For this geometry project, each student needs two sheets of ¼-inch Cartesian graph paper, a ruler, scissors, a colored pencil, a protractor and construction paper. Tell the students to draw and cut out four different geometric figures, approximately 1 inch by 1 inch, on the construction paper, such as squares, rectangles, triangles or a rhombus. Show them how to draw an x- and y-axis using the colored pencil. On the blackboard, write four sets of coordinates, one for each of their shapes. Tell the students to begin at (0,0), trace the shape, color it in and translate each shape to the appropriate coordinates. When the shape is translated to the appropriate coordinates, trace the shape and lightly color it in. Try this activity again, but use angles and distance to direct the translation.
To make a symmetrical design from an asymmetrical shape, you need ¼-inch Cartesian graph paper, a ruler, a protractor and colored pencils or crayons. Design an asymmetrical shape approximately 1 inch by 1 inch. Decide the rule for the translation, such as sliding the shape ¾ inch to the right. Whatever you do in one direction from the starting point, you must do in the opposite direction from the starting point. Creatively color the shapes.
A tessellation is a design of geometric shapes that completely covers a plane with no overlapping or gaps. To make a tessellation by translation, each student needs a piece tag board measuring 3 inches by 3 inches, a ruler, scissors, colored pencils or crayons and a 12-inch square piece of white paper. Tell the students to make an interlocking shape from the 3-inch square piece of tag board. They should cut a shape from one edge of the tag board and tape the shape to the opposite edge of the tag board. The students should cover the 12-inch square of paper by translating, or sliding, the shape in rows and tracing the shape in each position. When the tessellation is finished, they should creatively color the design.
To find examples of translations in the world around us, each student needs access to a digital camera. Tell the students to take a week to find five, or more, examples of translations, such as wallpaper designs, tile designs or the spacing of street lights. They should take a picture of each and download the photos to a class picture file. View the translation examples in class and discuss whether or not they meet the definition for this type of transformation.