Math Access for Teachers and Home Child Care Providers

Simply Symmetry

Children will explore the concept of symmetry and become more aware of symmetry in the world around them.

Content Area Standard Target
• Geometry
• Apply transformations and use symmetry to analyze mathematical situations
• Use visualization, spatial reasoning, and geometric modeling to solve problems
• Recognize and create shapes that have symmetry
• Recognize and apply slides, flips, and turns
• Create mental images of geometric shapes using spatial memory and spatial visualization
• Recognize and represent shapes from different perspectives
• Recognize geometric shapes and structures in the environment and specify their location
Obtain the Materials

• Book: Seeing Symmetry by Loren Leedy.
• Each child should have a picture of his or her self.  The picture should be an 8” by 12” color print (printed out from a computer). The picture should be cut in half, vertically (longways) so that half of his/her mouth, nose, one eye and one ear are on one side of the paper and the other half is on the other side of the paper.  Glue one half of the picture onto a blank piece of paper, leaving room for each child to draw the missing part of his/her face, head and neck.
• Some cut-out shapes (circle, heart, square, hexagon etc.) that you can use to model the definition of symmetry.
• An easel with a piece of paper that you can post your symmetrical shapes and a definition created by the children.

Note: Small parts create a choking hazard for children. Make sure that all materials you choose to use for an activity or lesson with children meet safety requirements. Small parts are not appropriate for children who are 5 years of age or younger.

Introduce the Activity

1. Elicit a definition of symmetry from the children.  Have the children gather on the rug and using the cut-out shapes, begin to fold the shapes symmetrically in half.  Fold a shape in half, unfold it, draw a line on the fold to emphasize it or cut the shape in half.
2. Ask the children: "What do you notice about what I have done to the shape?"
3. Say: “I’ve taken this shape of a heart and folded it down the middle."  Ask: "When I open up the shape, what do you notice?”  (You folded the shape in half)
4. Now cut the heart down the middle.  Take away one half of the heart and hold up the other half of the heart.
5. Ask: “Do you know what the other half of this heart looks like?”
6. Paste the ½ heart on your easel paper. Ask: “Can someone draw the other half of this heart?”  (pick a volunteer to come up to the easel and draw in the rest of the heart)
7. When the child is finished, ask the child, “How did you know what to draw? “Does this side of the heart help you draw the other side of the heart?” You are asking questions that will formulate the definition of symmetry.
8. Repeat the same activity with the other shapes.  Ask the same questions and model the activity with the shapes.
9. Say: “Symmetry is when you draw an invisible line through the middle of a shape and both sides match.”
10. Again, point to the shapes on the easel paper to emphasize this definition.  Write the definition on the easel paper.

Engage the Children

1. Explain to the children that now that they know what the definition of symmetry is, they are going to look for symmetry all around.
2. Introduce the book. Say: “Today we are going to read a book that will make us more aware of the symmetry around us.”  Have a small sheet of paper available when you read the book so you can cover up ½ of some of the objects in the book to further emphasize the idea of line symmetry.
3. Show the cover of the book.
4. Ask: “See the tiger and the butterfly?" Say: "Let’s draw an invisible line down the middle of the tiger and the butterfly.”  Cover up half of the tiger’s face and the butterfly with your piece of paper.
5. Ask: “Is the tiger’s face exactly the same on this side of our invisible line as it is on the other side of our line?”  (Yes)  Say: “The tiger’s face is symmetrical.”
6. Say: “Let’s try the butterfly’s wings and body.”  Again, cover up half of the butterfly with your piece of paper.  Ask: “Are the butterfly’s wings the same on this side of our invisible line as they are on the other side of our line?”  (Yes) Say: “The butterfly is symmetrical”
7. Say: “Let’s find out what other objects are symmetrical.
8. Read the book Seeing Symmetry.  Pause at pictures throughout the book and cover half of the picture and ask the children what they see and what they notice.  Cover up half of an object before the children see the picture and ask them what they think the other half of the picture will look like.  (Go through the book beforehand and tag the objects that you want to highlight with the children.  It is helpful to have a variety of objects – an animal, a toy, a design, something from nature.)  It is important to emphasize that symmetry is all around us.
9. Explain that there is even symmetry in all of us.  Show the children the pictures of their faces cut in half.
10. Ask: “Do you know what the other side of your face looks like by looking at this half of your face?”
11. Explain that using the picture half of their face as a guide, the children will now draw the other half of their face.
12. Pose prompting questions to help them get started.  Ask: “If your eyes are blue, what color are you going to draw your eye?”,  “If you have a lot of teeth in your smile, how are you going to draw the other side of your smile?”
13. Display their work.  This makes for a cute and engaging bulletin board.  It also adds to the content of the display, if you can include a picture of the book cover and a brief explanation of the activity.

