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0.3.14 Rotate and Tessellate Lesson Objectives Build and study complex patterns using the language of transformations Required Materials graph paper blank paper isometric graph paper copies of blackline master geometry toolkits Setup: Deducing Angle Measures (10 minutes) Access to geometry toolkits. Distribute one half-sheet (that contains 7 shapes) to each student. Statement Anticipated Responses Your teacher will give you some shapes. 1. 6, 1. How many copies of the equilateral triangle can you fit together around a single vertex, so that the triangles’ edges have no gaps or overlaps? What is the measure of each angle in these triangles? 2. Measures of angles: square: . hexagon: . parallelogram: and . right triangle: and . octagon: . pentagon: , , and . 2. What are the measures of the angles in the a. square? b. hexagon? c. parallelogram? d. right triangle? e. octagon? f. pentagon? Setup: Tesselate This (35 minutes) Access to geometry toolkits. Suggest students cut out a shape and trace it to make many copies. Show examples of tesselations and an example of specifying a translation that shows that a figure is a tessellation. Statement Anticipated Responses 1. Design your own tessellation. You will need to Answers vary. decide which shapes you want to use and make copies. Remember that a tessellation is a repeating pattern that goes on forever to fill up the entire plane. 2. Find a partner and trade pictures. Describe a transformation of your partner’s picture that takes the pattern to itself. How many different transformations can you find that take the pattern to itself? Consider translations, reflections, and rotations. 3. If there’s time, color and decorate your tessellation. Setup: Rotate That (35 minutes) Show an example of a figure that has rotational symmetry, and ask students to describe a rotation that takes the figure to itself. Provide access to geometry toolkits. If possible, access to square graph paper or isometric graph paper can also be helpful. Statement Anticipated Responses 1. Make a design with rotational symmetry. Answers vary. 2. Find a partner who has also made a design. Exchange designs and identify a transformation of your partner’s design that takes it to itself. Consider rotations, reflections, and translations. 3. If there’s time, color and decorate your design. Lesson Summary (5 minutes)