Curriculum topics:
 Symmetry &
Patterns
 Self –awareness
 SelfRepresentation
 Cultural
Exploration
MATHEMATICAL
SYMMETRY MODEL
These models combine symmetry and culture
Subjects:
Mathematics, Art,
Social Studies,
Language Arts
Grade range:
Pre-K - 2
Students create symmetrical models that are self-representational.
Designing the model facilitates students’ cultural exploration.
Completed models can be used as the basis of a story and/or play.
Who we are:
Resource Area for
Teaching (RAFT) helps
educators transform the
learning experience
through affordable
“hands-on” activities
that engage students
and inspire the joy and
discovery of learning.
For more ideas and to
see RAFT Locations
www.raft.net/visit-raft-locations
In collaboration with:
© 2014, RAFT
http://www.raft.net/raft-idea?isid=737
Materials required
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Tubes, at least 2.5 cm (~1”) in diameter, 1
per model
CD or equivalent (as a base), 1 per model
Cardstock circle, 10 cm (~4”) in diameter, 1
per model
Shapes, squares, circles, triangles, ~ 1 cm
(~½”), 2 of each shape per model (can use
paper or foam cut outs, stickers)
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Feathers, small, 4 or more (even number),
per model
Tape (double sided is best) and/or glue
Scissors
Colored markers
Pencils
Optional: Fabric scraps, colorful
Optional: mirror
Preparation before the activity
Note: Young students will need adult assistance.
Cut slits on
opposite
sides of the
tube
1
On one end of the tube, use scissors to cut two
1 cm (~½”) vertical slits on opposite sides, as shown.
2
Use tape or glue to attach the CD to the uncut end of the tube,
to form a base, as shown.
Attach CD to
the other end
of the tube
How to build it
1
Draw a light vertical line to divide the circle in half.
2
Select an even number of shapes and feathers.
3
Use half of the shapes and feathers to create half a face on
one side of the circle. Use symmetry to create a mirror image
on the other side of the circle with the other half of the
materials.
4
Slide the circle into the slits on the tube so that it is held
upright.
5
Slit
Optional: Use fabric scraps to decorate the tubes.
Mathematical Symmetry Model, page 2
© 2014, RAFT
To do and notice
1
Observe the model from a number of different
angles to see if and how the symmetry changes
with different perspectives.
Possible question to ask students:
What do you see?
Turn the model, now what do you see?
How does it look the same?
How does it look different?
What shapes can you see if you cover one eye?
2
Make a story about the model.
Possible details to include
(add more details, if desired):
Name:
Nickname:
Birthday:
Where the model was born:
How old is the model:
Favorite color:
Favorite shape:
3
Sample story
My Model
My name is LaNaé. My mom
sometimes calls me Naé. I was born
December 19th, 2001 in San Jose,
CA. My favorite color is green. My
favorite shape is a heart.
Share the story with the class, family, and/or friends.
Students can have models introduce “themselves” to
the other models.
The content behind the activity
Symmetry is a foundational part of geometry. In this activity, the following aspects of symmetry are
addressed: whole of a part, reflection, and central points.
Whole of a part: The student draws a line to divide the circle in half. One side of the circle is the same
as the other side. The dividing line is called a line of symmetry.
Reflection: The left side is the same as the right side.
Central points: The central point of symmetry remains the same even when observed from a different
perspective.
As students use symmetry to create self-representational models it encourages strong self-awareness
and mathematical awareness in the classroom and their community. It also increases awareness of
math in the surrounding world.
In some cultures, dolls are used as teaching models. Dolls can be used to illustrate aspects of the
culture for children. Many cultures have different ways in which they express history and play. For
example, Hopi Kachina (Katsina) dolls embody the characteristics of the ceremonial Kachina, or masked
spirits of the Hopi Native American Indian tribe.
In Africa, dolls are used both to teach and to entertain. Many dolls are unique, handmade, and are
traditionally handed down through generations.
Mathematical Symmetry Model, page 3
© 2014, RAFT
Curriculum
Standards:
Identity of self,
Awareness of diversity,
Socio-dramatic play &
Share space/ materials
(Early Education:
Desired Results Dev.
Profile(DRDP-R), SelfSocial Development,
1, 6, 9, & 12)
Shapes & Patterning
(Early Education:
Desired Results Dev.
Profile(DRDP-R),
Mathematical
Development,
36 & 37)
Learn more
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Related activities: See RAFT Idea Sheets:
Foam Dowel People –
http://www.raft.net/ideas/Foam Dowel People.pdf
Kaleidoscope Explorations http://www.raft.net/ideas/Kaleidoscope Explorations.pdf
Fine Motor Skills
(Early Education:
Desired Results Dev.
Profile(DRDP-R),
Physical Dev., 40)
Expression of self
through language &
Conversation
(Early Education:
Desired Results Dev.
Profile(DRDP-R),
Language & Literacy
Dev., 15, 16, 24)
Model Shapes in the
World & Attributes of
Shapes
(Common Core Math
Standards: Geometry,
Grade K, 5; Grade 1, 1)
Create, illustrate, & tell
stories
(Common Core English
Language Arts
Standards: Grades K-2,
Speaking & Listening, 4,
5, & 6)
Creative play,
materials, and making
(National Visual Arts
Standards: Creating:
Grades Pre K-1, 1.1;
Grades Pre K-2, 1.2)
Art, story, and culture
(National Visual Arts
Standards: Connecting:
Grades Pre K-2, 10.1;
Grades Pre K-2, 11.1)
Use yarn and beads to make necklace on the model.
Review the parts of a play with the students. Have students use the
models as characters in a play.
Use models to act out a story such as a nursery rhyme (e.g., Little Bo
Peep), fairy tale (e.g., The Three Little Pigs), or fable (The Tortoise and
the Hare).
Working together students create stories in which two or more models
interact. For example they could go on a trip, have a celebration, or
experience an adventure.
Mathematical Dream Catchers http://www.raft.net/ideas/Mathematical Dream Catchers.pdf
Resources
Visit www.raft.net/raft-idea?isid=737 for “how-to” video demos & more ideas!
See these websites for more information on the following topics:
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Math related teacher resources - http://www.nctm.org/

California Preschool Curriculum Framework –
http://www.cde.ca.gov/sp/cd/re/psframework.asp
Self-Awareness - Volume 1, pages 46-47
Patterning - Volume 1, page 264-265
Shapes - Volume 1, page 284-285
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California Preschool Learning Foundations –
http://www.cde.ca.gov/sp/cd/re/psfoundations.asp
Self-Awareness - Volume 1, page 6
Patterns - Volume 1, page 154
Geometry - Volume 1, page 157
 Katsina Doll Facts - http://www.heard.org/katsinadolls/faq.html
 Philadelphia Doll Museum – includes a short history of African-American
dolls and a virtual museum tour - http://www.philadollmuseum.com/
Acknowledgements:
A Make Build Play project, part of a collaboration between the Junior League of
San Jose and RAFT.
Mathematical Symmetry Model, page 4
© 2014, RAFT