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Mathematics |

Posted Mon Nov 1 19:50:54 PDT 2010 by Richard Lasky (Richard Lasky).

Wayne State University, Detroit, MI USA

Materials Required: Computer with Geometer's Sketchpad installed

Activity Time: 55 minutes

Concepts Taught: Basis Geometry

Lesson Plan Title: Using Geometer's Sketchpad to study triangles

Concept / Topic To Teach: Geometry/Sum of angles of a triangle equal 180°

Standards Addressed:

Michigan High School Mathematics Content Expectations Strand 3:Geometry and Trigonometry -- Standard G1.2.1 Prove that the angle sum of a triangle is 180° and that an exterior angle of a triangle is the sum of the two remote interior angles.

General Goal(s):

Using Geometer's Sketchpad, a virtual manipulative program that can be used for the teaching of Geometry the students will demonstrate that the sum of the inside angles of a triangle will always be 180° while the triangle changes shape and that the exterior angle will always remain the sum of the two remote interior angles.

Specific Objectives:

The students will be able to demonstrate how to calculate the sum of the inside angles and manipulate the shape to demonstrate that the total will not change. This will aid their ability to visualize the problem as the first step in proposing a proof.

Required Materials:

Computer with Geometer's Sketchpad software installed

Anticipatory Set (Lead-In):

Describe the problem to the students

The students will already have had a tutorial on the use of the software

Step-By-Step Procedures:

Procedure for calculating the sum of the inside angles of a triangle using Geometer's Sketchpad

1. Open Geometer's Sketchpad software by clicking on icon.

2. Select the open Polygon edges tool.

3. Create a triangle by dragging three points around to form the triangle.

4. Select the Translation tool -- arrow.

5. Start at the top vertex of the triangle and select each of the three vertices in counterclockwise order.

6. Select Measure and then Angle.

a. GSP will label the vertices

b. GSP will measure the angle ABC and display in the upper left corner

7. Repeat the process for the other two angles

8. Now calculate the sum of the angles

a. Select Number and then Calculate

9. Select each angle measurement and then the + sign in the Calculator object

a. Select all three angles in order with the + sign in between

b. Select OK

10. The total of the three angles will be displayed - 180°

11. Use the translation arrow tool to move any vertex and observe that the individual angles change but the total remains at 180°.

For the second part:

12. Select two points on an edge of the triangle and construct a line.

a. Select two points with the arrow

b. Select Construct then Line

13. Create a point on the line outside the triangle.

a. Select the line with the arrow

b. Select Construct then Point on the Line

c. If necessary, move the point outside the triangle

14. Select two points on the triangle adjacent to the point and then the point

15. Measure the outside angle

a. Select Measure then Angle

b. The outside angle measurement is displayed

16. Calculate the outside angle from the sum of the two remote angles.

a. Select Number and then Calculate

b. Select the first opposite angle in the upper left hand side of the window

c. Select + sign on the calculator object

d. Select OK on the calculator

e. The total angle will be displayed and will be the same as the exterior angle.

17. Use the arrow to move any vertex of the triangle

a. Observe that the sum of the two angles and the measurement of the outside angle remain the same even though the individual angles change.

The resulting construction is show on the attached page.

Plan For Independent Practice:

The students will be able to use the software at their next computer lab session to explore the construction method and the results

Closure (Reflect Anticipatory Set):

Using Geometer's Sketchpad provides the student with another tool to help understand Geometry concepts of all kinds

Assessment Based On Objectives:

Students will be asked to duplicate the project and produce a drawing similar to the one shown attached

Adaptations (For Students With Learning Disabilities):

Students with Learning Disabilities will be provided the accommodations required to provide them with access to the computer.

Extensions (For Gifted Students):

Gifted students can be provided assignments that require more complex use of the software.