Activity: Symmetry of Shapes

Let's find symmetry in shapes! You will need some shapes. You could buy some, or make your own like this: Print out Shapes (In Color) or Shapes (black and white) and cut them out.

Folding Test

You can find if a shape has a Line of Symmetry by folding it.

When the folded part sits perfectly on top (all edges matching), then the fold line is a Line of Symmetry.

Here I have folded a rectangle one way, and it didn't work.

So this is not a Line of Symmetry

But when I try it this way, it does work (the folded part sits perfectly on top, all edges matching):

So this is a Line of Symmetry

An Octagon

Let us try the Octagon (the 8-sided shape)

Is this a Line of Symmetry?

Let's try folding it:

Yes! When folded over, the edges match perfectly

So let us draw it on:

I found another way too::

Tried this	It works!	Draw it on

In fact I found 8 Lines of Symmetry:

Triangles

How about this Triangle?
I tried this fold, but it didn't work:

Can you find any Lines of Symmetry in that triangle? I couldn't.

But how about other types of triangle?

Your Turn

Now it is your turn ... pick a shape and find its Lines of Symmetry.

In fact, try them all! See what you discover.

Final Note: The Circle How about the Circle? Did you find any Lines of Symmetry? In fact the circle has infinite Lines of Symmetry, how about that! Click here for original source!

Math Meets Art: Symmetry Self-Portraits

Click here for original source!

Symmetry is one of my favorite parts of our geometry unit. We always begin by looking for symmetry in the world around us. The perfect book to begin my lessons on symmetry is Seeing Symmetry by Loreen Reedy. It opens my students’ eyes to symmetry that surrounds them in letters, words, nature, and even architecture.  After reading this book, my students love to design their own geometric animals, flowers, and buildings.

Beyond drawing the symmetrical butterfly, however, I like to show my students exactly how symmetrical they are. In order to do this we create symmetrical self-portraits, an activity that uses precise measurement to get beautiful results. Below, you’ll find the directions I had my students follow to create their “other half.”

Materials

• Closeup photo of each student
• 8.5 x 11 white paper for printing
• Paper cutter
• 9 x 12 white construction paper
• Glue sticks
• Rulers
• Shape templates (optional)
• Crayons and colored pencils for coloring.

Step-by-Step Directions

Step One: First, I took a closeup photo of each student. It’s best to take it straight on, making sure the head isn’t tilted to the left or right.

Step Two: Next, I downloaded the photos from my camera and resized them in Microsoft Word so that they took up most of a full page. Once they were resized, I printed them in color.

Step Three: Using scissors, I cut out each head. Having the head trimmed makes it easier to find the line of symmetry for the next step.

Step Four: Using the paper trimmer, I cut each photo in half, straight down the middle. I used the middle of the student’s nose to help me find the halfway mark on each student’s face.

Step Five: Students glued their half-heads onto a piece of 9 x 12 white construction paper.

This next part involves some modeling. Once you show the students how to measure, most can do it with ease.

Step Six: Using the ruler, students pick a starting point and measure how far it is from the line of symmetry. Then they measure that exact same distance on the opposite side, marking the spot with a dot.

For example, Eiki started with his eye. He measured and learned that the inside corner of his right eye was 1.25 cm from the line of symmetry. This helped him know that his left eye must also be 1.25 cm from the line of symmetry. So he measured 1.25 cm and made a dot there. Next he measured the distance from the center to the outside corner, making a dot on the opposite side.

Step Seven: Students continue to measure and mark dots all around the perimeter of their heads. Once they have generated a good amount of dots, I tell the class that they have made themselves into a dot-to-dot drawing and it is time for them to connect the dots! Once the dots are connected, they can really start to see their image emerge.

Step Eight: Next, students began coloring their portraits.

Step Nine: For the final step, students added a background of their choosing. Many used shape templates or rulers to draw symmetrical shapes and patterns. Getting the background symmetrical proved to be the trickiest part for my students, and I will definitely model this step more next time.

 

Symmetry Meets Technology

My class loves the free app Symmetry Lab Basic. This app quickly became a favorite during all the indoor recess we had over the cold winter months. Students use the touchscreen on the iPad to draw creative, symmetrical, kaleidoscope-like works of art.

On the desktop computers, my students enjoyed all the features of Polygon Playground that not only allowed them to create symmetrical shapes, but also introduced them to tessellations.

One of the easiest ways to show symmetry is through snowflakes. My students enjoy making them out of paper, but it is much faster (and neater!) to make them on the computer with Make a Flake.

Books to Try

 

Tangram App for 1st graders

Tangram Puzzles for Kids at ABCya!

This would be fun to use for centers or have students play when they finish classwork early.

1.G Grandfather Tang's Story

Alignments to Content Standards: 1.G.A.2

Student View

Task

Materials

• A copy of Grandfather Tang's Story by Ann Tompert
• One set of tangrams for each student (see note in commentary)
• A set of tangrams for the teacher (magnetic for the whiteboard or colored to use on a document projector)
• Character worksheet
• Crayons

Actions

• The teacher reads Grandfather Tang's Story to the class. As the teacher comes to each character in the story, note the picture of the animal that is an outline of a shape that can be made with tangrams. Students may need to spend some time looking to see how these outlines represent the animals since they are somewhat abstract. Ask the students if they see familiar shapes as components of the animal outlines--for example, the tail of the fox is a trapezoid and the wings of the hawk are triangles.
• After the class has read the story, the students choose animals from the story to make with the tangrams. The worksheet shows the tangram animals, and when they have made an animal, they color the corresponding shape on the worksheet.
• The teacher can demonstrate for students how to turn and place the tangram shapes as needed to support the students.
• After the students have worked on making 2 or more animals from the book, they can make their own animals.

