Students start with a simple figure like this pentagon. For all of these transformations, the student should make them on the geoboard, not just on the geodot paper. It tends to slow the student down so that they make fewer errors. Students learn that a transformation either slides, flips or turns a geometric figure. Above, the student flips, or reflects, the pentagon, first vertically and then horizontally. Before fourth grade, students called these transformations flips. The term used in fourth grade on is a reflection. Highlighting the "fl" in reflection is a way for students to relate
reflections to flips, a term that seems easier for students to grasp. Students who struggle to see the reflections can flip the geoboard over sideways. If the geoboard is the least bit translucent, the student can see what the figure looks like reflected. The geoboard can be flipped top to bottom to see the vertical reflection.
Students then translate the figure vertically and horizontally. Before fourth grade, this movement is called a slide. The term used in fourth grade on is a translation. Again, highlighting the "sl" connects the new term with the term slide, which is easier to understand. Students should also be shown that a slide can also be diagonal. A question to ask students is why the vertical reflection and translation look different, and why the horizontal reflection and translation look the same for this figure.
The final transformation is the rotation, which students have called turns before fourth grade. The students should definitely use the geoboard for their rotations, making sure that a point on the figure hits the center point. The student should then rotate the actual geoboard first clockwise, and then record on the paper what they see. They should then start from the original position and rotate the geoboard counterclockwise. The rotation is the hardest transformation for many students to see visually, so to avoid errors, students should use the geoboard as a tool.
