In this lesson, students use the language of transformations to produce, describe, and investigate patterns in the plane. This is a direct extension of earlier work with triangles, where three triangles were arranged in the plane to show that the sum of the angles in a triangle is 180 degrees, and where four copies of a triangle were arranged in a large square, cutting out a smaller square in the middle.

Throughout this unit, students have identified different types of rigid transformations, including translations, rotations, reflections, and sequences of these. They have also used rigid transformations to define congruence and investigate the sum of the angles in a triangle. In this lesson, students apply this learning in a creative way, as they examine patterns of shapes. 

Both of the activities in this lesson are optional. Depending on time, students can complete one or both activities. In the first optional activity, students create a tessellation using given shapes. In the second optional activity, students create a design of their choosing that highlights rotational symmetry. In both activities, students must use the structure of rigid transformations to create a design (MP7).