**Task**

Use the icons from the upper left panel to choose up to three
transformations to be successively applied to the red shape. The black
shape shows the resulting image. Use the icons from the lower left panel
similarly. The blue shape shows the results from successively
transforming the red shape using the lower left panel. Consider the red
shape in the interactive figure below. Drag it and observe the behavior
of its image after one or more successive transformations are applied
using the top left panel. Choose a different shape and observe the
behavior of its image under the same transformation or composition.
Change the shape of the red square or red triangle by dragging it from
an edge or vertex while pressing the Control key. Change their
orientation by dragging them from a corner. Which single transformation
or composition of transformations, if any, would have the same effect on
the original figure? Use the lower left panel to test your conjecture.

**Discussion**

Using dynamic geometry software, teachers can ask students to
consider what happens when transformations are composed. Teachers can
then ask students to make conjectures about which single transformation,
if any, would have the same effect on the original figure as the
composition does. A challenging assessment of students' understanding of
transformations can be given if two congruent shapes are given and
students are asked to specify a transformation or composition of
transformations that will map one to the other.

**Take Time to Reflect**

- What new
insights into transformations can students gain as they work on activities like
this?
- What are
specific ways in which middle-grades students can identify each of the
transformations or composition of transformations that would have the same
effect on the original figure as the composition does?
- What are some
ways in which teachers can assess students' understanding of transformations?