Document 95420

The Pattern Wizardry Portable Museum Kit is
based upon the exhibition Pattern Wizardry,
created by the Brooklyn Children’s Museum for
the Youth Museum Exhibit Collaborative (YMEC).
ive (YMEC.)
Beth Alberty
Sara DeAngelis
Patricia Hulse
Elizabeth Reich Rawson
Tim Hayduk
Kiyo Matsumoto
Britt Sheinbaum
Michael Sullivan
Esther J. Wahrhaftig
Nobue Hirabayashi
Rebecca Callan
Gloria Cones
Laurie DeAngelis
Edith Doron
Karen Jarmon
Deborah McDermott
William Fulbrecht
Aboriginal woman coiling tray—©Bill Bachman & Associates
Hurricane Hugo—©Tom Stack & Associates
Spider web—©Dietrich Stock Photos, Inc.
Brick wall—©Brooklyn Children’s Museum
Honeycomb—©Arthur Meyerson
Paving tiles—©Art Directors and TRIP Photo Library
Linear Repetition
Man block printing—©Art Directors and TRIP Photo Library
Sugar beet field—©Tom Stack & Associates
Woman weaving black and white pattern—©Brooklyn Children’s Museum
Branching Pattern
Blue oak—©Tom Stack & Associates
River—©Bill Bachman & Associates
Lightning—©Tom Stack & Associates
Woman making a mola—©Brooklyn Children’s Museum
Man painting decorative tiles—©Brooklyn Children’s Museum
Orchid stem—©Isaac Hernandez
National Science Foundationaon
All other rights reserved. Brooklyn Children’s Museum, 145 Brooklyn Avenue, Brooklyn, New York 11213
Copyright © 2002 by Brooklyn Children’s Museum
How to Use This Kit
Contents Checklist
Activity Matrix
Repeat After Me
Background for Teachers: Linear Repetition
Linear Repetition Activities
Tessellation Formations
Background for Teachers: Tessellations
Tessellation Activities
Spiral Spells
Background for Teachers: Spirals
Spiral Activities
Roots, Shoots, and Rivers
Background for Teachers: Branching
Branching Activities
Background for Teachers: Symmetry
Symmetry Activities
Teachers of Mathematics (NCTM) standards. Its
objects, images, and hands-on activities are
intended to work as an integrated unit that
focuses on three critical aspects of
understanding patterns:
• recognizing the concept of a pattern as
anything with a distinctive, consistent, and
repeating arrangement of units;
• identifying and describing linear and nonlinear types of patterns;
• creating, extending, and representing those
patterns in a variety of ways.
his Pattern Wizardry Portable Museum Kit
offers students and teachers a playful
introduction to some of the patterns that
surround us every day.
Produced by the Brooklyn Children’s Museum
for the Pattern Wizardry project, the kit’s
activities are designed for children ages five
through eleven. The kit can be used in
connection with the Pattern Wizardry
exhibition or on its own in a museum or
classroom setting. Individual instructors will
find it easy to adapt the kit to complement
their curricula and teaching methods. Please
feel free to photocopy individual pages or the
entire Teacher’s Guide for classroom use.
As you develop your lesson plans, think of this
guide as a resource you can use to link
patterns with the subjects you teach. You’ll
find we’ve pointed out many natural
connections between patterns and other
topics students are studying in the classroom,
including science, social studies, and math.
This kit has been designed to help students
meet the National Science Education
Standards (NSES) and National Council of
Before you begin using the kit, we recommend that you familiarize yourself with the Teacher’s
Guide, and the object and image checklist. The Teacher’s Guide and accompanying kit feature the
following components:
• Activity Descriptions: Step-by-step
instructions are provided in each section for
one pattern making activity, from preparation
to creation. Additional activities are outlined
at the end of each section. Use the activities
individually or in combination.
• Background Information: Offers a starting
point for lesson planning.
• Collection Objects and Images:
Resources to facilitate making connections
with patterns in culture and nature.
Note: A list of skills children will use during
each activity is highlighted at the beginning
of each activity description.
• Conversation Starters: Questions that
are intended to spark discussions around
the kit’s objects and images and help
students make connections to the
outside world.
Setting up the kit’s contents as a tabletop
mini-exhibit in your classroom can help to
generate excitement and provide context for
the topic. You will find relevant information
about the cultural and natural science
objects in the Collection Object Descriptions
section of this guide. Collection objects help
focus students’ attention and stimulate
children’s natural curiosity. Invite students to
bring in additional images and examples of
patterns. Then use the kit’s magnifiers and
mirrors to encourage more detailed
observations and experimentation with all
the patterns in your classroom display. Listen
to the music CD and talk about patterns in
sound as you study linear patterns.
Refer to the matrix on page 4 to see how the
activities in this guide meet the National
Science Education Standards (NSES) and the
National Council of Teachers of Mathematics
(NCTM) standards. The Book List on page 27
of this guide suggests books for further
reading. Visit the Brooklyn Children’s Museum
Web site at to find
more resources and Internet links to support
your classroom’s investigations of patterns.
The poems included in this guide were
written for the exhibition as examples of
linear patterns and rhythms and are a
wonderful language arts introduction to
pattern study. Feel free to photocopy and
use them in your lessons.
The objects in this kit are authentic and are
meant to be touched! Please demonstrate
careful handling for your students to ensure
that the objects are returned in good condition
for the next group that receives this kit.
These laminated photographs provide
contextual images that show patterns found
in nature and patterns made by people.
Finally, please photocopy, complete and return
the form on page 33 of this guide. Your feedback will improve our future kits.
Music is a type of pattern! Listen to repeated
sounds and make rhythmic patterns.
Please check that the kit includes all of the items on the checklist. Report any lost or missing items to the museum.
