I teach an engineering class entitles Engineering, Design and Development. My students are really excited about this project and need justification for their current problem. if you could take a minute out of your day to fill out their survey I would be very greatful. The link is here -> [link removed]
I used the integration method to calculate the following equation to find out the area between 1 and 4 was 51. The equation is 0.6666x^3 - x^2 + 8x + c.
However, when I use Trapezoidal rule and simpsons rule, the results are 82.
Th...See MoreOn 2/26/15, Tom wrote: > I used the integration method to calculate the following > equation to find out the area between 1 and 4 was 51. > The equation is 0.6666x^3 - x^2 + 8x + c. > > However, when I use Trapezoidal rule and simpsons rule, > the results are 82. > > Why there are such difference in result? >
Those numerical integration tools are approximations, and their accuracy is heavily influenced by the length of the intervals.
To get a sense of just how off these methods are when you try to apply them with such a large interval, as you have, you should draw the curve of the original function, f(x) = 2x^2-2x+8, which between x=1 and x=4 is a steeply increasing parabola. Now draw the trapezoid. Now look at the huge difference between the area of the actual curve and the area of the trapezoid that approximates that area.
These rules can be very accurate ways of doing numerical integration but you always have to look at the error analysis part of it to see how good the approximations are. To improve the accuracy you have to split the domain into smaller pieces and apply the trapezoid rule to each piece and then add up the little pieces of area you get. The smaller you make the intervals, the greater the accuracy.
If you do not have a good way of graphing the function so you can look at and compare the curve and trapezoid visually you might have a look at this program - it is free and it does a great job of graphing functions.
[link removed]
I have used this program for years with my students to help them "see" what is really going on, in questions like this.
I am wondering how people are implementing this model in their Mathematics program and what you are doing to help those students on whom you are focusing?
What is it?On 2/17/15, Erin wrote: > I am wondering how people are implementing this model in > their Mathematics program and what you are doing to help > those students on whom you are focusing?
A google search comes up empty on "Focus on Five". Do you have a link to something that explains what that model is?
Hello .. We are looking to adopt new math textbooks for our K-8 school. I haven't seen a lot of rave reviews on any of the common core aligned texts out there. Anyone already using a new "common core" aligned series. Do you love it? Hate it? Just in between? I'd love to hear some real world experiences.
We are currently beginning the process of researching and then will be deciding what to pilot. I am finding that many of the texts are similar, and most have an on-line piece which allows students to access the text on line and assessments which can be created and given on- line. One series I really like is Everyday Math from McGraw Hill. The materials are set up to allow the standards to drive the teaching, and give teachers differentiation information for classroom teaching and materials to supplement, but there is no "text" that is driving the instruction. This is a new way of teaching for most of us, but the CCSSM are asking us to learn to teach in a new way, and I believe with solid support this is one of the best resources I have seen yet. I am not finished previewing what is out there at this time.
Our school is pushing towards a general no-homework policy. Is there anybody out there successfully doing this, or tried it and can offer some feedback? I teach 8th grade pre-algebra.
Standardized learner: Student who's assessment of math learned falls within one standard deviation of class average for a particular class taught by same teacher.
Average homework: Homework that produces a reasonably normal distribution of correctness for a fixed amount of time, which is determined by the teacher. More or less time is not allowed for students.
Teacher grading to student working ratio: The amount of time the teacher needs to grade homework and enter grades. divided by the sum of each each student's time doing homework.
Relative rigor ratio: Level of math curriculum taught in relation to course syllabus.
Student ability level: Level of needed academic preparation to learn at average level in the specified class.
Student engagement index: Percentage of time student actually is attending an assigned learning activity in class.
Assessment integrity index: Percentage of work done by student's independent effort.
As some of my profs have said, "I leave the derivation of the formula as an exercise for you."
So, As you can see, the optimal production process is using continual formative assessment - as has been pointed out.
Note: If you are not sure of the exact formula, remember, you can use the Internet to get it. If you have trouble, most students can show you how for get the answer, even if it's wrong. Anyway, most teachers give completion grades to same grading time.
tag words involved with this question: [ &37; Operator, Matrices, remainder of division, Modulus/Cross-Product ]
tutoring request: Please help me understand the pattern of these results. What aspects of math or bit manipulation is occurring to result in these answers? Please help me visualize the process occurring to achieve these results. These answers are calculated by the Secondlife physics engine consistently.
so 16 mod 2 = 0 16 mod 8 = 0 17 mod 8 = 1 7...See More Mr/Ms Modulo Dec 30, 2014 That was a fantastically educational answer! and yes it took this long for me to get back into it considering the Christmas insanity! Thank you so much for a very helpful response! This is going to be very useful to me in my work! thank you! *happy hugs!* Good tutorial!
