mm-1062 === Subject: Re: How do get a scientific calculator to display 10^x.x >I have a standard scientific calculator and canÕt 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 canÕt 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 canÕt 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 doesnÕt 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. HereÕs 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 IÕm 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 observerÕs 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 EarthÕs axis of rotation, with respect to the perpendicular to the plane of EarthÕs orbit around the sun. There also is some minor effect from the eccentricity of EarthÕs orbit around the sun. The times also are affected slightly by atmospheric refraction, and by the observerÕs 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 IÕve seen is HalmosÕs places, including a book of essays edited by Steenrod: and a selection of HalmosÕs 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 wasnÕt >very relevant to my problem anyway- IÕm very sorry. >A better example would have been 5 - 3x = 5x. Again, IÕm very sorry. > Any help would still be appreciated. >> Well, other than the one mistake in subtraction, youÕre previous example was >> done perfectly. Is there something in particular that you donÕt think you >> understand? > Sometimes I get it to balance out, and sometimes I canÕt 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 donÕt 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- IÕm very sorry. > A better example would have been 5 - 3x = 5x. Again, IÕm 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 letÕs 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!!!!! IÕve 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 didnÕt 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. ItÕs 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)])Õ = cos(sqrt(x-x^3))*[sqrt(x-x^3)]Õ = cos(sqrt(x-x^3))*[(x-x^3)^(1/2)]Õ = cos(sqrt(x-x^3))*((1/2)(x-x^3)^(-1/2))*[x-x^3]Õ = 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 IÕll 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. IÕve 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. ThatÕs not necessarily so in the statement you are asked to explain. ItÕs 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. ThereÕs not really anything wrong with your explanation, it just doesnÕt 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 itÕs 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 canÕt 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 peoplesnames 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 ZÕs 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 donÕt 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 canÕt use calculators until they donÕt 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 donÕt 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 canÕt 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. ItÕs not only top-down policy. ItÕs bottom up. Math can be difficult to master, and itÕs 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. >ItÕs not only top-down policy. ItÕs bottom up. >Math can be difficult to master, and itÕs 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? IÕve heard the same jargon, but not about American education, about the system here. ItÕs 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 donÕt 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. IÕve 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? >IÕve heard the same jargon, but not about American education, about >the system here. ItÕs 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 donÕt think the remarks are > aimed at the American system in particular except to > perhaps express some real concern. Many kids today donÕt want to learn math and donÕt feel ashamed or guilty about not knowing any. ItÕs 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. IÕve 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 donÕt 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 donÕt 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 customersbills (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 donÕt 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 customersbills (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 couldnÕt 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 > donÕt 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? ThatÕs what my great grandmother said about electricity. > Once while working at a restaurant, the cash register failed. > No one, but I, could calculate the customersbills (including tax) > even WITH a calculator. Excellent point; the best argument for the usefulness of math knowledge, IÕve 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 >>donÕt 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 DomenicoÕs post, I was replying to yours. However, he did say that at least one student couldnÕt 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? ThatÕs what my great grandmother said > about electricity. And when the worldÕs 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 customersbills (including tax) >>even WITH a calculator. > Excellent point; the best argument for the usefulness of math knowledge, > IÕve 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 arenÕt 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 Ôtotalson 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 guestÕs 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 Ôlefton 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 Ôtotalson 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 guestÕs 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 >>donÕt 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? ThatÕs what my great grandmother said > about electricity. >>Once while working at a restaurant, the cash register failed. >>No one, but I, could calculate the customersbills (including tax) >>even WITH a calculator. > Excellent point; the best argument for the usefulness of math knowledge, > IÕve 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. IÕm suggesting the majority of people either do it without a problem, donÕt 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 donÕt 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 donÕt. >>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 havenÕt 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. IÕm suggesting the majority > of people either do it without a problem, donÕt 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 donÕt really care. Routine > money management is boring. Maybe you should be in charge of this countryÕs 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 donÕt. 