Teacher’s Guide
(notebook with activities pages)
Manganese Dendrite
Photo Album
3 Magnifiers
Green-Spotted Triangle Butterfly
3 Mirrors
Cultural Collection Objects
Imbenge Basket
India Printing Block
Drum! Music CD
Natural Science Collection Objects
Fossil Ammonite
Kente Cloth
Split Nautilus Shell
Maasai Necklace
Central Asian Tortoise Shell
American Quilt
Brush Coral
Mosaic Checkerboard
Lichtenburg Figure
Kuna Mola
The activities in the Pattern Wizardry Portable Museum Kit have been designed to help students
meet National Science Education Standards (NSES) and National Council of Teachers of
Mathematics (NCTM) standards. Refer to the matrix below as you create your lesson plans.
For further information, visit the following Web sites:
Once students recognize patterns, they will
see them all around the classroom and
beyond. There are many different kinds of
patterns; some are natural and others are
man-made. This kit focuses on the four
common pattern types most accessible to
children: linear repetition, tessellations,
spirals, and branching. In addition, we’ve
included a section on symmetry because so
many pattern types share this characteristic.
he human mind searches for patterns.
Patterns help us make sense of the world.
We see, hear, and feel patterns in the rhythms
and routines of our daily lives. Patterns are
anything with a unit—a shape, design, rhythm,
or motif —that repeats in an organized and
predictable way. We create and use patterns
in order to understand and share our
experiences. Because we find them everywhere,
patterns are a perfect interdisciplinary and
multidisciplinary topic to study. Pattern
recognition is at the heart of scientific
investigation, artistic creation, mathematical
calculation, and communication. Scientists
search for and study patterns in the natural
world. Mathematicians study and describe
patterns. Artists, musicians, and craftspeople
all over the world use patterns in their work.
As young children begin to investigate and
understand patterns, they are practicing
valuable inquiry skills. When students make
patterns, they practice cognitive and finemotor skills. Use the objects and activities in
this kit to help fuel classroom conversations,
questions, and discovery.
Use these questions along with the collection
objects to guide your class in a conversation
about linear repetition. In your discussion,
listen for ideas that could lead to interesting
classroom investigations.
inear patterns are easy to find; they occur
in art, music, and rhyme. Found in
materials, sounds, and cyclical events, linear
patterns repeat indefinitely in any direction
along a line. By looking and listening with your
students, you will discover a surprising
number of linear patterns: beads on a
necklace, woven materials, wallpaper borders,
stripes on clothing, zippers, walking footprints,
musical rhythms, the meter of poetry, the
passage of a day, and the changing seasons.
These examples all reflect patterns that are
created or extended by the regular repetition
of parts, sounds, or events. Linear patterns
can be simple or complex and are part of our
world’s natural rhythms. As a class, look for
examples of mathematical and scientific
patterns as well as those in art and music.
What do you notice about the linear patterns
of these objects? How are they the same and
how are they different? Create a list of words
describing what you see.
Where around the classroom do you see linear
patterns? Brainstorm a list of things that you
see, hear, and feel that repeat again and again.
Why do you think things use patterns that
repeat along a line?
1. Begin by looking at the different types of
pasta or noodles that the children will be
using as beads. Invite the children to look at
the “beads” carefully and describe the
features and patterns they observe.
homemade beads to experiment with
linear repetition.
Skills: artistic expression, creating and
extending patterns, comparing and
contrasting, making cultural connections,
using fine motor skills, and observing objects
2. Give each child one bead and a piece of
string or yarn. Tie the piece of pasta about five
inches from the end of the string as a stop.
Explain that a simple pattern can be created
using two types of beads, alternating one
after the other. Demonstrate a simple pattern.
Many children can easily master beading—a
great hands-on form of linear repetition. Use
commercial beads, or try beading with pasta
or noodles, cereal with holes, cut lengths of
colored drinking straws, buttons, paper
beads, and Styrofoam popcorn. Keep the
theme going by making a linear snack! Make
edible patterns by putting cut fruit on shishkebab skewers.
3. Invite children to design their own
patterns using two to five pasta beads. This
short arrangement is called a motif. Explain
that they will be repeating this pattern along
the length of their necklace. Have the
children begin threading the pasta one at a
time onto the string following their motif.
Have them repeat the pattern until the
necklace is complete.
It is easy to make dyed pasta using food
coloring. Prepare dyed pasta ahead of time.
Put uncooked noodles in a plastic bag with
food coloring and a teaspoon of rubbing
alcohol. Seal the bag and shake it to ensure
that the dye is evenly distributed. Lay the
pasta on a paper towel to dry overnight. For
young children, consider using one type of
pasta and multiple colors. For older children,
the more variety of forms and colors to
choose from the better.
Ask students to share how they created their
patterns, how they remembered how to
follow the pattern, and what they learned.
Have children look at the Maasai necklace in
the kit and discuss its pattern and origin.
Discuss ways in which the neck collar and
the other repeating pattern objects and
images are both similar to and different from
the pasta necklaces.
• string or yarn
• uncooked pasta or noodles (select varieties
that have holes, like ziti, penne, and rigatoni)
• food coloring and rubbing alcohol (optional)
• glue and glitter (optional)
Weave a work of art with paper and recycled
material! A linear repetition in action, weaving
is also a wonderful way to experiment with
materials and pattern making. Provide a wide
assortment of materials that can be cut into
similar length strips (e.g. paper, foil, giftwrap,
magazines, fabric, or ribbon) and encourage
children to experiment and be creative.
Examples of weaving can be found in many
cultures. Share some with your students.
Skills: creating and extending patterns,
learning cooperatively, comparing and
contrasting, making cultural connections,
using gross motor skills, observing objects,
and spatial awareness
Music is the linear repetition of sounds.
Explore how repeating simple rhythms like
clapping, snapping, and stomping can create
music. Demonstrate a simple rhythm made by
clapping (e.g., clap, clap, clap, pause, clap,
clap, clap; or clap, pause, clap, pause). Have
the whole group practice clapping the rhythm.
Vary the pattern by inserting a foot stomp
between claps. Choose a new leader and have
him or her invent a rhythm for the whole group
to follow. End by listening to examples of
linear repetition on the music CD provided.
Relate this activity to the rhythms found in
different cultures the class is studying.
