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.) ● ACKNOWLEDGEMENTS ● Beth Alberty Sara DeAngelis Patricia Hulse Elizabeth Reich Rawson Tim Hayduk Kiyo Matsumoto Britt Sheinbaum Michael Sullivan Esther J. Wahrhaftig Nobue Hirabayashi ● SPECIAL THANKS TO THE FOLLOWING EDUCATORS ● Rebecca Callan Gloria Cones Laurie DeAngelis Edith Doron Karen Jarmon Deborah McDermott William Fulbrecht ● PHOTO CREDITS ● Spirals Aboriginal woman coiling tray—©Bill Bachman & Associates Hurricane Hugo—©Tom Stack & Associates Spider web—©Dietrich Stock Photos, Inc. Tessellations 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 Symmetry Woman making a mola—©Brooklyn Children’s Museum Man painting decorative tiles—©Brooklyn Children’s Museum Orchid stem—©Isaac Hernandez ● FUNDING ● National Science Foundationaon USEOFTHESEMATERIAL S IS ENCOURAGED. U NLIMITED, NON- EXCLUSIVEREPRODUCTIONRIGHT S FORALL EDUCATIONALPURPOSE S AREHEREBY GRANTEDWITHOUT ROYALTY ORFEEPROVIDEDTHA T THE BROOKLYN C HILDREN’S MUSEUMRECEIVE S ADJACENTNAMECREDIT . All other rights reserved. Brooklyn Children’s Museum, 145 Brooklyn Avenue, Brooklyn, New York 11213 Copyright © 2002 by Brooklyn Children’s Museum CONTENTS TEACHER’S GUIDE INTRODUCTION How to Use This Kit Contents Checklist Activity Matrix AN INTRODUCTION TO PATTERNS PATTERN TYPES Repeat After Me Background for Teachers: Linear Repetition Linear Repetition Activities Tessellation Formations Background for Teachers: Tessellations Tessellation Activities 1 3 4 5 6 7 9 10 Spiral Spells Background for Teachers: Spirals Spiral Activities 13 Roots, Shoots, and Rivers Background for Teachers: Branching Branching Activities 17 Symmetry Background for Teachers: Symmetry Symmetry Activities 14 18 21 22 PATTERN MASTERS 25 BOOK LIST 27 COLLECTION OBJECT DESCRIPTIONS 28 KIT EVALUATION 33 TEACHER’S GUIDE INTRODUCTION 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. T 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 HOW TO USE THIS KIT 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. 1 ● TEACHER’S GUIDE INTRODUCTION ● PRESENTING PATTERNS 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. ADDITIONAL RESOURCES 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 www.brooklynkids.org to find more resources and Internet links to support your classroom’s investigations of patterns. POEMS 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. HANDLING OBJECTS 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. PHOTO ALBUM These laminated photographs provide contextual images that show patterns found in nature and patterns made by people. KIT EVALUATION Finally, please photocopy, complete and return the form on page 33 of this guide. Your feedback will improve our future kits. DRUM! MUSIC CD Music is a type of pattern! Listen to repeated sounds and make rhythmic patterns. 2 PATTERN WIZARDRY PORTABLE MUSEUM KIT CONTENTS CHECKLIST Please check that the kit includes all of the items on the checklist. Report any lost or missing items to the museum. CHECKLIST 1 Teacher’s Guide (notebook with activities pages) 11 Manganese Dendrite 2 Photo Album 12 Starfish 3 3 Magnifiers 13 Green-Spotted Triangle Butterfly 4 3 Mirrors Cultural Collection Objects 5 14 Imbenge Basket 15 India Printing Block Drum! Music CD Natural Science Collection Objects 6 Fossil Ammonite 16 Kente Cloth 7 Split Nautilus Shell 17 Maasai Necklace 8 Central Asian Tortoise Shell 18 American Quilt 9 Brush Coral 19 Mosaic Checkerboard Lichtenburg Figure 20 Kuna Mola 10 3 ACTIVITY MATRIX 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: NSES —http://www.nap.edu/readingroom/books/nses/html/ NCTM —http://www.nctm.org/standards/ 4 AN INTRODUCTION TO PATTERNS 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. T 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. 5 CONVERSATION STARTERS 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. BACKGROUND FOR TEACHERS: LINEAR REPETITION 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. L 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? 6 LINEAR REPETITION ACTIVITIES INSTRUCTIONS 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. PASTA PATTERNS ON PARADE—Use 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. AHEAD OF TIME 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. WRAP UP 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. MATERIALS • 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) 7 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. ADDITIONAL ACTIVITIES RHYTHM REPETITION 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. HANDPRINT PATTERNS 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. WEAVING WONDERS Skills: artistic expression, creating and extending patterns, making cultural connections, using fine motor skills, and observing objects 8 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. BACKGROUND FOR TEACHERS: TESSELLATIONS 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. A 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 9 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? CONVERSATION STARTERS 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 investigations. 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. TESSELLATION ACTIVITIES 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 MATERIALS • 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 10 2. Invite children to experiment with different AHEAD OF TIME 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 . WRAP UP 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. INSTRUCTIONS 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. 