Symmetry

Designed by: Kristin Reinfurt, Rosewood Elementary

Grade Level: Three      Subject: Mathematics

Core Curriculum: Identify symmetry in the environment and create designs with symmetry. (3GS3-2)

Overview: The students will discover the concept of symmetry by looking at various pictures of symmetry in nature (like in butterflies). In small groups, they will use hand mirrors to determine symmetry and lines of symmetry in the capital letters of the alphabet. They will identify at least three examples of symmetry in the environment and then create their own symmetrical designs with construction paper and other art supplies.

Focus Questions: 
Where can we see examples of symmetry in our world?
How can we create designs that show symmetry?

Time Frame: Two fifty minute class periods

Resources:

The Butterfly Alphabet By: Kjell B. Sandvet

By Nature's Design An Exploratorium Book Published by: Chronicles Books

Typed copy of the upper case letters of the alphabet (one for each student)

Hand mirrors (must have at least one flat edge - round ones won't work well)

Paper/pencil

Construction paper

Magic markers

Scissors, glue

Digital camera (optional)

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

www.geom.umn.edu/~demo5337/s97a/reflect.html (optional)

Culminating Assessment: The students will sketch three symmetrical objects/things from the environment and draw the line of symmetry for each. (If a digital camera is available, one of the three symmetrical objects could be taken with it instead of drawn.) Then they will create a design from construction paper that shows symmetry. The teacher will score the pictures and design using the following rubric:

Instructional Activities:

Activity One: Start by showing the wordless picture book, The Butterfly Alphabet. For each letter of the alphabet, there is a picture of a butterfly in whose wings that letter can be found. Elicit observations from the class about the pictures. Probably someone will notice that each butterfly has the same design on each wing so that if you fold it in half, the designs on the wings match up. Introduce that as the concept of symmetry and write the word symmetry on the board. Explain that the middle of the butterfly's body is called the line of symmetry because you could fold the butterfly in half on that line and the butterfly's wings would match and be identical. Discuss that a "line" of symmetry does not have to actually be drawn as part of the figure. Also you can draw/picture the line in any direction so that when the figure is folded on that line, the two parts match.

If available, also show some selected pictures from By Nature's Design to show other examples of symmetry found in nature. Discuss the various lines of symmetry found. Show some examples where a figure has more than one line of symmetry. You can also show the web site www.geom.umn.edu/~demo5337/s97a/reflect.html
which is a site with a few pictures and basic information about symmetry. Encourage the class to start thinking of other places/objects where they have seen something that has symmetry. (Do not share these ideas yet.)

Have students get into small groups and give each a hand mirror. (Group size depends on how many hand mirrors are available.) Hand each group member a manuscript copy of the upper case letters of the alphabet. Explain that each group is going to be using the hand mirror to determine which upper case letters of the alphabet have a line of symmetry. Model this on the board using a hand mirror with a few of the lower case letters. For example, draw a lower case w or x. Ask them to think about whether or not they think it has a line of symmetry. Ask if it has more than one. Remind them that the "line" of symmetry does not have to actually be drawn. They will make the line with the mirror. Remind them that lines of symmetry can go in any direction. Place a flat edge of the mirror standing up on the predicted line of symmetry and look at the image reflected in the mirror. If it is actually a line of symmetry, you will see the other half of the letter reflected in the mirror so that it appears that the whole letter is written correctly. Show a couple of examples of letters that do not have a line of symmetry like b or z and discuss why they do not have a line of symmetry.

Ask each group to work together to determine which of the capital letters has a line of symmetry using the hand mirrors to help them. Instruct them to take turns using the mirror. When they find a letter with symmetry, each group member should draw the line(s) of symmetry on their alphabet sheet. Remind them to look for more than one line on each letter since some do have two lines of symmetry or more. Monitor groups and give feedback and help as necessary. Discuss the results as a class. Remind them to be looking for other examples of symmetry for the rest of the day in other classes, at home, outside, etc.

Activity Two: Review the concept of symmetry and a line of symmetry. Tell the students that they are going to work with symmetry on their own today. For the culminating assessment, they have two jobs to do. Explain that the first part is to write down three things in the environment that they found to have symmetry. To get the full points, they must come up with objects/things that we did not discuss in class and they must sketch the object and draw the line(s) of symmetry on it. If a digital camera is available, ask that one of their object pictures be taken with the camera, instead of drawn.

For the second part, they are to create a design that shows symmetry. Provide materials such as construction paper, markers, scissors, glue, etc. for students to use. Demonstrate how to get started by showing how to fold a piece of construction paper in half and cut it (like one cuts a heart) so that when it is unfolded the two halves are identical. A good example is to cut out a capital B shape so that when it is opened it looks like a butterfly. Then cut out various shapes from construction paper cutting each through two thicknesses of paper so that the two shapes are congruent. Model how to glue them one to each half of the butterfly so that they are symmetrical. Encourage them to make their designs colorful and detailed to show that they understand the concept of symmetry. Offer extra credit to students who create a design with more than one line of symmetry.

Post the designs on a class bulletin board. Then go to the web site www.sci.mus.mn.us/sln/tf/s/symmetry/symmetry/html Click on the blue words Mrs. Smith's class found symmetry everywhere. Read through their examples of where they found symmetry. Then click on the words at the bottom of the page Have you spotted symmetry somewhere? to send an e-mail to the museum site about some of the places where your class spotted symmetry in the environment.

Extensions:

Math - Trace pattern blocks to use as shapes on the designs. Have students practice with naming the different two-dimensional shapes.

Health - Discuss whether or not the human body is symmetrical. Look at it from the outside and also discuss the insides and where some organs are. (There are two kidneys, lungs, etc. one on each side of the spine, but there is only one heart so your insides are not symmetrical.)

Social Studies/Science - With the symmetry web sites listed are activities to do with monarch butterflies such as tracing their migration patterns, looking at their life cycle, etc.