First time posting, I hope this is being done in the right location and format.
I am looking for software I can use, online, to show students how to work with different shapes (circles, squares, nets) and walk the student through how to find area and perimeter. I would like to have the shape on the screen, being able to change its orientation and size, and write on it (addition, explanations, labeling).
There are many out there, but I am not comfortable downloading unknown software.
Can anyone suggest something decent. I'm willing to pay, but if you know of a tried and true one which is free please let me know.
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?