Skills: artistic expression, creating and
extending patterns, learning cooperatively,
comparing and contrasting, using fine motor
skills, observing objects, and spatial awareness
Create a room-wrapping border of the entire
class’s handprints. Part of the fun of this activity
is coming up with many amusing and wild
variations using color, size, and arrangement,
and then seeing how they look when they
repeat. Have the class come up with as many
handprint patterns as possible. Select one to
begin with. Have the children print each new
pattern on a separate piece of paper. Then hang
the whole series of handprints around the room
as a fresco. Invite the students to look for
examples of this type of linear repetition in
design and decorating magazines, on buildings,
and around their homes.
Skills: artistic expression, creating and
extending patterns, making cultural
connections, using fine motor skills, and
observing objects
interlocking shapes as long as they fit together
without gaps or overlaps. The artist M. C.
Escher used fanciful geometric creatures to
create beautiful irregular tessellating patterns.
tessellation is a collection of individual units
that fit together without gaps or overlaps to
fill a two-dimensional space, like a tabletop, or a
three-dimensional space, such as a box. Floor
tiles, brick walls, and honeycombs are all
examples of tessellations. The word tessellation
comes from tessella, the Latin term for the small
stone tiles in ancient Roman mosaics.
Tessellations can extend in a two-dimensional
plane infinitely in every direction. Tessellating
shapes fill space efficiently without waste.
Some common tessellations are checkerboards
and floor tiles. Three-dimensional tessellations
are structurally strong. Honeycombs, for
example, use hexagonal tubes to provide the
maximum amount of storage space for honey,
with a minimum of material, beeswax. Other
examples of natural tessellations include corn
cobs, turtle shells, and soap bubbles.
There are two types of tessellations, regular and
irregular. Regular tessellations are made by one
repeating shape. There are only three shapes
that create regular tessellations: triangles,
squares, and hexagons. Irregular tessellations
can be made from a variety of repeating
Where around the classroom do you see
tessellations? Compare the tessellations that
you see around your classroom with those in
the kit. How are they the same, and how are
they different?
Use these questions to guide your class in a
conversation about tessellating objects and
images. In your discussion, listen for ideas
that could lead to interesting classroom
Make a list of some reasons why tessellating
patterns might be useful.
What do you notice about the tessellation
objects? How are they the same and how
are they different? Create a list of the
shapes you see.
remember, each piece should be the same
size.) Assemble all the finished squares on a
bulletin board to create a classroom quilt.
CRAZY QUILT—Explore tessellating patterns
while creating a classroom quilt.
Skills: artistic expression, creating and
extending patterns, learning cooperatively,
comparing and contrasting, making cultural
connections, using fine motor skills,
observing objects, and critical thinking
• pre-cut quilt pieces of assorted materials
• pre-cut cardboard or oaktag
• white glue
• scissors
Creating a classroom quilt is a great way for
children to experience a wonderful variety of
tessellations. Quilts are also a fun way to
connect math with culture. The instructions
below show two simple techniques for
creating quilting pieces that fit together. Try
experimenting with different types of quilt
materials like recycled giftwrap, colorful
magazines, fabric, and wallpaper.
Each participant should make one quilt
square approximately eight inches in size.
(You may want to adjust this size depending
upon the size of your bulletin board and the
number of students in your classroom, but
Continued on page 11
2. Invite children to experiment with different
Cut the quilt pieces. (Have an adult use the
technique below to prepare pieces in advance.)
combinations of shapes and colors until they
are pleased with their pattern. Older children
can be given the option of cutting down the
pattern shapes to create more intricate
tessellations. Remember that students’
patterns must be a tessellation—i.e., pieces fit
together without gaps or overlaps.
Help insure that all the quilt pieces fit
together neatly. Carefully stack three to five
pieces of the same sized material together.
Make a copy of the pattern master on page
25 to use as a template. Carefully pin all the
sheets and the template together using
straight pins or a stapler. Cut the sheets with
scissors. If you are comfortable using an
Exacto™ knife, you can also cut a stack of
paper by using a straight metal ruler (or a
wooden one with a metal edge) and aligning
it with the cutting lines on the master.
3. Instruct the children to glue each piece in
place on the cardboard form by carefully
lifting one piece at a time, applying glue, and
then replacing it in its former location. After
the whole class is finished gluing their
squares, have the children take a few
moments to look at each other’s work. Attach
the quilt squares to a bulletin board to make
a classroom quilt.
If you want the children to do some of the
cutting, photocopy the Pattern Master Quilt
Template on page 25 onto colored paper .
Ask students to share how they created their
quilt patterns, what shapes they chose to
use, and what they learned. Have children
look at the American quilt in the kit and
discuss its pattern and origin. Discuss ways
in which the quilt and the other tessellation
objects and images are both similar and
different from the quilt that the class made.
1. Start by giving each child an eight-inch
square piece of cardboard and a container of
white glue. Then have each child select a
variety of shapes from the cut quilt pieces.
Make place mats using craft paper, paint, and
pop-up sponges. First, have the children
design a tessellating shape from a three-inch
square and then create a template out of
cardboard. Use the templates to mark the
shapes to cut out on a sheet of pop-up craft
sponge. Then sponge-print a tessellating
pattern on a blank piece of 12˝ x 18˝ craft
paper. Once the paint is dry, laminate the final
artwork to keep the place mat food free.
Look for opportunities to connect tessellation
activities with math topics like geometry,
measurement, and number operations.
Skills: creating and extending patterns, learning
cooperatively, comparing and contrasting, using
gross motor skills, using fine motor skills,
observing objects, learning through inquiry,
spatial awareness, and critical thinkingTake a
field trip in the classroom by looking for
tessellation everywhere—from the ceiling to
the floor tiles! Play “I Spy” a tessellation as you
continue around the school and outside. Make
a list and create drawings of all the different
kinds of tessellations you discover. Remember
to look for tessellations found in nature as well
as those made by people. Follow up with a
tessellating snack—like crackers!
