The mathematics of this unit is based on the repeated use of just two geometric shapes: the square and the right isoceles triangle formed by cutting a square in half along its diagonal. These squares and triangles can be combined to form larger squares and triangles as well as many other geometric shapes. Many geometric designs are constructed by repeatedly using the same shapes or shape combinations in new locations, orientations and reflections. The element of the design which is repeated is called a unit of that design. Any movement or reflection of a shape that does not change the shape itself is called a transformation. Students use the terms slide, flip and turn to talk about the transformations they perform on geometric shapes. This unit encourages students to compare geometric designs to see how they are alike and different. When two geometric shapes are identical in all lengths and angles, they can be said to be congruent, or the same. If a shape does not change when it is reflected along a line through the center, it is said to have bilateral symmetry. When a shape does not change when it rotates through a particular angle, it is said to have rotational symmetry. Some of the designs students will create in this unit will have bilateral or rotational symmetry.