An Introduction to Perimeter and Area Using The Geometers Sketchpad

Objective:

Students will use the Geometers Sketchpad to construct squares and triangles. Students will use the Geometers Sketchpad to explore the perimeter and area of squares and triangles.

NCTM Standards:

This lesson incorporates the following NCTM standards: Standard 1: Mathematics as Problem Solving, Standard 3: Mathematics as Reasoning, Standard 7: Computation and Estimation, Standard 8: Patterns and Functions, Standard 12: Geometry, and Standard 13: Measurement.

Previous lessons:

Prior to this lesson, students will have had an introduction to the Geometers Sketchpad program. Students will be able to identify and name polygons. They also will have had experience measuring plane figures (squares and triangles) and calculating the perimeter and areas of those figures.

Lesson Overview:

This lesson is designed for sixth or seventh grade middle school students in their study of geometry. Students will use the program to explore and problem solve relationships between perimeter and area of squares and triangles. This is an introductory type of lesson and will use the grid portion of the program. This will allow for ease of constructing the polygons. It will also lead to a more indepth understanding of the perimeter and areas of the figures, as well as aid in estimating the perimeter and areas of the polygons. The following may be used as a worksheet guide for students.

This lesson will use the Geometers Sketchpad to help you construct squares and triangles. You will use the Geometers Sketchpad to explore the perimeter and area of squares and triangles. Before getting started, go to the top menu bar and pull down the menu under Graph. Drag down the cursor to Snap to Grid and then repeat, but this time Hide Axes. You will now have a grid of dots that look similar to a geoboard. The size of your computer monitor and the size of the window of your sketchpad will determine the size of the array of dots you have. Drag the bottom right hand square of your window until you have an 8 by 6 array of dots. You are now ready to explore perimeter and area!

1. Construct as many different size squares as possible. How many did you find?

2. Measure the perimeter and area of each square. (Remember to select each vertex of the polygon, using the shift key so that all are selected at the same time, pull down the Construct menu and highlight polygon interior. Next go to the Measure menu and highlight perimeter and repeat to measure the area.) What are the perimeter and area of each square? What do you notice about the area numbers? Did any of the squares have the same perimeter as area?

3. Start a new sketch. Remember to set up the grid as you did before. Explore with rectangles. Can you find any rectangles where the perimeter and area are the same? What are the dimensions? How many can you find?

4. Start a new sketch. Remember to set up the grid as you did before. Can you construct triangles with areas of 0.50, 1.00, 1.50, 2.00, 2.50, 3.00, 3.50? What are the perimeters of these triangles? Do any of the triangles have the same perimeter and area? Can you find any triangles where the perimeter and area are the same? You may need to uncheck the snap to grid command under the graph menu bar. Did you find a triangle where the perimeter and area are the same? What are the lengths of each side? What is the measure of the area and perimeter? What type of triangle is it?

Follow Up Lessons:

Upon completion of this lesson, students will continue to explore perimeter and area of other regular and irregular polygons. Students will also explore circumference and area of circles. Students could also construct more complex figures, such as a house or floor plan, and calculate the area. They could follow up by researching the cost of materials such as carpet, paneling or paint, and calculate the cost to remodeling a room or the entire house.

This lesson was written as part of a workshop on technology given at the University of Illinois - Urbana Champaign, in the summer of 1997. Thank you to all of the teachers, and university sponsers that made the workshop a success. If you have comments or some useful additions to this lesson, please email me, Kristen Morris, at this address
kbokenkamp@aol.com