Skills: learning cooperatively, comparing and
contrasting, observing objects, learning
through inquiry, and critical thinking
Engage students in a little imaginative roleplay by having them study cracker shapes and
design new ones. Bring in samples of different
shaped crackers. Demonstrate how many
cracker shapes fit together to create
tessellation patterns. Invite the children to
come up with a shape for a new cracker.
Skills: artistic expression, creating and
extending patterns, using fine motor skills,
and observing objects
distance between each successive coil is
always the same. They are found in many manmade products because their design conserves
space and resources. Golden, or equiangular,
spirals grow at an increasing rate like the shell
of a snail. The successive coil grows wider with
each rotation away from the starting point.
Many spirals found in nature are golden
spirals. They are the result of differential
growth, where the outside surface, the surface
farthest from the axis around which the coiling
is taking place, has more room to grow than
the inside edge. This gives golden spirals their
characteristic shape.
pirals are one of the most beautiful and
intriguing types of patterns. Although there
are many kinds of spirals, they all wrap around
a fixed point at a changing distance. They are
found in man-made and natural objects, such
as spider webs, nautilus shells, watch springs,
woven baskets, and coils of rope.
Two of the most common spirals are the
Archimedean and the golden spiral.
Archimedean spirals, named after the Greek
mathematician Archimedes, grow at a fixed
rate like a tightly wound coil of rope. The
A rchimedean spira l
golden spira l
What do you notice about these spirals? How
are they the same and how are they different?
Create a list of words describing what you see.
Use these questions to guide your class
in a conversation about the kit’s spiral
objects and images. In your discussion listen
for ideas that could lead to interesting
classroom investigations.
Where do you see spirals around the
classroom? Brainstorm a list of other things
that are spirals.
What reasons can you think of that things
might grow in a spiral pattern?
Mix the flour and salt together in a large bowl.
Slowly stir in the water and mix until the
mixture is the consistency of bread dough.
Use the clay immediately.
Allow your finished creations to dry for
48 hours.
SPIRAL SAUCERS—Explore many variations
of these simple spiral creations.
Skills: artistic expression, creating and
extending patterns, using fine motor skills,
and observing objects
Crafty Clay (Makes enough for six children)
1 cups cornstarch
1 1/2 cups cold water
2 cups baking soda
Two simple techniques for making spiral
crafts are outlined here. Feeling adventurous?
After you’ve created the saucers, have the
class serve up some fun by creating edible
spirals! Simply, roll up layers of cold cuts or
bread and jam then cut in one-inch pieces to
reveal the tasty spirals.
Combine cornstarch and baking soda in
a saucepan.
Add water and stir until the mixture is smooth.
For colored clay, add seven to ten drops of
food coloring.
Heat the mixture for five minutes over
medium heat.
Stir until it begins to thicken and turns to
dough-like consistency.
Remove from saucepan and allow to cool.
Knead clay for two to three minutes before
using. (To make sparkling creations, add
glitter while kneading.)
Allow your finished creations to air dry until
they are hard.
• Model Magic (fast drying molding clay),
Homemade Clay, or Crafty Clay
(see recipes below)
• food coloring and glitter (optional)
• wax paper
• dental floss
Homemade Clay Recipe
(Makes enough for eight children)
1 1/2 cups flour
1 1/2 cups salt
1 1/8 cups water
Continued on page 15
3. Once the full length of clay rope has been
1. Start with a fist-sized ball of clay
coiled, the children should gently press the
palms of their hands straight down on the
entire surface to help seal the clay together.
Allow the saucers to dry until hard.
material. Have children roll the ball back and
forth with their hands to form a thin rope of
clay at least 12 inches long.
2. Ask the children to choose one end of the
Ask students to share how they created their
patterns and what they discovered in the
process of making spirals. Have children look
at the imbenge basket in the kit and discuss
its pattern and origin. Discuss ways in which
the basket and the other spiral objects and
images are both similar to and different from
the spiral saucers.
rope of clay as the center of the spiral.
Demonstrate how to begin by gently coiling
around one end of the clay rope to form the
center of the spiral and by wrapping the
remaining rope around and around the
outside edge to form the spiral. Remind the
children that each coil should be in contact
along its full length with the previous coil.
1. This activity works best if you use two
different colors of clay. Start with lemonsized balls of each of the two colors of clay
material. Have the children flatten each ball.
Try to make both pieces about the same size
and thickness.
2. Place one of the two flattened pieces of
St a rting to coil saucer
clay on top of the other. Press the clay
together gently to seal the pieces together.
Cut the clay into a regular polygon like a
square or rectangle.
3. Begin at one edge of the square or
rectangle and roll the clay firmly so that
there are no gaps. Make multiple cuts in the
roll of clay about one inch apart. Each piece
of the “jelly roll” can then be flattened
carefully to form a spiral saucer.
Coiled saucer
Continued on page 17
leaving about eight inches of floss between.
Pull the floss tight. Choose a place to cut
the clay roll. Use the tips of your fingers to
help press the floss down through the clay
roll. Once you’ve reached the bottom, saw
back and forth a little. Then carefully lift the
floss straight up.
Try this dental-floss cutting technique
for a safe alternative to using a knife for
cutting clay!
Use a length of dental floss about two feet
long to cut the clay rolls. Loosely wrap the
floss around your left and right hands,
Make colorful spiral snakes to hang from the
classroom ceiling. Show some images of
snakes and talk about their characteristics.
Have the children draw an Archimedean spiral
on a paper plate, decorate it with paint or
markers, and then cut it out. Punch a hole at
the top of the spiral and thread it with yarn.
Hang the spirals by an open window and
watch what happens to the snakes!
Look for opportunities to connect your spiral
activities with life science, math, and cultural
Skills: artistic expression, using fine
motor skills, observing objects, and
literacy/language arts
Skills: learning cooperatively, comparing and
contrasting, making cultural connections,
using gross motor skills, observing objects,
spatial awareness, and critical thinking
Create translucent spiral spiderwebs using
string, glue, and glitter on wax paper. Spiders
create beautiful spiral webs. Have the children
look at and talk about spider webs found in
popular children’s stories and picture books
(e.g., Charlotte’s Web or The Spider Weaver:
Legend of Kente Cloth.) Use the string to
create the frame and central spokes of the
web. Use the glue to create its translucent
spiral. Hang the finished spider webs in a
classroom window.
