Does anyone know where logic c...See MoreI have been working on my web site to provide teachers a definitive free resource for the core curriculum for a while now. Many teachers are asking me to create Logic worksheets. I align all of my sheets to the Core Math Curriculum, to make it easier for teachers. I see no logic skills any where in the core.
Does anyone know where logic comes into play in the Core Curriculum. I can't believe that they would totally abandon logic as a skill.
Definition of a^(1/n) is the answer ------------------------------------ x=a^(1/n) is called as principle n^th real root of a and such root when it exists, is by definition either a positive number or zero, eg. 4^(1/2). When n is odd, the principle n^th real root may be a +ve or -ve number and it needs no special consideration since it can be easily found. eg. (-8)^(1/3) or (8)^(1/3).
Why consider only positive roots?
If x=8 then squaring operation such as x^2=64 introduces -8 as an extraneous root-meaning you start with x=8 to get x^2 = 64 but to get x back from x^=64 you get unintended x=-8. Thus, it is customary to consider only the principal n^th root in simplification of terms such as (16)^(1/4)=+2, (64)^(1/2)=+8 and exclude -2 and -8. Addressing the root in context as extraneous (and sometimes redundant, spurious or vacuous) seems appropriate since to derive x^2=64 from given x, x=8 is sufficient. Considering x=-8 does not generate any additional information in getting x^2=64 by the squaring operation.
Best regards.
Mohan Pawar Online Instructor, Maths/Physics MP Classes LLC -------------------------------------------------- US Central Time: 3:57 PM 2/22/2013
Mohan PawarOn 2/22/13, Mohan Pawar wrote: > On 2/20/13, Amanda wrote: >> I understand how the 4th root of 81 yields a positive and >> negative answer. When asked to evaluate 16^(3/4) why is >> there no negative answer? Thanks! > > Definition of a^(1/n) is the answer > ------------------------------------ > x=a^(1/n) is called ...See MoreOn 2/22/13, Mohan Pawar wrote: > On 2/20/13, Amanda wrote: >> I understand how the 4th root of 81 yields a positive and >> negative answer. When asked to evaluate 16^(3/4) why is >> there no negative answer? Thanks! > > Definition of a^(1/n) is the answer > ------------------------------------ > x=a^(1/n) is called as principle n^th real root of a and such > root when it exists, is by definition either a positive number > or zero, eg. 4^(1/2). When n is odd, the principle n^th real > root may be a +ve or -ve number and it needs no special > consideration since it can be easily found. eg. (-8)^(1/3) or > (8)^(1/3). > > Why consider only positive roots? > > If x=8 then squaring operation such as x^2=64 introduces -8 as > an extraneous root-meaning you start with x=8 to get x^2 = 64 > but to get x back from x^=64 you get unintended x=-8. Thus, it > is customary to consider only the principal n^th root in > simplification of terms such as (16)^(1/4)=+2, (64)^(1/2)=+8 > and exclude -2 and -8. Addressing the root in context as > extraneous (and sometimes redundant, spurious or vacuous) seems > appropriate since to derive x^2=64 from given x, x=8 is > sufficient. Considering x=-8 does not generate any additional > information in getting x^2=64 by the squaring operation. > > > Best regards. > > Mohan Pawar > Online Instructor, Maths/Physics > MP Classes LLC > -------------------------------------------------- > US Central Time: 3:57 PM 2/22/2013
Here is application of above explanation to your original question 16^(3/4)=+8. Why not -8 too?
16^(3/4) = ((16)^(1/4))^3 =(+2)^3 (By definition 16^(1/4)=+2 explained in my previous post) =+8
Best regards.
Mohan Pawar Online Instructor, Maths/Physics MP Classes LLC -------------------------------------------------- US Central Time: 4:18 PM 2/22/2013
My students are fussing about factoring, graphing, completing the square, etc. They say all they need is the quadratic formula, that older students have told them that's all that they used in College Algebra.
In Algebra 2, do you make them learn all the other ways? If so, what is the justification?
Back in the day I didn't get taught EITHER way, it was strictly trial and error, which stunk. I was so amazed to find out about the box method I never really looked beyond that. so I never tried the grouping method you suggest, and now I am teaching pre-algebra so I don;t have a chance to try it out.
> By the way, I love the way you start with factor finding.
Thanks. A lot of what I do is set the stage well beforehand so that they have fluency in key skills right before they need them. That is one of the reasons I am really enjoying teaching pre-algebra. Having taught algebra for many years I know exactly what they need to be successful in algebra and THAT is what I concentrate on, state test be d@mned.
n 3/01/13, Stella wrote: > Thank you very much for your replies. You are stating what I > believe, but since I am coming back to math after a long break, I > am sometimes unsure of myself, especially when the students just > can't seem to learn what we are studying. I needed some > reinforcement (and backbone). > > Their previous teacher mainly taught them how to use the > calculator to solve everything. We did factoring for weeks, and > half the class still could not do it. > > Even consultants who have come in focus on how to use the answer > choices to go backwards to the question. A good test taking > technique, but it makes the kids think what we do is irrelevant. > > Thank you again. >
On 2/23/13, Sue wrote: > Is anyone using one of the new common core textbooks or > planning on adopting something soon. I am winging it right > now without a textbook and the only decent one I can find > is "Math IN Focus". Unfortunatly it requires one hour per > day which my school is finding difficult to do. We need > something next year and not sure what to do. Any > suggestions?????
A lot of people have been redirected to that page. Something in your post must have caused the (lame, outdated) auto-filter to assume you were trying to break the law.
Don't worry about it. If everybody here who's seen that message were in danger of federal arrest, there would be half a dozen people left walking around free to post anything at all.
> Don't worry about it. If everybody here who's seen that > message were in danger of federal arrest, there would be half a > dozen people left walking around free to post anything at all.
Thanks so much for your reply; I thought I had some kind of malware on my computer! Wonder what I wrote that triggered it? I tried to use the square root symbol, maybe that did it
I ...See MoreAnother teacher shared with me something I hadn't thought of and am wondering what you all think...
Let x and y represent the factors of a given number, so that xy=n. Therefore, y=n/x. Put that into the calculator and the table will give the factors. Example xy=42, y = 42/x. Look at the table and it will give the factors of 42.
I like the way it reinforces transforming equations, but is it too much of a short cut?
We do not allow calculators at all. I am generally against doing anything with a calculator that the student couldn't, if need be, do by hand. To me that is the dividing line between a crutch and a tool.
mtinnjDoesn't seem like much of short cut. However, your function is missing one small detail for your table, which maybe you meant to be obvious. Domain={x| 1
If you are a middle or high school math teacher and available for a 15-20 minute conversation on this subject, I would like to learn how you use technology in your classroom.
I am a teacher, currently working on completing the research requirements for my doctorate in education. My study focuses on utilizing small group instruction techniques in mathematics classrooms patterned after proven techniques used in Reading classes. The study attempts to generate a working model that allows for appropriate differentiation of content while at the same time increasing student interest in mathematics. I am asking for your assistance.
If you have taught at least ten years and have experience teaching mathematics, I would be interested in your feedback concerning this model.
If you are interested, please email an I will send you the necessary information.
On 2/12/13, Taimur Murad wrote: > I need help with statistics i am a student