# Geometry and Transformations

Essential Questions:
• How has geometry inspired artists?
• How is geometry used in product design and graphic arts?
• How are geometric shapes defined and classified by their properties?
Content:
• Definitions for line, segment, ray, angle (acute, obtuse, right), non/collinear points, midpoint, complementary/supplementary angles, intersecting/parallel lines, regular/irregular, congruent, circle, triangles, quadrilaterals, and other polygons
• Use the correct notations for geometric terms
• Types & properties of triangles and quadrilaterals
• Angular measurements in circles, triangles, and quadrilaterals
• Formulas for finding area of quadrilaterals, triangles, and circles and how were they derived
• Types of translations: translation (slide), rotation (turn), reflection (flip)

Skills and Processes:

*Find missing angle measurements using complementary/supplementary properties, and 180 in a triangle and a line
*Calculate the degrees in a polygon and find each angle measurement for regular shapes
*Measure and draw angles accurately with a protractor
*Explain the differences between different types of triangles and quadrilaterals; know the properties of each
*Use the correct formulas for finding area of 2D shapes: quadrilaterals, triangles, circles
*Use a Mira to reflect and check for lines of symmetry
*Perform three types of transformations on a figure (slide, flip, turn)
*Combine transformations to create a tessellation

Assessment:
• Written Test
• Geometry Story: Write a short story that uses geometric shapes and properties symbolically (e.g. A love letter from a square to a circle)
• Tessellation Project
• Design packaging for a new product - find surface area from the 2D shapes that make the sides of the package.
Resources:
• Protractors, rulers, geometric shape kits (plastic/cut-out), tangram sets
• Tangram sets
• Origami constructions
• <Straw Polyhedra>
• Flatland by Edwin Abbott
• Slides, Flips, and Turns
• Examples of Escher tessellations
• Tessellation Exploration software (Tom Snyder Productions)
Multicultural Dimension:
• The work and life of MC Escher
• Extensions: Read Flatland - This book symbolically uses geometric shapes to connect with the social issues of caste systems and  fairness.
Integrated Learning:
• Geometry and Art: Tesselations
• The work of MC Escher
• Product design and packaging (Arts and Engineering)
• Graphic Arts
• Geometry Story (Language Arts)
• Extensions: Read Flatland. (Language Arts and Humanities)