The interactive pan balance uses multiple shapes with different values, allowing students to investigate what happens as different shapes are placed on the balance. This student interactive, from Illuminations, provides an interesting environment in which students can consider the concept of equivalence.

Students carry out an interactive, geometric "proof without words" for the algebraic technique of completing the square in this interactive. The page also includes directions and a link to the final solution.

Students use division skills to figure out how much each character gets. They also have the capability to design their own situation with dinosaurs dividing waffles, penguins sharing apples, or many other situations.

Students explore the relationship between theoretical and experimental probabilitiesin this student interactive, from Illuminations. Students use this "box model" as a statistical device to simulate standard probability experiments such as flipping a coin or rolling a die.

Students investigate how changes in the scale factor influence the ratio of perimeters and the ratio of areas between two figures.

Composing Transformations--This is part four of a four-part e-example from Illuminations that features interactive figures that allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. In this part, Composing Transformations, the users are challenged to compose equivalent transformations in two different ways. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math Investigations.

This applet simulates two runners moving along a track and creates a graph of the time-versus-distance relationship of their motion. Students then observe the simulated races as they happen and relate the changing positions of the two runners to dynamic representations that change as the events occur. Students can predict the effects on the graph of changing the starting position or the length of the stride of either runner. They can observe and analyze how a change in one variable, such as length of stride, relates to a change in speed. This computer simulation uses a familiar context that students understand from daily life, and the technology allows them to analyze the relationships in this context deeply because of the ease of manipulating the environment and observing the changes that occur.