so 16 mod 2 = 0 16 mod 8 = 0 17 mod 8 = 1 75 mod 50 = 25 75 mod 25 = 0 2 mod 490834752349 = 2
thank you for helping me understand! *^-^*
On 12/30/14, Modulo wrote: > The operator you are designating &37; is usually (in the US > anyway) called mod. So where you write 10 &37; 2 I would > normally write 10 mod 2. > > Basically what the value of "a mod b" is the remainder when > a is divided by b. > > Looking at some of your examples, the last 9 of them had a > value of 4 because if you divide 4 by a number that is > bigger than 4 you will always get a remainder of 4 > > You also had 2 mod 100 as 2, which makes sense since if you > divide 2 by 100 you have a remainder of 2. > > 18 mod 4 would be 2 (4 goes into 18 4 times (which we do > not care about) with a remainder of 2, which is the value > of the expression. > > The tricky ones are the negatives, but it still holds > together (as math should). Let's look at 4 mod -3. How > many times does 03 divide into 4? -1. And what is the > remainder? 1. > > 4 mod -2 : -2 goes into 4 -2 times with a remainder of 0 so > 4 mod -2 = 0 > > I hope this helps. This is one of those concepts that is > really simple once it clicks. Hopefully now it will click. > Feel free to ask follow-ups. > > On 12/29/14, ChristineBunny wrote: >> High-school education, >> Procedural-programing education, >> Fair bitwise-operation education, >> >> tag words involved with this question: >> [ &37; Operator, Matrices, remainder of division, >> Modulus/Cross-Product ] >> >> tutoring request: >> Please help me understand the pattern of these results. >> What aspects of math or bit manipulation is occurring to >> result in these answers? Please help me visualize the >> process occurring to achieve these results. >> These answers are calculated by the Secondlife physics >> engine consistently. >> >> 2 &37; 100=2 >> 3 &37; 100=3 >> 100 &37; 2=0 >> 100 &37; 3=1 >> 4 &37; -4=0 >> 4 &37; -3=1 >> 4 &37; -2=0 >> 4 &37; -1=0 >> 4 &37; 1=0 >> 4 &37; 2=0 >> 4 &37; 3=1 >> 4 &37; 4=0 >> 4 &37; 5=4 >> 4 &37; 6=4 >> 4 &37; 7=4 >> 4 &37; 8=4 >> 4 &37; 9=4 >> 4 &37; 10=4 >> 4 &37; 11=4 >> 4 &37; 12=4 >> 4 &37; 16=4
On 1/12/15, ChristineBunny wrote: > > > Mr/Ms Modulo Dec 30, 2014 > That was a fantastically educational answer! and yes it took > this long for me to get back into it considering the Christmas > insanity! Thank you so much for a very helpful response! This is > going to be very useful to me in my work! thank you! *happy > hugs!* Good tutorial! > > so > 16 mod 2 = 0 > 16 mod 8 = 0 > 17 mod 8 = 1 > 75 mod 50 = 25 > 75 mod 25 = 0 > 2 mod 490834752349 = 2 > > thank you for helping me understand! *^-^* > > > > On 12/30/14, Modulo wrote: >> The operator you are designating &37; is usually (in the US >> anyway) called mod. So where you write 10 &37; 2 I would >> normally write 10 mod 2. >> >> Basically what the value of "a mod b" is the remainder when >> a is divided by b. >> >> Looking at some of your examples, the last 9 of them had a >> value of 4 because if you divide 4 by a number that is >> bigger than 4 you will always get a remainder of 4 >> >> You also had 2 mod 100 as 2, which makes sense since if you >> divide 2 by 100 you have a remainder of 2. >> >> 18 mod 4 would be 2 (4 goes into 18 4 times (which we do >> not care about) with a remainder of 2, which is the value >> of the expression. >> >> The tricky ones are the negatives, but it still holds >> together (as math should). Let's look at 4 mod -3. How >> many times does 03 divide into 4? -1. And what is the >> remainder? 1. >> >> 4 mod -2 : -2 goes into 4 -2 times with a remainder of 0 so >> 4 mod -2 = 0 >> >> I hope this helps. This is one of those concepts that is >> really simple once it clicks. Hopefully now it will click. >> Feel free to ask follow-ups. >> >> On 12/29/14, ChristineBunny wrote: >>> High-school education, >>> Procedural-programing education, >>> Fair bitwise-operation education, >>> >>> tag words involved with this question: >>> [ &37; Operator, Matrices, remainder of division, >>> Modulus/Cross-Product ] >>> >>> tutoring request: >>> Please help me understand the pattern of these results. >>> What aspects of math or bit manipulation is occurring to >>> result in these answers? Please help me visualize the >>> process occurring to achieve these results. >>> These answers are calculated by the Secondlife physics >>> engine consistently. >>> >>> 2 &37; 100=2 >>> 3 &37; 100=3 >>> 100 &37; 2=0 >>> 100 &37; 3=1 >>> 4 &37; -4=0 >>> 4 &37; -3=1 >>> 4 &37; -2=0 >>> 4 &37; -1=0 >>> 4 &37; 1=0 >>> 4 &37; 2=0 >>> 4 &37; 3=1 >>> 4 &37; 4=0 >>> 4 &37; 5=4 >>> 4 &37; 6=4 >>> 4 &37; 7=4 >>> 4 &37; 8=4 >>> 4 &37; 9=4 >>> 4 &37; 10=4 >>> 4 &37; 11=4 >>> 4 &37; 12=4 >>> 4 &37; 16=4