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 havenÕt learned any mathematics. This seems to imply that if most learned some mathematics, our economy would shift from one thatÕs 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. IÕm suggesting the majority >> of people either do it without a problem, donÕt 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? IÕm 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 havenÕt learned any mathematics. ItÕs 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 donÕt need to know math to be functioning adults. > Maybe you should be in charge of this countryÕs budget. I couldnÕt 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 donÕt 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 donÕt 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 donÕt 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) couldnÕt 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 itssad 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 Ôlivefolks but some of the more prominent ones, too. Relatively speaking, there just isnÕt _that_ much mathematics needed by the average person that a four function calculator canÕt 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. ThatÕs not bad at all, especially for a relatively rural area as middle TN. Actually, itÕs _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. IÕm 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. > IÕm certain others can draw their own conclusions. Good teachers meet students at the studentslevels, which includes taking into account studentsreadiness to learn the mathematics topics of the day. Forcing students to do things the teacherÕs way when there are other options available doesnÕt work anymore, if it ever did. ThatÕs 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 donÕt 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) couldnÕt care less about your private emails! ThatÕs 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 itssad 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 Ôlivefolks but some of the more prominent ones, too. > Relatively speaking, there just isnÕt _that_ much mathematics needed by the > average person that a four function calculator canÕt 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 donÕt 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. ThatÕs not > bad at all, especially for a relatively rural area as middle TN. Actually, > itÕs _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 havenÕt learned any mathematics. > ItÕs 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 donÕt 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 donÕt need it to be functioning adults. Millions of Americans are unemployed, therefore they donÕt 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 donÕt need those freedoms to be functioning adults. *** PLONK *** >>Maybe you should be in charge of this countryÕs budget. > I couldnÕt 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 donÕt > need it to be functioning adults. > Millions of Americans are unemployed, therefore they donÕt 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 donÕt 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 canÕt 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 donÕt. -- 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 studentÕs 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. IÕm not sure what I as a new teacher can do about this. I mean at this point, itÕs 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! ItÕs $5.50 to get into the buffet, all they need to do is make change for a $10 or $20. This isnÕt hard math! Ok IÕm 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. LetÕs 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 isnÕt 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 isnÕt 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 isnÕt 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 wonÕt understand everything overnight. You will have more use for Ôewhen 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 isnÕt 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 itÕs the story of my life. I have heard of the idea that you really donÕt learn anything until youÕre 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 itÕs the story > of my life. I didnÕt 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 IÕd 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 donÕt learn anything until > youÕre 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 donÕt get it by the end of high school, repeating it once more in college doesnÕt 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 schoolÕs 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 donÕt get it by the end of high school, repeating it once more in >college doesnÕt 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 collegesassessments 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 itÕs the story >of my life. >I have heard of the idea that you really donÕt learn anything until >youÕre 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 countriesmath 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, Ôcindysaid: >> 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, IÕm almost certain this is it; It makes so much sense, but I just donÕt 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, IÕm almost > certain this is it; It makes so much sense, but I just donÕt > know. This has been bothering me forever, and a quick Just keep in mind that itÕs not the area itself that is squared, but the units; so itÕs 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. ItÕs 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, IÕm almost > certain this is it; It makes so much sense, but I just donÕt > 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 = canÕt simplify 4 in + 2 lb = canÕt add 4x * 2y = 8xy 4 in * 2 lb = 8 in-lb (An inch-pound is a unit of energy, if IÕm remembering my physics correctly. You donÕt see inch-pounds in practical computation very often, but foot-pounds are more commonly used.) IÕm emphasizing analogous to because you shouldnÕt 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 canÕt be simplified unless we learn something about the values of x and y. But 4 in + 2 lb is just plain wrong -- itÕs 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, IÕm almost >certain this is it; It makes so much sense, but I just donÕt >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. ItÕs 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, IÕm almost >certain this is it; It makes so much sense, but I just donÕt >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. wouldnÕt 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)?? WouldnÕt 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?? IÕm 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. wouldnÕt 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)?? WouldnÕt 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?? IÕm 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 