Barbara Perez

Lesson Plan #3

7/23/07

1. Title and Summary Pages

Unit: Perimeters and Areas of Similar Figures

Lesson: Perimeter and Area of Similar Figures

Author: Barbara Perez

Grade Level: 8th Grade Geometry

Classroom Layout:

Option 1.Students will be in groups of two with their desks adjacent to each other. Each student will have a laptop computer.

Option 2. Students will be in a computer lab and will work with a partner at an adjacent computer.

Prerequisite Knowledge for students:

  1. Students should be able to use a web browser to access Internet sites.
  2. Students should have some prior experience with GeoGebra.
  3. Students shouldunderstand the concept of similarity, how to determine if two geometric figures are similar, and how to write similarity ratios.
  4. Students should be able to find area and perimeter of geometric figures.

Prerequisite Knowledge for teacher:

  1. Teacher should be able to use a web browser to access Internet sites.
  2. Teacher should have some prior experience with GeoGebra.

Objective of the Lesson:

  1. Students will use proportions and ratios to find the perimeters and areas of similar figures.

Time Frame: 1 50-minute period

Materials:

Student

  • Computers with web browser and java installed (free from
  • GeoGebra Dynamic Worksheets
  • Rectangle.html
  • Triangle.html
  • Perimeter and Area Table Worksheet
  • Pencil
  • Calculator

Calculator

Teacher

  • Computer with web browser and java installed (free from
  • GeoGebra Dynamic Worksheets
  • Rectangle.html
  • Triangle.html
  • Projector

Short description of the content:

In this lesson students will learn how to determine the area and perimeter of similar figures if the area of one is known. Students will create their own area problems and solve them.

Sunshine State Standards: MA.B.1.4.3, MA.B.2.4.1, MA.C.2.4.1

Vocabulary/Key Words:

area, perimeter, similar, proportion, ratio, scale factor

2. Lesson Plan

Introduction to the lesson:

The concept of similarity will be reviewed. At this point, students already know how to determine if two figures are similar and how to write similarity ratios. Students will be given several examples of similar and non-similar pairs of figures. The students should be able to determine if the figures in each example are similar, and if so, be able to write the similarity ratios.

Explanation of the math involved:

As students experiment with polygons of different shapes and different scale factors, they have the opportunity to observe and interpret the changes in the perimeter and area. Students should be encouraged to focus on why the relationship between the scale factor and the ratio of perimeters of similar rectangles is linear, whereas the relationship between the scale factor and the ratio of areas of similar rectangles is nonlinear.

Teachers can help students develop their understanding by considering questions such as, Compare the ratio of the perimeters with the ratio of the areas for rectangles with various scale factors. What is the relationship between those two ratios?

It may also be beneficial for students to organize their data in a table. For various scale factors, record side lengths, perimeter, and area. This format may help students organize their information and assist in their developing an understanding of the relationship between scaling and perimeter and area.

Instructional Methods:

  • Whole group - lecture
  • Whole group – discussion
  • Small group – discovery
  • Small group - discussion
  • Small group – problem solving/practice

Procedure:

Step 1: Lecture/Review (Whole Group)

Teacher will review the concept of similarity with the students. The discussion should be focused on how we determine that two or more figures are similar.The teacher will do this with the whole class. The class will then do some examples together. Students will copy and solve the examples in their notes.

Step 2: Determine the relationship between perimeter and area of similar rectangles (Whole Class/Small Group)

Teacher will project the worksheet “Rectangle.html” to show students how the worksheet is used. This worksheet allows the length, width and scale factor to be changed so that many examples of can be shown. The students should find the area and perimeter of both rectangles. The answers can be checked by using the sliders to show the perimeters and areas.

Then students will use laptops to access the same worksheet (Rectangle.html). They will be paired up with another student. The students will manipulate the worksheet and try to make a conjecture about the relationship between scale factor and perimeter and area of similar figures.Then, students will complete the paper worksheet “Perimeter and Area.xls.” They will then discuss their conjectures with their partner. Finally, the whole group will discuss their conjectures.

Step 3: Determine the relationship between perimeter and area of similar triangles(Small Group)

Students will access the worksheet “Triangle.html.”This worksheet allows the base, height and scale factor to be changed so that many examples of can be shown. The area and perimeter is hidden so that the students can compute them on their own. Then the solution can be revealed. Students will create several examples and determine if the conjectures made in Step 2 apply to other geometric figures such as triangles.Then, students will complete the paper worksheet “Perimeter and Area.xls.” They will then discuss their conjectures with their partner. Finally, the whole group will discuss their conjectures.

Closure/Connections:

Students will review the concepts about similarity as it relates to perimeter and area that were learned in this lesson. Students will then be asked if what they discovered in this lesson about rectangles and triangles applies to all polygons. Each pair of students should come up with a different example using polygons other than rectangles and triangles. The class should discuss their findings and try to determine why this is true.

Assessments:

  1. Student created exercises and solutions on worksheets.
  2. Completed Perimeter and Area paper worksheet.
  3. Ability to create and solve an example for closure problem.

Extensions:

Have students investigate the relationship between similarity and surface area and volume of three dimensional figures.

3. Instructional Materials

  • GeoGebra Dynamic Worksheets
  • Rectangle.html
  • Triangle.html
  • Worksheet
  • Perimeter and Area.xls.