Make a game of searching for spirals around
the classroom and at home. Point out some
common examples like rolls of paper towels
and tape. Give bonus points for particularly
unique or surprising spirals such as cinnamon
sticks, patterns on clothing, or water as it goes
down the drain.
Skills: artistic expression, creating and
extending patterns, using fine motor skills,
and observing objects
arteries and veins! Branching patterns can also
be found in diverse man-made things including
roadways, decorative designs, and mobiles.
he most common type of branching pattern
is based on a series of three-way forked
joints, like a tree branch. These branching
patterns start from a single point and grow
outward in many directions. While branching
does not always follow the simple geometry of
other categories, it is an important and
recognizable pattern.
Use these questions to guide your class
in a conversation about branching objects
and images. In your discussion listen for
ideas that could lead to interesting
classroom investigations.
Branching patterns are very economical in that
they reach a large surface area using the
shortest path. For this reason, branching
patterns are formed by organisms, systems,
and structures that distribute or collect large
volumes of material. Many natural systems,
especially those involving liquids, have
branching patterns. Examples of branching
patterns include river systems (water
transport), lightning (electrical dissipation),
and plants (nutrient, gas, and water transport).
Our own blood travels in a branching pattern of
What do you notice about branching patterns?
How are they the same and how are they
different? Create a list of words describing
what you notice.
Where around the classroom do you see
branching? Make a list of branching patterns
you could find around your school or museum.
What do the things with branching patterns
share in common?
1. Start by going over some examples of
branching patterns. Explain that you will be
searching for examples of branching patterns
on your field trip. You may want to have the
children work with partners or as small
teams. Provide each student or team with a
copy of the Plant Pattern Survey Sheet on
page 26. Ask the students to record their
results clearly on the sheet.
PLANT PATTERN SURVEY—Take a mini field
trip to search for the branching patterns of
many plants and plant products.
Skills: learning cooperatively, comparing
and contrasting, using gross motor skills,
observing objects, learning through inquiry,
and critical thinking
Once you know what to look for, branching
patterns are easy to spot. Two variations of
this activity are described below. The first
involves a trip to a local playground,
schoolyard, or tree-lined street—anywhere
you can find plants. The second option, good
for winter and rainy days, can be done as a
take-home activity that challenges students
to survey either a refrigerator or grocery
store. You may want to use the Plant Pattern
Survey Sheet on page 26 as a template.
Once the survey has been completed, create
a chart with the class results.
2. Spend about 10 to 15 minutes outside
searching for examples of branching
patterns. Encourage children to look
carefully at the whole plant. Most plants
have at least some branching.
3. Bring the whole class together and share
the results of the children’s observations.
Ask: Where did you notice branching
patterns? Were all the branching patterns
the same? Did anyone find any hidden or
surprising branching patterns?
Observation and description are two skills
that every good scientist needs to learn.
Encourage the group to look carefully and
ask questions about all parts of the plants
they find. Since plants are alive, remind
children to be respectful of nature and leave
plants growing where they find them. At the
end of the survey you may want to show, as
an example, the branching root system of
one plant.
Ask students to share what they noticed
about the patterns they found, where the
patterns were located, and what they
learned. Have children look at the brush
coral in the kit. Discuss ways in which the
coral and the other branching objects and
images are both similar to and different from
the patterns they found.
• paper
• pencil
• tree and plant guides (optional)
2. Encourage the children to look carefully
1. Start by going over some examples of
branching patterns. Explain that each
student will be searching for examples of
branching patterns either at home or at a
grocery store. Provide each student or team
with a copy of the Plant Pattern Survey Sheet
on page 26. Ask the students to record their
results clearly on the sheet.
for examples of whole plants and parts of
plants that have branching patterns.
3. Ask the class to share the results of their
at-home surveys. Ask: Where did you notice
the branching patterns? Were all the
branching patterns the same? Did anyone find
any hidden or surprising branching patterns?
Schematic plant showing bra n c h i n g
of trees or plants they are reminded of. Add
colorful flowers, leaves, or fruit to the trees by
gluing tufts of colored tissue to the branches.
Look for opportunities to connect your
branching activities with math, physical
science, and life science topics being studied
in your classroom.
Skills: artistic expression, comparing and
contrasting, using fine motor skills, and
observing objects
Skills: creating and extending patterns,
comparing and contrasting, using fine motor
skills, observing objects, and spatial awareness
Make a mobile using leaf shapes. First, have
students look at examples of mobiles by an
artist such as Alexander Calder. Then distribute
pipe cleaners and string to the class and invite
them to create a simple mobile armature.
Complete the mobiles by attaching either leaf
rubbings, leaf shapes, or images of branching
patterns cut from recycled magazines.
Make leaf rubbings to reveal natural branching
patterns. Begin by having students use
magnifiers to look at some fallen leaves that
you have collected. Then invite children to use
thin paper and the side of a crayon to create
the rubbings. Have children cut out their leaf
rubbings and hang them up on a bulletin
board. (Tree-shaped silhouettes mounted on a
bulletin board work well for this activity.) Or,
make leaf mobiles by tying several of the
rubbings to pipe cleaners with string (see
Mobile Movements).
Skills: artistic expression, creating and
extending patterns, comparing and
contrasting, using fine motor skills, and
observing objects
Create naturalistic branching patterns by
blowing ink on paper. Place a drop of ink at the
bottom of a piece of plain paper and have
children use a straw to blow the ink around in a
branching pattern. Ask the children which types
number of repetitions. Natural examples of
rotational symmetry can be found in starfish,
flowers, and snowflakes. Many cultural objects
exhibit rotational symmetry including tile
work, basket patterns, and kaleidoscopes.
ymmetry is a way that units of pattern are
organized. A figure is symmetric if you can
pick up a copy of it, move it to a new location
or orientation, and set it down so that it
exactly matches. There are twenty-four twodimensional symmetries. In this kit we
examine two: mirror and rotational symmetry.
