s and 30s? > answer: isnt it 0.006 km/s^2 ? > My daughter insists that it is 0.8 km/s^2 > Please help. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration > I am helping my daughter with her math/science but i am > confused myself. > given data > distance(km), time(s) > 0 0 > 5 10 > 12 20 > 20 30 > 30 40 > 42 50 > 56 60 > ----------------- > question: what is the acceleration between 20s and 30s? > answer: isnt it 0.006 km/s^2 ? > My daughter insists that it is 0.8 km/s^2 The _speed_ between 20s and 30s averages 0.8 km/s. The speed between 10s and 20s averaged 0.7 km/s. The speed between 30s and 40s averaged 1.0 km/s. Theres no way to tell the speed _at_ 20s or 30s, so theres really no way to know what the _average_ acceleration was between 20s and 30s. There doesnt seem to be a smooth curve that describes the speed over time. If the speed at any time was the average of the average speeds before and after it - as reasonable an assumption as any - then we can assign a speed at 20s of 0.75 km/s and at 30s of 0.9 km/s, which yields an average acceleration between 20s and 30s of 0.015 km/s^2. But thats just based on the assumption. What year is your daughter in? --Jeff -- It is only those who have neither fired a shot nor heard the shrieks and groans of the wounded who cry aloud for blood, more vengeance, more desolation. War is hell. --William Tecumseh Sherman Egotism is the anesthetic that dulls the pain of stupidity. --Frank William Leahy -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration The velocity at 20 km is .6666 km/s, the velocity at 30 km is .75 km/s. The difference is .0833 km/s over 10 seconds, which would be .00833 km/s*s = ..00833 km/s^2. Have fun! John > distance(km), time(s) > 0 0 > 5 10 > 12 20 > 20 30 > 30 40 > 42 50 > 56 60 > ----------------- > question: what is the acceleration between 20s and 30s? > answer: isnt it 0.006 km/s^2 ? > My daughter insists that it is 0.8 km/s^2 -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration Could you read the question once more? Its asking for acceleraton between 20 sec and 30 sec. > The velocity at 20 km is .6666 km/s, the velocity at 30 km is .75 km/s. The > difference is .0833 km/s over 10 seconds, which would be .00833 km/s*s = > ..00833 km/s^2. > Have fun! > John > distance(km), time(s) > 0 0 > 5 10 > 12 20 > 20 30 > 30 40 > 42 50 > 56 60 > ----------------- > question: what is the acceleration between 20s and 30s? > answer: isnt it 0.006 km/s^2 ? > My daughter insists that it is 0.8 km/s^2 -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: acceleration >The velocity at 20 km is .6666 km/s, the velocity at 30 km is .75 km/s. Those are the average rates over those intervals from time zero. He has to use finite differences to get an average speed over the preceding 10 sec interval [the smallest recorded], the interval in question and the next interval. Then finite differences will give an average acceleration in the interval. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Grade 10-12 Math review book trigonometry, functions, probability...). Would you have a suggestion on a math book that would cover all three grades. I do not want the students to by a different book each year. John -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Grade 10-12 Math review book Are all/most students going to finish Math 12? If so: just have them buy the Math 12 book and you provide the extra materials for a lead up to the Math 12 course. If most students are only going to do up to Math 10 or Math 11 - have the school rent out copies of the textbooks. Here in British Columbia, we use the MathPower book series and the Frog math books -- they have a frog on the cover -- I cant remember the series name. The number one problem with adult students seems to be social embarrassment when making a mistake in class -- yet blackboard work and verbal responses are important. -- Casey -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Grade 10-12 Math review book but ... it is quite impossible that you can stick to the same book every year to cover the three grades. I happened to post a link that covers some topics you mentioned yesterday: http://www.scienceoxygen.com/mathnote/index.html Probably the best way is: you compile your teaching materials together and publish... (algebra, >trigonometry, functions, probability...). Would you have a suggestion >on a math book that would cover all three grades. I do not want the >students to by a different book each year. >John -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Grade 10-12 Math review book > (algebra, >>trigonometry, functions, probability...). Would you have a > suggestion >>on a math book that would cover all three grades. I do not want the >>students to by a different book each year. > but ... it is quite impossible that you can stick > to the same book every year to cover the three grades. Why is this impossible? The three years of material are really only one year worth of material, with lots of repetition. Id look for a good algebra+trig book, and supplement with probability from another source, if you cant find a single book that covers it all. You may have to visit some used book stores in college towns, and try to find older books---they tended not to be synced to state standards and so covered more. (The standards seem to be used by publishers as excuses for dumbing down or leaving out material.) ------------------------------------------------------------ Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus Professor of Biomolecular Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Senior member, IEEE Board of Directors, ISCB (starting Jan 2005) life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Grade 10-12 Math review book Fascinating. watch out for punctuation errors. mrtatterscratch@earthlink.net -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Math testing online I am a graduate student and have been working on a math testing project for use especially in elementary and middle schools. The software (now a website) is a suite of simple math tests which can be given online. Since its all computer based, the teacher receives complete grade reports and record keeping of the tests his/her students take. So far I have developed tests for basic arithmetic, times tables, inequalities, fractions, exponents, roots, and calculating area and perimeter of rectangles, triangles and circles. There are practice tests for students, and more advanced options for teachers who want to assign tests and have automatic grading. Its completely free and school-friendly (no ads). If you think you might be interested please have a look at it : http://www.thatquiz.com Lyczak -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Jump-Tutoring University of Canada (located at the University of Regina, Regina, Saskatchewan). A few weeks ago I heard a presentation about Jump-tutoring. This tutoring concept originated in Ontario and has been designed to help students with their math skills. The tutors are ordinary people from the school community area that work in conjunction with the teacher to help the students. The tutors do not need to be particularly good in presentation, the goals of the program are twofold. One - to get the community involved in supporting the kids education, and two - to help the kids with their math problem areas. I would like to get some feedback from you as to your opinion about this type of program. Do you think that it will be advantageous to the school, the community, and ultimately to the students? Cordially, Robert Cropp -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Jump-Tutoring >University of Canada (located at the University of Regina, Regina, >Saskatchewan). >A few weeks ago I heard a presentation about Jump-tutoring. This >tutoring concept originated in Ontario and has been designed to help >students with their math skills. The tutors are ordinary people from >the school community area that work in conjunction with the teacher to >help the students. The tutors do not need to be particularly good in >presentation, the goals of the program are twofold. One - to get the >community involved in supporting the kids education, and two - to help >the kids with their math problem areas. >I would like to get some feedback from you as to your opinion about >this type of program. Do you think that it will be advantageous to >the school, the community, and ultimately to the students? >Cordially, Robert Cropp Sounds like a wonderful idea. Different students need different kinds of help. For some, simply being put in an environment where some real work is expected will help. Parental expectations can help. And if the adults are learning, too, and then sharing what they learned with the kids, great. I suspect that a very high percentage of those of us who were successful academically would point to the home environment as being critical. And that doesnt mean the specific subject knowledge of the parents, but the atmosphere of expectation and encouragement. Of course, there are limits to what this approach can achieve. But the point is to emphasize how it can help some students do better than they would have done without this support. It would be interesting to know how this program evaluates their own efforts. bob -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Jump-Tutoring >University of Canada (located at the University of Regina, Regina, >Saskatchewan). >A few weeks ago I heard a presentation about Jump-tutoring. A quote form the site: JUMP believes that all children can be led to think mathematically, and that with even a modest amount of attention every child will ßourish. By demonstrating that even children who are failing math or are labeled as slow learners can excel at math, we hope to dispel the myths that have caused us to neglect our children. And by offering inner-city children effective and consistent help in mathematics (and eventually reading and other subjects), we hope to break the cycle of ignorance that lies at the root of all poverty. Well, it that doesnt soothe anxious parents I dont know what will. Wow. He can do, through the use of volunteer help, what the rest of society fails to do, and all with just a handful of donations and volunteers. So, wheres the proof of the above claim? Believe half of what you hear and none of what you see. It sounds very much like the companies who will imply a guarantee of a high paying job to anyone who takes their seminars ...at a small fee. The truth is that there are no guarantees in this world, and the truth is that not all people can play professional hockey, or concert piano, or excel in math. The truth is that they should not then feel badly about that and get on with their lives. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Jump-Tutoring Some students will benefit from having somebody actively involved in helping them to do their math, because the student lacks the self-discipline to do it on his/her own. However, there is a good reason why somebody teaching math needs to be at least 2 or 3 grade levels above -- because a good way to see if a student is grasping the concepts is to teach them a few concepts from the next grade level and see if they grasp that. AND Somebody from a higher grade level will know what concepts need to be mastered, so that one has at least a chance to pass the next grade level. I read a study, that said after graduation, math skills were the first to go, compared to other skills. -- Casey -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Jump-Tutoring > However, there is a good reason why somebody teaching math needs to be > at least 2 or 3 grade levels above -- because a good way to see if a > student is grasping the concepts is to teach them a few concepts from > the next grade level and see if they grasp that. I believe that math is progressive. I think of a ladder. When you climb a ladder you will do best by stepping on each rung rather than skipping. An example is that you are asking for failure if you try to teach a pupil long division before he or she has mastered subtraction. I prepare students for the GED test. When they first come to class, they all have an opinion on where they should begin. For example, students tell me they want to study percents right away. Before I teach percents, I want them to understand proportions, before proportions, ratios, before that fractions etc. I find that finding and filling the holes in their knowledge is much more effective than making them start where all the other students are. I would certainly not teach them a few higher level concepts until the lower level concepts are mastered. Having an individual tutoring program is a great opportunity to build up students set of basic concepts before advancing to the next level. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: How do get a scientific calculator to display 10^x.x I have a standard scientific calculator and cant figure out what mode would allow me to display this. Right now it only allows me to display powers in integers. I would like to do a problem like 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x Can anyone tell me how? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How do get a scientific calculator to display 10^x.x Druid (sniffmyhand2@yahoo.com) stated: : : I would like to do a problem like 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x : It has been have pointed out that this is just a common logarithm: x = Log(10^3.2 + 10^4.6 * 10^8.7) However, due to round off errors, the calculator just gives x=13.3 We can get more digits by rearranging a little: x = Log[ (10^13.3)*(1+10^(-10.1)) ] Factor out a large power of 10. = 13.3 + Log[1+10^(-10.1)] Log Law, Product becomes Sum. = 13.3 + Ln[1+10^(-10.1)]/Ln(10) Change of Base from 10 to e. Now apply the Taylor series: Ln(1+n) = n - n^2/2 + n^3/3 - n^4/4 + ... To get: x = 13.3000000000344972369... Thats about the best I can do with a basic scientific calculator. Robert |)|/| || Burnaby South Secondary School || |orewood@olc.ubc.ca || Beautiful British Columbia Mathematics & Computer Science || (Canada) -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How do get a scientific calculator to display 10^x.x I have a question: Where can I get a basic scientific calculator that will give 21 digits of accuracy? Previouly, I had posted: *** *** *** Heres the simple procedure: Just use your calculator to find 10^3.2 + 10^4.6 * 10^8.7 -- I take it you know how to do that. Then take log base 10 of that answer. This is your x.x . UNFORTUNATELY, when I did this procedure, it came up with 13.3 for the x.x. Notice that 13.3 is the sum of the last two exponents 4.6 and 8.7 -- this happens because you are adding a number 10^3.2 to a product equal to 10^13.3, and as far as the calculator is concerned, it has used up all its digits of accuracy with the 10^13.3 part. Think of it this way: 10^13.3 is approximately 1 followed by 13 zeros. Your calculator, probably like mine, can only keep track of 10 or so digits, so the last 3 or 4 digits of a number like 10^3.3 are lost forever (ignored), and that is exactly where the digits due to 10^3.2 would be. *** *** *** > Druid (sniffmyhand2@yahoo.com) stated: > : > : I would like to do a problem like 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x > It has been have pointed out that this is just a common logarithm: > x = Log(10^3.2 + 10^4.6 * 10^8.7) > However, due to round off errors, the calculator just gives x=13.3 > We can get more digits by rearranging a little: > x = Log[ (10^13.3)*(1+10^(-10.1)) ] Factor out a large power of 10. > = 13.3 + Log[1+10^(-10.1)] Log Law, Product becomes Sum. > = 13.3 + Ln[1+10^(-10.1)]/Ln(10) Change of Base from 10 to e. > Now apply the Taylor series: Ln(1+n) = n - n^2/2 + n^3/3 - n^4/4 + ... > To get: x = 13.3000000000344972369... > Thats about the best I can do with a basic scientific calculator. > Robert > |)|/| || Burnaby South Secondary School > || |orewood@olc.ubc.ca || Beautiful British Columbia > Mathematics & Computer Science || (Canada) -- Delete the second o to email me. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How do get a scientific calculator to display 10^x.x Joseph Sroka queried: : I have a question: Where can I get a basic scientific calculator : that will give 21 digits of accuracy? Short answer: Between your ears. The longer answer requires a review of Druids original problem: :> I would like to do a problem like 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x To which others responded: x = Log(10^3.2 + 10^4.6 * 10^8.7) I suggested the rearrangement: x = Log[ (10^13.3)*(1+10^(-10.1)) ] Factor out a large power of 10. = 13.3 + Log[1+10^(-10.1)] Log Law, Product becomes Sum. = 13.3 + Ln[1+10^(-10.1)]/Ln(10) Change of Base from 10 to e. And the Taylor series: Ln(1+n) = n - n^2/2 + n^3/3 - n^4/4 + ... To get x=13.3000000000344972369... Here is just a little more detail, substituting that Taylor series into the above expression for Ôx: x = 13.3 + 10^(-10.1)/Ln(10) - 10^(-20.2)/(2Ln(10)) + ... = 13.3 + 10^(.9)/Ln(10) * 10^-11 - 10^(.8)/2Ln(10) * 10^-21 + ... Then I get lazy and use that basic scientific calculator to find that: 10^(.9)/Ln(10) = 3.449723692 (plus or minus 10^-9) So, using just the first two terms to estimate Ôx: x = 13.3 + 3.449723692*10^-11 (plus or minus 10^-9 * 10^-11) Anyone who understands scientific notation well enough to use a scientific calculator should realize that the above is just: x = 13.30000000003449723692 (with that last 2 suspect) Calculator round off error makes that last digit suspect. There is also a truncation error: - 10^(.8)/2Ln(10) * 10^-21 + 10^(.7)/3Ln(10)*10^-31 - ... However, the series is alternating with terms of decreasing magnitude, so the truncation error is smaller than the first omitted term (about 10^-21), which is already smaller than the round off error above (about 10^-20). So I state with confidence that: x = 13.3000000000344972369 (with 21 digits accuracy) A better scientific calculator would give only a few more digits accuracy. More than that would require a better idea. Robert |)|/| || Burnaby South Secondary School || |orewood@olc.ubc.ca || Beautiful British Columbia Mathematics & Computer Science || (Canada) P.S. Here is a small calculation challenge: really easy, even without any calculator. It takes a little more thought to find the 2005-th decimal place. (A calculator might be helpful, but isnt necessary if you know a bit of calculus.) -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How do get a scientific calculator to display 10^x.x No, the calculator is between *your* ears, Robert. As you probably know, my question was intended to poke fun at your l e n g t h y explanation, which was ostensibly aimed at poor Druid. And, of course, to point out that you re-assembled two answers between *your* ears to get 13.3000000000344972369, a 21 digit answer, an answer that poor Druid will never see *displayed* on *his* basic scientific calculator, unless you happen to lend him your special calculator. --- Joe > Joseph Sroka queried: > : I have a question: Where can I get a basic scientific calculator > : that will give 21 digits of accuracy? > Short answer: Between your ears. > The longer answer requires a review of Druids original problem: > :> I would like to do a problem like 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x > To which others responded: > x = Log(10^3.2 + 10^4.6 * 10^8.7) > I suggested the rearrangement: > x = Log[ (10^13.3)*(1+10^(-10.1)) ] Factor out a large power of 10. > = 13.3 + Log[1+10^(-10.1)] Log Law, Product becomes Sum. > = 13.3 + Ln[1+10^(-10.1)]/Ln(10) Change of Base from 10 to e. > And the Taylor series: Ln(1+n) = n - n^2/2 + n^3/3 - n^4/4 + ... > To get x=13.3000000000344972369... > Here is just a little more detail, substituting that Taylor series > into the above expression for Ôx: > x = 13.3 + 10^(-10.1)/Ln(10) - 10^(-20.2)/(2Ln(10)) + ... > = 13.3 + 10^(.9)/Ln(10) * 10^-11 - 10^(.8)/2Ln(10) * 10^-21 + ... > Then I get lazy and use that basic scientific calculator to find > that: 10^(.9)/Ln(10) = 3.449723692 (plus or minus 10^-9) > So, using just the first two terms to estimate Ôx: > x = 13.3 + 3.449723692*10^-11 (plus or minus 10^-9 * 10^-11) > Anyone who understands scientific notation well enough to use > a scientific calculator should realize that the above is just: > x = 13.30000000003449723692 (with that last 2 suspect) > Calculator round off error makes that last digit suspect. > There is also a truncation error: > - 10^(.8)/2Ln(10) * 10^-21 + 10^(.7)/3Ln(10)*10^-31 - ... > However, the series is alternating with terms of decreasing > magnitude, so the truncation error is smaller than the first > omitted term (about 10^-21), which is already smaller than > the round off error above (about 10^-20). So I state with > confidence that: > x = 13.3000000000344972369 (with 21 digits accuracy) > A better scientific calculator would give only a few more > digits accuracy. More than that would require a better idea. > Robert > |)|/| || Burnaby South Secondary School > || |orewood@olc.ubc.ca || Beautiful British Columbia > Mathematics & Computer Science || (Canada) > P.S. Here is a small calculation challenge: > really easy, even without any calculator. It takes a little > more thought to find the 2005-th decimal place. (A calculator > might be helpful, but isnt necessary if you know a bit of > calculus.) -- Delete the second o to email me. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How do get a scientific calculator to display 10^x.x >I have a standard scientific calculator and cant figure out what mode >would allow me to display this. >Right now it only allows me to display powers in integers. I would >like to do a problem like 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x >Can anyone tell me how? I would be quite surprised if any standard scientific calculator will do that. They are intended for scientific/exponential notation, which uses a mantissa of one digit before the decimal place and an integer exponent. You should be able to enter numbers of the type you showed by using the power key (y^x). You should be able to calculate the value you show as x.x by taking the log(10) of the answer. bob -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How do get a scientific calculator to display 10^x.x > I have a standard scientific calculator and cant figure out what mode > would allow me to display this. > Right now it only allows me to display powers in integers. I would > like to do a problem like 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x > Can anyone tell me how? On an HP calculator with reverse-polish notation (RPN), you would enter 10 3.2 10 4.6 + 10 8.7 + Similar steps (with different key orders) are possible on almost any scientific calculator. If you only have and not you can do 10 / on an RPN calculator (I use that trick all the time to get log_2). ------------------------------------------------------------ Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus Professor of Biomolecular Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Senior member, IEEE Board of Directors, ISCB (starting Jan 2005) life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How do get a scientific calculator to display 10^x.x >I have a standard scientific calculator and cant figure out what mode >would allow me to display this. >Right now it only allows me to display powers in integers. I would >like to do a problem like 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x >Can anyone tell me how? First change the mode to allow decimals. Order of operations : 10 exp 8.7 = x 10 exp 4.6 = M+ 10 exp 3.2 M+ MR These might differ for one calculator to another. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How do get a scientific calculator to display 10^x.x > I have a standard scientific calculator > and cant figure out what mode would > allow me to display this. > Right now it only allows me to display > powers in integers. I would like to do > a problem like > 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x > Can anyone tell me how? Usually there is no such mode. If numbers are big enough, the display will change to scientific notation automatically. However, you can retrieve the desired form easily by taking the common log (base ten) of your displayed answer. Consider your example, 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x. Compute the left side in the usual way and the display may show 10^x.x in integer form. Now take the common log, which gives log(10^x.x) = x.x*log(10) = x.x, and you have the correct exponent. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How do get a scientific calculator to display 10^x.x > I have a standard scientific calculator and cant figure out what mode > would allow me to display this. > Right now it only allows me to display powers in integers. I would > like to do a problem like 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x > Can anyone tell me how? Hey Druid, I remember you from your question about calculating exponential growth/decay using your calculator. Why do you want to do this type of calculation? I ask this question for two reasons: First reason: It doesnt seem like any problem from a course that would ask you to calculate exponential growth/decay. Second reason: The answer to your question involves a pretty simple procedure on your standard scientific calculator, which gives only an *approximate* answer, which approximate answer you could obtain in about 5 seconds using only a pencil, or less. Heres the simple procedure: Just use your calculator to find 10^3.2 + 10^4.6 * 10^8.7 -- I take it you know how to do that. Then take log base 10 of that answer. This is your x.x . UNFORTUNATELY, when I did this procedure, it came up with 13.3 for the x.x. Notice that 13.3 is the sum of the last two exponents 4.6 and 8.7 -- this happens because you are adding a number 10^3.2 to a product equal to 10^13.3, and as far as the calculator is concerned, it has used up all its digits of accuracy with the 10^13.3 part. Think of it this way: 10^13.3 is approximately 1 followed by 13 zeros. Your calculator, probably like mine, can only keep track of 10 or so digits, so the last 3 or 4 digits of a number like 10^3.3 are lost forever (ignored), and that is exactly where the digits due to 10^3.2 would be. So, back to the question: Why do you want to do this type of calculation? Have fun. -- Delete the second o to email me. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How do get a scientific calculator to display 10^x.x Actually, you could use logarithmic function. You seem to want a base of 10, so you want the logarithm for your first result; you will use your scientific calculator to find 10 to what exponent gives you your first result. Your second result may be integral or it may be mixed decimal, or it may be decimal. Simple example, you want 10^2.0 + 10^3.0, which first will equal 1100. NOW, with 1100 in your display (on a scientific calculator), press the [LOG] button. You will see 3.0413927... So, your final answer then means, 10^3.04, that being rounding the exponent to the nearest hundredths. G C >Right now it only allows me to display powers in integers. I would >like to do a problem like 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x >Can anyone tell me how? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How do get a scientific calculator to display 10^x.x sniffmyhand2@yahoo.com wants to know how to use the requested format on calculators: >Right now it only allows me to display powers in integers. I would >like to do a problem like 10^3.2 + 10^4.6 * 10^8.7 = 10^x.x >Can anyone tell me how? Actually, you can at least USE numbers in that format. Receiving displayed results in such format, I do not know. You could enter an arithmetic expression using numbers in your requested format into a graphing calculator; but Im not sure you can obtain an evaluation value in that format. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: project for high school student Here is a possible project for a high school junior or senior who likes math and physics. It would need to be started in early December, and it would last until early January. It includes a chance to do some study and measurements in astronomy, and to make a presentation to the class or to a school extracurricular club. Course credit seems appropriate. The times of sun rise and sun set exhibit some apparently strange behavior around the shortest and longest days of the year. According to standard time, The sun sets earliest a few weeks before the shortest day of the year, and rises latest a few weeks after the shortest day of the year. The sun sets latest a few weeks after the longest day of the year, and rises earliest a few weeks before the longest day of the year. These effects are quite noticeable to a person who is outside at the same time every day. The exact amount of a few weeks depends mainly on the observers latitude, and changes very slightly from year to year. In the continental United States, it is about 2 weeks. These effects are caused mainly by the inclination of Earths axis of rotation, with respect to the perpendicular to the plane of Earths orbit around the sun. There also is some minor effect from the eccentricity of Earths orbit around the sun. The times also are affected slightly by atmospheric refraction, and by the observers elevation. An interested student can note the time and azimuth of sun-set every day, beginning in late November, and continuing through early January. Then the student can compute the expected times and azimuths from solar data, compare the expected values with the observed values, explain the effects, and make a presentation to his class, or to his school science or math or astronomy club, or to a high school science fair. The solar data can come from an ephemeris, or from US Naval Observatory Web pages of varying complexity according to how far the student wants to go into analysis. Requirements are that the student be at home every late afternoon during that whole period, have an unobstructed view reasonably close to the horizon, and have clear weather most of the time. A Christmas vacation trip more than a few days long, would disqualify the student. The student will need to have studied (and liked) trigonometry, and must have access to good calculating power (a high-end scientific calculator, or spread-sheet software with scientific calculating power). The student will need to know his latitude and longitude, which generally are readily available. If the student and her faculty advisor are not familiar with this phenomenon, then probably considerable contact, preferably by telephone conference-calling and fax, will be necessary. There also are some apparently strange effects with the moon, like harvest moon during the summer and fall seasons; but those effects generally take much longer to observe, and are not as spectacular as the times of sun rise and sun set. WARNING! Never, absolutely NEVER, look at the sun without proper eye protection. To do so, can cause severe and permanent eye damage. Dick Alvarez alvarez at alumni dot caltech dot edu -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Older student going back to school. I have to do an internet chat room interaction project for my intermediate algebra class. It is hard enough doing algebra, after not having had it since high school, 35 years ago. It is even harder to do this computer project for this algebra class. I have never been on the internet before, much less a chat room. It has taken 6 weeks and 5 people to help me get this far. I am really frustrated. Does any one have any recommenations, technology wise, for an older student going back to school? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Older student going back to school. > I have to do an internet chat room interaction project for my > intermediate algebra class. It is hard enough doing algebra, after > not having had it since high school, 35 years ago. It is even harder > to do this computer project for this algebra class. I have never been > on the internet before, much less a chat room. It has taken 6 weeks > and 5 people to help me get this far. I am really frustrated. Does > any one have any recommenations, technology wise, for an older student > going back to school? Yes, find a school that teaches what you need, rather than insisting on using chat rooms. While it is useful to learn how to use the internet (particularly productive use of time. ------------------------------------------------------------ Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus Professor of Biomolecular Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Senior member, IEEE Board of Directors, ISCB (starting Jan 2005) life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Older student going back to school. > I have to do an internet chat room interaction project for my > intermediate algebra class. It is hard enough doing algebra, after > not having had it since high school, 35 years ago. It is even harder > to do this computer project for this algebra class. I have never been > on the internet before, much less a chat room. It has taken 6 weeks > and 5 people to help me get this far. I am really frustrated. Does > any one have any recommenations, technology wise, for an older student > going back to school? > Yes, find a school that teaches what you need, rather than insisting > on using chat rooms. > While it is useful to learn how to use the internet (particularly > productive use of time. > ------------------------------------------------------------ > Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus > Professor of Biomolecular Engineering, University of California, Santa Cruz > Undergraduate and Graduate Director, Bioinformatics > Senior member, IEEE Board of Directors, ISCB (starting Jan 2005) > life member (LAB, Adventure Cycling, American Youth Hostels) > Effective Cycling Instructor #218-ck (lapsed) > Affiliations for identification only. It seems strange that the school would make an algebra class a writing class. There are so many classes that you write in already, (like english, speech, research, reports, etc.) it just does not make sense for a math class. No matter what you go into, you have to take the same basic requirements, some of which could be writing classes. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Older student going back to school. > It seems strange that the school would make an algebra class a writing > class. There are so many classes that you write in already, (like > english, speech, research, reports, etc.) it just does not make sense > for a math class. No matter what you go into, you have to take the > same basic requirements, some of which could be writing classes. It does not seem strange to me that a math class would require writing, but the writing they require should be mathematical writing, which is a distinct style not taught in other classes (and unfortunately rarely taught anywhere, with the result that most people, even trained mathematicians, cannot write mathematics well). Requiring a chat room seems rather irrelevant for a math class---it is not as if chat rooms were good mechanisms for tutoring or peer discussions on math. A study group with a blackboard would be far more useful, since equations can be written on a board with much greater facility than they can be typed in a chat room. ------------------------------------------------------------ Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus Professor of Biomolecular Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Senior member, IEEE Board of Directors, ISCB (starting Jan 2005) life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Older student going back to school. > It seems strange that the school would make an algebra class a writing > class. There are so many classes that you write in already, (like > english, speech, research, reports, etc.) it just does not make sense > for a math class. No matter what you go into, you have to take the > same basic requirements, some of which could be writing classes. > It does not seem strange to me that a math class would require > writing, but the writing they require should be mathematical writing, > which is a distinct style not taught in other classes (and > unfortunately rarely taught anywhere, with the result that most > people, even trained mathematicians, cannot write mathematics well). > Requiring a chat room seems rather irrelevant for a math class---it is > not as if chat rooms were good mechanisms for tutoring or peer > discussions on math. A study group with a blackboard would be far > more useful, since equations can be written on a board with much > greater facility than they can be typed in a chat room. > ------------------------------------------------------------ > Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus I am not sure what mathatical writing is. What is an example, or where can I find an example of mathmatical writing? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Older student going back to school. >> It does not seem strange to me that a math class would require >> writing, but the writing they require should be mathematical writing, >> which is a distinct style not taught in other classes (and >> unfortunately rarely taught anywhere, with the result that most >> people, even trained mathematicians, cannot write mathematics well). > I am not sure what mathatical writing is. What is an example, or > where can I find an example of mathmatical writing? Mathematical writing is found in math books and journals. Just as with science writing, there are several different types of writing, depending on who the audience is. There are trade books aimed at the general public, text books for students at all levels, and math The best essay about mathematical writing Ive seen is Halmoss places, including a book of essays edited by Steenrod: and a selection of Halmoss writing: Selecta: Expository Writings ------------------------------------------------------------ Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus Professor of Biomolecular Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Senior member, IEEE Board of Directors, ISCB (starting Jan 2005) life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Solving equation >That was a bad example, I made mistake in subtraction- and it wasnt >very relevant to my problem anyway- Im very sorry. >A better example would have been 5 - 3x = 5x. Again, Im very sorry. > Any help would still be appreciated. >> Well, other than the one mistake in subtraction, youre previous example was >> done perfectly. Is there something in particular that you dont think you >> understand? > Sometimes I get it to balance out, and sometimes I cant get it to > work. Like here: > -2(3y+1)=3(1-6y)-9 > I get rid of parantheses > -6y - 2 = 3 - 18y - 9 > Now I combine like term > -6y - 2 = 18y - 6 > Then I add two to both sides > -6y = 18y - 10 > And this is where I get stuck. I dont see where to go from here. I > can devide 18/-6 and get -3, but I still have -10. Am I doing this > right so far and just overlooking something, or making mistake? -2(3y+1)=3(1-6y)-9 -6y - 2 = (3 -18y) - 9 -6y - 2 = -6 - 18y -6y - 2 +18y = -6 -18y + 18y 12y - 2 = -6 12y -2 + 2 = -6 + 2 12y = -4 12 y / 12 = -4 / 12 y = -1/3 -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Solving equation >> Hello - I am new to pre/algebra, and I have difficulty understanding >> how to do equations with variables on both sides. >> Like this: >> 7r - 1 = 5r - 13 >> I get rid of one and have: >> 7r = 5r - 12 >> Then I get rid of 5r and have: >> 3r = -12 (2r = -12) >> r = -4 ? (r = -6) > very relevant to my problem anyway- Im very sorry. > A better example would have been 5 - 3x = 5x. Again, Im very sorry. > Any help would still be appreciated. 5 - 3x = 5x 5x = 5 - 3x 5x + 3x = 5 - 3x + 3x 8x = 5 8x / 8 = 5 / 8 x = 5 / 8 -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Solving equation > Hello - I am new to pre/algebra, and I have difficulty understanding > how to do equations with variables on both sides. > Like this: > 7r - 1 = 5r - 13 > I get rid of one and have: > 7r = 5r - 12 > Then I get rid of 5r and have: > 3r = -12 > r = -4 ? > Could someone tell me where I go wrong with this? Appreciate any > response. Well, assuming you are solving for r... 7r - 1 = 5r -13 7r - 1 - 5r = 5r - 13 - 5r 2r - 1 = -13 2r - 1 + 1 = -13 + 1 2r = -12 2r / 2 = -12 / 2 r = -6 -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Simplify by combining like terms > I trying to figure out the equation below. Please help and give > details. > 1/2(X + 3) + 1/3(3x = 6) You have a typo in there somewhere. What you have typed makes no sense. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Simplify by combining like terms > I[Ôm] trying to figure out the equation below. Please help and give > details. 1/2(X + 3) + 1/3(3x = 6) Certainly there is a typo in the problem above for which we will graciously forgive. We are all human here. However, the correct problem may be easily derived. Perhaps the problem should read as follows: 1/2(X+3)+1/3(3X)=6 If this in fact the problem which was supposed to be written, then we have an easy solution. There are a few ways of solving this equation, but lets do it this way. Start with the distributive property. 1/2 times X and 1/2 times 3. Then, 1/3 times 3X. We end up with the following (if we stay in fraction form): 1/2X + 3/2 + X = 6 Combine terms and solve. 3/2X + 3/2 = 6 3/2X = 9/2 X = 3 We can check our answer by substituting the answer into our original problem. 1/2(3+3) + 1/3[3(3)] = 6 -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Square Root Help > Hey!!!!! Ive been having trouble lately with my homework, dealing > with squares and square roots. If anyone has an answer to my request, > please e-mail me(above) THANX!!!!!!! :) You didnt make a request. You made a statement. What is your question? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Square Root Help Also remember that when dealing with square roots, you can take a number and actually raise it to certain power to get the same answer if you squared it. For example, we know that the square root of 4 is 2. But we can also write it 4^(1/2). The answer is 2. This works with nearly any power. For example, with cubes. We know that the cube of 64 is 4. And we can write it 64^(1/3). In this example, 3 represents the root and 1 represents the exponent, or basically how many 64s there are. Further, 64^(2/3) is 16 because 64 squared or 64^2 equals 4096 and the cube of that is 16. Church -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Derivative of Sin K (X) Please check my answer: sin Sqrt(X - X^3) = sin sqrt X - sqrt x^3 = sin X^1/2 - X^3/2 = sin 1/2 X^-1/2 - 3/2 X^1/2 = sin 1 / 2sqrt X - 3 sqrt X / 2 = 1/2 sqrt X - 3sqrt X / 2 . cos sqrt X-X^3 Jason -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Derivative of Sin K (X) You started off making a fundemental error. It is a common error. Sqrt(x-x^3) does not equal Sqrt x - Sqrt x^3 Try plugging in numbers, any numbers Sqrt (100-25), does it equal Sqrt 100 - Sqrt 25?? Sqrt (100-25)=8.6600... Sqrt 100 - Sqrt 25= 10-5 = 5 So try again. If ever you wonder if you can do an operation, try numbers you know first. This should help you out. ~John >Please check my answer: sin Sqrt(X - X^3) >= sin sqrt X - sqrt x^3 >= sin X^1/2 - X^3/2 >= sin 1/2 X^-1/2 - 3/2 X^1/2 >= sin 1 / 2sqrt X - 3 sqrt X / 2 >= 1/2 sqrt X - 3sqrt X / 2 . cos sqrt X-X^3 >Jason -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Derivative of Sin K (X) You started off making a fundemental error. It is a common error. Sqrt(x-x^3) does not equal Sqrt x - Sqrt x^3 Try plugging in numbers, any numbers Sqrt (100-25), does it equal Sqrt 100 - Sqrt 25?? Sqrt (100-25)=8.6600... Sqrt 100 - Sqrt 25= 10-5 = 5 So try again. If ever you wonder if you can do an operation, try numbers you know first. This should help you out. ~John >Please check my answer: sin Sqrt(X - X^3) >= sin sqrt X - sqrt x^3 >= sin X^1/2 - X^3/2 >= sin 1/2 X^-1/2 - 3/2 X^1/2 >= sin 1 / 2sqrt X - 3 sqrt X / 2 >= 1/2 sqrt X - 3sqrt X / 2 . cos sqrt X-X^3 >Jason -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Derivative of Sin K (X) sin[sqrt(x-x^3)] You made up non-rules to simplify this expression, which is not going to be simplified. Its structure is like this: trig[square root(polynomial)]. You treat it as a trig function, then as a power function, then as a polynomial function, one inside the other with regard to the Chain Rule. (sin[sqrt(x-x^3)]) = cos(sqrt(x-x^3))*[sqrt(x-x^3)] = cos(sqrt(x-x^3))*[(x-x^3)^(1/2)] = cos(sqrt(x-x^3))*((1/2)(x-x^3)^(-1/2))*[x-x^3] = cos(sqrt(x-x^3))*((1/2)(x-x^3)^(-1/2))*[1-3x^2] = cos(sqrt(x-x^3))*(1/(2sqrt(x-x^3))*[1-3x^2] = cos(sqrt(x-x^3))*((1-3x^2)/(2sqrt(x-x^3)) = ((1-3x^2)/(2sqrt(x-x^3))cos(sqrt(x-x^3)) -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Algerbra History Does any one know when Algerbra was first taught in Michigan High Schools? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Algerbra History ha ha ha, Just kidding. Try contacting the Dept of Education or Dept of Public instruction >Does any one know when Algerbra was first taught in Michigan High >Schools? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Sproket Problem, I need help! This problem has to do with speeds & sprockets. If anyone can come up with an easy solution to this problem, it would be greatly appreciated! Carol Here is the problem: The front sprocket of a 3-speed bike is 6.8a in diameter. The diameters of the back sprockets for the 1st, 2nd, and 3rd speeds are 4.8a, 3.8a, and 2.8a respectively. The diameter of the back wheel is 25.8a. For each speed, calculate how many times the back wheel will turn and how far the bike will move when the pedals move around once. Solutions should include diagrams and explanations. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Sproket Problem, I need help! look at it like this. The front sprocket is 6-pi the back sprockets are 2 -pi, 3-pi, 4-pi in circumfrence 1 revolution on the front sprcket will turn the back sprockets 3 rev, 2 rev, 1.5 rev respectively. Since the back tire is 25 in dia, the circumfrence is 25-pi so depending on the sprocket you have the chain on you could go 3x25-pi, 2x25-pi, or 1.5x25-pi I hope this helps. I will leave the drawing up to you. ~John >This problem has to do with speeds & sprockets. If anyone can come up >with an easy solution to this problem, it would be greatly >appreciated! >Carol >Here is the problem: > The front sprocket of a 3-speed bike is 6.8a in diameter. The >diameters of the back sprockets for the 1st, 2nd, and 3rd speeds are >4.8a, 3.8a, and 2.8a respectively. The diameter of the back wheel is 25.8a. >For each speed, calculate how many times the back wheel will turn and >how far the bike will move when the pedals move around once. >Solutions should include diagrams and explanations. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Sproket Problem, I need help! >This problem has to do with speeds & sprockets. If anyone can come up >with an easy solution to this problem, it would be greatly >appreciated! >Carol >Here is the problem: > The front sprocket of a 3-speed bike is 6=94 in diameter. The >diameters of the back sprockets for the 1st, 2nd, and 3rd speeds are >4=94, 3=94, and 2=94 respectively. The diameter of the back wheel is 25= =94. = >For each speed, calculate how many times the back wheel will turn and >how far the bike will move when the pedals move around once. = >Solutions should include diagrams and explanations. Your units are not showing here, so Ill assume inches. Can you say how many times the 2 sprocket will turn for every turn of the 6 sprocket? That is the basis of the problem. Having found the number of turns, that is also the number of turns of the wheel, and you know its diameter, so you can find its circumference. The circumference meets the road over every turn of the wheel, so that gives the distance travelled. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Very difficult problem with mixtures Can anyone help me with this problem? Toothpaste in the Basement Elana mixes the tootpastes in large tanks in her basement after school. Both ßavors are made from only four ingredients, which we.89ll call A, B, C, and D to preserve Elana.89s trade secrets. Ingredients A, B, and D are pumped into Tank 1 and mixed to make Candy Madness, which requires 2 gallons of B and 3 gallons of D for every gallon of A. Two-thirds of this mixture are drained and packaged, but one-third is pumped into Tank 2 where it is mixed with other ingredients to make Maple Sugar Supreme. This second recipe requires three times the amount of A used in Candy Madness, and it is ßavored with 2 gallons of C for every 3 gallons of A. If Elana.89s process produces 21 gallons of Maple Sugar Supreme per hour, how many gallons of Candy Madness are produced per hour? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Very difficult problem with mixtures >Can anyone help me with this problem? = How many gallons would you have if you mixed 1 of a, 2 of B and 3 of D? How many times will this total divide into 21? Multiply each by the result to get the amount of each in 21 gallons. Since 2/3 are packaged, what fraction remains? OK, I Ôll tell you that one, 1/3. So find 1/3 of each of A,B, D, to find what remains. You now know how much of A there is available. Can you figure out how much of A is needed [Hint: 3 times the amount you calculated for A initially, of which 1/3 is already there.] Now you can figure out how much of A is needed by the difference of the two. The amount for C is dependent on the total required for A, which is 3 times the original amount for A. the amount for C will be 2/3 of the amount for A. >Elana mixes the tootpastes in large tanks in her basement after >school. Both ßavors are made from only four ingredients, which we=92ll= >call A, B, C, and D to preserve Elana=92s trade secrets. Ingredients A,= >B, and D are pumped into Tank 1 and mixed to make Candy Madness, which >requires 2 gallons of B and 3 gallons of D for every gallon of A. = >Two-thirds of this mixture are drained and packaged, but one-third is >pumped into Tank 2 where it is mixed with other ingredients to make >Maple Sugar Supreme. This second recipe requires three times the >amount of A used in Candy Madness, and it is ßavored with 2 gallons >of C for every 3 gallons of A. > If Elana=92s process produces 21 gallons of Maple Sugar Supreme per >hour, how many gallons of Candy Madness are produced per hour? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Alternative to Kumon Math I have recently discovered Dreamchievers for my 13 year old son. It has programs for math & language. Let me know if you would like more information, I will be glad to help. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Alternative to Kumon Math >I have recently discovered Dreamchievers for my 13 year old son. It >has programs for math & language. >Let me know if you would like more information, I will be glad to >help. Please clarify: is Dreamchievers a tutoring institution, or is it a software program, or is it a textbook intensive reteaching system? G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: career advice Hello all, I am a practicing engineer about to make a leap (well, as a snail might see it) into teaching high school math. Ive been doing some class observation hours, and right now I believe that my final aspiration is to teach an AP-track math series in a rural or (maybe) inner-city school. That and have some significant summer time to spend :-) However, I percieve that this will not be a career path that is easy to accomplish in any short order. I expect I will enjoy teaching most math/science courses along the way as I have enjoyed tutoring a wide variety of students, but I doubt I will be satisfied until I am teaching an AP course of some ßavor, or moving on to post-secondary roles. All you out there teaching along the path to AP math... what is your background like? Are opportunities to teach advanced-track courses more a matter of seniority or was something else involved? Any advice? Anyone think this way when they started, but change focus? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Inequality help! Hi I am having trouble with this question I saw in a problem solving book, could someone please help me. I know its hard to read inequalities nicely so I have also put a picture of the question on the internet here. http://img44.exs.cx/img44/2759/q24.jpg It says if f(x) => g(x) for a integral of g(x) in the range a to b. Then it says if p>q>0 and x>= 1 then prove 1/p*(x^p -1) => 1/q(x^q - 1) and show this also holds when p>q>0 and 0<=x<=1. then lastly it says prove that if p>q>0 and x=>0, then 1/p*(x^p/(p+1) -1) => 1/q(x^q/(q+1) - 1) this is what I have done so far. Really brießy this is to do with every value of f(x) is bigger then or equal to g(x) so if we take the integral to mean the area under the graph then it is clear the integral of f(x) is bigger then g(x) as it is the same length under the graph but every value is more. Then I am not sure if this is correct but for part 2, if we consider the integral from 1 to x of t^(p+1) and same integral of t^(q+1), it gives us the result from the first part. as t^(p+1)>t(q+1). Is this correct? Then for the p>q>0, if we multiply the integral in part 1 by -1 then change the 1 and the x around in the integral we get the desired result (I hope). But then the last part I have no idea what to do, could someone please help. thank you -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Inequality help! > Hi I am having trouble with this question I saw in a problem solving > book, could someone please help me. > I know its hard to read inequalities nicely so I have also put a > picture of the question on the internet here. > http://img44.exs.cx/img44/2759/q24.jpg > It says if f(x) => g(x) for a f(x) => integral of g(x) in the range a to b. Nearly. What it says is: If f(t) => g(t) for a integral(from a to b) g(t)dt. <... this is what I have done so far. > Really brießy this is to do with every value of f(x) is bigger then > or equal to g(x) so if we take the integral to mean the area under the > graph then it is clear the integral of f(x) is bigger then g(x) as it > is the same length under the graph but every value is more.<...> Interpreting a definite integral as an area requires certain conditions be in place. For instance, the function must be nonnegative. Thats not necessarily so in the statement you are asked to explain. Its not a requirement that the functions be nonnegative in order for the statement to be true so personally I would avoid the area explanation, but YMMV. Theres not really anything wrong with your explanation, it just doesnt justify the general case of the theorem (only specific cases for nonnegative functions.) Try this. If you already have access to the these facts (IOW you can use these in your explanation): int(a to b) f(t)dt => 0 for f nonnegative and integrable on [a,b] ....which also says something about the area interpretation and... int(a to b) [f(t) +- g(t)] dt = int(a to b) f(t)dt +- int(a to b) g(t)dt then... f(t) => g(t) implies f(t)-g(t) => 0, thus... int(a to b) [f(t) - g(t)] dt => 0 rewrite... int(a to b) f(t)dt - int(a to b) g(t)dt => 0 adding the second integral to both sides.... int(a to b) f(t)dt => int(a to b) g(t)dt That is essentially the proof of the theorem, but its short enough to also be the explanation, too. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Inequality help! trouble proving the inequalities though. Could you please help me with that? it isnt for a class, just seen it in a book of problems and I cant do it. I think I am supposed to show it some how by using the integration information about functions being bigger then each other, and deduce it. No induction or anything though -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Inequality help! What class is this for? Is this a discrete class where you will have to prove by induction or other methods. I need just a little more information to help you out. ~John >Hi I am having trouble with this question I saw in a problem solving >book, could someone please help me. >I know its hard to read inequalities nicely so I have also put a >picture of the question on the internet here. href=http://img44.exs.cx/img44/2759/q24.jpg>http://img44. exs.cx/img44/27 59/q24.jpg g(x) for af(x) => integral of g(x) in the range a to b. >Then it says if p>q>0 and x>= 1 then prove >1/p*(x^p -1) => 1/q(x^q - 1) >and show this also holds when p>q>0 and 0<=x<=1. >then lastly it says prove that if p>q>0 and x=>0, then >1/p*(x^p/(p+1) -1) => 1/q(x^q/(q+1) - 1) >this is what I have done so far. >Really brießy this is to do with every value of f(x) is bigger then >or equal to g(x) so if we take the integral to mean the area under the >graph then it is clear the integral of f(x) is bigger then g(x) as it >is the same length under the graph but every value is more. >Then I am not sure if this is correct but for part 2, >if we consider the integral from 1 to x of t^(p+1) and same integral >of t^(q+1), it gives us the result from the first part. as >t^(p+1)>t(q+1). >Is this correct? >Then for the p>q>0, if we multiply the integral in part 1 by -1 then >change the 1 and the x around in the integral we get the desired >result (I hope). >But then the last part I have no idea what to do, could someone please >help. >thank you -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Runs in a random sequence The Badger 5 game allows players to pick 5 of the numbers from 1 to 31, and a player wins if their ticket matches the 5 numbers randomly selected by the state. What is the probability that the winning numbers will have at least two consecutive numbers? Any hints on how to aproach this?? Repeats are not allowed, and order doesn.89t matter. That is, if the state picks 8 .9a 3 .9a 28 .9a 6 .9a 16, and your ticket says 3 .9a 6 .9a 8 16 .9a 28, you win. Go to www.wilottery.com to see what an actual Megabucks result looks like. HELP!!! -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: a gift exchange Ten friends organize a gift exchange. The ten names are put in a hat, and the first person draws one. If they pick their own name, they return it to the bag and draw again, until they have a name that is not their own. Then the second person draws, again returning their own name if they draw it. This continues down the line. What is the probability that when the 10th person draws, only their own name will be left in the bag? any help!!! -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: a gift exchange > Ten friends organize a gift exchange. The ten names are put in a hat, > and the first person draws one. If they pick their own name, they > return it to the bag and draw again, until they have a name that is > not their own. Then the second person draws, again returning their > own name if they draw it. This continues down the line. What is the > probability that when the 10th person draws, only their own name will > be left in the bag? > any help!!! Suppose more generally that n people (with distinct names) are involved in the gift exchange, where n > 1. Let f(n) be the number of ways that these peoples names can be distributed among them such that no one gets their own name. Given the way the names are drawn, the first (n-1) people will not have their own name. So, the number of ways that the n-th person can draw his own name is f(n-1). On the other hand, if he does not draw his own name, this can happen in f(n) ways. This exhausts all cases. Clearly, each outcome is equally likely. Therefore, the probability that the last person draws their own name is the ratio f(n-1) / [f(n-1) + f(n)] This reduces your problem to finding a formula for f(n), calculating f(9) and f(10), and substituting them into the formula. There is a nice recursion formula for f(n). According to my calculations, the answer to your question is about 9.09% Hope this helps. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: a gift exchange > Ten friends organize a gift exchange. The ten names are put in a hat, > and the first person draws one. If they pick their own name, they > return it to the bag and draw again, until they have a name that is > not their own. Then the second person draws, again returning their > own name if they draw it. This continues down the line. What is the > probability that when the 10th person draws, only their own name will > be left in the bag? > any help!!! What are the odds that each person before Z picks Zs name from the hat? Add up those probabilities and subtract from 1. --Jeff -- It is only those who have neither fired a shot nor heard the shrieks and groans of the wounded who cry aloud for blood, more vengeance, more desolation. War is hell. --William Tecumseh Sherman Egotism is the anesthetic that dulls the pain of stupidity. --Frank William Leahy -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: a bar bet Someone offers to bet you that if you ßip a coin twenty times, you will get at least two heads in a row at least once. They are paying 200 to 1 odds, so if you bet a dollar, they will pay $200 if you win. Is this a good bet? Hummm -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Witzzle Pro Mail In Math Contest Kaidy has a new mail-in contest for you and your children. It is a unique individual or class contest. The Fall Witzzle Pro Mail-In Math and/or teachers will be notified in January, 2005. Witzzle Pro Games have been the basis for almost 10 years of math contests. Students up to grade 8 may enter. Teachers may enter whole classes in one step. Each winner and teacher, if school based entry with school email, gets a prize. It is a great game that lets students play to learn while they learn to play! Visit http://mathfun.com/WitzzleProMailInContest.html for the contest information! Kaidy and MathFun.com are dedicated to promoting math awareness, learning and success for all children! Check back in February 2005 for our Spring contest. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: It has to be right: I used my calculator! The continuing pseudo-education of American students is demonstrated clearly by the mushrooming college enrolments in remedial mathematics courses. A key component of this pseudo-education is the widespread, deliberate over reliance on calculators--with no expectation that students understand elementary concepts--whereby students punch numbers into their calculators and are required to simply write down the last display. At the beginning of this semester, in one of my remedial courses, I reviewed how to perform manual operations with simple fractions. The following operations were to be done manually, with all the steps written down. One student, among many, used his graphing calculator to obtain the following three correct answers. When I asked him to do (5/6)(9/10) = 3/4 [45/16] (3/4):(7/8) = 6/7 [28/32] (: indicates division symbol) (7/6)-(3/8) = 19/24 [(7-3)/48 = 5/48] When I pointed out that the following answer was wrong, (3/4)+(5/12) = 14/15 he immediately snapped: It has to be right: I used my calculator! The majority of the students in this class had graphing calculators. I would not be surprised if their pseudo-education was promoted with the bogus slogans and empty boasts of pseudo-educators: using technology to solve real-world problems, twenty-first century mathematics, world-class education, calculators free the mind to solve more difficult problems. Dom Rosa -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! Domenico...you must have my 8th graders. I dont allow calculators unless it is a problem that has large numbers and I want the results quickly. I even teach my 8th graders (in a two year algebra course to learn and master fractions) In my Algebra 1 class they cant use calculators until they dont need them! Ginny J > The continuing pseudo-education of American students is demonstrated > clearly by the mushrooming college enrolments in remedial mathematics > courses. A key component of this pseudo-education is the widespread, > deliberate over reliance on calculators--with no expectation that > students understand elementary concepts--whereby students punch > numbers into their calculators and are required to simply write down > the last display. > At the beginning of this semester, in one of my remedial courses, I > reviewed how to perform manual operations with simple fractions. The > following operations were to be done manually, with all the steps > written down. One student, among many, used his graphing calculator to > obtain the following three correct answers. When I asked him to do > (5/6)(9/10) = 3/4 [45/16] > (3/4):(7/8) = 6/7 [28/32] (: indicates division symbol) > (7/6)-(3/8) = 19/24 [(7-3)/48 = 5/48] > When I pointed out that the following answer was wrong, > (3/4)+(5/12) = 14/15 > he immediately snapped: It has to be right: I used my calculator! > The majority of the students in this class had graphing calculators. I > would not be surprised if their pseudo-education was promoted with the > bogus slogans and empty boasts of pseudo-educators: using technology > to solve real-world problems, twenty-first century mathematics, > world-class education, calculators free the mind to solve more > difficult problems. > Dom Rosa -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! What you are using to support your rant? > At the beginning of this semester, in one of my remedial courses,... ....a remedial course; are these students up to speed? > I reviewed how to perform manual operations with simple fractions. Did *they* review it or better yet, did they ever learn it? > The following operations were to be done manually, with all the steps > written down... Those, who never learned fractions, decimals and percents in the 6th, 7th, 8th, 9th, 9th, 10th, 11th, 12th, 12th grades, will be using calculators. If you dont like it, quit teaching (remedial math courses). In your frustration, do you want to torture students for what you perceive as sins of the system? > One student, among many, used his graphing calculator to > obtain the following three correct answers.... I see. You are attacking the competence of one functioning remedial student, who can complete almost all the problems, using a calculator. > in brackets. Let sleeping dogs lie, unless you want to go the extra mile. Forget it, if you cant teach your way out of a paper bag. > (5/6)(9/10) = 3/4 [45/16] > (3/4):(7/8) = 6/7 [28/32] (: indicates division symbol) > (7/6)-(3/8) = 19/24 [(7-3)/48 = 5/48] > When I pointed out that the following answer was wrong, > (3/4)+(5/12) = 14/15 > he immediately snapped: It has to be right: I used my calculator! You are down to focusing on one remark made by one remedial student. > The majority of the students in this class had graphing calculators... Is this a crime? > I would not be surprised if their pseudo-education was promoted with the > bogus slogans and empty boasts of pseudo-educators: using technology > to solve real-world problems, twenty-first century mathematics, > world-class education, calculators free the mind to solve more > difficult problems. You made up this part, right? Is there any evidence that teachers or even most mathematicians ever did this or that anyone claims this? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >> I reviewed how to perform manual operations with simple >> fractions. >Did *they* review it or better yet, did they ever learn it? >> The following operations were to be done manually, with all the >> steps written down... >Those, who never learned fractions, decimals and percents >in the 6th, 7th, 8th, 9th, 9th, 10th, 11th, 12th, 12th grades, >will be using calculators. This is exactly my point! The fact that so many students never learned and were probably _never taught_ these elementary concepts is indicative of the pseudo-education that is being promoted in the U.S. today. Dom Rosa -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! > This is exactly my point! The fact that so > many students never learned and were > probably _never taught_ these elementary > concepts is indicative of the pseudo-education > that is being promoted in the U.S. today. You are putting the cart before the horse. Its not only top-down policy. Its bottom up. Math can be difficult to master, and its not a critical activity in the daily lives of most citizens. As we know, even memorizing multiplication tables can be a herculean task. I hope you are not blaming teachers. That would be like blaming toll-booth workers for the state of the subway system. Otherwise, you sound like Chicken Little. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >> This is exactly my point! The fact that so >> many students never learned and were >> probably _never taught_ these elementary >> concepts is indicative of the pseudo-education >> that is being promoted in the U.S. today. >You are putting the cart before the horse. >Its not only top-down policy. Its bottom up. >Math can be difficult to master, and its not a >critical activity in the daily lives of most citizens. >As we know, even memorizing multiplication >tables can be a herculean task. >I hope you are not blaming teachers. >That would be like blaming toll-booth workers >for the state of the subway system. >Otherwise, you sound like Chicken Little. I do not blame the teachers, most of whom must follow the directives of internal curriculum specialists and directors of instruction; and of high-ßown outside consultants retained by Boards of Education. Dom Rosa -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >> I would not be surprised if their pseudo-education was promoted with the >> bogus slogans and empty boasts of pseudo-educators: using technology >> to solve real-world problems, twenty-first century mathematics, >> world-class education, calculators free the mind to solve more >> difficult problems. >You made up this part, right? Is there any evidence that teachers or >even most mathematicians ever did this or that anyone claims this? Ive heard the same jargon, but not about American education, about the system here. Its common promotion of the proponents of massive and dependent use of the calculator and computer. We have similar problems here in my part of the world, and likely elsewhere, so I dont think the remarks are aimed at the American system in particular except to perhaps express some real concern. Surely there must be some concern, or there is no room for further change, so I suspect he is a concerned American. A LOT of people here are quite concerned especially about recent changes. Ive been tutoring children here in calculus who have a bare minimum knowledge of geometry, are weak in algebra, and have little trig to speak of, except as an appendix in their high school graduation year introductory calculus text. They are having a very tough time of it, especially when they do graduate and move on to college. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! > I would not be surprised if their pseudo-education was promoted with the > bogus slogans and empty boasts of pseudo-educators: using technology > to solve real-world problems, twenty-first century mathematics, > world-class education, calculators free the mind to solve more > difficult problems. >>You made up this part, right? Is there any evidence that teachers or >>even most mathematicians ever did this or that anyone claims this? >Ive heard the same jargon, but not about American education, about >the system here. Its common promotion of the proponents of massive >and dependent use of the calculator and computer. You are absolutely correct! The first three slogans appear in numerous leading promoter of math reform who used to be a mathematics consultant with the Connecticut State Department of Education. I read the fourth slogan in a newsletter from an elementary school. Dom Rosa -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! > We have similar problems here in my part of the world, > and likely elsewhere, so I dont think the remarks are > aimed at the American system in particular except to > perhaps express some real concern. Many kids today dont want to learn math and dont feel ashamed or guilty about not knowing any. Its too bad for us. These are tough times. The esthetics go first. The golden age of mathematics teaching is over. > Surely there must be some concern, or there is no room > for further change, so I suspect he is a concerned American. Maybe not in our lifetimes. > A LOT of people here are quite concerned especially about > recent changes. Ive been tutoring children here in calculus > who have a bare minimum knowledge of geometry, are weak > in algebra, and have little trig to speak of, except as an > appendix in their high school graduation year introductory > calculus text. They are having a very tough time of it, > especially when they do graduate and move on to college. Tutors will be doing well. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! > >At the beginning of this semester, in one of my remedial courses,... > ....a remedial course; are these students up to speed? > > I reviewed how to perform manual operations with simple fractions. > Did *they* review it or better yet, did they ever learn it? >>The following operations were to be done manually, with all the steps >>written down... > Those, who never learned fractions, decimals and percents > in the 6th, 7th, 8th, 9th, 9th, 10th, 11th, 12th, 12th grades, > will be using calculators. If you dont like it, quit teaching (remedial > math courses). In your frustration, do you want to torture students > for what you perceive as sins of the system? Except that 1) most of them probably dont know how to use a calculator, and 2) calculators will not always be available to them. Once while working at a restaurant, the cash register failed. No one, but I, could calculate the customers bills (including tax) even WITH a calculator. All of these people had completed high school. That is pretty abysmal. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >Except that 1) most of them probably dont know how to use a calculator, >and 2) calculators will not always be available to them. Once while >working at a restaurant, the cash register failed. No one, but I, could >calculate the customers bills (including tax) even WITH a calculator. >All of these people had completed high school. That is pretty abysmal. Here they gave credit for work done outside the school. One got a job teller]. She couldnt make change. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! > Except that 1) most of them probably > dont know how to use a calculator, Domenico never claimed that, did he? The level for him seems to be post high school. Maybe you were thinking of your classes. > and 2) calculators will not always be available > to them. Why not? Thats what my great grandmother said about electricity. > Once while working at a restaurant, the cash register failed. > No one, but I, could calculate the customers bills (including tax) > even WITH a calculator. Excellent point; the best argument for the usefulness of math knowledge, Ive heard in years. It underscores, though, the simple truth that there are very few everyday applications of mathematics, speaks to the acceptability of math ignorance, and gives an example showing experts always will be around to do elementary calculations. > All of these people had completed high school. That is pretty abysmal. Okay. You are appalled by the state of mathematics knowledge. Youth is going to hell in a handbasket. In these times, one must justify pursuit of knowledge to the philistines. The problem is, Mathematics is an esthetically-pleasing, elitist discipline that life can be conducted without, although life will be poorer for it. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >>Except that 1) most of them probably >>dont know how to use a calculator, > Domenico never claimed that, did he? > The level for him seems to be post high school. > Maybe you were thinking of your classes. Uhh... I was not replying to Domenicos post, I was replying to yours. However, he did say that at least one student couldnt work one of the problems with the aid of a calculator, which supports my first point. >>and 2) calculators will not always be available >>to them. > Why not? Thats what my great grandmother said > about electricity. And when the worlds oil and coal reserves have been depleted, your grandmother may be proven correct. >>Once while working at a restaurant, the cash register failed. >>No one, but I, could calculate the customers bills (including tax) >>even WITH a calculator. > Excellent point; the best argument for the usefulness of math knowledge, > Ive heard in years. It underscores, though, the simple truth that there > are very few everyday applications of mathematics, Really??? If there are so few applications of mathematics, then where did it originate? It did not come from scholars in their ivory towers. It was developed out of necessity --- counting, business transactions, carpentry, engineering, etc. How many people in the U.S. have checking accounts? To balance your books, you need to be comfortable with decimal arithmetic. Do you suggest that the majority of people turn over their checkbooks and receipts to experts every couple of days to balance their books? How would one go about verifying that the auditor did his arithmetic correctly? What is 15% gratuity on a meal that costs $17.84? Few applications indeed. > speaks to the > acceptability of math ignorance, and gives an example showing experts > always will be around to do elementary calculations. >>All of these people had completed high school. That is pretty abysmal. > Okay. You are appalled by the state of mathematics knowledge. Youth is > going to hell in a handbasket. In these times, one must justify pursuit of > knowledge to the philistines. The problem is, Mathematics is an > esthetically-pleasing, elitist discipline that life can be conducted > without, although life will be poorer for it. Elitist discipline --- that takes the cake. Climb down out of the ivory tower. We arent talking about stochastic processes. We are talking about basic arithmetic. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! <... How many people in the U.S. have checking accounts? Considerably more than know how to properly balance one. <... What is 15% gratuity on a meal that costs $17.84? $1.78 plus half that, but ask yourself how many people (to include those that _can_ make that calculation,) actually do. Also ask yourself why the industry does not provide two Ôtotals on the receipt, one with no tip and one with the customary 15% tip automatically calculated and totaled. The only restaurant receipts that include a tip entry _at all_ are for credit cards (for convenience of the guests record keeping) but they leave the amount blank. In Germany (and presumably some other countries) the customary gratuity is included. Tipping is considered rude, especially so when Ôleft on the table. Only small tips, handed directly to the waiter, are ever socially acceptable. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >> What is 15% gratuity on a meal that costs $17.84? > $1.78 plus half that, but ask yourself how many people (to include those > that _can_ make that calculation,) actually do. Also ask yourself why the > industry does not provide two Ôtotals on the receipt, one with no tip and > one with the customary 15% tip automatically calculated and totaled. The > only restaurant receipts that include a tip entry _at all_ are for credit > cards (for convenience of the guests record keeping) but they leave the > amount blank. I eaten in many restaurants in the US that automatically add a service charge for parties of 6 or more---often 18%, which is more than the usual tip. One of the restaurants I frequent does include a comment at the bottom of each bill indicating how much a 15% and a 20% tip would be. ------------------------------------------------------------ Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus Professor of Biomolecular Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Senior member, IEEE Board of Directors, ISCB (starting Jan 2005) life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! > One of the restaurants I frequent does include a comment at the bottom > of each bill indicating how much a 15% and a 20% tip would be. Interesting. I have not seen that yet myself. It would be interesting to know if this resulted in less, more, or the same tippage over the long run. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >>Except that 1) most of them probably >>dont know how to use a calculator, > Domenico never claimed that, did he? > The level for him seems to be post high school. > Maybe you were thinking of your classes. >>and 2) calculators will not always be available >>to them. > Why not? Thats what my great grandmother said > about electricity. >>Once while working at a restaurant, the cash register failed. >>No one, but I, could calculate the customers bills (including tax) >>even WITH a calculator. > Excellent point; the best argument for the usefulness of math knowledge, > Ive heard in years. It underscores, though, the simple truth that there > are very few everyday applications of mathematics, speaks to the > acceptability of math ignorance, and gives an example showing experts > always will be around to do elementary calculations. >>All of these people had completed high school. That is pretty abysmal. > Okay. You are appalled by the state of mathematics knowledge. Youth is > going to hell in a handbasket. In these times, one must justify pursuit of > knowledge to the philistines. The problem is, Mathematics is an > esthetically-pleasing, elitist discipline that life can be conducted > without, although life will be poorer for it. Oh come on. That same argument can be made about reading and writing. There are people in their 30s, 40s, 50s, etc. who have somehow managed to get through life without ever learning to read or write. What are you advocating here? That we dismantle the school system? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! > Oh come on. That same argument can be made > about reading and writing. Literacy is a *more* critical skill to have. Have you ever heard of a person suing their educational institution because they cannot prove the Pythagorean Theorem? > There are people in their 30s, 40s, 50s, etc. who > have somehow managed to get through life without > ever learning to read or write. What are you > advocating here? That we dismantle the school system? School systems are the most conservative of public institutions, the last, not the first, to change. They experience a trickle down effect with respect to cultural attitudes towards learning. More from Brett: > Really??? If there are so few applications of mathematics, then > where did it originate? It did not come from scholars in their > ivory towers. People learn necessary arithmetic, when they need to use it. > It was developed out of necessity --- counting, business > transactions, carpentry, engineering, etc. We have become almost exclusively a service economy. > How many people in the U.S. have checking accounts? To > balance your books, you need to be comfortable with > decimal arithmetic. Nooo. You need to make enough money. > Do you suggest that the majority of people turn over their > checkbooks and receipts to experts every couple of days > to balance their books? This is trivial, not really mathematics. Im suggesting the majority of people either do it without a problem, dont bother to do it at all, or get assistance. Remember, most students will not have any difficulty when the time comes, whether or not they learn anything about it in school. > How would one go about verifying that the auditor did his > arithmetic correctly? If they have ballpark figures, most dont really care. Routine money management is boring. > What is 15% gratuity on a meal that costs $17.84? Who cares? Just plunk down $3, $4, or $5. It is to the benefit of waiters and waitresses anyway. ;-) Nobody needs to know the difference between the check and, say, 10sqrt(pi). -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >>Oh come on. That same argument can be made >>about reading and writing. > Literacy is a *more* critical skill to have. > Have you ever heard of a person suing > their educational institution because they > cannot prove the Pythagorean Theorem? Why do people need to read? After all, we have television. Furthermore, there will always be a reading expert around. >>There are people in their 30s, 40s, 50s, etc. who >>have somehow managed to get through life without >>ever learning to read or write. What are you >>advocating here? That we dismantle the school system? > School systems are the most conservative of public > institutions, the last, not the first, to change. They > experience a trickle down effect with respect to > cultural attitudes towards learning. > More from Brett: >>Really??? If there are so few applications of mathematics, then >>where did it originate? It did not come from scholars in their >>ivory towers. > People learn necessary arithmetic, when they need to use it. No. They dont. >>It was developed out of necessity --- counting, business >>transactions, carpentry, engineering, etc. > We have become almost exclusively a service economy. Maybe that is because most people havent learned any mathematics. >>How many people in the U.S. have checking accounts? To >>balance your books, you need to be comfortable with >>decimal arithmetic. > Nooo. You need to make enough money. Impossible in a service economy. >>Do you suggest that the majority of people turn over their >>checkbooks and receipts to experts every couple of days >>to balance their books? > This is trivial, not really mathematics. Im suggesting the majority > of people either do it without a problem, dont bother to do it > at all, or get assistance. Remember, most students will not have > any difficulty when the time comes, whether or not they learn > anything about it in school. Absurd. I personally know hundreds of adults who cannot subtract integers, much less decimals. When does the time come? >>How would one go about verifying that the auditor did his >>arithmetic correctly? > If they have ballpark figures, most dont really care. Routine > money management is boring. Maybe you should be in charge of this countrys budget. >>What is 15% gratuity on a meal that costs $17.84? > Who cares? Just plunk down $3, $4, or $5. It is to the benefit > of waiters and waitresses anyway. ;-) Nobody needs to know > the difference between the check and, say, 10sqrt(pi). -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! <...> People learn necessary arithmetic, when they need to use it. > No. They dont. Well, than they must not really _need_ it that bad. >It was developed out of necessity --- counting, business >transactions, carpentry, engineering, etc. >> We have become almost exclusively a service economy. > Maybe that is because most people havent learned any mathematics. This seems to imply that if most learned some mathematics, our economy would shift from one thats predominantly service oriented to something else. That sounds unlikely. >How many people in the U.S. have checking accounts? To >balance your books, you need to be comfortable with >decimal arithmetic. >> Nooo. You need to make enough money. > Impossible in a service economy. There are some really good paying service oriented jobs. For that matter, there are some even better paying illegal jobs. >Do you suggest that the majority of people turn over their >checkbooks and receipts to experts every couple of days >to balance their books? I, for one, would not suggest that, but I do suggest that most people do use a calculator or some such vs. doing the arithmetic by hand. >> This is trivial, not really mathematics. Im suggesting the majority >> of people either do it without a problem, dont bother to do it >> at all, or get assistance. Remember, most students will not have >> any difficulty when the time comes, whether or not they learn >> anything about it in school. > Absurd. I personally know hundreds of adults who cannot subtract > integers, much less decimals. When does the time come? Im sure you do, but apparently that was not in question. The knowlege of (manually) subtracting decimals, or even integers, is not a requirement to balance a checkbook, and as was mentioned not all that have checkbooks actually balance them. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >> We have become almost exclusively a service economy. > Maybe that is because most people havent learned any mathematics. Its more a matter of NAFTA economics. Between 1945 and 1960 Japan and Germany were out of commission. The U.S.of A. was the leading manufacturer of automobiles and televisions but let its dominance slip away through shoddy workmanship and a lack of research and development. > Absurd. I personally know hundreds of adults who > cannot subtract integers, much less decimals. Exactly. People dont need to know math to be functioning adults. > Maybe you should be in charge of this countrys budget. I couldnt do worse for the poor middleclass. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >> Absurd. I personally know hundreds of adults who >> cannot subtract integers, much less decimals. >Exactly. People dont need to know math to be functioning adults. I believe he said they were alive, not functioning, except at menial tasks. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >Absurd. I personally know hundreds of adults who >cannot subtract integers, much less decimals. >>Exactly. People dont need to know math to be functioning adults. > I believe he said they were alive, not functioning, except at menial > tasks. Be careful how you reply. I just discovered that if you disagree with N. Silver, he will send you a private e-mail full of filthy language. Be forewarned. - Brett -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >Exactly. People dont need to know math to be functioning adults. >> I believe he said they were alive, not functioning, except at menial >> tasks. > Be careful how you reply. I just discovered that if you disagree with N. > Silver, he will send you a private e-mail full of filthy language. Be > forewarned. I (and I suppose most) couldnt care less about your private emails! In all seriousness, perhaps you are misinterpreting a little what he and I may be trying to tell you. Speaking strictly for myself, please understand that although I do think its sad that the world has come to what it is, the facts are that many people do not know much mathematics at all. By that I mean not just the Ôlive folks but some of the more prominent ones, too. Relatively speaking, there just isnt _that_ much mathematics needed by the average person that a four function calculator cant handle for him. It would be _nice_ of everyone was proficient not only in basic arithmetic but a little algebra as well. Actually, a little statistics and what not that have direct applicability to the average life would be ideal. The facts, however, are that many people simply are not as proficient in math as they should be, yet society functions. We have made places for these people, and these places include not only trash collectors but some of the best paying jobs around. Some factory workers in this area (particularly Nissan) start out at $25 per hour some with no diploma or GED. Thats not bad at all, especially for a relatively rural area as middle TN. Actually, its _much_ higher than a new college instructor with a masters degree. More than not, of course, it is who you know, not what you know. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! (snip.) > In all seriousness, perhaps you are misinterpreting a little what he and I > may be trying to tell you. I misinterpret nothing. I do indeed have some idea why certain people would come the k12.ed.math newsgroup to repeatedly post their view that it is a proßigate waste of time to attempt to teach people mathematics. Im certain others can draw their own conclusions. (snip.) -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! > I misinterpret nothing. I do indeed have some idea why certain > people would come the k12.ed.math newsgroup to repeatedly > post their view that it is a proßigate waste of time to attempt to > teach people mathematics. > Im certain others can draw their own conclusions. Good teachers meet students at the students levels, which includes taking into account students readiness to learn the mathematics topics of the day. Forcing students to do things the teachers way when there are other options available doesnt work anymore, if it ever did. Thats why I take issue with the original post. I have no illusions about my own popularity. On the other hand, your views may not be so widely shared as you might think. Sometimes those, who know mathematics, are less threatened or more ßexible about making changes in their approaches to teaching. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >>Exactly. People dont need to know math to be functioning adults. >I believe he said they were alive, not functioning, except at menial >tasks. >>Be careful how you reply. I just discovered that if you disagree with N. >>Silver, he will send you a private e-mail full of filthy language. Be >>forewarned. > I (and I suppose most) couldnt care less about your private emails! Thats funny. You cared enough to mention it. > In all seriousness, perhaps you are misinterpreting a little what he and I > may be trying to tell you. Speaking strictly for myself, please understand > that although I do think its sad that the world has come to what it is, the > facts are that many people do not know much mathematics at all. By that I > mean not just the Ôlive folks but some of the more prominent ones, too. > Relatively speaking, there just isnt _that_ much mathematics needed by the > average person that a four function calculator cant handle for him. How exactly does a calculator handle mathematics for someone? If I open an algebra book and put a calculator beside it --- it just sits there. Oh, I have to push the BUTTONS. Right there is the problem; and the O.P. also mentioned this. As the saying goes, Garbage in, garbage out. > It would be _nice_ of everyone was proficient not only in basic arithmetic > but a little algebra as well. Actually, a little statistics and what not > that have direct applicability to the average life would be ideal. The > facts, however, are that many people simply are not as proficient in math as > they should be, yet society functions. Society functions at what level? When people dont understand accounting, interest, loans, etc., how do they plan for the future? Why do we have Social Security? Everybody ends up paying. > We have made places for these > people, and these places include not only trash collectors but some of the > best paying jobs around. Some factory workers in this area (particularly > Nissan) start out at $25 per hour some with no diploma or GED. Thats not > bad at all, especially for a relatively rural area as middle TN. Actually, > its _much_ higher than a new college instructor with a masters degree. > More than not, of course, it is who you know, not what you know. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! >We have become almost exclusively a service economy. >>Maybe that is because most people havent learned any mathematics. > Its more a matter of NAFTA economics. Between 1945 and 1960 > Japan and Germany were out of commission. The U.S.of A. was > the leading manufacturer of automobiles and televisions but let its > dominance slip away through shoddy workmanship and a lack of > research and development. >>Absurd. I personally know hundreds of adults who >>cannot subtract integers, much less decimals. > Exactly. People dont need to know math to be functioning adults. Hmmm. By your logic, the following isomorphic arguments should also be valid: Millions of Americans have no health insurance, therefore they dont need it to be functioning adults. Millions of Americans are unemployed, therefore they dont need to be employed to be functioning adults. Millions of people around the globe do not enjoy freedom of speech or freedom of religion, therefore they dont need those freedoms to be functioning adults. *** PLONK *** >>Maybe you should be in charge of this countrys budget. > I couldnt do worse for the poor middleclass. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! > Hmmm. By your logic, the following isomorphic arguments should also be > valid: > Millions of Americans have no health insurance, therefore they dont > need it to be functioning adults. > Millions of Americans are unemployed, therefore they dont need to be > employed to be functioning adults. > Millions of people around the globe do not enjoy freedom of speech or > freedom of religion, therefore they dont need those freedoms to be > functioning adults. Good points all three and all three are, of course, true. Did you happen to catch that IQ test that was on TV a while back? They divided the audience into four groups, I believe, which were doctors/nurses, educators, students, and unemployed. I cant remember the IQ scores but IIRC there was not THAT much difference to speak of between the groups. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! > The continuing pseudo-education of American students is demonstrated > clearly by the mushrooming college enrolments in remedial mathematics > courses. A key component of this pseudo-education is the widespread, > deliberate over reliance on calculators--with no expectation that > students understand elementary concepts--whereby students punch > numbers into their calculators and are required to simply write down > the last display. > At the beginning of this semester, in one of my remedial courses, I > reviewed how to perform manual operations with simple fractions. The > following operations were to be done manually, with all the steps > written down. One student, among many, used his graphing calculator to > obtain the following three correct answers. When I asked him to do > (5/6)(9/10) = 3/4 [45/16] > (3/4):(7/8) = 6/7 [28/32] (: indicates division symbol) > (7/6)-(3/8) = 19/24 [(7-3)/48 = 5/48] > When I pointed out that the following answer was wrong, > (3/4)+(5/12) = 14/15 > he immediately snapped: It has to be right: I used my calculator! > The majority of the students in this class had graphing calculators. I > would not be surprised if their pseudo-education was promoted with the > bogus slogans and empty boasts of pseudo-educators: using technology > to solve real-world problems, twenty-first century mathematics, > world-class education, calculators free the mind to solve more > difficult problems. > Dom Rosa I am in complete agreement. Sometimes my students ask Can we use calculators? To which I say, Do you know HOW to use a calculator? Most of them dont. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! One method of skill assessment is to require the student to list the sequence of calculator keys to perform a calculation. A group of questions should be dedicated to this. Another idea, not certain if other people use this, is to present an incorrect equation of arithmetic, and tell the student to explain what error was used to obtain the incorrect result. This would be a useful type of question for assessment because (1) you can really check the students understanding of arithmetic, and (2) one of the purposes of using mathematics is to communicate, both through speech and through writing. This essay method is likely to be difficult for most students. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: It has to be right: I used my calculator! Hi there, I agree with you, but it seems hopeless. During a recent interview I was asked: What do you think about all freshmen being required to buy and use a calculator? My response was: I do not think all students should have calculator unless they have demonstrated the basics first. Towards the end of the interview, I was told at xxx district all incoming freshmen are required to buy and use a calculator. So this is coming down from the administration. Im not sure what I as a new teacher can do about this. I mean at this point, its better for me to just go with whatever the district wants so I can get a job! However, I do not like this prospect. I saw the results first hand, there was a problem with the register in the cafeteria at school this week and the kid running it was unable to make change! Its $5.50 to get into the buffet, all they need to do is make change for a $10 or $20. This isnt hard math! Ok Im done. John > The continuing pseudo-education of American students is demonstrated > clearly by the mushrooming college enrolments in remedial mathematics > courses. A key component of this pseudo-education is the widespread, > deliberate over reliance on calculators--with no expectation that > students understand elementary concepts--whereby students punch > numbers into their calculators and are required to simply write down > the last display. > The majority of the students in this class had graphing calculators. I > would not be surprised if their pseudo-education was promoted with the > bogus slogans and empty boasts of pseudo-educators: using technology > to solve real-world problems, twenty-first century mathematics, > world-class education, calculators free the mind to solve more > difficult problems. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: times tables program I have begun using a new times tables program that a really enjoy. The kids really like it too. You can download a free sample from their web site www.tabledrills.com. You can even make copies for the students to take home. Shiela -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: times tables program Shiela, OK, but it is only times tables. Have you seen http://www.thatquiz.com which is times tables, arithmetic, inequalities, geometry, fractions, decimals, place value, telling time, shape identification, AND offers free grading and record keeping for teachers? This site is more comprehensive. Javier > I have begun using a new times tables program that a really enjoy. > The kids really like it too. You can download a free sample from > their web site www.tabledrills.com. You can even make copies for > the students to take home. > Shiela -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: trigo How do you do, i turn some circle as of hours. Of how to write [sin](x+pi/3)+[sin](x-5pi/6) under the form A[sin](t+o). -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: trigo > How do you do, i turn some circle as of hours. > Of how to write [sin](x+pi/3)+[sin](x-5pi/6) > under the form A[sin](t+o). sin(x+pi/3)+sin(x-5pi/6) = sin(x+pi/3)+cos(x+pi/3) = sqrt(2)[sin(x+pi/3)cos(pi/4)+cos(x+pi/3)sin(pi/4)] = sqrt(2)sin(x+pi/3+pi/4) = sqrt(2)sin(x+(7pi/12)) -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Simplifying Radical Expressions but for some reason the solution is eluding me. SQRT(3 + 2 * SQRT(2)) - SQRT(3 - 2 * SQRT(2)) I know that this expression simplifies to 2, but I cannot figure out why. Any suggestions on how to approach this type of problem would be most appreciated. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Simplifying Radical Expressions sqrt(3+2*sqrt(2))-sqrt(3-2*sqrt(2))=x; x^2=(3+2*sqrt(2))-2*sqrt(3+2*sqrt(2))*sqrt(3-2*sqrt(2))+ (3-2*sqrt(2))=6-2*1=4 x^2=4 and x>0; i.e. x=2; Valery. Joseph Sustar ???????/???????? ? ???????? ?????????: > but for some reason the solution is eluding me. > SQRT(3 + 2 * SQRT(2)) - SQRT(3 - 2 * SQRT(2)) > I know that this expression simplifies to 2, but I cannot figure out > why. Any suggestions on how to approach this type of problem would be > most appreciated. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Simplifying Radical Expressions Joseph Sustar (jcsustar@msn.com) asked how to simplify: : : SQRT(3 + 2 * SQRT(2)) - SQRT(3 - 2 * SQRT(2)) A couple of clever approaches have been posted, but noone has mentioned what seemed fairly obvious to me: 3 + 2*Sqrt(2) = 2 + 2*Sqrt(2) + 1 = [Sqrt(2)]^2 + 2*(1)*Sqrt(2) + 1^2 = [ Sqrt(2) + 1 ]^2 and 3 - 2*Sqrt(2) = 2 - 2*Sqrt(2) + 1 = [Sqrt(2)]^2 - 2*(1)*Sqrt(2) + 1^2 = [ Sqrt(2) - 1 ]^2 are both perfect squares, which simplifies the original expression quickly and easily. This approach is not be as general as some of the others. However, when facing a square root, is it not natural to ask whether the quantity inside is a perfect square? Then, one just needs: (a+b)^2 = a^2+2ab+b^2 and a tiny bit of cleverness. Robert |)|/| || Burnaby South Secondary School || |orewood@olc.ubc.ca || Beautiful British Columbia Mathematics & Computer Science || (Canada) -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Simplifying Radical Expressions > SQRT(3 + 2 * SQRT(2)) - SQRT(3 - 2 * SQRT(2)) > I know that this expression simplifies to 2, but I cannot > figure out why. How do we eliminate radicals? We square them. If the expression really is equal to 2, then squaring it should help. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Simplifying Radical Expressions > but for some reason the solution is eluding me. > SQRT(3 + 2 * SQRT(2)) - SQRT(3 - 2 * SQRT(2)) > I know that this expression simplifies to 2, but I cannot figure out > why. Any suggestions on how to approach this type of problem would be > most appreciated. Joseph, Try this: square the quantity that you are given, and show that this simplifies to 4. That is, show that {SQRT(3 + 2 * SQRT(2)) - SQRT(3 - 2 * SQRT(2))}^2 = 4. It really helps to be quite familiar with the formulas (A - B)^2 = A^2 - 2AB + B^2 and (A - B)(A + B) = A^2 - B^2 There is another trick that works for problems somewhat similar to this one, when a complicated expression of the form A - B appears in the numerator, (or the denominator) of a rational expression. The trick that often works is to multiply numerator and denominator of the rational expression by the conjugate A + B of the numerator. --- Joe P.S. If one of the homework doers completes this problem in detail, try to ignore their help until you try it yourself, using just the hint, above. I did notice that you said suggestions and approach. Lets hope that the homework doers restrain themselves from providing a detailed solution complete with punctuation. -- Delete the second o to email me. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Simplifying Radical Expressions > but for some reason the solution is eluding me. > SQRT(3 + 2 * SQRT(2)) - SQRT(3 - 2 * SQRT(2)) > I know that this expression simplifies to 2, but I cannot figure out > why. Any suggestions on how to approach this type of problem would be > most appreciated. 1. Let x = SQRT(3 + 2 * SQRT(2)) - SQRT(3 - 2 * SQRT(2)) 2. Square both sides 3. Expand the RHS using the fact that (a - b)^2 = a^2 - 2ab + b^2 4. Solve for x -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Simplifying Radical Expressions > but for some reason the solution is eluding me. > SQRT(3 + 2 * SQRT(2)) - SQRT(3 - 2 * SQRT(2)) > I know that this expression simplifies to 2, but I cannot figure out > why. Any suggestions on how to approach this type of problem would be > most appreciated. Let a = sqrt(3 + 2 sqrt(2)) and b = sqrt(3 - 2 sqrt(2)). Then a^2 = 3 + 2 sqrt(2) and b^2 = 3 - 2 sqrt 2, and so a^2 b^2 = 1. Hence ab = 1 as a and b are the positive square roots. Now consider (a-b)^2. This equals a^2 - 2ab + b^2 = 4. As a > b then a - b > 0 so that a - b = 2. -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html His mind has been corrupted by colours, sounds and shapes. The League of Gentlemen -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Are Imaginary Numbers Fairy Tales? My name is C. Church and I am attending the College of the Delta where I regularly sit in a math class. It seems that when I start to get the hang of things in Algebra class, the topic takes a turn for the more complex and more confusing. Speaking of imaginary numbers, i isnt that confusing I have to admit, but e is. Can any one explain to me the idea of e.? Hopefully this request makes sense. Gracias. Church -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Are Imaginary Numbers Fairy Tales? >Can any one explain to me the idea of e.? e: The Story of a Number by Eli Maor Princeton University Press, 1994 is a very enjoyable, elementary, yet comprehensive book. Alexander Bogomolny http://www.cut-the-knot.org -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Are Imaginary Numbers Fairy Tales? Here is the skinny on e. if you take y=e^x every point on the curve will have a slop equal to the y value. for example at x=0 the point (0,1) is plotted. The slope of the line at that point is 1 then e^0=1 Bingo!!!!! ~John >My name is C. Church and I am attending the College of the Delta where >I regularly sit in a math class. >It seems that when I start to get the hang of things in Algebra class, >the topic takes a turn for the more complex and more confusing. >Speaking of imaginary numbers, i isnt that confusing I have to >admit, but e is. Can any one explain to me the idea of e.? >Hopefully this request makes sense. >Gracias. >Church -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Are Imaginary Numbers Fairy Tales? >My name is C. Church and I am attending the College of the Delta where >I regularly sit in a math class. >It seems that when I start to get the hang of things in Algebra class, >the topic takes a turn for the more complex and more confusing. >Speaking of imaginary numbers, i isnt that confusing I have to >admit, but e is. Can any one explain to me the idea of e.? >Hopefully this request makes sense. Look up continuously compounded interest on money [not yearly, monthly, weekly ... but continuous.] -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Are Imaginary Numbers Fairy Tales? Mr. Church, Did you finish elementary or introductory algebra successfully yet? Are you in intermediate algebra right now? The imaginary number, i, and the base for the natual logarithm, e, are probably new to you now; just continue studying and reviewing. You wont understand everything overnight. You will have more use for Ôe when you study calculus. Right now, just use e as a real, irrational number. Other people can more reliably talk about the way in which you can express e using arithmetic. Also, you may be able to read about this number in a college algebra book (college algebra is a study of algebra at a somewhat higher level than intermediate; in many ways, these courses have very much in common). G C >I regularly sit in a math class. >It seems that when I start to get the hang of things in Algebra class, >the topic takes a turn for the more complex and more confusing. >Speaking of imaginary numbers, i isnt that confusing I have to >admit, but e is. Can any one explain to me the idea of e.? >Hopefully this request makes sense. >Gracias. >Church -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Welcome to High School College I was talking with one of my relatives the other day about classes, and she raised a certain kind of interesting question. She said to me, in the form of a question, why do students in college have to take nearly the same classes they took in high school? Being the academic skeptic that I am, I smiled with glee at the thought of not being in school, or not being in school anymore--it seems that its the story of my life. I have heard of the idea that you really dont learn anything until youre out of school. I have experienced learning in my profession through experience. Would it be too awful to throw students into a working environment and have them pick up the skills they need to make it in that profession? That idea sounds barbaric, or does it? Any responses? Church *Church is a student of Life and Delta College, the smallest and biggest institution of high learning in the TriCities. He currently attends Algebra on Tuesday and Thursday mornings. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Welcome to High School College > I was talking with one of my relatives the other day about classes, > and she raised a certain kind of interesting question. She said to me, > in the form of a question, why do students in college have to take > nearly the same classes they took in high school? Being the academic > skeptic that I am, I smiled with glee at the thought of not being in > school, or not being in school anymore--it seems that its the story > of my life. I didnt take the same classes in college as in high school (except that I retook calculus---my high school class had not had enough seats for all the calculus students, and so Id spent the year in the library, just going to class for exams, I used my AP exam results to get into the honors calculus class, rather than skipping the first quarter). The only people who take the same classes in college as in high school are those who failed to learn the material in high school and are taking remedial classes (or are just marking time to keep from having to find a job). > I have heard of the idea that you really dont learn anything until > youre out of school. I have experienced learning in my profession > through experience. Would it be too awful to throw students into a > working environment and have them pick up the skills they need to make > it in that profession? That idea sounds barbaric, or does it? > Any responses? There are jobs that require essentially no skills---you can throw people into those without problems. Other jobs (medicine, engineering, mechanics, plumbing, police, ...) require considerable training before the practitioner is safe and competent. Not all the training needs to happen in school, but it does need to happen. ------------------------------------------------------------ Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus Professor of Biomolecular Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Senior member, IEEE Board of Directors, ISCB (starting Jan 2005) life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Welcome to High School College > The only people who take the same classes in college as in >high school are those who failed to learn the material in high school >and are taking remedial classes (or are just marking time to keep from >having to find a job). The ßaw there is that in high school, students may learn the material but would not have retained what they learned. The studied material does not all stay with the student unless or until the student restudies. Especially for mathematics, four years of high school with each year dedicated to a different subject within mathematics presents many different concepts and skills. After finishing highschool, some students do not retain it all. If these sort of students attend college and are forced to repeat those preparatory courses, they now become much easier to learn. The student then is not likely to have any great difficulty in retention until reaching new material never that he previously studied. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Welcome to High School College >> The only people who take the same classes in college as in >>high school are those who failed to learn the material in high school >>and are taking remedial classes (or are just marking time to keep from >>having to find a job). > The ßaw there is that in high school, students may learn the material but > would not have retained what they learned. The studied material does not all > stay with the student unless or until the student restudies. Especially for > mathematics, four years of high school with each year dedicated to a different > subject within mathematics presents many different concepts and skills. After > finishing highschool, some students do not retain it all. If these sort of > students attend college and are forced to repeat those preparatory courses, > they now become much easier to learn. The student then is not likely to have > any great difficulty in retention until reaching new material never that he > previously studied. I can see this argument for geometry, which is distinctly different from the other years of high school math, but all the rest are minor variations on the same theme (algebra, algebra+trig, polynomials, linear algebra, ...), so the skills are repeated over and over. If they dont get it by the end of high school, repeating it once more in college doesnt seem to help much. The re-entry students who have been out of school for five or more years are a different category---they may have lost skills due to lack of practice, and refresher courses for them can bring back the skills, often even to a higher level, since they are no longer distracted from study by adolescence. ------------------------------------------------------------ Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus Professor of Biomolecular Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Senior member, IEEE Board of Directors, ISCB (starting Jan 2005) life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Welcome to High School College Karplus @ discusses mathematical subjects and retention in response to chergarj@ response about retaining high schools college preparatory mathematics: >I can see this argument for geometry, which is distinctly different >from the other years of high school math, but all the rest are minor >variations on the same theme (algebra, algebra+trig, polynomials, >linear algebra, ...), so the skills are repeated over and over. If >they dont get it by the end of high school, repeating it once more in >college doesnt seem to help much. People vary regarding what they retain at the end of high school. The repetition in high school overlap of topics was helpful, but finally by the end some students may still have less than fair retention of most things beyond experience. Certainly, I retained less than 5% of Geometry instruction. (that 5% is just a guess/judgement). Maybe I was unusual about so quickly loosing much of what I studied in high school. In college, I DID NEED TO REPEAT ALL of the same high school math coursework, but now, in community college. Everything was much easier to study this time. Thoroughly repeating those studies this way helped enourmously. I never had any real mathematical trouble until PreCalculus. After that, the reason for retaining somewhat more of intermediate algebra and trigonometry was that (1) they were used in Calculus and (2) they were used in other coursework, too. Today, I still retain much of them because I restudy on my own from time to time. I assume, without knowing about the details of so many people, that most people would either be talented and achieve very much in mathematics, or they will do everything possible to avoid any more study or review of mathematics than necessary. This periodic restudying process is very helpful, and probably not normal. I did not read your second paragraph yet; will do next. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Welcome to High School College In college, the imposed requirements are specified general education course for transfer or graduation credit; and pre-requisite courses determined through the colleges assessments of the incoming students. Test-taking is tough, and many students will not retain what they studied in high school. Then, they are forced to re-enroll in a few of the same courses in college that they already passed in high school. THIS time, although the courses may be remedial at the college , the student can learn them much more effectively than when they were in high school. Repeated study of hard courses makes those courses easier to study the second time. G C Churchill@......... .com said this: >I was talking with one of my relatives the other day about classes, >and she raised a certain kind of interesting question. She said to me, >in the form of a question, why do students in college have to take >nearly the same classes they took in high school? Being the academic >skeptic that I am, I smiled with glee at the thought of not being in >school, or not being in school anymore--it seems that its the story >of my life. >I have heard of the idea that you really dont learn anything until >youre out of school. I have experienced learning in my profession >through experience. Would it be too awful to throw students into a >working environment and have them pick up the skills they need to make >it in that profession? That idea sounds barbaric, or does it? >Any responses? >Church >*Church is a student of Life and Delta College, the smallest and >biggest institution of high learning in the TriCities. He currently >attends Algebra on Tuesday and Thursday mornings. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Square Why square a number? What is its basic purpose? For ex: the square of 3 is 9. Why would I want to reach 9? What would I use it for? Same reason, why would I want to know the square root of a number and what would I use it for? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Square >Why square a number? What is its basic purpose? >For ex: the square of 3 is 9. Why would I want to reach 9? What would >I use it for? >Same reason, why would I want to know the square root of a number and >what would I use it for? That is troubling you? Multiplication is a more efficient way to add the same number repeatedly. Sometimes you have a number, x, and you may want to find x of x. You multiply. This can be represented graphically with a square. Nobody responded yet, but I believe the question was not serious; then, maybe it was? Algebryonic -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Square > Why square a number? What is its basic purpose? > For ex: the square of 3 is 9. Why would I want to reach 9? What would > I use it for? Because if you have a square of something that is three (inches, feet, meters, kilometers) on a side then the area will be nine (square inches...). --Jeff > Same reason, why would I want to know the square root of a number and > what would I use it for? -- It is only those who have neither fired a shot nor heard the shrieks and groans of the wounded who cry aloud for blood, more vengeance, more desolation. War is hell. --William Tecumseh Sherman Egotism is the anesthetic that dulls the pain of stupidity. --Frank William Leahy -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: U.S.math students compared to others. My name is Cindy, and I am a student at Delta College. I have to do an interaction project on the internet for my Intermediate Algebra class. I was wondering how American students do on mathmatic scores compared to students in other parts of the world. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: U.S.math students compared to others. >My name is Cindy, and I am a student at Delta College. I have to do >an interaction project on the internet for my Intermediate Algebra >class. I was wondering how American students do on mathmatic scores >compared to students in other parts of the world. Explain! Will such an internet interaction project about american math students compared to other countries math students help you to solve absolute value inequalites, or logarithmic relations more effectively? Why are you required to do such a project? Algebryonic -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: U.S.math students compared to others. > My name is Cindy, and I am a student at Delta College. I have to do > an interaction project on the internet for my Intermediate Algebra > class. I was wondering how American students do on mathmatic scores > compared to students in other parts of the world. I looked into this not too long ago. I went to the window should appear already set on net rather than images, groups, news or froogle. Type in something like: international math scores or TIMSS and click on search. You will be giving a list of web sites that have last couple international tests, including a ranking of countries. and I will try to talk you through it. blacksalt -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: U.S.math students compared to others. > My name is Cindy, and I am a student at Delta College. I have to do > an interaction project on the internet for my Intermediate Algebra > class. I was wondering how American students do on mathmatic scores > compared to students in other parts of the world. What does an interaction project on the internet have to do with Intermediate Algebra? What is Delta College teaching? The information you are looking for is probably TIMMS (Trends in International Mathematics and Science Study) http://timss.bc.edu/ ------------------------------------------------------------ Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus Professor of Biomolecular Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Senior member, IEEE Board of Directors, ISCB (starting Jan 2005) life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: U.S.math students compared to others. Delta College (in where, Michigan??) may be a community college; it has certificate and associates degree programs in some technical and vocational fields. Their intermediate algebra course description and course objectives are available for download. That description corresponds well to what would be expected for intermediate algebra. No reference in that description for using the internet was expected and none was found. G C Under the quotes, Ôcindy said: >> My name is Cindy, and I am a student at Delta College. I have to do >> an interaction project on the internet for my Intermediate Algebra >> class. I was wondering how American students do on mathmatic scores >> compared to students in other parts of the world. Karplus@cheep.cse.ucsc.edu then eventually responded: >What does an interaction project on the internet have to do with >Intermediate Algebra? What is Delta College teaching? >The information you are looking for is probably TIMMS >(Trends in International Mathematics and Science Study) >http://timss.bc.edu/ -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Square feet Hello. I was just hoping someone here could explain to me why, when defining the area of an object, the answer is squared or cubed. I use A = 4*2 to find area of a 4 2 rectangle, and my answer is supposed to be 8^2 (64?); Is that to say there are 64 little units of the given measurement in my rectangle? I guess a cubed number would then be used for the volume of 3 dimensional object? After writing this, Im almost certain this is it; It makes so much sense, but I just dont know. This has been bothering me forever, and a quick -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Square feet > Hello. I was just hoping someone here could explain to me > why, when defining the area of an object, the answer > is squared or cubed. > I use A = 4*2 to find area of a 4 2 rectangle, and my > answer is supposed to be 8^2 (64?); Is that to say there > are 64 little units of the given measurement in my rectangle? > I guess a cubed number would then be used for the volume of > 3 dimensional object? After writing this, Im almost > certain this is it; It makes so much sense, but I just dont > know. This has been bothering me forever, and a quick Just keep in mind that its not the area itself that is squared, but the units; so its 8 inches squared. otherwise, you are correct - the squared indicates how many 1 inch by 1 inch squares fit into your rectangle. And the cubes are likewise. Its how many small cubes of whatever unit (Unit cubes) will fit into the cube you are finding the volume of. Good Luck -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Square feet > Hello. I was just hoping someone here could explain to me > why, when defining the area of an object, the answer > is squared or cubed. > I use A = 4*2 to find area of a 4 2 rectangle, and my > answer is supposed to be 8^2 (64?); Is that to say there > are 64 little units of the given measurement in my rectangle? > I guess a cubed number would then be used for the volume of > 3 dimensional object? After writing this, Im almost > certain this is it; It makes so much sense, but I just dont > know. This has been bothering me forever, and a quick Keep the units (inches in this case) in all manipulations. So a 4 inch by 2 inch rectangle has area A = (4 inch)x(2 inch) = 8 inch x inch = 8 inch^2. [I wonder when America will grow up and use metric units?] -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Square feet >I use A = 4*2 to find area of a 4 2 rectangle, and my >answer is supposed to be 8^2 (64?); Is that to say there >are 64 little units of the given measurement in my rectangle? You are confusing two things: the numeric computation and the units of the result. You are multiplying (4 inches) by (2 inches). The numeric part of the result is 4*2=8. The unit part is inches*inches = square inches. Computation with units is >> analogous to <<<< (not the same as) computation with variables. 4x + 2x = 6x 4 in + 2 in = 6 in 4x * 2x = 8x^2 4 in * 2 in = 8 in^2 4x + 2y = cant simplify 4 in + 2 lb = cant add 4x * 2y = 8xy 4 in * 2 lb = 8 in-lb (An inch-pound is a unit of energy, if Im remembering my physics correctly. You dont see inch-pounds in practical computation very often, but foot-pounds are more commonly used.) Im emphasizing analogous to because you shouldnt get the idea that a unit is a quantity, in the way that a variable represents a (perhaps unknown) quantity. So, for example, 4x+2y is a perfectly valid expression, just one that cant be simplified unless we learn something about the values of x and y. But 4 in + 2 lb is just plain wrong -- its never meaningful to add inches and pounds. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Square feet >Hello. I was just hoping someone here could explain to me >why, when defining the area of an object, the answer >is squared or cubed. >I use A = 4*2 to find area of a 4 2 rectangle, and my >answer is supposed to be 8^2 (64?); Is that to say there >are 64 little units of the given measurement in my rectangle? >I guess a cubed number would then be used for the volume of >3 dimensional object? After writing this, Im almost >certain this is it; It makes so much sense, but I just dont >know. This has been bothering me forever, and a quick I am just trying to understand how someone can be so clearly well educated, and literate and well-spoken in expression, adult even, yet so lacking in such a fundamental concept in arithmetic; the difference between quantity and unit. Its beyond belief. People who I have known, and there are enough, who are so lacking in arithmetic are not nearly so well educated, and certainly can not express themselves so clearly either in other areas. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Square feet >Hello. I was just hoping someone here could explain to me >why, when defining the area of an object, the answer >is squared or cubed. >I use A = 4*2 to find area of a 4 2 rectangle, and my >answer is supposed to be 8^2 (64?); Is that to say there >are 64 little units of the given measurement in my rectangle? >I guess a cubed number would then be used for the volume of >3 dimensional object? After writing this, Im almost >certain this is it; It makes so much sense, but I just dont >know. This has been bothering me forever, and a quick Almost. By writing down your question in some detail, you almost talked your way thru a good explanation. The only quibble is with your actual calculation. The area of a 4 inch by 2 inch rectangle is 8 sq in. You can see this with a little picture. Draw the rectangle you said, and mark off one inch increments in each direction. You have 8 little squares, each 1 inch by 1 inch = 1 sq inch area. * of them means 8 sq in for the total rectangle. Your extension to volume having units cubed is right on. A cube of side 2 inches has volume = 2 inches * 2 inches * 2 inches = 8 cubic inches. bob -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Weighted Averages (Question) weighted averages. Suppose I have the following formula for per-pupil revenue in a given state: Total Revenue (in a given state)/Average Daily Attendance (in a given state). Now if I want to find the average per-pupil revenue across the whole U.S. wouldnt I take the sum of all total revenues in the U.S.(sum each of the 50 states) and divide that by the sum of all Average Daily Attendance figures in the U.S. (sum each of the 50 states)?? Wouldnt this be a weighted average of per-pupil revenue that is more accurate than taking the sum of all total revenues and dividing by the number of states?? Im just having problems relating this calculation to the basic weighted average formula (sum of weight*quanitities/sum of quantities). Is the weight in my calculation the Average Daily Attendance?? Similarly, suppose the formula for Average Daily Attendance (for a given state)= aggregate number of days pupils (in a given state) attend class/total number of days in school year (for a given state). If I want a national average for average daily attendance, rather than summing the Average Daily Attendance for each state and dividing by 50, would I sum the aggregate number of days pupils attend class in each state and divide by the cumulative number of days in a school year for all states? Is this correct and would this be considered a weighted average?? Would the weight be the total number of days in a school year (for a given state)?? Again, I am having problems seeing how the basic weighted average formula applies to this calculation. Another problem I anticipate having is that not all states use the above formula for average daily attendance (i.e. some have complex formulas incorporating summer school students, actual number of hours students attended class rather than number of days, etc.) In this case, would simply taking the sum of Average Daily Attendance and dividing by number of states be the best way to calculate Average Daily Attendance or is there another weighted mean that is Juile -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Weighted Averages (Question) >weighted averages. Suppose I have the following formula for per-pupil >revenue in a given state: Total Revenue (in a given state)/Average >Daily Attendance (in a given state). Now if I want to find the average >per-pupil revenue across the whole U.S. wouldnt I take the sum of all >total revenues in the U.S.(sum each of the 50 states) and divide that >by the sum of all Average Daily Attendance figures in the U.S. (sum >each of the 50 states)?? Wouldnt this be a weighted average of >per-pupil revenue that is more accurate than taking the sum of all >total revenues and dividing by the number of states?? Im just having ^^^^^ [should say per-pupil] >problems relating this calculation to the basic weighted average >formula (sum of weight*quanitities/sum of quantities). Is the weight ^^^^^^^^^^ [should be weights] >in my calculation the Average Daily Attendance?? Everything you say is correct, apart from the two small mistakes noted above. In your computation, you are starting with the figures for total revenue and for ADA, for each state. So its clearly right to add total revenues (straightforwardly) and add ADAs (with the caveats you mention later in your message). But suppose you happened to be given the per-pupil revenues rather than the total revenues. In that case, you might be tempted to add the per-pupil revenues, since thats what you have! And the weighted average formula is telling you that youre not allowed to do that, but must instead recover the total revenues by multiplying each states per-pupil revenue by its ADA. In the vocabulary of the formula, you weight each states per-pupil revenue by its population (which is essentially what ADA measures, since for this purpose population means population attending school). As for computing the average ADA, given the complexities in the formulas used, Id be inclined to say that there is *no* honest way to average such unlike numbers. Instead youd have to compute your own ADA figures for each state, using the same formula for each, starting from their raw daily attendance numbers. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: multiply Can you think of a way to use doubling to multiply 6 x 7? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: multiply >Can you think of a way to use doubling to multiply 6 x 7? half of 6 is 3; what is 3 x 7? 6 x 7 is twice 3 x 7. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: multiply > Can you think of a way to use doubling to multiply 6 x 7? Yes, double 7 to get 14, double that to get 28. Add 14 and 28 to get 42. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Pre-Algerbra and Geometry are subjects in which my son needs help. what is a divided by b=b divided by a -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Pre-Algerbra and Geometry are subjects in which my son needs help. lil_ozark_gurl23@yahoo.com asks this: >what is a divided by b=b divided by a Apparantly you are asking does a divided by b equal b divided by a? The answer is, NO. A fancy reason is that division is not commutative; just try comparing 10 divided by 5 with 5 divided by 10. They are not the same! One condition and only one condition permits your question an affirmative answer; that is when a=b. Only when a=b, a divided by b is equal to b divided by a; and the quotient will be 1. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Pre-Algerbra and Geometry are subjects in which my son needs help. > lil_ozark_gurl23@yahoo.com asks this: >>what is a divided by b=b divided by a An equation! To be more precise, its a conditional equation. It is a true statement under the condition that a and b are such that the equation is true. Not just any ol values fort a and b will do, but certain values will indeed make that a true statement. > Apparantly you are asking does a divided by b equal b divided by a? > The answer is, NO. A fancy reason is that division is not commutative; > just > try comparing 10 divided by 5 with 5 divided by 10. They are not the > same! The answer is sometimes. It depends on the values of a and b, so try to determine the conditions in which that can happen. Clearing fraction (say, by crossmultiplying) can be your friend here. > One condition and only one condition permits your question an affirmative > answer; that is when a=b. Only when a=b, a divided by b is equal to b > divided > by a; and the quotient will be 1. Sorry, but thats just wrong. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Pre-Algerbra and Geometry are subjects in which my son needs help. > Only when a=b, a divided by b is equal to b >> divided >> by a; and the quotient will be 1. >Sorry, but thats just wrong. I wouldnt say wrong, but Id say inadequate, or incomplete. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Pre-Algerbra and Geometry are subjects in which my son needs help. >> Only when a=b, a divided by b is equal to b > divided > by a; and the quotient will be 1. >>Sorry, but thats just wrong. > I wouldnt say wrong, but Id say inadequate, or incomplete. Apparantly you did not approve of my choice of words. No offense intended, but I think wrong is an accurate description, even if you wouldnt say it. Not the only description by any means, but definitely an accurate one. There are many legitimate words one can use in place of wrong if one so chooses. ToMAYto, toMAHto. No big deal. Plus, its no fun when everyone says the same thing :-). I believe what you were trying to get across, which is a very legitimate point, is that a/b=b/a is not *always* true the way ab=ba is always true, but simply botched the explanation. An honest mistake, but certainly worth pointing out so that the OP does not leave with unchallenged, incorrect information. Since you brought it up, incomplete definitely would be an incorrect (IOW, wrong) description. Omitting the word only in your above statement would qualify it as being incomplete since the statement would actually be true, just lacking in some very relevant details. The above, as written, is simply untrue. The first word makes the entire sentence untrue. What you said was close to being true but Ôclose only counts in horseshoes and hand grenades :-). -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Pre-Algerbra and Geometry are subjects in which my son needs help. Still somewhat confusing, but the difficulty is in language more than the algebra or the logic. Im not overly worried. We can examine these equations and apply fairly low level facts and transformations; then we can struggle with bringing in the precise language of natural English to discuss the situation. G C dr6583@comcastsnip.net discusses: >Apparantly you did not approve of my choice of words. No offense intended, >but I think wrong is an accurate description, even if you wouldnt say it. >Not the only description by any means, but definitely an accurate one. >There are many legitimate words one can use in place of wrong if one so >chooses. ToMAYto, toMAHto. No big deal. Plus, its no fun when everyone >says the same thing :-). >I believe what you were trying to get across, which is a very legitimate >point, is that a/b=b/a is not *always* true the way ab=ba is always true, >but simply botched the explanation. An honest mistake, but certainly worth >pointing out so that the OP does not leave with unchallenged, incorrect >information. >Since you brought it up, incomplete definitely would be an incorrect (IOW, >wrong) description. Omitting the word only in your above statement would >qualify it as being incomplete since the statement would actually be true, >just lacking in some very relevant details. The above, as written, is >simply untrue. The first word makes the entire sentence untrue. What you >said was close to being true but Ôclose only counts in horseshoes and hand >grenades :-). >-- >Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Pre-Algerbra and Geometry are subjects in which my son needs help. > Only when a=b, a divided by b is equal to b >> divided >> by a; and the quotient will be 1. >Sorry, but thats just wrong. >> I wouldnt say wrong, but Id say inadequate, or incomplete. >Apparantly you did not approve of my choice of words. No offense intended, >but I think wrong is an accurate description, even if you wouldnt say it. >Not the only description by any means, but definitely an accurate one. Perhaps made the more accurate if it was more descriptive, like very wrong, mostly wrong, partly wrong, a little bit wrong ... but not just wrong. ? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Pre-Algerbra and Geometry are subjects in which my son needs help. > lil_ozark_gurl23@yahoo.com asks this: >>what is a divided by b=b divided by a > Apparantly you are asking does a divided by b equal b divided by a? > The answer is, NO. A fancy reason is that division is not commutative; just > try comparing 10 divided by 5 with 5 divided by 10. They are not the same! > One condition and only one condition permits your question an affirmative > answer; that is when a=b. Only when a=b, a divided by b is equal to b divided > by a; and the quotient will be 1. > G C Correction: a/b = b/a admits solutions satisfying a^2 = b^2, where neither a nor b is zero, of course. Thus, for example, a=3 and b=-3 satisfy the original equation. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Pre-Algerbra and Geometry are subjects in which my son needs help. cauchy_1@yahoo.com contributes further detail: >Correction: a/b = b/a admits solutions satisfying a^2 = b^2, where >neither a nor b is zero, of course. Thus, for example, a=3 and b=-3 >satisfy the original equation. Most of us fail to think carefully enough about that situation. You are certainly correct in discussing this alternative situation for a/b = b/a. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Freeware Berkeley Logo 5.4 released Release 5.4 of Berkeley Logo is now available by anonymous FTP or Web. This release is available only for Unix (including MacOS X) and Windows, until I get back to California where my Classic Mac and my DOS machine live. Version 5.3 remains available for Classic Mac and DOS. Berkeley Logo (a/k/a UCBLogo) is FREE SOFTWARE, with source code included. ------------- Logo is the educational programming language best known for its turtle graphics but also featuring easy and powerful facilities for computing with words and sentences. Sample projects included with the Berkeley Logo distribution range from a tic-tac-toe game to a Pascal compiler and a Logo implementation of Student, Daniel Bobrows program that solves algebra word problems. Berkeley Logo is distributed under the terms of the GNU General Public License: You may redistribute it freely, and you may use it as a base for developing additional free software, but you may not use it as a base for commercial software products. The exact details are included in the distribution, in the file named GPL. Advantages of Berkeley Logo: * Its free. * It comes with source files (in C). * Logo programs are completely compatible among Unix, PC, and Mac. Disadvantages of Berkeley Logo: * Its relatively slow. * It doesnt do anything fancy about graphics. (One turtle.) This announcement has four more parts: * How to get Berkeley Logo. * Installation instructions. * Details about this release. * Pointers to other peoples Berkeley-Logo-related distributions. ---------------------------------------- HOW TO GET BERKELEY LOGO: ---------------------------------------- FTP to ftp.cs.berkeley.edu and get any of the following files: pub/ucblogo/ucblogo.tar.gz Unix sources and documentation (gzip format) pub/ucblogo/ucbwlogosetup.exe Windows version, self-installing, with executable UCBWLOGO.EXE pub/ucblogo/macosx-ucblogo-Installer.hqx MacOS X version, self-installing, BinHex. pub/ucblogo/usermanual Just the documentation file. Be sure to use BINARY transfer mode when retrieving the archive files! Alternatively, you can download Berkeley Logo from the World-Wide Web. Youll find pointers on http://http.cs.berkeley.edu/~bh/logo.html (The filenames above are links to filenames that include the version number, e.g., ucblogo-5.4.tar.gz; either name is okay. Anything other than the current version, if still online, is in the subdirectory pub/ucblogo/old.) ----------- The Mac version is in the form of a BinHex-converted self-extracting StuffIt archive. To install it, just copy to your hard disk, un-BinHex it (this may be done automatically by your file transfer program), and double-click on it. ----------- The Unix version is a gzipped tar file. To install it, copy to your machine, then say gunzip ucblogo.tar tar -xf ucblogo.tar cd ucblogo configure make ----------- The Windows and Mac versions include a SOURCE subdirectory containing the C source files used to compile Berkeley Logo. If you dont want to play with the code, you can delete this directory and all its contents. You can also delete some or all of the contents of the DOCS directory, which has the usermanual in various formats (Postscript, PDF, HTML, INFO, TEXI). The HTML files are particularly huge, if youre looking for something to delete. (In the Unix version, the source files are in the top-level directory of the distribution.) In the source directory, the file plm is a Program Logic Manual that documents some of the inner mysteries of this interpreter. You should read _Structure and Interpretation of Computer Programs_ before you read plm. Also included is evaluator.ps, a beautiful one-page simplified ßowchart of the evaluator to admire while reading plm. In the Unix version, if you want to save space, you can delete the entire ucblogo directory created by tar once youve done make install. ---------------------------------------- INSTALLATION INSTRUCTIONS: ---------------------------------------- Unix version: the makefile compiles with optimization turned off. This is necessary to avoid mysterious garbage collection failures. (NOTE: On my HP 712, for reasons I dont understand, I had to compile the entire interpreter without optimization. But on other platforms, such as PCs running Linux and FreeBSD, its sufficient merely to un-optimize mem.c. If that works on your machine, you can remove the -O0 at the end of the CFLAGS line at the beginning of the makefile, after running configure.) --------- The Windows version, named UCBWLOGO.EXE, requires Windows 95/98/Me/NT/2000/XP or later (not 3.1; sorry). It is distributed as a self-installing setup file. --------- The Mac installer puts Logo in /usr/bin/logo and puts runtime support files and documentation in /usr/lib/logo. To run Logo, you must start X11, then type logo into an xterm window. The installer puts the source files in, by default, /ucblogo-5.4 but thats movable. The installer has an uninstall option as well as a custom install to select only the desired components. ---------------------------------------- THIS RELEASE: ---------------------------------------- All platforms: Fix bug that embedded null characters in print-to-buffer generated strings. Fix graphics routines that didnt call prepare_to_draw (has different effects on different platforms). Change the print-to-string feature so that you can OPENWRITE a string, then SETWRITE to and from it repeatedly, then CLOSE it, just like a file, and all output is accumulated correctly. If you CLOSE the current reader or writer, then the reader or writer is changed to stdin or stdout. If a file named startup.lg exists in the initial working directory, it is loaded when Logo starts. Check for zero arg to MOD or REMAINDER. (RANDOM 3 8) is equivalent to (RANDOM 6)+3. Fatal error messages get printed (instead of causing another fatal error). compare_node() can handle quoted list without crashing. Fixed bug about procedures defined with DEFINE of literal lists sharing code. (DEFINE now deep-copies its second input.) An instruction line starting with #! is taken as a comment. This allows a Logo program file to be shell-executable if you put #! /usr/local/bin/logo as its first line. (This only benefits Unix users, but the feature applies to all platforms.) New operation PRIMITIVES returns the a list containing the names of all primitive procedures, including synonyms created with COPYDEF. New infix operators <=, >=, and <> and new operations LESSEQUALP, GREATEREQUALP, and NOTEQUALP. FPUT and LPUT will now accept a word as the second input, provided that the first input is a one-letter word. (This restriction preserves the fact that FPUT and FIRST are opposites.) TO in the middle of a line gives a correct title line to the resulting procedure. Also, COPYDEF FOO TO works. COPYDEF of a defined procedure generates a correct title line (with the new name instead of the old), and, therefore, no longer buries the new procedure. ASCII now handles backslashed characters (in particular, the ones returned by READCHAR for control characters) correctly. The CSLSLOAD command loads a file from the directory containing the _Computer Science Logo Style_ example programs. (Added because the Windows version now starts in the users Documents directory rather than in the Logo installation directory.) The SETCSLSLOC command can be used to change Logos idea of where it is. Fixed a bug about redrawing graphics with consecutive turtle moves with the pen up. (This led to a crash in Windows and a premature end of drawing on all platforms.) Windows: The installer and Logo agree on the registry name HELPFILE for the help file installation directory. Logo now starts in the users My Documents folder rather than in C:UCBLOGO and/or wherever the shortcut is found. This should help with users on shared systems prevented from saving by file access restrictions. The installer now offers the option of making UCBLogo the default application for .lg files, so they can be double-clicked to start Logo. Fixed a bug in the parsing of command-line arguments that prevented giving Logo a quoted filename to run. The desktop icon is now installed for all users, like the start menu entry, if the installer runs with Administrator privilege. Unix/MacOS X: Default editor is emacs instead of jove (mainly for the sake of MacOS, whose X11 installation includes emacs but not jove). Ôconfigure sets up makefile to use gmake if available, else make. names from the user manual, one per line, for use by emacs logo-mode procedure coloring. New emacs logo-mode version 3.0 with syntax checking. MacOS X version now has a double-clickable installer that puts the files needed to run Logo in /usr/bin and /usr/lib/logo; source files are by default in /ucblogo-5.4 but can be moved. (Note, Logo itself isnt double-clickable.) In the Unix tarball, docs files are no longer inside the emacs directory. ---------------------------------------- OTHER UCBLOGO-RELATED DISTRIBUTIONS: ---------------------------------------- MSWLogo is a free port of Berkeley Logo to Microsoft Windows done by George Mills. He has added a lot of Windows-specific capability to the language, so you can do cool multimedia stuff with it. Look in http://www.softronix.com/logo.html --- Adaptation francaise pour MSWLogo et UCBLogo: A startup file and documentation for UCBLogo in French is at http://www.algo.be/logo1/MSWlogo-fr.html --- -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Partitioning of numbers Does anyone know how numbers are partitioned or where I can go to get more information on partitioning of numbers? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Partitioning of numbers > Does anyone know how numbers are partitioned or where I can go to get > more information on partitioning of numbers? George E s The Theory of Partitions published by Cambridge University Press is the classic. Any good book on number theory will have a chapter or two on the subject. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Partitioning of numbers >Does anyone know how numbers are partitioned or where I can go to get >more information on partitioning of numbers? http://mathworld.wolfram.com/Partition.html -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Partitioning of numbers http://www.virtuescience.com/partitions.html Try Googling number partitions -- Casey -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Are Imaginary Numbers Fairy Tales? This website gives a fairly easy to read explanation fo why e comes from and why it is useful. It is not a number we just made up to work. It is actually a number that was disovere to do majical math work. There are also other majic numbers: pi, golden ration (aka Divine ratio), ... ~John -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Introduction to calculas - Limits I think should we differential equation to solve this. 4*2*x-0 / 1-0, and replace x with 3 Ans=24 >ok what u have to is first factorize the 4x^2-36 >ans= 4(x-3)(x+3)/(x-3) subsitute the 3 >in. >>I have just started learning calculas and need a few tips. >>Q1 >>lim 4x^2 -36 >>x app 3 -------- (x approaches 3) >> x - 3 >>= (4 x (3)^2) - 36 >> ---------------- >> 3 - 3 >>= (4 x 9) - 36 >> ------------ >> 0 >>= 36 - 36 >> --------- Book answer = 24 >> 0 >>*************** -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Introduction to calculas - Limits >I think should we differential equation to solve this. Is that supposed to be a sentence? >4*2*x-0 / 1-0, and replace x with 3 >Ans=24 This method is called LHospitals rule, and it is not at all appropriate for a student who has just started learning Ôcalculas . --Lynn -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Why does m = slope? >I am an eighth grade teacher and was discussing slope with my >Algebra I class and one of my students asked, Why did they >chose the letter m to represent slope? Why not s or another >variable? I know that s is referred to as distance in other >mathematics, but why m? I have searched and all I can find is >the explanation on how to derive slope, not why that specific >variable was chosen. Does anyone know the answer? Please >e-mail me the answer if you know why. My kids and I would >really appreciate it! Also, if you know of a source I could >Janene Shearburn >jshearbu@pen.k12.va.us >Sutherland Middle School >Charlottesville, VA I am a 8th grade student and our class had this same question. I found this website that had some possible answers for why m is used for slope, but they do not know for sure how it came along. If u would like to take a look at the website some parts are very interesting. The website is: http://www.math.duke.edu/education/webfeats/Slope/ Slopederiv.html -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Why does m = slope? There is no more reason to use m rather than slp as the name for the slope of a line than there is for you to name your cat Max. Whatever shorthand name you use for a math object never makes any difference to the math, though some names might tend to confuse or upset the reader. The only important exception is that, in any one particular discussion of math, the same name may not be used for two different objects. (Not a good idea to have two cats named Max.) ---------------------------------------------------------- >>I am an eighth grade teacher and was discussing slope with my >>Algebra I class and one of my students asked, Why did they >>chose the letter m to represent slope? Why not s or another >>variable? I know that s is referred to as distance in other >>mathematics, but why m? I have searched and all I can find is >>the explanation on how to derive slope, not why that specific >>variable was chosen. Does anyone know the answer? Please >>e-mail me the answer if you know why. My kids and I would >>really appreciate it! Also, if you know of a source I could >>Janene Shearburn >>jshearbu@pen.k12.va.us >>Sutherland Middle School >>Charlottesville, VA >I am a 8th grade student and our class had this same question. I found >this website that had some possible answers for why m is used for >slope, but they do not know for sure how it came along. If u would >like to take a look at the website some parts are very interesting. >The website is: href=http://www.math.duke.edu/education/webfeats/Slope/ Slopederiv.html>h ttp://www.math.duke.edu/education/webfeats/Slope/ Slopederiv.html -------------------------------------- -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Why does m = slope? Slope may be similar in character to mountain (but not Ôcliff). Think of words like mountain, montan~a, monte, mont, mount. ... Someone who understood one of the latin-derived languages must have come to decide to use Ôm for Ôslope in the equation for a line. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Why does m = slope? > .... > I am a 8th grade student and our class had this same question. I found > this website that had some possible answers for why m is used for > slope, but they do not know for sure how it came along. If u would > like to take a look at the website some parts are very interesting. > The website is: > http://www.math.duke.edu/education/webfeats/Slope/ Slopederiv.html > .... That web page is essentially copied from http://www.pballew.net/arithme3.html and you may also like to look at a page of the best web site for origins of mathematical words: http://members.aol.com/jeff570/geometry.html On both of these, scroll down to find the right section. Ken Pledger. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Qualities of a good math teacher I just began reading the postings in this part of the Math Forum, so I hope I am not too late to help you find the information you need about the qualities of good math teachers. There are many research studies about this topic and that is where I would suggest you look first. Everyone has an opinion based on their personal experiences, but these may not be supported by research that is based on sound methodology. You should be able to search ERIC through your university library and will find an abundance of resources available on this topic there. I think it is reasonable to assume that quality teachers provide quality instruction and for information regarding quality math information below will help you locate a an ERIC digest version. There is also a second part that explains how to implement the ten research based practices into the classroom.--Improving Student Achievement in Mathematics, Part 1: Research Findings. ERIC Digest. Grouws, Douglas A.; Cebulla, Kristin J.; ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH., 2000 (ED463952) Additionally, I would suggest you visit the Education Trust website and read their K-16 reports Good Teaching Matters and The Real Value of Teaching. Both of these may be found at http://www2.edtrust.org/edtrust/product+catalog/main Best wishes for your success as a quality math teacher of the future. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Qualities of a good math teacher > There are many research studies about this topic and that is where I > would suggest you look first. Everyone has an opinion based on their > personal experiences, but these may not be supported by research that > is based on sound methodology. You should be able to search ERIC > through your university library and will find an abundance of > resources available on this topic there. I agree that reviewing research may be helpful, but there is research that supports just about everything and anything. Be careful to make sense and experience are the best sources of information. I would successful teachers. Kris -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Math Educators Math Educators of the World Unite! I have been hired by the website www.TheMathWebSite.com to correlate the content of this website with the current math textbooks being used in the high schools in Canada and the USA. Other countries will be added if they express interest in this project. The above website is primarily for high/secondary school math educators in a classroom and we are working to take some of the drudgery out of their day. We plan to enable teachers to simply input the textbook page number of their next math lesson, and the website will refer them to the appropriate sheets to use for their next math class - lesson sheets, study sheets, quiz sheets, homework practice sheets, and test sheets .9a all ready to be printed out and used. So, if you are a math educator, would you please email the following information to software@TheMathWebSite.com Use .8bTextbooks.8a as the topic. - Your Math Textbook Name/Title and Publisher - For Grade 9/10/11/12 and Level Basic/Intermediate/Advanced - Your City and State/Province and Country - Type of School Board .9a Public/Separate/Private - Any other information that you feel is relevant further in this matter. - My name is Shasta. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Math Educators Shasta, I went to your web site and none of the topics were active hyperlinks. Will they be in the future? Is there a charge for this service? By the way I teach Algebra 1 and Geometry in middle school...so dont leave out 8th grade in your target. Algebra 1 is the standard for Grade 8 in California. (Not that all students study Algebra 1) We use the California Edition of Prentice Hall Algebra and an older text for Geometry, An Integrated Approach published by D. C. Heath. These are the same texts used by the high schools in our district. Ginny J > Math Educators of the World Unite! > I have been hired by the website www.TheMathWebSite.com to correlate > the content of this website with the current math textbooks being used > in the high schools in Canada and the USA. Other countries will be > added if they express interest in this project. > The above website is primarily for high/secondary school math > educators in a classroom and we are working to take some of the > drudgery out of their day. > We plan to enable teachers to simply input the textbook page number of > their next math lesson, and the website will refer them to the > appropriate sheets to use for their next math class - lesson sheets, > study sheets, quiz sheets, homework practice sheets, and test sheets .9a > all ready to be printed out and used. > So, if you are a math educator, would you please email the following > information to software@TheMathWebSite.com Use .8bTextbooks.8a as the > topic. > - Your Math Textbook Name/Title and Publisher > - For Grade 9/10/11/12 and Level Basic/Intermediate/Advanced > - Your City and State/Province and Country > - Type of School Board .9a Public/Separate/Private > - Any other information that you feel is relevant > further in this matter. > - My name is Shasta. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Trigonometry If sin x = 1/3 and pi/2 < X < 2pi Find: (i) tan x (ii) cos x therefore x is in the 3rd quadrant as sin x = 1/3 = O/H (+) so as per pythag if a^2 = b^2 + c^2 then c^2 = a^2 - b^2 = 3^2 - 1^2 = 8 so sqrt of 8 approx= 2.83, so tan = O/A = 1/2.83 and cos = A/H = 2.83/3 is this correct? Jason -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry > If sin x = 1/3 and pi/2 < X < 2pi > Find: > (i) tan x > (ii) cos x > therefore x is in the 3rd quadrant as > sin x = 1/3 = O/H (+) No, x is in the 2nd quadrant. B * y | | * | | * 3 | 1 | * | | * | |---------* ------------ A -sqrt(8) O Reading from the diagram, we get: x = angle(AOB) sin(x) = 1/3 cos(x) = -(sqrt(8))/3 = (-2/3)sqrt(2) tan(x) = -1/sqrt(8) = -1/(2sqrt(2)) = (-1/4)sqrt(2) -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry > If sin x = 1/3 and pi/2 < X < 2pi > Find: > (i) tan x > (ii) cos x > therefore x is in the 3rd quadrant as sin x = 1/3 = O/H (+) > so as per pythag if a^2 = b^2 + c^2 then c^2 = a^2 - b^2 = > 3^2 - 1^2 = 8 so sqrt of 8 approx= 2.83, so tan = O/A = 1/2.83 and > cos = A/H = 2.83/3 > is this correct? cos x = sqrt(1 - sin^2 x) = sqrt(8/9) = (2/3)sqrt(2). tan x = (sin x)/cos x = 1/3 * 3/2 *sqrt(1/2) = 1/2 * sqrt(1/2). It is my belief that you should _not_ write approximate answers (e.g. 1/2.83) when precise ones (e.g. 1/2 * sqrt(1/2) are calculable. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry > If sin x = 1/3 and pi/2 < X < 2pi > Find: > (i) tan x > (ii) cos x > therefore x is in the 3rd quadrant as sin x = 1/3 = O/H (+) > so as per pythag if a^2 = b^2 + c^2 then c^2 = a^2 - b^2 = > 3^2 - 1^2 = 8 so sqrt of 8 approx= 2.83, so tan = O/A = 1/2.83 and > cos = A/H = 2.83/3 > is this correct? > Jason Looks good to me, except if you are going to approximate the square root of 8, why not estimate tan x as 0.35 and cos x as .94. Otherwise, write them in terms of the square root of x, tan x = sqrt(8)/8 and cos x = sqrt(8)/3. Aaron -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Trigonometry >> If sin x = 1/3 and pi/2 < X < 2pi >> Find: >> (i) tan x >> (ii) cos x >> therefore x is in the 3rd quadrant as sin x = 1/3 = O/H (+) >> so as per pythag if a^2 = b^2 + c^2 then c^2 = a^2 - b^2 = >> 3^2 - 1^2 = 8 so sqrt of 8 approx= 2.83, so tan = O/A = 1/2.83 and >> cos = A/H = 2.83/3 >> is this correct? >> Jason >Looks good to me, except if you are going to approximate the square root of >8, why not estimate tan x as 0.35 and cos x as .94. Otherwise, write them in >terms of the square root of x, tan x = sqrt(8)/8 and cos x = sqrt(8)/3. Or... sqrt(8) = 2sqrt(2). tan(x) = 1/[2sqrt(2)] = sqrt(2)/4 -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Learning Math Hello everyone I have a website dedicated to helping people learn any type of math and physics. At first it started out as a website helping people how to do proofs, but then I expanded out to physics as well: http://fsc729.ifreepages.com/ I have a forum with textbook reviews, learning techinques, and more. In addition I have a link to totally free online textbooks. Please visit my website and if you have any ideas you want to share you can sign my guestbook or post in my forum. It is completely free. John G. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Inequality help! bump for the last parts anyone? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: 50 Questions Math SAT Preparation Test freely available on the Internet !!! Another excellent site with free sat math prep samples is http://www.xlmath.com. This site has an incredible question generating engine and icludes questions on the new sat 2005 math section. You will be able to sign up for free at the site and purchase if you like it. I highly recommend this site if you are looking for a quick and smart way to study for the SAT test. Best SAT practice questions I have seen so far. Check it out at xlmath.com. >Poliplus Software is proud to introduce our new Algorithmically >Generated Self-Scoring Math SAT practice Exam. The latest in >Dynamic mathematics from Poliplus Software. >Features include: >* 50 questions in only 30K >* Ideal for wireless networks and/or quick downloads >* Infinite number of exams from one template >* Automatic multiple choice shufßing of each question >* Self-Scoring >Take our SAT for a test drive at, href=http://www.poliplus.com/eBooks/launcher.htm>http:// www.poliplus.com /eBooks/launcher.htmWe welcome your comments and look forward to your feedback. >Carlos Bazzarella >Poliplus.com for all your interactive online math needs! -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Inequality help! Hey could someone please help me with the last parts thank you very much -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Number Recognition I am doing a short research paper on how to teach number recognition. I tutored a third grade student who was unable to look at the number 22, for example, and tell me what that number was. He could create numbers using base ten blocks, but he could not look at any number and tell me what that number was. When I research online, it tells me how to teach a toddler number recognition, but that is not appropriate for this situation. Could someone please give me some resources to help with this paper. I greatly appreciate it. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Number Recognition >I am doing a short research paper on how to teach number recognition. >I tutored a third grade student who was unable to look at the number >22, for example, and tell me what that number was. He could create >numbers using base ten blocks, but he could not look at any number and >tell me what that number was. When I research online, it tells me how >to teach a toddler number recognition, but that is not appropriate for >this situation. Could someone please give me some resources to help >with this paper. I greatly appreciate it. Maybe the online research information you found really does fit this third-grade student. If you try that method that you found, and repeat it a couple of times, and if this works for your student, then the two of you win. Also, keep in mind that this third grade student may develop slower than the other students of his age; maybe he will understand better in a couple of years. He may not be doomed to failure just for lack of understanding right now. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Suggested Math Software? You can try a free software called DeadLine. DeadLine solves equations graphically and numerically. The freeware finds the real roots of an equation, evaluates functions and the first two derivatives extremely fast and accurately, finds extrema of the function. http://deadline.3x.ro -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Riemann surface of w=log(e^z-1) >How can I get a handle on the riemann surface of w=log(e^z-1)? I have >some idea of what it looks like - a stack of sheets piled on top of >one another and joined together in a certain way. But how do I >formalize this and work with it. Youre in luck here: your surface is easily described as being a subset of C^2, namely its the set of pairs (z,w) with exp(w)=exp(z)-1. The covering map from the surface to the plane is just the projection (z,w) -> z. This much is the same as the as the algebraic setting. But youll have more trouble with compactness here because the exponential map does not extend to a map from the Riemann sphere to itself. You can construct your Riemann surface by hand in this example. Its pretty and no, its nothing like the low-genus examples you asked about. View the surface as the set of points (x,y,u,v) with exp(u) cos(v) = exp(x) cos(y) - 1 and exp(u) sin(v) = exp(x) sin(y) or equivalently exp(x) sin(v-y) = sin(v), exp(u) sin(v-y) = sin(y) . Note that the signs of all the sines must agree. Now, what does this surface look like? You can get a pretty good idea of the graph by plotting x+u as a function of v and y, that is, from the graph of log( sin(v)/sin(v-y) ) + log( sin(y)/sin(v-y) ) . Because of the periodicity it is sufficient to draw the portion of the surface where -pi <= y, v <= pi and then glue copies of those together appropriately. Within this one patch, we must have either v > y > 0 or v < y < 0 or v = y = 0. The projection to either vyx or vyu space can be visualized as a long rectangle with a half-twist in it lying over the vy-plane. (The line v=y=0 is where the twisted rectangle becomes vertical; the four edges, in order, lie over the lines v=-pi, y=0, v=pi, y=v.) This twisting makes a smooth surface out of something that projects in the vy plane to a pair of triangles meeting only at the corners. Now make copies of that surface lying over each pair of black squares in an infinite checkerboard, and perform the same trick at every point where two squares touch. Thats your Riemann surface. >This comes up as a change-of-variable: z in (0,infty) -> w in >(-infty,infty), to apply before appling the trapezoidal rule, and >need to integrate over the boundary of a region surrounding >(-infty,infty)... Im sorry, I dont understand this. dave === Subject: Re: lagrange and continued fractions > I was wondering about the following: take two continued fractions >[a0;a1,a2,...] and [b0;b1,b2,...] (converging to irrationals x1 and >x2), such that > (1) there exists N : an=bn for n>=N > (2) sum(ak-bk)=0 > If (2) then the respective convergents pn/qn and cn/dn lie on the >same horizontal line in the Stern-Brocot tree (for n>=N). If (1) >then Lagrange showed that x2=f(x1) where f(x)=(ax+b)/(cx+d) with >integer coefficients (if I remember correctly). > Question 1: is there en explicit form for f (for instance >knowing ak,bk for ksends pN/qN on cN/dN? (I bet not...) It is. Let y_k = [a_k; a_{k+1}, a_{k+2}, ...] and z_k = [b_k; b_{k+1}, b_{k+2}, ...], so x1 = y_0 and x2 = z_0. Let s_k be the Mobius transformation u -> a_k + 1/u and t_k the Mobius transformation u -> b_k + 1/u. Then y_k = s_k(y_{k+1}) and z_k = t_k(z_{k+1}). By assumption y_N = z_N. Thus x1 = s_0 o ... o s_{N-1} o t_{N-1}^{-1} o ... o t_0^{-1} x2. Since the Mobius transformations form a group, T = s_0 o ... o s_{N-1} o t_{N-1}^{-1} o ... o t_0^{-1} is a Mobius transformation (and easily computed from a_0, ..., a_{N-1}, b_{N-1},...,b_0). Of course this doesnt depend on a_N, a_{N+1}, ..., so it would be the same if a_N = a_{N+1} = ... = 0, and thus T(c_N/d_N) = p_N/q_N. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Has anybody encountered the following strange object ... > Hi everybody, > has anybody seen an object like this > =c d(x-v) d(y-u) > where c is a number, d stands for the Dirac-Deltafunction, and > the <> is a functional average over the function f. Does anyone know > a name for this? Has anyone done some work using/involving this? > We are doing research in physics and do not know how to deal with > this object and wonder if any of you mathematicians have ideas. By functional average over the function f do you mean something like the integral over a domain (possibly with some weight function g) ? If I understand well then, you are being given a point (u,v) say in R^2, and your expression is zero except if x=v and y=u. This means that it is zero unless your domain contains the point (x,y)=S(u,v) where S is the reßexion w.r.t. the diagonal of R^2. The effect of the weight g you have in your average is thus to detect such a reßexion point. Unfortunately Im too ignorant to know if this has a name, but it might have popped up in signal analysis. Hope this helps. -- thomas. === Subject: Paper published by Geometry and Topology The following paper has been published: Geometry and Topology, Volume 9 (2005) Paper no. 1, pages 1--93 URL: http://www.maths.warwick.ac.uk/gt/GTVol9/paper1.abs.html Title: Monopoles over 4-manifolds containing long necks, I Author(s): Kim A Froyshov Abstract: We study moduli spaces of Seiberg-Witten monopoles over spin^c Riemannian 4-manifolds with long necks and/or tubular ends. This first part discusses compactness, exponential decay, and transversality. As applications we prove two vanishing theorems for Seiberg-Witten invariants. Secondary: 57R57 Keywords: Floer homology, Seiberg-Witten, Bauer-Furuta, compactness, monopoles Proposed: Dieter Kotschick Seconded: Simon Donaldson, Tomasz Mrowka Author(s) address(es): Fakultaeat fuer Mathematik, Universitaet Bielefeld Postfach 100131, D-33501 Bielefeld, Germany Email: froyshov@mathematik.uni-bielefeld.de === Subject: Re: Uniqueness of implicit functions Epigone-thread: zhoabrarshel >Im not sure what you mean by a regular curve in R^(n-1). Its >certainly not a curve. Perhaps what you have in mind is something >like this: >Suppose theres a continuous function r(x_1,...,x_{n-1}) on a >subset A of R^(n-1) such that for (x_1,...,x_n) in A and x_{n-1} in R, >g(x_1,...,x_n) = 0 iff x_n = r(x_1,...,x_{n-1}). >Then h(x_1,...,x_n) = g(x_1,...,x_{n-1},x_n+r(x_1,...,x_{n-1})) >is a continuous function on A x R such that >h(x_1,...,x_n) = 0 iff x_n = 0 >and g(x_1,...,x_n) = h(x_1,...,x_{n-1},x_n-r(x_1,...,x_{n-1})). Mikhail === Subject: Re: Banach space Of Analytic Functions Epigone-thread: gumfikend >Of Course I Search for a NON STANDARD topology for some Functional >Space(For Example schwars maps) which is invariant under the action of >a polynomial vector field X (As a Bounded operator ) In a certain sense, such spaces have *only one* natural topology: complete, separable, metrizable, and described without resort to the Axiom of Choice. But I guess it takes a logician to specify what that sense is. === Subject: Re: Banach space Of Analytic Functions >[...] >But Exponentials Are Tempered Distributions. QED! Just in the interest of accuracy, of course that should have been But Bounded Exponentials (IE Characters) Are Tempered Distributions. QED! ************************ David C. Ullrich === Subject: Re: modular elliptic curves over number fields? posting-account=I5OE7A0AAABFXgfTwWarqxMzHqMkyhHC > The problem with the question is that it is sufficiently vague to admit > several answers. If the questioner defines precisely what he/she means > by modular then it would be possible to give a better answer. The problem > is that its very hard to make the question rigorous in general! The question Im really interested in is, is there a sensible definition of Heegner points on elliptic curves over number fields? Of course, its just as vague as asking for modular curves... === Subject: Re: Schatten Class Operators Yet another suggestion: J. Ringrose, Compact non-self-adjoint operators. (English) Van Nostrand Reinhold Mathematical Studies. 35 (1971). > Hi all, > Could someone please give me a good reference on the Schatten Class > Operators? I read about this kind of Operators in the book Operator > theory in function spaces by K. Zhu but I cant figure out how to > show that S_p (the p-Schatten Class Operators) is a complete normed > space for 1<=p definition of the norm of an operator T (in the above book) depends on > the canonical representation of the square root of T*T. Though, I > could prove that S_p is complete for p=1 or 2 because in these cases, > the book provides good definitions for the norms. > Trieu. === Subject: Re: Schatten Class Operators Hello Trieu Leu, try this paper: C.A. MCCARTHY, $c_p$, Israel J. Math. 5 (1967), 249-271 Or these books: J. WEIDMANN, Linear Operators in Hilbert Spaces, Springer 1980 R. MEISE / D. VOGT, Introduction to Functional Analysis, Oxford University Press 1997 Markus > Hi all, > Could someone please give me a good reference on the Schatten Class > Operators? === Subject: Re: Schatten Class Operators >Could someone please give me a good reference on the Schatten Class >Operators? I read about this kind of Operators in the book Operator >theory in function spaces by K. Zhu but I cant figure out how to >show that S_p (the p-Schatten Class Operators) is a complete normed >space for 1<=pdefinition of the norm of an operator T (in the above book) depends on >the canonical representation of the square root of T*T. Though, I >could prove that S_p is complete for p=1 or 2 because in these cases, >the book provides good definitions for the norms. Try: Simon, Barry Trace ideals and their applications. London Mathematical Society Lecture Note Series, 35. Cambridge University Press, Cambridge-New York, 1979. viii+134 pp. ISBN 0-521-22286-9 Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Recurrence relation, part 3 This option I certainly knew and this is not what I am looking for. Any finite and elegant formula? Alex