Big Idea:

Big Idea 3

Congruent parts of a polygon map to its congruent parts under a rotation or reflection.

1 week

Evidence of Understanding

  • describe qualities of polygons
    • use examples and non-examples to justify a figure is a polygon
    • distinguish irregular and regular polygons using congruent sides and congruent angles
    • create and justify all of the lines of symmetry for a regular polygon (use paper folding, drawing, reflective devices, etc.)
    • use isosceles triangles to understand qualities about regular polygons
      • decompose regular polygons into congruent triangles
      • use properties of circles to construct an equilateral triangle
      • use properties of circles to construct a regular hexagon inscribed in a circle
         
  • explore congruent parts of regular polygons using lines of reflection and center of rotation
    • demonstrate how rotational symmetry and line symmetry carry a polygon onto itself
      • describe rotations as preserving congruence (isometry) and orientation
    • use tools to justify that the line of symmetry, or line of reflection, is the perpendicular bisector
      • construct the perpendicular bisector
      • explain that the distance of each point of the figure from the line of reflection (line of symmetry) is the same
    • generalize qualities about regular polygons using rotational and line symmetry
      • Example: connect lines of symmetry with congruent parts within a polygon and the degree of rotation that carries a polygon onto itself
    • specify the reflection or rotation that carries a polygon onto itself
      • calculate the degree measures that can carry a polygon onto itself
      • use the coordinate plane to write the equation of a horizontal or vertical line that carries a polygon onto itself

Develop conceptual understanding:

polygon, regular polygon, irregular polygon, equilateral, inscribed, rotate, reflect, rotational symmetry, line symmetry, isometry, orientation, line of symmetry, line of reflection, perpendicular bisector

Supporting terms to communicate:

examples, non-examples, congruent, side, angle, triangle, square, pentagon, octagon, preserve, perpendicular, bisect, degree measure, clockwise, counterclockwise

Core Resource

A core resource supports multiple days of instruction.

Instructional Routine: Sharing Skepticism

The primary goal of this instructional routine is to support students in constructing and critiquing mathematical arguments.
 

  • Counting Triangles
    Students will use transformations implicitly to count the number of shaded triangles in a diagram. During sharing of strategies and through annotation, the transformations used will be made explicit.
    Resource:
    Counting Triangles

    Students will use transformations implicitly to count the number of shaded triangles in a diagram. During sharing of strategies and through annotation, the transformations used will be made explicit.

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