Use these questions to guide your class in a
conversation about symmetry objects and
images. In your discussion, listen for ideas
that could lead to interesting classroom
Mirror or reflection symmetry divides a figure or
design into halves that are mirror images. The
axis can be located either vertically or
horizontally. Mirror symmetry is found in both
natural and man-made objects. Butterflies are
good examples of mirror symmetry. Human
faces have symmetry! In fact, most animals and
plants exhibit some form of symmetry in their
body shape and their markings.
What do you notice about the symmetrical
objects? How are they the same and how are
they different? Create a list of words
describing what you see.
Where around the classroom do you see
symmetry? What type of symmetry do
you see? Make a chart categorizing the
symmetry objects. Which type of symmetry
is most common?
Rotational symmetry occurs when an object is
turned a certain number of degrees around a
center point and still looks the same (i.e., it
matches itself a number of times while it is
being rotated). The number of repeated
elements in this type of symmetry can vary
significantly, although three is the minimum
Why do you think things have symmetry?
SYMMETRY MASKS—Create a mask with
mirror symmetry.
This technique produces fun, random results.
Skills: artistic expression, comparing and
contrasting, making cultural connections,
using fine motor skills, and observing objects
1. Have children turn the paper so the long
edge is at the top, then fold the paper in
half, like a book (the two short edges should
be together). Have them press along the fold
to create a sharp crease. Then open the
paper completely and lay it flat.
Start your conversations about symmetry by
discussing the objects and images in the kit.
Introduce the concept of mirror symmetry by
having the children experiment with the
mirrors and various pictures, letters, and
drawings. Demonstrate rotational symmetry
by placing two mirrors together. Play with the
angle between the two mirrors and discuss
what happens to the reflected image.
2. Put paint on one half of the paper. Be
careful not to get paint on both halves. It is
okay if the paint is thickly applied. While the
paint is still wet, fold the undecorated side of
the paper onto the painted side. Press down
gently, but firmly, along the whole surface.
Open the two halves of the paper to reveal the
symmetrical pattern. Allow the paint to dry.
Mask making is a playful way to introduce
the concept of mirror symmetry. Consider
connecting this activity with cultural and life
science topics the class is studying.
3. Ask the children to look at the images
they have created and to envision them as
masks. Ask: Where is the top? Do they need
any further decoration? Invite students to
cut out the masks’ outlines and eyeholes.
Punch holes on both sides of the masks and
attach ribbons. Encourage children to wear
their unique creations.
• construction paper
• string, yarn, or ribbons
• scissors
• markers
• paints
• glue
• one-hole punch
Continued on page 23
Ask students to share how they created
their patterns, if what they created surprised
them, and what they learned. Have children
look at the Green-Spotted Triangle Butterfly
in the kit and discuss its pattern and origin.
Discuss ways in which the butterfly and the
other symmetry objects and images are both
similar to and different from the masks.
sketch a design in pencil on one half of the
paper and cut out the shapes. (The images
that are used in the design can be drawn from
any topic the class is currently studying.) Glue
the banners to a string along their top edge as
shown. Use the finished papel picado strings
to decorate the classroom!
Look for opportunities to connect your
symmetry activities with cultural studies, math
topics like geometry, and life science topics
like life cycles.
Skills: artistic expression, creating and
extending patterns, making cultural
connections, using fine motor skills, and
observing objects
In Mexico, papel picado (perforated paper)
banners are cut from colorful paper in
whimsical and symbolic patterns to decorate
for festivals like the Day of the Dead. The
patterns of papel picado can be simple or very
ornate. To make banners for the classroom,
have each student fold one or more pieces of
colorful tissue paper in half. Ask them to
Skills: artistic expression, creating and
extending patterns, using fine motor skills,
observing objects, and spatial awareness
Skills: artistic expression, creating and
extending patterns, using fine motor skills,
observing objects, and spatial awareness
Illustrate mirror symmetry by making playful
butterflies. Have children research different
kinds of butterflies and moths, looking at
examples of the symmetry within the
patterning of butterfly wings. When students
are ready, have them fold pieces of
construction paper in half. Tell them to cut out
the shape of a half of a butterfly, leaving the
folded area of their paper intact. (You may want
to create simple templates for the children to
follow.) Have the children decorate their unique
butterflies’ wings.
Make playful pinwheels to illustrate rotational
symmetry. Pinwheels are bright, eye catching,
kinetic, and demonstrate rotational symmetry.
Create an “x” in the middle of each square of
paper by folding opposite corners together.
Open the paper and cut the creases to within
one inch of the center. Invite children to
decorate their pinwheels, creating the same
pattern in each of the four quadrants. (You
may want to suggest children use imagery
from ongoing science or cultural studies.) Fold
one flap from each corner to the center, as
shown, without creasing the paper. Affix the
corners in place. Attach the pinwheel to a craft
stick or straw with a brass fastener and blow.
Watch how the pattern spins!
Describe what the branching
pattern is on or a part of.
Draw the branching pattern you see.
● Patterns! Action Math by Ivan Bulloch. New York, NY: Two-Can Publishers, 2002.
● Arabic Geometrical Pattern and Design by Jules Bourgoin. New York, NY: Dover Publications, 1973.
● Beach Patterns: The World of Sea and Sand by Stella Snead. Barre, MA: Barre Publishing, 1975.
● By Nature’s Design by Pat Murphy. Vancouver, B.C: Raincoast Books, 1993.
● Forms and Patterns in Nature by Wolf Strache. New York, NY: Pantheon Books, 1973.
● Kente Colors by Deborah M. Newton Chocolate. New York, NY: Walker and Company, 1996.
● Lots and Lots of Zebra Stripes: Patterns in Nature by Stephen R. Swinburne. Honesdale, PA: Boyds Mills
Press, 1998.
