Geometry

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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?
  • Where did the Platonic Solids come from?
Content: 
  • Definitions for line, segment, ray, angle (acute, obtuse, right), complementary/supplementary angles, intersecting/parallel lines, regular/irregular polygons, circle, triangles (scalene, isoceles, right), quadrilaterals (parallelograms, rectangles, squares, rhombus, trapezoid), and the relationship between the terms.
  • Platonic solids and their relationship to each other, Euler's Law relating edges and vertices
  • Similarity vs. Congruence
  • Symbols for geometric terms
  • Types & properties of triangles and quadrilaterals
  • Formulas for finding area of quadrilaterals, triangles, and circles and how were they derived

 

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
*Build platonic solids and combine various shapes

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)
  • Straw Polyhedra 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
Multicultural Dimension: 
    Extensions: Read Flatland - This book symbolically uses geometric shapes to connect with the social issues of caste systems and  fairness.
Integrated Learning: 
  • Product design and packaging (Arts and Engineering)
  • Evolution of the Platonic Solids (Math History)
  • Geometry Story (Language Arts)
  • Extensions: Read Flatland. (Language Arts and Humanities)