LESSON PLAN

Name: Reem Kattura

Title of lesson: Symmetry and its Application to Nature

Date of lesson: Fall 2006

Length of lesson: 50 minutes

Description of the class

                     Name of course: Geometry

                     Grade level: 9^th/10^th

                     Honors or regular: Regular

Source of the lesson:

• PBI Spring 2005: Math in Architecture – Lesson 2 “Symmetry Fun” by Sara Waldrip
• http://www.geom.uiuc.edu/~lori/symmetry/teacher.html

TEKS addressed:

§111.34. Geometry
(G.2) (A)  use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships
(G.3) (B)  construct and justify statements about geometric figures and their properties.
(G.5) (C)  use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations

I. Overview

Students will learn about two kinds of symmetry: line and rotational. Line symmetry is investigated using Geometer’s Sketchpad and rotational symmetry is explored through a hands-on activity. The class should have some prior knowledge of what these terms are.  This is an important concept to learn because symmetry is seen in nature, the main theme of this unit.

II. Performance or learner outcomes

Students will be able to:
1. Define reflectional symmetry in terms of its properties.
2. Define rotational symmetry.
3. Identify if an object has reflectional or rotational symmetry.
4. Realize that symmetry is seen in many real world objects.

III.Resources, materials and supplies needed

Computers with the Geometer’s Sketchpad file loaded (A copy of which is found on the website provided)

Cut out pictures for rotational symmetry exploration

IV. Supplementary materials, handouts.

Homework Worksheets
Found at: http://www.geom.uiuc.edu/~lori/symmetry/ref-ws.html
http://www.geom.uiuc.edu/~lori/symmetry/rot-ws.html

Five-E Organization

Teacher Does                    Probing Questions                    Student Does      

Engage/Explore/Explain Learning Experience(s) Students will begin thinking about reflectional symmetry (aka line/mirror symmetry). Teacher holds up a blank piece of paper vertically along her nose. Students are broken up into groups of 3. Students go through the geometer’s sketchpad exercise which will be loaded on each computer. This will allow them to make observations on reflectional symmetry. Students discuss their observations from the reflectional symmetry exercise. This provides them with the properties of this kind of symmetry. Teacher shows pictures from nature (with and without line symmetry) and asks students to identify whether they have line symmetry. Teacher gives definition of reflectional symmetry: ”An image has Reflectional Symmetry if there is at least one line which splits the image in half so that one side is the mirror image of the other. Reflectional symmetry is also called line symmetry or mirror symmetry because there is a line in the figure where a mirror could be placed, and the figure would look the same. Sometimes reflectional symmetry is referred to as a FLIP”

Critical questions 1. If I put this blank piece of paper across my nose vertically, what would you see? 2. What similarities do you notice on the right and left hand side of my face? 3. Would it make a difference if I turned the paper horizontally? 4. Will these be similar? (Teacher will go around to make sure that students understand the exercise and are writing down their observations) 5. How many reflections does it take to go back to the original image? 6. Does reflection preserve distances between the points of an image? 7. How can you find a reflection? 8. Do you think it’s possible to have more than one line of reflectional symmetry? 9. Do you think nature has reflectional symmetry? 10. Which of these pictures from nature have line symmetry?

Expected Student Responses/Misconceptions 1. Both sides of your face. 2. Both sides have the same shapes and features. 3. You would see the top and bottom of your face. 4. No 5. 2 reflections. 6. Yes. 7. Draw a perpendicular line between the point and the line of reflection then extend that line past the reflection line. 8. Yes/No/Maybe. 9. Answers vary depending on picture 10. Answers vary depending on picture.

Evaluate
The completion of the computer exercise and participation in the discussion of the results from the activity. Teacher will interrupt with any misconceptions.

Engage/Explore/Explain Learning Experience(s) Students will start thinking about rotational symmetry. Tack a cut out triangle in its center (the point where all of the lines of symmetry meet) to a piece of white paper on a bulletin board or other surface. Trace the outline of the triangle onto the white paper. Then rotate the shape until it matches the traced outline again. Students will remain in their groups from the line symmetry activity. Give each group the cut out pictures. They are to figure out whether each picture has rotational symmetry. Students discuss their observations from the activity. Teacher shows pictures from nature (with and without rotational symmetry) and asks students to identify whether they have rotational symmetry. Teacher explains to the students that: “An object has rotational symmetry if there is a center point around which the object is turned a certain number of degrees (this would be its angle of rotation) and still looks the same (matches itself) a number of times while being rotated. Rotational symmetry preserves distances between the points in the new image. If a shape “matches” itself only once in a full rotation, it does not have rotational symmetry.”

Critical questions 1. How many times will the triangle match the outline as you spin it completely around once? (Teacher visits with each group to ensure they are on task and understanding the activity) 2. Did all the pictures have rotational symmetry? 3. What was special about the pictures that had rotational symmetry? 4. Which of these pictures from nature have rotational symmetry?

Expected Student Responses/Misconceptions 1. Three times 2. No 3. Every time you rotated them a certain angle, the picture looked the same. 4. Answers vary depending on picture.

Evaluate
The students categorize the pictures as having/not having rotational symmetry correctly, and explain why they came to their conclusions. Teacher will interrupt with any misconceptions.

Extend / Elaborate Learning Experience(s) Students learn that reflectional and rotational symmetry can occur at the same time.

Critical questions 1. Can reflectional and rotational symmetry occur at the same time? 2. Can you give me some examples from nature?

1. Yes/No/Maybe. 2. Snowflakes, daisies, sunlowers, etc.

Evaluate
The purpose of this section is to show the students that both line and rotational symmetry can occur at the same time in an object. Students then brainstorm for examples in nature.

Wrap Up/Evaluate: Lesson Objective(s) Teacher summarizes lesson by asking a set of questions to check for the students’ understanding. Teacher gives students homework worksheets.

Critical questions 1. What are two types of symmetry we looked at today which exist in nature? 2. What are some of the properties of line symmetry? 3. What is rotational symmetry? 4. If a shape “matches” itself only once in a full rotation, does it have rotational smmetry? 5. Can an object have both line and rotational symmery?

Expected Student Responses/Misconceptions 1. Reflectional/line and rotational symmetry. 2. It takes 2 reflections to go back to the original image; the distance is preserved between in points in the new image; there can be more than one line of reflectional symmetry. 3. When an object has a center point around which it is turned at some angle (angle of rotation) but still looks the same. The distances between the points are also preserved in this kind of symmetry. 4. No. 5. Yes.

Pictures for Rotational Symmetry Exploration Activity