● Mathematics: The Science of Patterns by Keith Devlin. New York, NY: Scientific American Library, 1997.
● Math For Fun: Discovering Patterns by Andrew King and Tony Kenyon. Brookfield, CT: Copper Beech Books, 1998.
● Math in Science and Nature: Finding Patterns in the World Around Us by Robert Gardner. New York, NY:
Franklin Watts, 1994.
● The Nature and Science of Patterns by Jane Burton and Kim Taylor. Milwaukee, WI: Gareth Stevens
Publishing, 1998.
● Nature’s Paintbrush: The Colors and Patterns Around You by Susan Stockdale. New York, NY: Simon and
Schuster Children’s Publishing Division, 1999.
● On the Surface of Things by Felice Frankel and George M. Whitesides. San Francisco, CA: Chronicle Books, 1997.
● Once Upon a GEMS Guide: Connecting Young People’s Literature to Great Explorations in Math and
Science by Lawrence Hall of Science. Berkeley, CA: University of California, 2000.
● Patchwork Patterns by Jinny Beyer. McLean, VA: EPM Publications, 1979.
● Symmetry in Chaos: A Search for Pattern in Mathematics, Art, and Nature by Michael Field and Martin
Golubitsky. New York, NY: Oxford University Press, 1992.
● The Spider Weaver: A Legend of Kente Cloth by Margaret Musgrove. New York, NY: Blue Sky Press, 2001.
● What’s Next, Nina? (Math Matters) by Sue Kassirer. New York, NY: Kane Press, 2001.
This stamp or block, made of teak or a similar wood, is decorated with a design that
is used to create a repeating pattern in textile printing. Wood block textile printing is
still done in some places in India. A printer dips the surfaces of the stamp into a tray
filled with dye and repeatedly presses it onto the cloth, taking care to line up each
impression. Elaborate patterns may require multiple blocks each with an element for
a particular design—for example, one block for the outline, another for filler, and a third for highlights.
To create a multicolored pattern, each block is dipped in a different color and then stamped one on
top of the other, creating the final design. Both chemical and vegetable dyes are used.
The process of textile weaving is a form of linear repetition in action. The
designs of many textiles are also linear repeating patterns. Traditional kente is
handwoven in three to four inch wide strips on a horizontal treadle loom by the
Asante peoples of Ghana, Africa. The strips are then assembled into large
pieces of cloth that are wrapped around the body to make dresses or robes.
Traditionally kente is a high-status garment worn for ceremonial occasions. Patterns are named
and colors may be symbolic. Today’s kente may be printed rather than woven. Kente cloth has
become very popular. Contemporary kente may be found in a wide array of products from
backpacks to baseball caps.
This necklace, created by a cooperative of Maasai women for export, is similar to
traditional Maasai neck collars. With their bold geometric patterns, beaded collars
are a good example of linear repetition. Maasai women often wear many collars at
one time. Maasai women shave their heads, which makes their decorative
ornaments especially striking. Neck collars with jingles, like this one, are worn during
singing ceremonies. The women perform stylized head movements and the jingles add another
musical layer to their songs. Maasai girls make beaded jewelry to catch the attention of Maasai
warriors. Beads were introduced to the Maasai about 200 to 250 years ago. Since then, patterned
beadwork has played an important role in the lives of Maasai women. The tradition of creating
beadwork is passed along from mother to daughter.
This mosaic checkerboard is a regular tessellation. Each square piece is fitted
together without any gaps, and the pattern goes in all directions. This contemporary
piece of mosaic work is part of a much longer mosaic tradition; and while not all
mosaics are tessellations, many are. Mosaic work dates back to 4,000 B.C. in ancient
Mesopotamia. The first mosaics were bits of shell, rock, and clay. Later mosaic work
incorporated stone and colorful glass. This checkerboard was made in India of precisely-cut and
inlaid stones. Game boards like this have been used to play chess, checkers, and draughts for
centuries. There are even images of checkerboards on ancient Greek urns and in Egyptian tombs!
Testudo horsfieldi
The Central Asian tortoise, also called the Russian tortoise, is found in the semi-arid
grasslands and rocky hillsides throughout southern Russia and parts of the Middle
East. The protective shell of the Central Asian tortoise is made of a bone
substructure, covered by pieces of hard horn-like material. These tessellating plates
are called scutes. As the shells of turtles and tortoises grow, the diameter of each
of the scutes increases. A hardy plant eater, the Central Asian tortoise feeds on the dried grasses
and twigs of the harsh Central Asian landscape.
If you look closely you can see that the tessellating pattern of this quilt is made up
of triangles, squares, and long rectangles. This is a good example of a typical
American-style quilt from the 1930s. Women of the Catskills region of New York
made the quilt on consignment for sale at Russell’s General Store in Bovina, New
York. The popular art of making pieced quilts dates back to the 1800s in America
when machine-made fabric became widely available. In principal, quilting is very simple. To create
a bed covering, small pieces or scraps of fabric are sewn together. In practice, however, master quilt
makers demonstrate their skills and artistry through highly complex patterns and designs.
Like the living nautilus, this ammonite grew its spiral shape slowly, adding
successively larger segments to the coil as the animal matured. Ammonites are the
fossil relatives of the living octopus, squid, and nautilus. Ammonites became
extinct, together with the dinosaurs, at the end of the Cretaceous period about 65
million years ago. Ammonite fossils help paleontologists determine the age of
certain sedimentary rocks. Among the most beautiful fossils, ammonites were once animals that
lived deep in the open water of the world’s oceans. Paleontologists have found many species of
them, including long knife-shaped and spiral-shaped forms. The largest ammonites grew to a
diameter of over six feet!
Nautilus pompilius
Nautiluses, part of an ancient line of sea-dwelling creatures, have been on Earth for
500 million years. Like ammonites, nautiluses are cephalopods and are related to
octopuses and squid. The hard spiral-shaped outer shell consists of a series of
chambers separated by curved cross plates; the last and largest chamber houses
the living animal. As the nautilus grows, a new and larger chamber is added. Each
chamber is connected by a small hole or septa. It is believed that nautiluses control their buoyancy
by filling the smaller, empty chambers with gas. Because nautiluses live deep in the ocean, their
life and habits are something of a mystery to scientists.
