Roller Coaster is a simulation where you can design a roller coaster course by changing several variables such as the height of two hills, the size of the loop, initial speed, the mass of the car, friction and gravity. You then run the simulation to see if the car makes it to the end, falls off the track, gets stuck part way, or hovers in the air (as my children discovered when they lowered gravity too much.)

Although Roller Coaster does not have a grade associated with it, it would be most effective as a classroom learning tool at a grade 8 - 10 or level. My kids (grades 2 and 4) loved it and played with it for a long time, but I'm not sure how much learning was taking place.

In terms of knowledge representation, a roller coaster simulation is a great way to introduce students to physics concepts. A lot of information in physics can be very dry and difficult to understand and visualize, so having a simulation that allows students to change variables and immediately see the results is very beneficial.

The virtual geometry manipulatives are a set of tools on a site dedicated to math manipulatives from K - 12. One activity that particularly impressed me was the congruent triangles activity. Students can build triangles using SSS, SAS and other rules. With geometry especially, it is important for students to be able to visualize objects. In the past, students could use represent their ideas through sketches and models. With technology, a rule like SSS becomes much clearer when students actually have the opportunity to manipulate the sides of a triangle and build it themselves.

References:

Davis, R., Shrobe, H., & Szolovits, P. (1993). What is a knowledge representation? Retrieved March 30, 2005 from http://medg.lcs.mit.edu/ftp/psz/k-rep.html

National Library of Virtual Manipulatives for Interactive Mathematics (Utah State University) http://matti.usu.edu/nlvm/nav/category_g_2_t_3.html

Roller Coaster http://www.funderstanding.com/k12/coaster/