1. Have the children go on a Symmetry Hunt around the room.  They can identify symmetrical objects around the room and draw these objects in a notebook.  Children should have a Math Journal readily available to record their mathematical thinking, reasoning and observations.  Share their findings.  Make a classroom chart of symmetrical objects in the room.
2. Give the children gingerbread men cutouts.  Divide the cut out in half, the long way.  Have one child color in his/her face, what he/she is wearing, shoes, hands etc. When they are finished coloring in and adding detail to one half of the cut out person, have children switch cut outs and finish what someone else began.  The children must replicate what the other child began.  The children must replicate the original design so that the both halves of the gingerbread men are symmetrical.

Encourage Vocabulary

• SymmetricalThe two sides of the whole are exactly like one another (e.g., "Is the tiger’s face exactly the same on this side of our invisible line as it is on the other side of our line?" "The tiger’s face is symmetrical.")
• Half – One of two equal parts of the shape, the whole (e.g., "When we divide this shape in half, we have two of the same shapes on each side of the dividing line.")

Glossary of MATH vocabulary

Supporting Children at Different Levels

Toddlers   Pre-K

Toddlers may:

• Need some assistance in recognizing the various details of their photo so they can better duplicate those details in their mirrored drawing.
• Need some additional symmetrical examples shown to them.

Pre-K Children may:

• Grasp the concept of symmetry and look for additional ways to extend their knowledge.

Home child care providers may:

• Help point out the symmetrical objects within the photo.  “You have an eye on this side of your face. Will you need an eye on the other side of your face?  Where should that eye go?
• Continue to point out the symmetry in objects around the room or in books.

Home child care providers may:

• Have the children go on a Symmetry Hunt around the room.  They can identify symmetrical objects around the room and draw these objects in a notebook.  Children should have a Math Journal readily available to record their mathematical thinking, reasoning and observations.  Share their findings.  Make a classroom chart of symmetrical objects in the room.
• Give the children gingerbread men cutouts.  Divide the cut out in half, the long way.  Have one child color in his/her face, what he/she is wearing, shoes, hands…. When they are finished coloring in and adding detail to one half of the cut out person, have children switch cut outs and finish what someone else began.  The children must replicate what the other child began.  The children must replicate the original design so that both halves of the gingerbread men are symmetrical.

Books

• Seeing Symmetry by Loren Leedy (New York: Holiday House, 2012)
• What is Symmetry in Nature by Bobbie Kalman (New York: Crabtree Pub Co., 2010)
• It Looked Like Spilt Milk by Charles G. Shaw (New York: Haperfestival, 1992)

Music and Movement

Outdoor Connections

• Go on a Symmetry Hunt outside.  Have the children bring their Math Journals with them so that they can write down or draw all of the symmetrical objects that they notice.  If possible, collect some symmetrical objects to bring inside and investigate further.
• Read What is Symmetry in Nature? by Bobbie Kalman.  Allow the children to make connections to what they read in the book to that of their surrounding area outside.

Web Resources

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