South Carolina ETV

South Carolina ETV
1101 George Rogers Boulevard
Columbia, SC 29201-4761
Phone: 803-737-3545

Up for a Change? (Grade 8)

Master Teacher

Rebecca Ginn

Time Allotment

Three 45-minute class periods

Overview

Does the size of similar objects affect the perimeter, angle and area of the objects? How is it affected? In this lesson, students will participate in a series of hands-on, multimedia and online activities to examine how the edge length affects the angle measures, perimeters and areas of similar regular polygons.

Subject Mattter

Geometry

Learning Objectives

The student will find the perimeter, area, and angle measures of various regular polygons.
The student will describe how a change in edge length affects the angle measures, perimeters, and areas of similar regular polygons.
The student will use geoboards and writing to justify how areas and perimeters change when edge length increases or decreases.

South Carolina Standards

(From the South Carolina Mathematics Curriculum Standards, grade 8, Geometry, available online at http://www.myscschools.com)

I.B. 1.Describe how a change in the edge length affects the angle measures, perimeters, and areas of similar regular polygons. (8 th Grade Geometry I.B.1.)

Media Components

Video

Project Mathematics: “Similarity, Similar Triangles”

To access this video segment, log on to your account at the United Streaming Web page. In the search by keyword box, type Project Mathematics: Similarity. Click on the Similarity lesson and download the “Similar Triangles” video clip to your computer desktop and preview it.

(Note to Teacher: If you don’t have an account with StreamlineSC, check with your media specialist about signing up for your own account.)

Web Sites

NCTM Electronic Examples: Side Length and Area of Similar Figures at http://standards.nctm.org/document/eexamples/chap6/6.3/index.htm This Web site contains an applet with similar rectangles that gives the scale factor, the perimeter, and the area of the rectangles.

PACT Writing Rubric located at http://www.richlandclicks.org/PACT/writing_rubric.htm and a Word document (“PACT_Writing_Rubric.doc”)

Materials

For each student:

Graph paper – two sheets
Geoboards

For the class:

One floppy disk to save all of the data sheets on.

For each group of four students:

Computer with the bookmarked Web site http://standards.nctm.org/document/eexamples/chap6/6.3/index.htm

Prep for Teachers

Prior to teaching this lesson, bookmark the Web site used in the lesson on each computer you are planning to use.

Download the video clip from StreamlineSC.

Create a data sheet for use by the students in the lesson to record the different measurements of the figures they create

Create a writing rubric for her and the students use in assessing the work done in the final activity. The teacher should use the PACT Writing Rubric cited in the Web sites from which to choose specific elements.

When using media, provide students with a FOCUS FOR MEDIA INTERACTION, a specific responsibility to complete during or after viewing of video, Web sites, or other multimedia elements.

Introductory Activity

Step 1: The teacher will have the video ready to show the class, and will have the state standard written on the board.

Step 2: The teacher will introduce the lesson by reading the standard and telling the students that they will be examining this standard for the next few days, and that the first thing they are going to do is to watch a video clip from United Streaming. Tell the students that the video clip will be paused from time to time for clarification of understanding.

Step 3: The teacher will play the video clip. PAUSE the clip after hearing, “You always get a triangle twice as large, but with the same shape.” Provide your students with a FOCUS FOR MEDIA INTERACTION, asking your students why do you always get a triangle twice as large, but with the same shape? Check for student comprehension because the angles have not changed. CONTINUE playing the clip and STOP the clip at 3:33 after you hear, “Ratios of corresponding sides are called the scalene factor, and the triangles are called similar.” Provide your students with a FOCUS FOR MEDIA INTERACTION, asking your students when are polygons similar? Check for student comprehension (Answers may vary, but should relate to angles are the same, but the sides, area, and perimeter may vary.).

Step 4: The students will go to the Web site that is bookmarked. The teacher may have to group the students according to the availability of computers. Provide your students with a Focus for Media Interaction, telling your students probing activities such as notice what happens to the angles when you change the rectangle and why. Notice any other changes. Provide the students with some time to experiment with the applet that shows how measures change when the rectangle changes. Then ask the questions so they answer the points made in your Focus for Media Interaction.

Learning Activities

Step 1: The teacher will pass out one sheet of graph paper to each student. The teacher will tell the students that they will be drawing three triangles on the graph paper – one small, one twice as big as the first, and one three times as big as the first. The teacher will direct the students to draw a right triangle on the graph paper. After this is done, the teacher will then direct the students to draw another right triangle, which is twice as big as the first one. After this is done, the teacher will direct the students to draw a third right triangle, which is three times as big as the first one. The teacher will be walking around and observing what the students are drawing and directing as necessary. The teacher may have to explain what makes an object twice and three times as big.

Step 2: The teacher will have the students find the length of the sides of the three triangles using units as the standard unit of measure. The students will write the lengths of the sides of each triangle on each side of each corresponding triangle. Then the students will find the area of each triangle, writing the area beside or in each corresponding right triangle. Then the students will find the perimeter of each right triangle, writing the perimeter beside or in each corresponding right triangle. Lastly, the students will measure the angles of each triangle and write the measures every angle.

Step 3: The student will write a few sentences about what they found out about the right triangle. There needs to be enough sentences to explain how each right triangle was affected due to the changes in perimeter, area, angle measures, and side length.

Step 4: The teacher will pass out a data table for the students to use to fill in their information on their shapes. The students will write on the paper. Later they will be required to input the data in Word and save it to a class disk.

Step 5: The students will repeat Steps1, 2 and 3, except they will be using an scalene triangle instead of a right triangle.

Step 6: The students will repeat Steps 1, 2 and 3, except they will be using an isosceles triangle instead of a right triangle.

Step 7: The teacher will pass out another sheet of graph paper for the students to use.

Step 8: The students will repeat Steps 1, 2 and 3, except they will be using a square instead of a right triangle.

Step 9: The students will repeat Steps 1, 2 and 3, except they will be using a rectangle instead of a right triangle.

Step 10: The students will repeat Steps 1, 2 and 3, except they will be using a pentagon instead of a right triangle.

Step 11: The students will repeat Steps 1, 2 and 3, except they will be using a hexagon instead of a right triangle.

Step 12: The students will repeat Steps 1, 2 and 3, except they will be using an octagon instead of a right triangle.

Step 13: The students’ will transfer their information into the data table provided in Word. The student will then save the data sheet as “data_sheet_firstname_lastname” onto the disk provided for the class.

Culminating Activity

Step 1: Each student will write a paper about what they found out and what they learned. The paper should be long enough to explain how each shape was affected due to the changes in perimeter, area, angle measures and side length. The paper should include at least six paragraphs: one introductory paragraph, one paragraph per concept (how each figure was affected by the perimeter, angle measures, side length, and length of the sides), and one concluding paragraph. Every paper should include the introduction and conclusion paragraph. The middle paragraphs can be done at the discretion of each student. The above can be used as a suggestion. Another suggestion could be a paragraph on each shape. The paper will be graded using the PACT writing rubric.

Step 2: The teacher will divide the class into groups of four or five. Each group will create a PowerPoint about this lesson.

Step 3: Each group will present their PowerPoint to the class. A rubric will be provided for grading the presentation. While each group is presenting, the other students, who are not presenting, will fill in their grades for each group using the same rubric that the teacher is using. The provided rubric will have a place for the teacher’s evaluation score and the students’ evaluation score.

Cross-Curricular Extensions

Language Arts: Ask students to write a five-paragraph paper describing what they have learned (already incorporated in the lesson). The first paragraph should be the introduction. The middle paragraphs should be on each concept. The last paragraph should be the conclusion. The middle paragraphs could be on each shape (how each figure was affected by the perimeter, angle measures, side length, and length of the sides) or each concept (how each perimeter, angle measure, side length, and length of the sides were affected by making the figure twice as big and three times as big).

Art: Choose a subject and paint a picture using only similar polygons.

Community Connections

Invite a contractor into the classroom and have her discuss how changes to a blueprint affects the design of a house.

Student Materials

Graph Paper (recommended, but will be provided by the teacher if the student doesn’t have any)
PACT writing rubric (located at http://www.richlandclicks.org/PACT/writing_rubric.htm and a Word document (“PACT_Writing_Rubric.doc”)