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Building and into standards-based learning

Mathematics K through 6

Ron De Long, M.Ed. Janet B. McCracken, M.Ed. Elizabeth Willett, M.Ed.

© 2007 Crayola, LLC Easton, PA 18044-0431 Acknowledgements Table of Contents

This guide and the entire Crayola® Dream-Makers® series would not be possible without the expertise and tireless efforts Crayola Dream-Makers: Catalyst for Creativity! ...... 4 of Ron De Long, Jan McCracken, and Elizabeth Willett. Your passion for children, the , and creativity are inspiring. Thank you. Special thanks also to Alison Panik for her content-area expertise, writing, research, and curriculum develop- Lessons ment of this guide. Garden of Colorful Counting ...... 6 Crayola also gratefully acknowledges the teachers and students who tested the lessons in this guide: In the Face of ...... 10 Analysis of symmetry Barbi Bailey-Smith, Little River Elementary School, Durham, NC Gee’s-o-metric Wisdom ...... 14 Geometric modeling Rob Bartoch, Sandy Plains Elementary School, Baltimore, MD of Love Beads ...... 18 Algebraic patterns Susan Bivona, Mount Prospect Elementary School, Basking Ridge, NJ A Bountiful Table—Fair-Share Fractions ...... 22 Fractions Jennifer Braun, Oak Street Elementary School, Basking Ridge, NJ Barbara Calvo, Ocean Township Elementary School, Oakhurst, NJ Whimsical Charting and Checking ...... 26 Chart, estimate, analyze data Pat Check, Spring Garden Elementary School, Bethlehem, PA Shaping Up With Shapes ...... 30 Spatial measurement Trish Davlante, Michael Jordan Community School, Chicago, IL Toying Around With ...... 34 Geometric forms Regina DeFrancisco, Liberty Corner Elementary School, Basking Ridge, NJ Measure Twice, Create Once ...... 38 Measurement and scale Beth Delaney, Fredon Township School, , NJ It’s About Time…Average Time! ...... 42 Elapsed time Carly Doughty, Little River Elementary School, Durham, NC Purchasing Flower Power! ...... 46 Money and estimates Amanda Warner Grantz, Oakhurst Elementary School, Fort Worth, TX Personal Math Motto Banners ...... 50 Equations and proofs Barbara Grasso, John J. Jennings Elementary School, Bristol, CT Animals: A Brood, a Clutter, a Drift, and More! ...... 54 Algebraic relationships Craig Hinshaw, Hiller Elementary School, Madison Heights, MI Keeping Track of Time ...... 58 Time measurement Janice House, Little River Elementary School, Durham, NC Spin a Radial Design ...... 62 Radial symmetry Charlotte Ka, PS 132K, Brooklyn, NY Nancy Knutsen, Triangle School, Hillsborough, NJ Balls: Classify, Roll, and Bounce ...... 66 Measurement Kay La Bella, Foothills Elementary School, Colorado Springs, CO Secret Castles: Solve the Number Mysteries! ...... 70 Problem solving Kamyee Ladas, Mount Prospect Elementary School, Basking Ridge, NJ Mazes and Labyrinths: Design Your Pathway ...... 74 Geometric patterns Cara Lucente, Gayman Elementary School, Plumstead, PA The Math of Maps ...... 78 Coordinate geometry Jenna Makos, Catholic Charities After- School Program, Phillipsburg, NJ Estimate a Pot’s Capacity ...... 82 Volume and capacity Elyse Martin, Michael Jordan Community School, Chicago, IL What Are the Chances? ...... 86 Probability Annette Mauer, Freeman Elementary School, Phillipsburg, NJ Symmetrical Starburst ...... 90 Transformational symmetry Marge Mayers, Barley Sheaf School, Flemington, NJ Stock-Smart ...... 94 Value and investments Val Negra, Mountain Way Elementary School, Morris Plains, NJ Geometric ...... 98 Relationships of patterns Jen O’Flaherty, Sandy Plains Elementary School, Baltimore, MD Alison Panik, Trinity Kids Club, Trinity Wesleyan Church, Allentown, PA Choosing Crayola Art Supplies ...... 102 Jennifer Parks, T. J. Lee Elementary School, Irving, TX Kathy Prichard, Feeeman Elementary School, Phillipsburg, NJ Nancy Rhoads, Curlew Creek Elementary School, Palm Harbor, FL Lynn Schatzle, Wood Creek Elementary School, Farmington Hills, MI Karen Sommerfeld, Foothills Elementary School, Colorado Springs, CO Neila Steiner, CS 102, Bronx, NY Tom Tschumper, Princeton North Elementary School, Princeton, MN The language and concepts of and art are intrinsically linked, with both using symmetry, proportion, geometry, symbols, reasoning, linear , and more. From Greek and Roman architects, to arts and inventors such as Leonardo do Vinci, Roy Lichtenstein, Kendall Shaw, and the Gee’s Bend quilters, students explore our world, , and order in principles of art and design based on these concepts. We hope that these lessons will aid you in building children’s creative problem-solving skills, and a deeper, memorable understanding of mathematics by experiencing and seeing these concepts through learning activities. Nancy A. De Bellis Director, Education Marketing Crayola

Crayola Dream-Makers is a series of standards-based supplemental ©2007 Crayola, LLC. All rights reserved. curriculum resources that contain lesson plans for educators Permission inquiries should be directed to: teaching kindergarten through 6th grade. Each guide uses visual Crayola art lessons to stimulate critical thinking and problem-solving for Attn: Content Editor individual subject areas such as Math, Language Arts, Science, and 1100 Church Lane Social Studies. Students demonstrate and strengthen their knowledge Easton, PA 18044-0431 while engaging in creative, fun, hands-on learning processes. www.crayola.com/educators Printed in the of America ISBN: 0-86696-327-8 Building fun and creativity into standards-based learning  Mathematics Mathematics  Crayola® Dream-Makers®: Catalyst for Creativity!