itÕs 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 thatÕs what you have! And the weighted average formula is telling you that youÕre not allowed to do that, but must instead recover the total revenues by multiplying each stateÕs per-pupil revenue by its ADA. In the vocabulary of the formula, you weight each stateÕs 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, IÕd be inclined to say that there is *no* honest way to average such unlike numbers. Instead youÕd 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, itÕs 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 olvalues 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 thatÕs 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 thatÕs just wrong. I wouldnÕt say wrong, but IÕd 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 thatÕs just wrong. > I wouldnÕt say wrong, but IÕd 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 wouldnÕt 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, itÕs 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 Ôcloseonly 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. IÕm 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 wouldnÕt 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, itÕs 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 Ôcloseonly 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 thatÕs just wrong. >> I wouldnÕt say wrong, but IÕd 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 wouldnÕt 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 BobrowÕs 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: * ItÕs free. * It comes with source files (in C). * Logo programs are completely compatible among Unix, PC, and Mac. Disadvantages of Berkeley Logo: * ItÕs relatively slow. * It doesnÕt 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 peopleÕs 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. YouÕll 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 donÕt 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 youÕre 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 youÕve 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 donÕt understand, I had to compile the entire interpreter without optimization. But on other platforms, such as PCs running Linux and FreeBSD, itÕs 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 thatÕs 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 didnÕt 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 userÕs Documents directory rather than in the Logo installation directory.) The SETCSLSLOC command can be used to change LogoÕs 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 userÕs 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). Ôconfiguresets 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 isnÕt 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 AndrewsThe 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 LÕHospitalÕs 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 ÔcliffÕ). 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 Ômfor Ôslopein 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 IÕve read this book and did not take it personally. It is a research paper that states the differences in teachersunderstanding of fundamental mathematics in China and the United States. I really donÕt think the aim of a research paper is to sugar coat information in order not to hurt feeling. Was it really surprising the results were that many US Math teachers do not have a strong understanding in basic mathematical concepts? ItÕs a real good book and I highly recommend it. >> Good Morning Patricia, >> I donÕt know what makes a good math teacher, but IÕm certain that a >> profound understanding of elementary mathematics is very important. >> See the book Knowing and Teaching Elementary Mathematics by Liping >> Ma. >But do be prepared to feel put down if you read that book. I have read it >and I am not a math teacher nor have any aspirations to become one. (I am >a Ph.D. student and part of my fellowship required reading that book.) >I was a little disturbed because I had gone through the traditional U.S. >way of schooling and seemed to have turned out just fine. It seems, from >reading the book, my teachers were horrible teachers and I didnÕt learn >anything about math. >Sure, it is true that less and less U.S. students are going to graduate >school in math (see the MAA reports) and many students do not have the >basic math skills, so there is some truth to the book. However, Liping Ma >is short on tact. >One of my professors had a chance to talk with Liping and he asked her if >she realized many elementary school teachers thought her book was an attack >on them. He told me that she said that wasnÕt her intent, but just to show >the differences between the two ways of learning, or something like that. > - Tim >-- >Timothy M. Brauch >NSF Fellow >Department of Mathematics >University of Louisville >email is: >news (dot) post (at) tbrauch (dot) 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: 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 donÕt 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: 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: Math problem that I canÕt work out :/ The first number was simply 1. The next, 11. Then, 21, 1,211, and 111,221. -- 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: Corporate Model in St. Louis School System Some members of this NG may be interested in the following Washington http://mathforum.org/epigone/math-teach/treldkerlcrau Dom Rosa ------------------------------------------- Corporate Model Proves an Imperfect Fit for School System In St. Louis, Some Question Whether Bankruptcy FirmÕs Fix Is Working By Michael Dobbs Washington Post Staff Writer -- 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: learning math website. Actually, I am a graduate math student at a univerity already, I just want to help anyone and everyone learn math. John G. >If you want to be led through traditional school math step by step try >EPGY at Stanford. href=http://hypatia.stanford.edu/epgy/>http:// hypatia.stanford.edu/epgy/ it is recognized for AP credit. >Sounds to me like youÕre ready for calculus and could probably finish >a standard intro calculus book this summer. Might as well get it out >of the way - it seems to be a rite of passage. >If you want to see some stuff that a lot of HS teachers donÕt even >know exists try: >Group Theory and physics by Sternberg >Intro to number theory by Flath >The book of numbers by Conway and Guy >The Universal Turing Machine.... (pub. by Springer Verlag) >DONÕT be discouraged if some of these books are too hard for you now - >look at them as goals, contact a math professor or Ask Dr. Math or >this forum for guidance in getting the background to go where itÕs >interesting to you to go. -- 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