For centuries, Zulu men of South Africa have been famous for their sturdy and
beautiful spiral baskets woven from grasses and palm leaves. During apartheid,
Zulu men often worked as watchmen at construction sites. These workers, who could
not find traditional natural materials like palm fronds, began to use materials that
they found—including colorful, plastic-coated wires discarded from telephone
installation. The practice of using this recycled material caused some problems, however,
as craftspeople began to disassemble telephone hardware to gather material for their weaving.
Salvaged telephone wire is now supplied directly to the weavers. Traditional imbenge are small
baskets used to store dry food or as beer pot covers. The construction and patterning of today’s
imbenge baskets have been adapted from traditional Zulu designs and are made by women as
well as men.
Pocillopora species
Stony corals, like this branching brush coral, form the backbone of the world’s coral
reefs. Surprisingly, each coral is a colony of very tiny animals, called polyps. The
branching shape of these corals probably helps the organisms in the colony to
receive an adequate supply of food. As each new generation of coral animals grows,
it adds to the branching shape of the colony. Over the course of thousands of years,
the calcareous skeletons of corals, algae, and sponges have cemented together, forming the giant
coral reefs. You can see the location of each tiny polyp by looking at an empty coral under a
magnifier. As they grow, coral polyps secrete a hard structure called chitin. The chitin anchors the
coral and protects the living polyps from predators. The polyps open up at night and filter food
from the surrounding ocean waters. All living coral is part of a very fragile ocean community that is
in danger from the by-products of industries such as agriculture, fishing, and recreational diving.
The beautiful tree-like branching pattern seen inside this plastic cube is the result of
discharged electricity. To create the pattern, tiny negatively-charged particles called
electrons were fired at the plastic, traveling at almost the speed of light using a
Linear Particle Accelerator. When the plastic could not hold any more, the electrons
escaped along the shortest path, leaving a branching figure behind. In a sense, a
Lichtenberg figure is captured lightning. The first Lichtenberg figures were discovered by accident by
the pioneering German electrical experimenter, Georg Christoph Lichtenberg (1742–1799).
Dendrites look like fossil ferns, but they are really a special type of mineral crystal.
Many minerals can form dendrites when conditions are right. This specimen was
formed by the mineral called manganese oxide. Dendrites are most commonly
found in sedimentary rocks and form when those rocks come in contact with
mineral-rich waters. Over time the minerals from the liquid migrate up thin fractures
in the rock. Small amounts of mineral attach to the flat surfaces of the rock. The random process of
attachment and growth is part of the reason that dendrites have a very organic looking form. Like
snowflakes, no two dendrites are exactly the same!
Asteroidea sp.
Starfish are rotationally symmetrical creatures with five to six legs. Some species can
have up to twenty legs! Starfish are perhaps the best known of a group of animals
called echinoderms. (Echinoderms include sea cucumbers, sand dollars, and sea
urchins.) With no front or back, starfish can move in any direction without turning.
They use a series of tiny tube-like feet on their underside to slowly cruise along sand
or rocks in search of mollusks. Once they find potential food, starfish wrap themselves around it,
pulling the mollusk open. Once the mollusk has been opened a crack, the starfish inverts its stomach
outside of its own body and forces it inside the mollusk’s open shell. It then digests the mollusk.
This bold and colorful mola has a symmetrical pattern. Molas are a form
of reverse appliqué traditional to the Kuna people of Panama. Kuna
women wear identical molas in pairs as the front and back of a decorative
blouse. (The term mola refers to both the panel and the blouse.) The
pattern is made by sewing together layers of cloth of different colors and
cutting parts away. The artists who create molas are inspired by almost anything they come in
contact with including nature, village life, dreams, cartoons, books, fantasy and, recently, global
popular culture. The most traditional molas are composed of geometric patterns and were
developed from ancient body painting designs. Many mola patterns exhibit symmetry.
Graphium agamemnon
All butterfly and moth wings are examples of mirror symmetry. This type of mirror
symmetry is common in many animals. In biology it is called bilateral symmetry.
The Green-Spotted Triangle, also called the Tailed Jay Butterfly, has apple-green
spots on speckled brown ground and “stubby tails” on its two lower wings. The
“tail” of the female is longer than that of the male butterfly. The underside of the
wing is gray brown with green markings. It is one of a number of related butterflies that live across
Asia, the Pacific Islands, and the tropical northeast coast of Australia. The adult butterflies have a
wingspan between three and four inches. The adult butterfly is a fast flyer that can be seen
frequenting flowers and will also land at puddles and springs to drink water. This specimen is part
of a special rainforest conservation project where indigenous people rear butterflies and moths to
sell rather than cut down the forest for agriculture.
Your comments about the Teacher’s Guide and the kit’s collections are extremely important to us. Please help us in
the creation of future activity kits by making a photocopy of this questionnaire, filling it out, and sending it the
attention of: Senior Exhibition Developer—Pattern Wizardry Kit, The Brooklyn Children’s Museum, 145 Brooklyn
Avenue, Brooklyn, NY 11213.
Rate the criteria from 1 to 5, with 5 being the highest:
Overall usefulness of the Pattern Wizardry Portable Museum Kit
Introduction to Patterns
Repeat After Me
Tessellation Formations
Spiral Spells
Roots, Shoots, and Rivers
Book List
Addresses math and science
Addresses art, music, and culture
Addresses variety of learning styles
Text easy for teacher to follow
Text easy for students to follo w
Encourages critical thinking skills
Useful for small, cooperative learning groups
Ease of integrating into existing curriculum
Stimulates and captures students’interest
Did you use the kit in conjunction with a visit to the Pattern Wizardry exhibition?
What was the single most helpful aspect of the entire kit?
What aspect, if any, worked least well?
Is there anything you would have liked that wasn’t offered?
Additional Comments: