Students can rotate, flip, reflect and slide their own creations while exploring symmetry. Give each student a paper with grid lines or dots approximately every centimeter. Instruct them to draw or shade in a design in the center of the paper. They must then draw the symmetrical reflection of that design next to the original. The vertical flip can be done by drawing the symmetrical reflection of the design on top of the original. Allow students time to explore and re-create the design in a variety of ways. A repeated shape that is arranged without overlap is called a tessellation. Discuss examples of symmetry on volunteers' papers.
Purchase transparent mirrors at a teacher supply stores or online. These tools allow mathematicians to look through the glass of the mirror, viewing both the reflection and the design on the other side of the mirror. Photocopy one half of a black-line master sketch of a design, such as a butterfly. With the transparent mirrors, students should draw the reflection of the butterfly completing the picture. Instruct them to draw one half of an image on blank paper and trade papers with a partner. Using the transparent mirror, students can complete their partner's sketch.
Symmetry is everywhere in nature. Ask students to clip out pictures of symmetry in nature found in magazines, calendars and newspapers. Using transparent mirrors, instruct students to draw the line of symmetry through each picture. A line of symmetry is the imaginary line that divides a shape in half with both sides of the line being balanced in size and shape. Prepare students to expect that symmetry may not be precise in nature, so they will need to be slightly forgiving with the images. Before moving on to the next image, remind students that many objects in nature may have more than one line of symmetry.
Arrange for your class to borrow a set of almanacs from the library or take the class to the school library with pencils and paper in hand. Have students study the great variety of flags that represent countries and states throughout the world. They should take notes on the forms of symmetry they find on the flags. Point out how color, images and shapes are used in symmetrical designs on flags. Referring to their notes, invite students to design a new flag on a blank paper. Remind them to include symmetry using any combination of color, images and shapes.