Module Design Format:

 

Name of Module:         Properties of various types of triangles

 

Topic (S):                           Constructions of Equilateral, Isosceles, Scalene triangles using Geometer Sketchpad.

 

Courses:                             Math 299---Geometry and Trig.

 

Designed by:                     Panagos Papageorgiu, Vinay Duggal

 

 

Duration:                            1 Hour and 45 minutes

 

Brief Description:         This module focuses on various types of triangles and investigates their properties, through constructions. Students will work in small groups using geometer sketchpad software as well a traditional means such as compass straight edge and protractor.

 

 

Prospective teachers will be taught in a manner similar to the way they should teach. Students are encouraged to discuss and collaborate among themselves and with their instructor. The use of technology as a problem solving tool and applications in art and physics will be incorporated.

 

                                                  

                                                  

 

Description of Learners: Potential middle school teachers with strong background in

                                                   College Algebra.

 

 

Goals:                   To make students appreciate the power of strict geometric constructions and the logical reasoning in which constructions are based.

 

Objectives:        Students will be able to:

a)       Construct various types of triangles using the geometer sketchpad.

b)      Derive logical conclusions based on the construction process.

c)      Understand the generalizations that define the properties of various types of triangles.

d)      Apply properties of triangles in art and physics.

 

 

 

 

Instructional Strategies: Step 1: Teacher demonstrates the construction of an

equilateral triangle using geometer sketchpad.

 

Step 2: Students organized in groups will work on the following questions. “Justify the claim that the triangle we constructed is an equilateral.”, “Use similar approach to construct an isosceles triangle and then a scalene one”

 

Step 3: Students demonstrate their findings and come up with conclusions and generalizations: “ The Intersection of three identical circles make equilateral triangle, intersection of three circles with only two being identical makes an isosceles triangles and the intersection of three different circles makes a scalene triangle.”

 

Step 4: Students will use the geometer sketch pad to create an art involving triangles and circles (art integration).

 

Step 5:

 

I) For Home work do the same constructions using only compass and straight edge.

 

                                                   II)            Use the geometer sketch pad to construct a regular hexagon.

                                                  

III)               Find samples of Etchers work involving circles and triangles.

 

Assessment:                      1) Teachers collects hard copies of the groups’ final outcome. The work is evaluated for clarity and accuracy.

 

                                                   2) Students will write a paragraph describing the work done in the classroom. (Writing across the curriculum)                   

                                                  

3) A rubric will be used to record and evaluate the students’ behavior during class.

 

4) A quiz will be given during the next class.

 

 

 

 

 

 

 

 

Resources:                         1) Geometer sketch pad software.

 

                                                   2) Geometric instruments

 

                                                   3) Art samples involving circles and triangles.

 

                                                   4) Handouts outlining the steps involved in the constructions.

 

 

Site Map:                             A “Smart classroom”.

 

 

On-Line Components:

 

1)      The entire module posted on blackboard.

2)      Using the discussion board on Blackboard for issues related to their homework assignments.

 

Content Outline:            

 

                                                   Types of triangles: -    

- Equilateral

                                                                                                      - Isosceles

                                                                                                     - Scalene

 

                                                   Constructions of the above using points of intersection of circles.

 

Intersection of forces applied on the three vertices of triangles. (Application of math in physics)

 

 

Suggested next Step:                     1) Types of polygons.

 

                                                                    2) Construction of regular polygons.