Symmetry

Designed by:  Jeanna Hoffman and Christi Jones
Satchel Ford Elementary School

1) Core Curriculum Objective: Identify and/or draw line(s) of symmetry for a given object or representation.  (2GS3-4)

Grade level:    Second          Subject:  Math

2) Overview:  Students will find the lines of symmetry for pattern blocks after being shown examples from symmetry web pages and discussing the meanings of symmetrical and line of symmetry.  Students will construct symmetrical designs using pattern blocks.  Students will identify and draw lines of symmetry for alphabet letters.

3) Focus Question:  How can we find lines of symmetry?

4) Time Frame:  3 class periods (60 minutes each)

5) Resources/ Materials:  triangle-shaped grid from

http://math.rice.edu/~lanius/Patterns/design2.html

overhead pattern blocks

overhead projector

yard stick

student supplies:  pattern blocks, paper, crayons, rulers

mathedology.ed.asu.edu/teachers/ahern/129/start.html

www.sci.mus.mn.us/sln/tf/s/symmetry/symmetry.html

www.bonita.k12.ca.us/schools/gladstone/merica/wow.htm  

www.geom.umn.edu/~demo5337/s97a/img/nature.html

www.earthsbirthday.org/activitykit/unit4-e.html

math.rice.edu/~lanius/Patterns/design2.html

www.geom.umn.edu/java/Kali/program.html

6) Culminating Assessment:  Students will  identify the letters of the alphabet that have lines of symmetry and draw these lines.  Note to the teacher:  The symmetry that is taught in this lesson is reflective symmetry.  *Sixteen letters have reflective symmetry (A, B, C, D, E, H, I, K, M, O, T, U, V, W, X, Y).  Teacher will check the letters using the following rubric:

Symmetry Rubric  

· Symmetry of the letters B and K  often depends on how they are written.

7) Instructional Activities:

Activity One: Prior to teaching the lesson, view the video at the web site http://mathedology.ed.asu.edu/teachers/ahern/129/start.html
To introduce symmetry,  demonstrate the making of a symmetrical heart from a folded piece of paper.  Discuss the terms line of symmetry and symmetrical.  Explain that a shape or design is symmetrical if it can be divided so that each part matches.  Cut the heart in half along the line of symmetry.  Show how the parts are exactly the same.  Ask the students if they’ve ever folded paper and made something (i.e. snowflakes).  Let them share their experiences.

Show students some examples of symmetry using the  web site http://www.sci.mus.mn.us/sln/tf/s/symmetry/symmetry.html  or http://www.bonita.k12.ca.us/schools/gladstone/merica/wow.htm
or http://www.geom.umn.edu/~demo5337/s97a/img/nature.html
Use an Averkey to show the site on TV screen so that all students will be able to see it better.  Have students use a yardstick to "draw" the line of symmetry on the computer screen.

Give students a set of pattern blocks and a ruler.   Have the students find a line of symmetry in each pattern block using the ruler to represent the line. Observe and assist students as needed.  Using overhead pattern blocks, model how to make new shapes that have symmetry by combining pattern blocks.  Demonstrate how to show the line of symmetry using a ruler.  Students construct symmetrical designs using pattern blocks.  Have students place their rulers to show the line of symmetry for their  designs.  Assist as needed.  Let students look at the designs of others.

HOMEWORK:  Students are to find 3 examples of symmetry outside of school.  Brainstorm some ideas with the class (i.e. tile on the floor, clothing, rugs).  They should copy them and write down where they found them.

Activity Two:  Pair students and give each pair a set of pattern blocks, ruler, and piece of drawing paper.  Instruct students to fold the paper in half, open it, and use the ruler to draw a straight line in the crease.  This will be the line of symmetry.  Have one partner create a design using pattern blocks on the upper half of the paper, at least one pattern block should touch the line.  The other partner then builds the other half so the design is symmetrical.   Observe the students as they are working.  

While they’re working, create a design on the overhead that has more than one line of symmetry.  Share this with the class and have students come to the overhead  and use a ruler to point out the lines of symmetry.  See if any pair thinks their design has more than one line of symmetry.  Allow the students to walk around the room and use their rulers to find the lines of symmetry in other designs.  Challenge the students to see if any of the designs have more than one line of symmetry. 

Have students clear their papers.  Give each student the paper with the triangle-shaped grid.  Students will fold the paper in half, open it, and use the ruler to draw a straight line in the crease.  (Hint:  have students use a black crayon so the line will really show.)  Each student will create a design using pattern blocks on one side of the line.  He/She traces and colors the blocks on the paper. 

Exchange papers and instruct the students to build the symmetrical design on the other side of the line using pattern blocks.  Students then trace and color the design.  Allow the students to share their papers and let the rest of the class decide if it is a symmetrical design and check for more than one line of symmetry.  Post these completed designs on the school web page and in the hall.

Close the activity by leading a discussion about where symmetry is found in our world.  Discuss the examples students found from the previous night’s homework.

Activity Three:

Print the letters of the alphabet in uppercase letters on the board.  Give the students a piece of paper and instruct them to copy the letters as neatly as possible, leaving space in between letters and skipping lines.  (Depending on the level of the students, the teacher may want to have these already printed and copied for the students, a sample is included below.)  Instruct the students to draw one line of symmetry for all the letters that have them.  They should circle the letters that do not have a line of symmetry.  Tell the students that they can earn extra credit by finding more than one line of symmetry in some of the letters. Collect these and score them using the rubric.

Extension Activities:  The web site http://www.earthsbirthday.org/activitykit/unit4-e.html
contains an art activity using the symmetry of butterflies.

Use the following web sites as center activities for the students:

Interactive site for constructing symmetrical designs using pattern blocks. http://math.rice.edu/~lanius/Patterns/design2.html

Interactive site where students can draw lines and make designs that are automatically made symmetrical.  http://www.geom.umn.edu/java/Kali/program.html

ALPHABET SYMMETRY