Very simply, geometers examine a pair of rectangles on graph paper and find a translation and rotation to demonstrate their congruence. A couple of questions follow to stimulate critical thinking about other possibilities.

Young mathematicians investigate the use of symmetry in graphic design. After first learning about reflection, translational, and rotational symmetry, children use this new knowledge to identify symmetry in letters of the...

A triangle rests in quadrant two, from which your class members must draw reflections, both over x=2 and x=-2. This focused exercise strengthens students' skills when it comes to reflection on the coordinate plane.

Model real-life structures with mathematics. A project-based lesson presents a problem situation requiring classes to develop a function to model the St. Louis Arch and the Rainbow Bridge in Arizona. They create their models by...

Young geometers flex their transformation muscles in this brief but powerful exercise using dilations and translations to develop the similarity of circles. The plan provides guidelines to help learners navigate a pair of...

Two triangles are displayed on a coordinate plane. Youngsters apply a reflection and a translation to demonstrate their congruence. This exercise makes a terrific tool for teaching these concepts, or a way to assess learning.

While it may seem incredibly obvious to the geometry student that congruent sides make congruent triangles, the proving of this by definition actually takes a bit of work. This exercise steps the class through this kind of proof by...

Comparing the movement of graphs geometrically when small changes are made to the parent function motivates this collaborative discussion on the transformations of functions to their various forms. Vertical and horizontal shifts due to...

The task at hand is to partition a hexagon into two, four, and eight congruent figures. Make sure to give your wizards a sheet of triangle grid paper on which to decompose the hexagons. Have them explain which rotations, reflections, or...

Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great...

Geometers prove that triangle PQR is congruent to triangle ABC by describing any combination of rotations, reflections, and translations that would prove it so. There is only this single task on the handout, but a detailed explanation of...

Students will be in groups and plot given points. From the given points the students will plot the appropriate reflection or translation.

Twelve problems offer practice working with the translations and reflections of trigonometric graphs. They are given with each step to the solution cleverly revealed one at a time. You can work each step of the problem then click the...

An introductory look at the interactive Geometer's Sketchpad in terms of using it to explore rotations, translations, and reflections. Only a beginner's amount of skill with the program is needed. Exploration questions are given for the...

In this activity, students will investigate the relationship among the three types of rigid transformations - translations, rotations, and reflections.

This site is a Geometer's Sketch Pad lesson plan where students explore tessellations through reflections, rotations, and translations.

Students will discover how to move a function up, down, to the right or left or reflect it.

Students move their cursor in this activity center to occupy a unique point on a background letter "F" in quadrant 1. Students then together follow a rule for going to a different point (such as "use the opposite of the original x...

Shodor Education Foundation provides an applet that "allows the user to explore the world of transformations, reflections, and rotations. It allows the user to translate triangles, squares, and parallelograms on both the x and y-axes."

Find a quick, concise explanation of the transformations of graphs: translations, reflections and rotations. Examples are given and clearly explained for each transformation.

This site presents information on the three basic transformations of figures in a plane: Reflections, Rotations, and Translations.

In this activity, students describe how to move a shape from one place to another in a plane. They learn about translations, rotations, and line reflections. [Requires Adobe Reader.]

This activity is designed to reinforce the concepts of reflections and translations by having the students create a virtual puppet using Cabri Jr. As they construct their puppets, students will reinforce their understanding of...