Investigating+geometry


 * Quadrilaterals Unit**

__**Goal**__: Students investigate different types of quadrilaterals and apply knowledge of triangles to classify, describe and prove their characteristics.

A. Students will define quadrilaterals, distinguish between examples and nonexamples (Construct a concept, communication and comprehension)
 * __Objectives__**:

B. Students investigate different types of quadrilaterals, and observe their properties. They use deductive reasoning to prove their observations (willingness to try, discover relationship)

C. Students will learn (visual, auditory and kinesthetic learning) and be able to appropriately use the words: quadrilateral, parallelogram, rectangle, rhombus, square, trapezoid, kite, and describe the differences between them. (comprehension and communication)

D. Students will be able to visualize a Venn diagram of different classes of quadrilaterals.

E. Students use their understanding of the area of a rectangle to develop expressions for areas of: parallelogram, square, rhombus, trapeziod, and kite. (discover the relationship, creative thinking)

F. Students recall the formulas for the areas of the different quadrilaterals. (simple knowledge)

G. Given some information about a quadrilateral, students finds necessary data to calculate its area and perimeter. (algorithmic skill)

H. Students use their knowledge to slove problems that involve applying theorems they have proved and formulas they have found. (application)

Lesson plan for objective B

Have Students discover the relationships of quadrilaterals to the properties of diagonals and interior angles by: (See worksheets) Discuss the concepts with the students to create a chart that shows the relationships of diagonals and interior angles of the different quadrilaterals. (See graph)
 * 1) Starting with the relationships of the diagonals, find a specific quadrilateral.
 * 2) Starting with the relationships of quadrilaterals, find the relationship of the diagonals.
 * 3) Starting with the relationships of the interior angles, find the specific quadrilateral.
 * 4) Starting with the diagonals of parallel sides and the relationships of the interior angles of created, find the specific quadrilateral.

**Have students learn properties by repetition**