IM Commentary

The purpose of this task is for students to compose two-dimensional shapes to create a composite shape using the 7 tangram pieces. It is essential that the language the teacher uses during the task is precise to support students' academic vocabulary development. For example, "turn the square so one side is lined up with the shorter side of the rhombus to create the tail of the squirrel."

Trying to make the animals without the internal lines is very challenging, so the worksheet shows how the pieces are composed for each animal. This helps students see the shapes both as a single figure (consisting of the outline and a single region filled inside it) and as a composite shape that can be decomposed into smaller shapes. If the teacher wants to challenge the students, then they can try to make the animals just looking at the outline shown in the book.

As an extra challenge, see if the students can combine their tangrams into the original shape of a large square.

Note: The tangrams can be plastic machine-made sets or students can make them in a preceding lesson. There is a template for creating tangrams attached to this task. If the students create their own tangrams, they will see that the 7 pieces originate from a large square. Making the tangrams for themselves also helps students develop the ability to compose and decompose figures.

Not all of the characters are included on the character worksheet. The students can build these as time permits.

Attached Resources

Character worksheet

Tangram Template

Solution

• If the student completes the fox fairy, hawk, and squirrel, then they will color those three figures:

• There is no single solution for each of the students' own pictures

Click here for original source

Triangle-Circle Clown

By Keren Perles

If your child is just learning the difference between different types of shapes, you can review them by making a triangle-circle clown. Your child will enjoy creating an entire picture out of nothing but circles and triangles of different sizes. This clown craft also makes a good activity for birthday parties or other gatherings with several young children.

What You Need:

• Construction paper
• Craft foam, fabric scraps and other materials
• Scissors
• Poster board (optional)

What You Do:

1. Before the activity, cut out circles and triangles of various sizes. A few of them should be about the size of an adult hand, some of them should be the size of an adult fist, some of them should be the size of a child’s fist, and some of them should be even smaller than that. Cut the shapes out of various materials – whatever you have handy.
2. Tell your child that you'll be making a picture of a clown using only triangles and circles. Ask your child which shape would work best for the clown’s head. Then ask which one would work best for the clown’s hat. Have her try out the combination by putting two of the largest shapes together and see if it looks like a clown’s head with a clown’s hat. Adjust as needed.
3. Help your child glue these two pieces onto a piece of construction paper or a large piece of poster board to make the clown’s head and hat.
4. Now ask your child which shapes would work best as the clown’s body. His feet? His hands? There is no right answer to these questions, but help your child arrange the pieces until she's satisfied with how her choices look, and then glue them down. Keep in mind that strings of circles may work for arms or legs.
5. Follow this same process to add two eyes, a nose, and a mouth to the clown. Then help your child decorate the rest of the clown’s body with smaller circles and triangles. Voila! A circus clown made from shapes!

If your child has also learned about squares or other shapes, you can include those on the picture as well.

Best Children's Books for Teaching Shapes

When a Line Bends, a
Shape Begins
(use it to teach 10 different
2D shapes)by Rhoda Gowler Greene
preschool - 2nd grade

Shape by Shape
(use it to teach basic 2D shapes
with a little mystery added)
by Suse MacDonald
preschool - 1st grade math

A Circle Here, A Square There
(use it to teach basic 2D shapes)
by David Diehl
preschool - kindergarten

Skippyjon Jones Shape Up
(use it to teach early intro to shapes)by Judy Schachner
preschool - Kindergarten

Captain Invincible and
the Space Shapes
(space adventure that's great
for teaching 3D shapes)
by Stuart Murphy
kindergarten - 4th grade

Cubes, Cones, Cylinders,
and Spheres
(uses photographs to teach children that 3D shapes all around us)
by Tana Hoban
preschool - 4th grade

If You Were a Polygon
(teaches all about polygons)
by Marcie Aboff
illustrated by Sarah Dillard
1st grade - 2nd grade

Icky Bug Shapes
(uses bug bodies to teach shapes)
by Jerry Pallotta
illustrated by Shennen Bersani
preschool - 2nd grade

Shapes, Shapes, Shapes
(uses photographs to teach kids
that shapes all around us)
by Tana Hoban
good for all ages

So Many Circles, So
Many Squares    
(uses photographs to teach kids
that shapes all around us)
preschool - 1st grade

Museum Shapes
(teaches basic shapes by
showing famous artworks)by the Metropolitan Museum of Art
kindergarten - 3rd grade

Round is a Mooncake
(great to teach basic shapes and
a little about Chinese culture)by Roseanne Thong
preschool - kindergarten

I Spy Shapes in Art
(teaches basic shapes by
showing famous artworks)
by Lucy Micklethwait
preschool - 2nd grade

Tyrannosaurus Math
(dinos explore shapes and
other math concepts)
by Michelle Markel
Kindergarten - 3rd grade

Circle Dogs
(story about dogs that can be
used to teach shapes)
by Kevin Henkes
preschool - Kindergarten

Windows, Rings, & Grapes:
a Look at Different Shapes
(crazy cats teach geometry shapes)
by Brian Cleary
Grade 1 & Up

The Greedy Triangle
(little triangle sees what it's like
to live as other 2D shapes)
by Marilyn Burns
preschool - 2nd grade

A Cloak for the Dreamer
(tailors make cloaks using different shapes of fabric--which is best?)
by Aileen Friedman
Kindergarten - 3rd grade

Not a Box
one simple box = possibilities!
(click link to see lesson idea using this book to teach basic shapes)
by Antoinette Portispreschool - 1st grade shapes

Click for Original Source