## Simply Symmetry

In this lesson, children will explore the concept of symmetry and become more aware of symmetry in the world around them.

### Math Lesson for:

Toddlers/Preschoolers
(See Step 5: Adapt lesson for toddlers or preschoolers.)

Geometry

### Learning Goals:

This lesson will help toddlers and preschoolers meet the following educational standards:

• Apply transformations and use symmetry to analyze mathematical situations
• Use visualization, spatial reasoning and geometric modeling to solve problems

### Learning Targets:

After this lesson, toddlers and preschoolers should be more proficient at:

• Recognizing and creating shapes that have symmetry
• Recognizing and applying slides, flips and turns
• Creating mental images of geometric shapes using spatial memory and spatial visualization
• Recognizing and representing shapes from different perspectives
• Recognizing geometric shapes and structures in the environment and specifying their locations

## Simply Symmetry

### Lesson plan for toddlers/preschoolers

#### Step 1: Gather materials.

• The book, Seeing Symmetry by Loren Leedy
• A photograph of each child (The photo should be an 8” x 12” color computer printout cut in half vertically, so that half of the child’s mouth and nose, as well as one eye and one ear, are on each half. Glue one half of the picture onto a blank piece of paper, leaving room for each child to draw in the missing part of his/her face, head and neck.
• Some cut-out shapes (e.g., circle, heart, square, hexagon) that you can use to model the definition of symmetry.
• An easel with a piece of paper that you can use to post your symmetrical shapes and a definition created by the children.

Note: Small parts pose a choking hazard and are not appropriate for children age five or under. Be sure to choose lesson materials that meet safety requirements.

#### Step 2: Introduce activity.

1. Elicit a definition of symmetry from the children. Have the children gather on the rug and, using the cutout shapes, begin to fold the shapes symmetrically in half. Fold a shape in half, unfold it and 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. Ask: “What do you now notice about this heart?” (It’s half of a heart.)
5. Ask: “Do you know what the other half of this heart looks like?”
6. Paste half of the heart onto 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 help the children formulate the definition of symmetry.
8. Repeat the same activity with the other shapes. Ask the same questions and model the activities 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.

#### Step 3: Engage children in lesson activities.

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 that you can cover up half 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 middle of 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 each 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 photo halves of their faces as guides, the children will now draw the other halves of their faces.
12.  Pose prompting questions to help the children 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, identify symmetrical objects 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 cutouts in half the long way. Have the children color in only one side of the gingerbread man’s face, hands, clothes, shoes, etc. When they are finished coloring in and adding detail to one half of the gingerbread man cutouts, have the children switch cutouts and finish what someone else began. The children must replicate the original design so that both halves of the gingerbread men are symmetrical.

#### Step 4: Math vocabulary.

• Symmetrical: The 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.”)

#### Step 5: Adapt lesson for toddlers or preschoolers.

###### Toddlers may:
• Need some assistance in recognizing the various details of their photos so that they can better duplicate those details in their mirrored drawing
• Need some additional symmetrical examples shown to them
###### 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
###### Preschoolers may:
• Grasp the concept of symmetry and look for additional ways to extend their knowledge
###### Home child care providers may:
• Have the children go on a “symmetry hunt” around the room, identify symmetrical objects 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 cutouts in half the long way. Have the children color in only one side of the gingerbread man’s face, hands, clothes, shoes, etc. When they are finished coloring in and adding detail to one half of the gingerbread man cutouts, have the children switch cutouts and finish what someone else began. The children must replicate the original design so that both halves of the gingerbread men are symmetrical.

### Suggested 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)

### 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 between what they read in the book and what they see in their outdoor environment.