This lesson is an investigation of
four-sided polygons, aka quadrilaterals.
Lesson objective: To develop a quadrilateral hierarchy with definitions.
Quadrilaterals under investigation: Square,
Rectangle,
Trapezoid, Isosceles Trapezoid, Parallelogram, Rhombus, and Kite.
NCTM Standards (2000):
Analyze
characteristics – understand
the
relationships among the angles, side lengths, perimeters, areas, and
volumes of
similar objects.
Specify
locations – use coordinate
geometry
to examine special geometric shapes, such as regular polygons or those
with
pairs of parallel or perpendicular sides.
Use
visualization – use geometric
models to
represent and explain numerical and algebraic relationships.
Teacher Section
Lesson Plan
Assessment
Assignment 1:
Informal
Investigation of Area
Sketchpad Student
File Sketchpad Reference File
Assignment 2: Investigation of Area Formulas
Sketchpad File
Assignment 3: Investigation of Diagonal Properties
Assignment 4: Flowchart Development (additional options)
Assignment 5: In Class Graphing
Exercise
Student Section
Assignment 1:
Informal Investigation of Area
Assignment 2:
Investigation of Area
Formulas
Assignment 3:
Investigation of
Diagonal Properties
Sketchpad
File
Assignment 4:
Flowchart Development
Summary of Assignments
Assignment 1: Students are asked to determine the area of semi-novel
quadrilaterals using their knowledge of squares and triangles in
Geometer's Sketchpad®.
Assignment 2: Students are asked to investigate the formulas of
quadrilaterals given the formula of a trapezoid using Geometer's
Sketchpad®.
Assignment 3: Students are asked to investigate the properties of the
diagonals and complete a summary chart.
Assignment 4: Students are asked to complete a quadrilateral hierarchy
chart and justify placement of polygons.
Assignment 5: Students investigate how a generic quadrilateral is
related to more specific quadrilaterals in this in-class graphing
exercise.