11 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. ADDITIONAL ACTIVITIES Look for opportunities to connect tessellation activities with math topics like geometry, measurement, and number operations. TESSELLATION FIELD TRIP 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! CRACKER FACTORY CHALLENGE 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. SPONGE PRINT PLACE MATS Skills: artistic expression, creating and extending patterns, using fine motor skills, and observing objects 12 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. BACKGROUND FOR TEACHERS: SPIRALS 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. S 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 13 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. CONVERSATION STARTERS 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? SPIRAL ACTIVITIES 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. MATERIALS • 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 14 3. Once the full length of clay rope has been INSTRUCTIONS: CLAY-COIL TECHNIQUE 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 WRAP UP 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. INSTRUCTIONS: JELLY ROLL TECHNIQUE 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 15 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! ADDITIONAL ACTIVITIES Look for opportunities to connect your spiral activities with life science, math, and cultural topics. SPIDERWEB SUN CATCHER Skills: artistic expression, using fine motor skills, observing objects, and literacy/language arts SPIRAL SEARCH 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. SPIRAL SNAKE MOBILE Skills: artistic expression, creating and extending patterns, using fine motor skills, and observing objects 16 arteries and veins! Branching patterns can also be found in diverse man-made things including roadways, decorative designs, and mobiles. BACKGROUND FOR TEACHERS: BRANCHING 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. T CONVERSATION STARTERS 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? 17 BRANCHING PATTERNS ACTIVITIES INSTRUCTIONS 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. WRAP UP 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. MATERIALS • paper • pencil • tree and plant guides (optional) 18 2. Encourage the children to look carefully BUNCHES OF BRANCHES: AT-HOME ACTIVITY 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 19 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. ADDITIONAL ACTIVITIES Look for opportunities to connect your branching activities with math, physical science, and life science topics being studied in your classroom. MOBILE MOVEMENTS Skills: artistic expression, comparing and contrasting, using fine motor skills, and observing objects LEAF RUBBING 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). INK-BLOWN BRANCHING 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 20 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. BACKGROUND FOR TEACHERS: SYMMETRY 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. S CONVERSATION STARTERS 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 investigations. 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? 21 SYMMETRY ACTIVITIES SYMMETRY MASKS—Create a mask with mirror symmetry. INSTRUCTIONS 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. MATERIALS • construction paper • string, yarn, or ribbons • scissors • markers • paints • glue • one-hole punch Continued on page 23 22 WRAP UP 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! ADDITIONAL ACTIVITIES Look for opportunities to connect your symmetry activities with cultural studies, math topics like geometry, and life science topics like life cycles. PAPEL PICADO 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 23 BUTTERFLIES SYMMETRY PINWHEELS 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! 24 PATTERN MASTER QUILT TEMPLATE 25 PLANT PATTERN SURVEY SHEET Describe what the branching pattern is on or a part of. Draw the branching pattern you see. 26 BOOK LIST ● 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. 27 COLLECTION OBJECT DESCRIPTIONS LINEAR REPETITION INDIA PRINTING BLOCK 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. KENTE CLOTH 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. MAASAI NECKLACE 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. 28 ● COLLECTION OBJECT DESCRIPTIONS ● TESSELLATIONS MOSAIC CHECKERBOARD 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! CENTRAL A SIAN TORTOISE SHELL 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. AMERICAN QUILT 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. 29 ● COLLECTION OBJECT DESCRIPTIONS ● SPIRAL OBJECTS FOSSIL AMMONITE 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! SPLIT NAUTILUS SHELL 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. IMBENGE BASKET 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. 30 ● COLLECTION OBJECT DESCRIPTIONS ● BRANCHING OBJECTS BRUSH CORAL 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. LICHTENBERG FIGURE 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). MANGANESE DENDRITES 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! 31 ● COLLECTION OBJECT DESCRIPTIONS ● SYMMETRY OBJECTS STARFISH 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. KUNA MOLA 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. GREEN-SPOTTED TRIANGLE BUTTERFLY 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. 32 KIT EVALUATION 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: CRITERIA 1 2 Overall usefulness of the Pattern Wizardry Portable Museum Kit Introduction to Patterns Repeat After Me Tessellation Formations Spiral Spells Roots, Shoots, and Rivers Symmetry 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: 33 3 4 5 N/A
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