Each Crayola Dream-Makers guide provides elementary classroom and art teachers with 24 arts-focused lessons that extend children’s learning and enhance academic skills. Align these lessons with your school district and state curriculum standards. Stay flexible in your teaching approaches with adaptations like these.

• Be prepared. Read through the lesson first. Create an art sample so you understand the process. Children learn in many different ways • Discover new resources. Each lesson contains background , and craft examples, representative student artwork, vocabulary builders, and discussion ideas. Use these suggestions as a spring- Howard Gardner has identified eight types of intelligences and board to find resources that address your students’ interests and are pertinent to your community. Search may add others. Arts-integrated learning experiences enable Web sites such as Google Image to locate fine art. Stretch student imaginations and their awareness of the children to more fully develop a wide range of skills and world around them. understandings. • Seek creative craft materials. Ask children’s families and local businesses to recycle clean, safe items • Linguistic intelligence involves sensitivity to spoken and for project use-and take better care of the environment, too. Recycle, Reuse, Renew! written language, the ability to learn languages, and the • Showcase student achievements. Create banners to accompany curriculum project displays in your capacity to use language to accomplish certain goals. class, school, or community. Post the lesson’s standards-based objectives with displays to demonstrate • Logical-mathematical intelligence consists of the capacity broad-based student learning. Demonstrate how children’s accomplishments have personal meaning and to analyze problems logically, carry out mathematical promote life-long learning through portfolio documentation. operations, and investigate issues scientifically. • Make this book your own. Jot down your own ideas as you plan and reflect on students’ learning • Musical intelligence involves skill in the performance, experiences. Combine art techniques and lesson content to fit goals for your students and classroom. composition, and appreciation of musical patterns. Substitute other transformative craft materials. With students, make content webs of possibilities for • Bodily-kinesthetic intelligence entails the potential of using extending learning opportunities. one’s whole body or parts of the body to solve problems. • Build connections. Collaborate with your students, other teachers, administrators, in residence, • Spatial intelligence involves the potential to recognize and and community groups to plan lessons that are unique. Work together to promote creative thinking! use the patterns of wide space and more confined areas. • Write DREAM statements. As part of the assessment process, students are asked to reflect on their • Interpersonal intelligence is concerned with the capacity work in a dream journal. Before the lesson, Dream statements are expected to, capture children’s prior to understand the intentions, motivations, and desires of other knowledge about each topic. After each lesson, students state in writing how they will use what they people. It allows people to work effectively with others. have learned and dream about possibilities for future exploration.. • Intrapersonal intelligence entails the capacity to understand • Funding resources. Crayola Dream-Makers lesson plans have been used in school programs funded by oneself, to appreciate one’s feelings, fears, and motivations. a variety of federal, state, local, and private grants. For more information about grants and grant writing • Naturalist intelligence enables human beings to recognize, visit The Foundation Center at www.fdncenter.org. categorize, and draw upon certain features of the environment. (Gardner, 1999: pp. 41-43, 52) The lessons in this book are intended to address content benchmarks and grade-level expectations in mathematics along with a heavy concentration of key art concepts. All lessons are teacher- and Find More Resources at www.crayola.com/educators student-tested and follow a consistent Supplementary materials for Dream-Makers guides include: format to support you in planning creative, fun learning opportunities for your students. • Printable certificates for recognizing children’s participation and adults’ support • Thousands of images of children’s art Benefits of Arts Integration • Demonstration videos for teaching arts-integrated lessons The 2006 report Critical Evidence–How Benefit • Lesson-by-lesson correlations to California, New York, Texas, Student Achievement, published by the National Assembly Illinois, and Florida standards of State Arts Agencies in collaboration with the Arts Education • Printable resource guides for educators and administrators Partnership, identifies a number of ways that arts learning experiences • More than 1,000 free, cross-curricular lesson plan ideas on wide- benefit students. Teachers who consciously integrate arts-based practice into ranging topics, all developed by experienced educators. Sign up for their teaching bring these benefits to their students. free monthly newsletters to keep you abreast of the newest Crayola products, events, and projects. “Certain arts activities promote growth in positive social skills, including self-confidence, self-control, conflict resolution, collaboration, empathy, and social tolerance. Research evidence Bibliography demonstrates these benefits apply to all students, not just the gifted and talented. The arts can a key role in developing social competencies Gardner, H. (1999). Intelligence Reframed: Multiple Intelligences for the 21st Century. New York: Basic Books. among educationally or economically disadvantaged youth who are at greatest Marzano, R.J. (March 2005). ASCD Report–Preliminary Report on the 2004-05 Evaluation Study of the ASCD Program risk of not successfully completing their education.” (p. 14) for Building Academic Vocabulary. Reston, VA: Association for Supervision and Curriculum Development. National Assembly of State Arts Agencies (NASAA) in collaboration with the Arts Education Partnership. (2006). According to Diane Watanabe and Richard Sjolseth, co-directors of the Institute of Learning, Teaching, and the Critical Evidence–How the ARTS Benefit Student Achievement. Washington, DC: Author. Human Brain, when there is joy in learning, student achievement soars. Smith, M.K. (2002). Howard Gardner and multiple intelligences. The encyclopedia of informal education, “When students find joy in their creative outlets, there is a positive carryover to school in general. http://www.infed.org/thinkers/gardner.htm. Retrieved from http://www.infed.org/thinkers/gardner.htm May 9, 2007. Emotion, interest, and motivation promote learning and memory. Brain research shows the brain Reprinted with permission. produces as least three pleasure chemicals when joy is present: endorphins, dopamine, and serotonin. Watanabe, D., & Sjolseth, R. (2006). Lifetime Payoffs: The Positive Effect of the Arts on Human Brain Development. These chemicals account for the emotional states produced by self-satisfaction, positive self-image, Miami, FL: NFAA youngARTS. Reprinted with permission. passion for one’s art, and joy in learning.” (2006, p. 20)

Building fun and creativity into standards-based learning  Mathematics Mathematics  Garden of Colorful Counting

Objectives Multiple Intelligences Artwork by students from St. Theresa School, Students recognize sets of objects and understand numbers Hellertown, . Logical-mathematical Spatial and ways of representing them. Children create and count beds of garden flowers in Naturalist colorful collages to demonstrate that they understand sets Spatial and their representations. Naturalist

National Standards Visual Arts Standard #3 Mathematics Standards Chooses and evaluates a Number and Operations range of subject matter, Understand numbers, ways of representing numbers, relationships among numbers, and number systems symbols, and ideas Understand meanings of operations and how they relate to one another Compute fluently and make reasonable estimates Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and in other contests Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving

Background Information Vocabulary List In April 1887 a spectacular marvel occurred. A shipment of 20 Use this list to explore new vocabulary, create idea webs, glass flowers arrived in from Dresden, Germany. or brainstorm related subjects. The flowers were the first of 847 life-size glass models that were created and shipped to Harvard University in Cambridge, • Math concepts Fraction Organize Massachusetts. Two German artists, Leopold Blaschka and his Classify Collection Group Pair son Rudolf, created these garden marvels that included models Compare Less Percentage of plants, flowers, and other botanical specimens. Decimal More Set Today the more than 3,000 glass flowers and plants are Dozen Number Skip counting used mostly as teaching tools for students studying the plant Equal Numeral Sort sciences at Harvard. In addition to being stunningly accurate Even Odd to the smallest detail, these spectacular wonders are in bloom all year. The Ware Collection of Glass Models of Plants, as the • Art concepts collection is known, is housed in two rooms on the third floor Collage Rubbing Texture of the Botanical Museum of Harvard University. It is the only collection of its kind in the world. • Science concepts Bulb Petal Stamen Flower Pistil Stem Resources Leaf Seed Alison’s Zinnia by Anita Lobel Dazzling display of botanically correct illustrations arranged in an alphabet book format. Collection of detailed flowers of various colors, shapes, and sizes. Planting a Rainbow by Lois Ehlert Colorful collage- illustrations. Inspires children and adults alike to plant gardens of blooms both in soil and on paper. Rich language and high- artwork supplement early elementary studies of plants, flowers, color, and counting. Rooster’s Off to See the World by Eric Carle Rooster collects—and counts—companions along his travels. Carle’s colorful collages lead early elementary children through Artwork by students from an addition and subtraction adventure of counting up and Little River Elementary School, Monet’s Garden counting down. Durham, North Carolina. Photo by R. De Long Floral Motif Textile The Glass Flowers at Harvard by Richard Evans Schultes Teachers: Barbi Bailey-Smith, from Kashmir, and William A. Davis Carly Doughty, Janice House Contemporary, For upper-elementary and middle school students. Photo essay date unknown presents Harvard’s unique collection of amazing glass flowers Artisan unknown and the story of how they were made. Private Collection.

Building fun and creativity into standards-based learning  Mathematics Mathematics  Garden of Colorful Counting

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Show three flowers in a plastic Show a box with three clay Show a garden diagram with Process: Create flowers Preparation vase and two others loose. Guide pots inside and two outside. Ask four equal sections, each section Session 3 . Cut simple, small flower shapes from the textured rubbing papers. Create multiples of several kinds of flowers. and children to create number sentences children to write math sentences labeled with a different type of 20-30 min. Make some flowers unique. Create new species of flowers that are not known to science. Add stems and leaves identifying how many flowers they identifying how many clay pots flower. Ask students to create to the flowers. Store flowers in plastic bags. Discussion count in total and how many are they count in total, and how many mathematical statements about in the sets in and out of the vase. are in sets inside and outside the this garden using fraction, decimal, Process: Build a set garden Build a multiplication garden Build an equivalent Arrange different sets in the vase box. Try different combinations of and percentage computations. to practice this skill. same size sets in and out of the box. Change the diagram to offer Session 4 6. On paper, students write num- 6. On paper, students write a fraction garden ber phrases such as 3 + 4 + 2. multiplication fact. Collect visual examples of different Encourage the use of multiplication. different computation opportunities. 20-30 min. 6. On paper, students write an types of flowers, both real and in Display a bouquet of flowers and Display a variety of examples . Fold another sheet of paper . Glue flowers grouped in sets equivalent fraction fact. photographs and other art. Display books of flowers for children to look of flowers, real ones, books, and in half. Along the fold draw a inside beds to reflect the . Teams of students glue flower pictures of flower gardens and at and use to make flower sketches. catalogs about flowers, and art garden divider, such as a fence multiplication fact. groupings reflecting equivalent gardens with multiple beds of plants. Invite children to choose which depicting flowers. Invite students to post, scarecrow, or birdhouse, 8. Use to outline blossoms. fraction facts on craft paper to Read the book Rooster’s Off to flowers are their personal favorites explore these resources to prepare to separate two garden beds. Draw flower features such as create a garden . See the World aloud. Stop at various and explore why. Is it the color, to design their own garden plots. 8. Glue flowers into place to show stems and leaves. Add other points in the story to ask questions size, shape, fragrance, design of the the number phrases. Air-dry garden objects to each bed. such as, “If we had two small sheds, flower, or some other attribute that the glue. how many animals could we put appeals to them? in each shed?” Invite children to Assessment • Children count the number of • Children write math sentences • Students write mathematical explain how they would group flowers they drew in both beds describing the flowers in their descriptions of their garden the animals. and write the numerals on their collages in different ways. plans. Ask them to use fraction, drawings or on a separate paper. Encourage them to try to decimal, and percentage terms ® Crayola • Crayons • School Glue • Scissors • Children write math sentences write addition, subtraction, to describe the ways they could Supplies describing the flowers in their multiplication, and division plant different flowers in their collages in different ways. Check sentences. Check for accuracy. gardens. Interview students Other • Construction paper • Plastic bags that seal • Tag board, poster board, or recycled file folders for accuracy. as needed. Materials • Textured materials such as leaves, plastic sink mats, very coarse sandpaper, screens, netting, or latch-hook mats • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things • Rolled craft paper they learned.

Set-up/Tips • Cover any sharp edges on textured materials (such as screens) with thick layers of masking tape. Extensions Children create a collage depicting Students design their own gardens with colored , stamps, rulers, a garden. Display gardens in pairs on and markers. Encourage students to choose their favorite flowers and • Students label plastic bags with their names. a bulletin board with a strip of paper calculate percentages, fractions, and decimal descriptions of the use of (fence) separating each pair. Invite space in their virtual gardens. Calculate perimeter and area. Fence in the Process: Create sets Use multiples and division Use equivalent fractions children to count and compare the garden with toothpicks. Session 1 1. Students put a variety of objects 1. Students show multiplication 1. Students show equivalent number of flowers of different types Plan, plot, and plant flower gardens in a schoolyard, community park, or at 20-30 min. into sets, such as crayons, and division of sets of objects fractions with concrete models. (colors, sizes, shapes) in each pair a local retirement community. Solicit flower donations from local nurseries desks, and people. with concrete models such as Use cut shapes to experiment. of gardens. and businesses. Use math skills to plan and calculate how flower beds will . Students justify why they marbles or books to achieve . Create a number representation Plant mini gardens. Fill recycled be divided and filled with color. Visit the garden, photograph the beds, and created the sets. Combine multiplication facts such as of the model for equivalent containers with soil. Use craft sticks use math to describe the results. sets and record the findings. 2 x 3 = 6. fractions such as 1/4 + 1/4 + to divide each mini garden into Take a different view of flowers with lesson plans such as Table for Two . Students demonstrate correct 1/4 + 1/4 = 1; 2/8 + 4/16 + two beds. Plant seeds in each bed. or Fluttering Focus on Crayola.com. results. 1/2 = 1. Record number of seeds planted. As plants grow, continue to record . Challenge students to demon- the number of seedlings on each strate a proof. half, the number of leaves, flowers, Process: Create texture rubbings and other details. Sketch the plants’ . Session 2 . Place construction paper on top of flat textured materials. Rub over the paper with the side of an unwrapped Keep excitement for gardens 20-30 min. . Press hard to achieve dramatic color effects. Encourage children to experiment. growing! Check out the Underground Garden lesson plan on Crayola.com! Create blended-color rubbings Create shadow rubbing effects . For unique multicolor effects, . Experiment with different rub two different colors over effects: Move the paper slightly the same texture. and rub a second time with a different color. Or rub over a different textured item.

Building fun and creativity into standards-based learning  Mathematics Mathematics  In the Face of Symmetry

Objectives Multiple Intelligences What Does It Mean? Artwork by students from Children identify geometric shapes and differentiate St. Theresa School, Logical-mathematical Logical-mathematicalAsymmetry: when one Hellertown, Pennsylvania. the attributes of symmetry and asymmetry in a variety of side of a point, line, or different shapes. Naturalist Spatialplane is arranged so that Children in grades 3 to 6 research their facial images with Spatial it differs from and does mirrors to prove symmetry or asymmetry. Spatial not balance with the Children in grades 5-6 sculpt a symmetrical 3-D model of opposite side their 2-D drawing. Bas-relief: short 3-D Children design a face whose details demonstrate symmetry. projections on a , as in or weaving Symmetry: when one National Standards side of a point, line, or Visual Arts Standard #2 Mathematics Standards plane balances another, Uses knowledge of structures and functions Geometry with opposite sides Apply transformations and use symmetry to demonstrating identical analyze mathematical situations or similar arrangement, form, and size Grades 3-6 Reasoning and Proof Select and use various types of reasoning and methods of proof

Background Information When Pigasso Met Mootisse by Nina Laden Alexander Calder, “Sandy” to his friends, was born near Feuding animal artists turn their neighboring farms into dueling Philadelphia, Pennsylvania, to a family of artists. When works of art. Bold colors, contrasting portrait and Sandy was only 5 years old, he made little wood and wire styles, and clever humor appeal to students in all grades. people and animals. At age 8, he made jewelry for his Provides details about the parodied artists, Picasso and Matisse. sister Peggy’s doll. Sandy always liked to think of new contraptions. In the fourth grade he made an -blotting Concept List pad to hang on the side of his desk. As an adult he invented Use this list to explore new vocabulary, create idea webs, many new and playful ways to make sculpture, including or brainstorm related subjects. portraits out of wire; hanging, moving mobiles; and giant standing steel stabiles. Many of the shapes observed in this • Natural symmetry Animals & insects Leaves art illustrate asymmetry. Human faces Joan Mirò was born in 1893 in Barcelona, Spain, in a region known as Catalonia. He began to make art at the • Symmetry in the arts Performing arts Visual arts age of 8. As a young man, a serious illness ended his career Mime Oriental and as a bookkeeper and contributed to his decision to dedicate Persian rugs himself to painting. Like other artists of the early 20th century, he was drawn to Paris, France, where he met many other important artists. His art is marked by his use of • Explore symmetry Capital letters Symmetrical expressive colors, lines, and large shapes, often arranged on Palindromes plane figures a simple background, conveying a dreamlike atmosphere. Reflection & Mirò always stayed close to his Catalan roots, and often mirror image incorporated the people, places, and images of his Artwork by students native land in his work. Like Calder, many of the shapes • Terms Assymetry Symmetrical balance observed in Mirò’s art depict asymmetry. from Catholic Charities Balance Symmetry After-School Program, Bilateral symmetry Three dimensional Phillipsburg, New Jersey. Congruence Two dimensional Teacher: Jenna Makos Resources Line of symmetry It Looked Like Spilt Milk by Charles G. Shaw Near symmetry Splotches of spilt milk against a blue background inspire Radial symmetry all ages to envision other images such as a rabbit, a squirrel, or a tree. Illustrations lead students to see the world in a new way. The Essential Alexander Calder by Howard Greenfield Artwork by students from Hanging, dangling, harmoniously asymmetrical mobiles Foothills Elementary School, accompany an account of Calder’s life. Fascinating facts, Colorado Springs, Colorado. compelling quotes, and background about cultural Teachers: Kay La Bella, Karen Sommerfeld influences appeal to upper elementary students.

Building fun and creativity into standards-based learning 10 Mathematics Mathematics 11 In the Face of Symmetry

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Ask children to name basic shapes. Review symmetry. Challenge Discuss that a line of symmetry Process: Find a face and add details Add details Preparation List all the shapes children can find students to identify which English can exist in two AND three dimen- Session 2 6. Study positions of painted shapes. Search for a face among the shapes. . Add additional symmetrical in the classroom. capital letters are symmetrical. sions. Think of examples. and 20-30 min. . Fill areas around the face shape with Overwriters Under-Color Markers details if necessary. Discussion Read It Looked Like Spilt Milk Explore symmetry in the human The human face appears flat in or a similar title. Children cut or face and nature. Use mirrors to photographs but really it is a three to bring out facial features. Outline shapes with lines of color. 6. Add color to the various shapes tear assorted colored paper shapes. review and explore the concept. dimensional (3-D) object. It has 8. Embellish and strengthen the face concept by adding details with both of the face keeping consistent Imagine what the shapes could be. Fold magazine pictures of face in height, width, and depth. Under- and Over-Color Markers. with the idea of symmetry. Draw lines or fold down the middle half and place fold against mirror 3-D objects can be represented of shapes to illustrate symmetry to see symmetry of the full face. with 2-D symbols but 3-D objects Process: Research symmetry and Create a 3-D model and asymmetry. Are all faces symmetrical or are quite different. A circle can Session 3 near symmetry . Using the 2-D plan as a guide, near symmetrical? Take a digital represent a sphere. A square a cube, 15-20 min. . Position artwork with line of create a 3-D model of the photograph of each student’s full a triangle a , a rectangle a symmetry along a mirror to monster face with Model face. Print each photo on copy rectangular prism. reveal whether it is perfect Magic compound on tag board. paper. Fold sheets in half on the symmetry. Compare reflection Determine the line of symmetry. face’s line of symmetry and place with actual artwork. 8. Create 3-D forms, such as fold against a mirror to compare spheres where circles were used symmetrical face with actual face. 10. Slide mirrors across artwork to see new symmetrical faces in 2-D. Glue pieces in place. Look at reproductions of art created by Joan Mirò and Alexander Calder. and designs. . Add symmetrical details Display portraits by Matisse and Picasso. Read When Pigasso Met Mootisse with markers. or another appropriate book. Talk about how symmetry and asymmetry 10. Display 2-D drawings with 3-D affect the balance of shapes and features. models and objectives.

Crayola® • Markers • Overwriters® Markers • • Paint Brushes • Colored Pencils • Markers Assessment • Children identify shapes in their • Older children draw faces with increasing levels of detail. Supplies • Model Magic® • School Glue own artwork and the artwork • Students explain how their own artwork is symmetrical in a written or of classmates. oral proof, citing evidence proving the symmetrical features in the faces Other • Paper towels • Recycled newspaper • Water containers • Tag board • White paper • Children explain the details they created. Materials • White drawing paper that make their face designs • Students recognize where plan modifications were necessary for symmetrical. completion of the project. Set-up/Tips • Cover painting surface with recycled newspaper. • Draw first half of face on one side • Students identify details that create asymmetry in each other’s artwork. • Encourage children to load brush so they have enough paint to make of paper using heavy marks. substantial shapes, but not so much that strokes are hard to control. Fold paper in half and hold to window. Trace other half of • Students correctly represented 2-D drawing on opposite side of paper. shapes with 3-D forms to sculpt a bas-relief model of their plans. Process: Paint shapes and fold Draw symmetrical Session 1 1. Fold paper in half. Crease. Open paper flat. monster face • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things they learned. 20-30 min. . Use an Overwriters Under-Color Marker to draw a line along the fold. 1. Fold paper in half. Crease. Open flat. . Paint a variety of shapes on one side of the fold. Extensions Make symmetrical cloud books. Students make symmetrical names. Print first names using all capital . While the paint is still wet, fold paper closed. Press down gently with . Draw one half of monster face Children paint several symmetrical letters. Identify letters that are symmetrical. Draw lines of symmetry through palm and fingers. Be careful not to push paint beyond the edges of using geometric shapes on one cloud shapes on small squares of each symmetrical letter. Next fold colored paper (one piece for each letter), the paper. side of the fold. blue paper. Attach dry cloud designs crease, and open flat. Paint one half of each symmetrical letter along the to every other page of a folded fold and press closed. Open. Paint asymmetrical letters on one side of the . Open the paper. Are painted designs on both sides of the paper . Fold drawing back to opposite side of paper. paper book. Children write or draw fold line, being sure one edge of the letter is on the fold. Press paper closed. symmetrical or asymmetrical? Air-dry painted designs. about what they see in each design. Open to reveal the new letter design. Air-dry all letters. Cut out letters and . Hold up the drawing to a glue names on colored poster board. window and trace the Younger children and those drawing on the opposite side with visual or visual processing Expand symmetry research into the third dimension with the Sweet of the page. Open to reveal a impairments may find it helpful to Symmetry craft on Crayola.com. complete symmetrical face. trace the dried paint shapes with Encourage children with exceptional talents to identify symmetry in a their fingers, one on each side. variety of art forms, letters or characters in other languages, vehicle design, and other challenging topics.

Let symmetry studies take flight with the Insect Symmetry lesson plan on Crayola.com.

Polish Paper Cuttings unknown Cut colored paper 9" x 9" Private Collection. Building fun and creativity into standards-based learning 12 Mathematics Mathematics 13 Gee’s-ometric Wisdom

Objectives Multiple Intelligences What Does It Mean? Students identify increasingly advanced geometric shapes and Linguistic Logical-mathematicalBalance: equal distribution demonstrate how several shapes can be combined to create new of colors, lines, textures, and different shapes. Logical-mathematical and shapes to give parts of Students experiment with various geometric designs to create Spatial a composition equal visual aesthetically pleasing paper quilts using their own original weight or emphasis patterned papers. Congruence: the harmoni- Children use the language of mathematics appropriate to their ous relationship between grade and ability levels to write and talk about geometric relation- figures that are the same ships in quilt designs created by themselves and their classmates. size and the same shape Symmetry: when one side of a point, line, or National Standards plane balances another Visual Arts Standard #4 Mathematics Standards with opposite sides Understanding the visual arts in relation to Geometry demonstrating identical history and cultures Use visualization, spatial reasoning, and or similar arrangement, Visual Arts Standard #6 geometric modeling to solve problems form, and size Making connections between visual arts and Communication other disciplines Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

Background Information Vocabulary List People create quilts to keep themselves covered and warm. Use this list to explore new vocabulary, create idea webs, Quilts can also be objects of . The women of Gee’s or brainstorm related subjects. Bend—a small, remote community in rural Alabama—have • Geometric terms Circle Perpendicular created hundreds of quilt masterpieces for about 100 years. Congruence Rectangle They traditionally work with used, discarded, or rejected bits Hexagon Square of cloth and follow linear patterns that combine shape and Octagon Symmetry color, often with the flavor of the African textile traditions Parallel Triangle handed down from their ancestors. Gee’s Bend (and many Parallelogram other) quilts are products of everyday life, mental agility, deep sensitivity, and geometric genius. Gee’s Bend quilts • Visual arts vocabulary Arrangement Light are even featured on U.S. postage stamps! Balance Artwork by students from Border designs T.J. Lee Elementary School, Contrast Grandmother’s Irving, Texas. Resources Design Flower Garden Teacher: Jennifer Parks Shapes, Shapes, Shapes by Tana Hoban Hue Log Cabin Wordless picture book. Challenges young students to find Illusion Wedding Ring geometric shapes in everyday life. Shapes include circles, Juxtaposition Quilting frame parallelograms, triangles, and . Shadow The Quilts of Gee’s Bend by John Beardsley, William Arnett, Pauljane Arnett, & Jan Livingston Older elementary students enjoy these stories of the lives of the quilters of Gee’s Bend, Alabama. Illustrated with color photographs of the geometric quilts made by these women. The Rag Coat by Lauren A. Mills Readers learn that patterned fabric scraps are more than just the sum of their shapes, sizes, and colors. Touching story for Artwork by students from all ages. Mount Prospect Elementary School Basking Ridge, New Jersey. Teachers: Susan Bivona and Regina DeFrancisco

Artwork by students from T.J. Lee Elementary School, Irving, Texas. Building fun and creativity into standards-based learning Teacher: Jennifer Parks 14 Mathematics Mathematics 15 Gee’s-ometric Wisdom

K-2 3-4 5-6 K-2 3-4 5-6 Suggested With students, prepare a display of quilts or quilt pictures. Show shapes such as rectangles, squares, triangles, Process: Cut triangles Color patterns Preparation circles, parallelograms, and a rhombus near the quilt display. Session 2 . Fold a square diagonally, then open flat. Cut along fold line to create . Plan color for the concept. and 20-30 min. two triangles. Fold a few triangles in half and cut along folds to create Make sure color patterns Invite students to identify Review increasingly more complicated geometric shapes. Introduce smaller triangles. support the concept and add Discussion basic geometric shapes in their vocabulary of geometric relationships such as angles, symmetry, adjacent, to design effectiveness. environments. parallel, perpendicular, and congruent. Experiment with how paper Demonstrate the illusionary effects of juxtaposing light and dark . Fill the patterns with color. shapes can be combined to make contrasting shapes. Create more triangles Create additional shapes new shapes. Who can put two Research several sophisticated quilt designs. Identify all of the shapes triangles together to form a square? used. How are the shapes oriented to create the designs? How does the . Cut other squares into a variety . Fold some squares in other What shape is formed when several quilt design demonstrate balance and symmetry? Can students find of triangle sizes and shapes. directions. Cut shapes such squares are set side by side? congruent shapes within the quilt designs? as smaller squares, rectangles, and parallelograms. Encourage Demonstrate how cutting one Ask students to find and describe examples of shapes within shapes. shape can transform it into others. students to make a variety of shapes.

Examine and discuss quilt display. What connections can students make between geometry and quilt design? Process: Design with triangles Design with shapes . Experiment with various arrangements of quilt squares Discuss number concepts includ- Session 3 . Children arrange triangles on . Students experiment with on mounting paper. ing multiplication fact families, 20-30 min. the 9-inch paper to form new various arrangements of shapes fractions, decimals, percentages. decorative squares. on the 9-inch paper to create How could these concepts be new patterns and designs. represented visually? Brainstorm and illustrate examples. 6. Encourage children to rotate, slide, and reposition shapes to see various effects. Invite them to look at each other’s arrangements and exchange ideas. Settle on a final design. Glue shapes on the paper. Crayola® • Colored Pencils • Markers • School Glue • Scissors . Mount square to a larger sheet in a contrasting color. Supplies 8. Punch several holes across top and bottom borders of mounting paper. Tie yarn through holes.

Other • Construction paper • Hole punch • Ruler • Sealable plastic bags • Yarn Process . Children orally explain their . Students write paragraphs describing the mathematical thinking used Materials Session 4 design decisions using geomet- in designing their projects. How did they decide which shapes to 20-30 min. ric and visual arts terms. combine? What were the results? What revisions did they make and Set-up/Tips • Store papers between sessions in labeled, sealable plastic bags. 10. Students write one or two why? Encourage use of mathematical terms. Display projects and sentences describing the colorful paragraphs together. Process: Design paper Prepare quilt squares project. Display projects and 10. Invite students to orally compare and contrast their projects. What Session 1 1. Children measure and cut at least four 4-inch paper squares and one 1. Children measure and cut at colorful sentences together. similarities and differences do they notice? What are some particularly 15-20 min. 9-inch square. least six 6-inch paper quilt effective designs? Why? . Fill the small squares with decorative lines, shapes, and patterns in a squares and one mounting variety of contrasting hues. paper large enough to hold Assessment • Are students able to recognize and identify increasingly more sophisticated geometric shapes within each other’s all the paper squares without quilt designs? Can older students identify elements that show balance, symmetry, and congruence? Do patterned overlapping. papers include an ever-increasing variety of colors and designs? . Select a math concept to • Do projects reflect an understanding of overall math concepts? Do projects reflect an understanding of how represent. Draw the concept different shapes can be combined to form new shapes? Do project designs reflect a complexity commensurate Detail of quilt pattern a different way in each quilt with the ages and abilities of the students who created them? Did students in grades 3 to 6 use a variety of shapes illustrates how geometric square. in their designs? Did students in grades 5 and 6 identify and accurately represent concepts in their quilt designs? shapes are pieced together • Do students use appropriately precise vocabulary in describing their design procedures orally and/or in writing? to create a pattern. • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things they learned. Extensions Create a class quilt with Crayola Fabric Crayons or Fabric Markers. Use design concepts learned from the paper quilt project. Ask parents to iron students’ patterns on fabric squares. Recruit a community volunteer to sew fabric squares together. Display quilt and/or donate it to a local charity. Invite students with an interest in research to investigate and present quilting traditions of various cultures. Discuss similarities and differences. Invite a local quilter to show quilt samples and demonstrate design and sewing techniques. Check out quilt-related lesson plans on Crayola.com such as Patchwork Quilt Lesson and Amish Quilters. Provide colorful wooden pattern blocks for students who learn best from kinesthetic exercises.

Quilt, Circa 1965, by Mary L. Bennett Quilt, circa 1955, by Sue Willie Seltzer of Gee’s Bend, Alabama. of Gee’s Bend, Alabama. Cotton and cotton/polyester blend. 77" x 82" Cotton and synthetic blends. 80" x 76" Reproduced by permission of Tinwood Ventures. Reproduced by permission of Tinwood Ventures. Building fun and creativity into standards-based learning 16 Mathematics Mathematics 17 Patterns of Love Beads

Objectives Multiple Intelligences What Does It Mean? Children sculpt three-dimensional geometric beads for 1960s Interpersonal Marbleize: knead at hippie-style necklaces. least two colors a little to Students compare and order their formed beads in various Logical-mathematical achieve a marble effect color, shape, and sizes to represent patterns (grades K-2), Musical Pattern: orderly, repeated multiplication (grades 3-4), and algebraic equations (grades 5-6). Spatial designs

National Standards Visual Arts Standard #1 Mathematics Standards Understands and applies (Grades K-6) media, techniques, and Understand patterns, relations, and functions processes Geometry (Grades K-6) Use visualization, spatial reasoning, and geometric modeling to solve problems Connections (Grades K-6) Recognize and apply mathematics in contexts outside of mathematics Number and Operations (Grades 3-4) Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Background Information Vocabulary List Beads have been made and used by humans for a variety Use this list to explore new vocabulary, create idea webs, of purposes for centuries. In an article in Lapidary or brainstorm related subjects. Journal, Lynda McDaniel wrote, “Beads were among • Pattern concepts humans’ earliest expression of abstract ideas. Although Concrete objects Pairs Sequence not functional in the sense of a tool or a weapon, beads Form Prediction Sets carry strong symbolic significance.” Movement Problem-solving Skip-counting In the late 1960s, young people used necklaces of “love Relationships Tables beads” to show their rejection of violence and their hopes Numbers Repetition for peace, reflecting the mood of the times. Although both men and women wear necklaces today, in the 1960s young • Multiplication concepts men who wore love beads were making a social statement Equivalent sets Fact families Factors of protest against war and expressing their desire for universal fellowship. These necklaces were often hand- • Algebra concepts made and exchanged as signs of love and friendship. Cause and effect Integers Variables Artwork by students from Spring Garden Elementary School, Resources • Geometry concepts Bethlehem, Pennsylvania. Congruence Space figures Space figures (contd.) Teacher: Pat Check A String of Beads by Margarette S. Reade Cone Rectangular prism Picture book for early elementary students. Beads are Size Cube Sphere celebrated as little pieces of the world with stories to tell. Cylinder Triangular prism Cheerful story presents facts about the history of beads Elongated sphere and beading. • Bead concepts Beads of the World by Peter Francis, Jr. History Materials Techniques Atlas of colorful photographs of hundreds of beads, with Decoration Clay Baking Czech Molded Bead Necklace Artist unknown origins and uses. Younger students enjoy the photographs. Socialization Glass Carving Storytelling Seed Firing 24" Descriptions pique interest in world cultures for older Monofilament and glass students. Trade Stone Stringing Worship Wood Private Collection. The Storyteller’s Beads by Jane Kurtz Based on personal accounts of Ethiopian refugees in the A 1980s. Upper-elementary novel presents the stories of two refugee girls on a pilgrimage to Sudan. One girl relies on her grandmother’s beads to remind her of the many stories of her ancestors’ bravery. B

Math bead pattern necklaces A. Multiplication—8x4 B. Reflective Symmetry C C. Red Bead Forms—Pyramid, Cone, Cube, Sphere, Cylinder D D. Fractions—1/8, 1/4, 1/2, 1, 1/2, 1/4, 1/8 Building fun and creativity into standards-based learning 18 Mathematics Mathematics 19 Patterns of Love Beads

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Define the word pattern by Display one or two plastic bead Create an assortment of plastic Process: Plan simple patterns Plan multiplication patterns Plan algebraic patterns Preparation showing examples. Ask children necklaces demonstrating multiples bead necklaces demonstrating Session 1 1. Sketch necklace patterns. Plan 1. Students choose multiplication 1. Students write algebraic equa- and to find patterns in their everyday of one number (3 red, 3 blue, 3 algebraic equations. Choose 20-30 min. the colors and shapes that will facts to demonstrate in their tions describing the necklace Discussion lives, such as clothing, calendars, yellow). String others that demon- statements such as these: repeat to form patterns. necklace designs. patterns they plan to create. and seasons. Refer to concrete strate more complex multiples (2 2(2a +3b + 4c) examples whenever possible. green, 3 purple, 2 green, 3 purple). . Children work in pairs to check . Draw plans for the use of shape, . Draw necklace design plans 3(5x + 2y) each other’s design patterns. size, and color to show the using color, shape, and/or Make a list of places where Have corresponding math flash- 7(a + b + 2c) children see, hear, or experience cards on hand. Challenge students . Demonstrate how to chant a math facts in bead patterns. size as the variables of the patterns. to match flashcards with necklaces. where different bead colors, shapes, pattern: “Red, blue, yellow! . Trade bead pattern plans with algebraic equations. Ask students to figure out how or sizes represent variables. Red, blue, yellow!” as a way to partners. Challenge partners to . Partners check each other’s bead patterns and multiplication Challenge children to identify the feel the pattern’s rhythm. identify the math fact in the bead design plans to be sure are related. equations in bead patterns. pattern plan. they represent the algebraic equations accurately. Discuss the ways artists use patterns and repetition in their art as they repeat designs, colors, and figures. A good example of the use of patterns in art is the bead necklaces, called hippie or love beads, worn in the 1960s. Display Process: Create beads images or reproductions of hippie-era bead necklaces with patterns. Invite children to share observations about Session 2 . Select a marble-size amount of Model Magic compound for each bead. Add marker color, mix colors, or patterns they see. 30-40 min. marbleize if desired. ® Make a sample bead necklace to show students. Use colored Crayola Model Magic compound to form several . Wrap bead around a plastic straw piece. Shape it into one of the following forms: sphere, cone, cylinder, cube, marble-size geometric figures. String the beads in patterns of figures and colors. rectangular prism, pyramid, or elongated sphere. Crayola® • Colored Pencils • Markers • Model Magic® • Scissors 6. Make quantities of each bead form according to the plan. Air-dry beads at least 24 hours. Supplies Process: Design the necklace Other • Clear adhesive tape • Cotton cord or heavy string • Modeling tools • Paper plates Session 3 . Sort similar beads into piles. String beads on cotton cord according to the bead design plan. Check the accuracy of the pattern. Materials • Plastic drinking straws • Pony beads (available at most craft stores) 20-30 min. 8. Tape the cord ends together for wearing. Set-up/Tips • Children help cut drinking straws into 1-inch (2 cm) pieces so they extend beyond the ends of the modeled beads. Each student will use about 20 pieces. Trim straws with scissors after beads dry. Assessment • Ask students to identify the • Students create multiplication • Students exchange necklaces and patterns in their classmates’ flashcards to correspond with write algebraic expressions for • Mix white Model Magic compound with color from washable markers to make new hues. necklaces. Each child creates a their necklaces. Play matching bead patterns. • To create marbled beads, combine small amounts of two or three Model Magic colors. Knead and twist modeling chart of patterns observed on five to identify bead patterns Chart patterns, including a compound with fingers for desired marble effect. • or more classmates’ necklaces. and the multiplication facts they column to record what each • For longer necklaces, use pony beads to separate Model Magic beads or bead pattern segments. Write student names in one represent. Check for accuracy. variable represents (specific column. Draw or write about • Work and air-dry beads on paper plates labeled with children’s names. shape, color, or size of bead the pattern that is repeated in written as a =, b =, c =). Check Seal string ends with tape so children can wear beads. Close adult supervision is essential whenever children wear • each necklace. for accuracy. anything around their necks. • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things Round Ceramic Glazed Beads Turquoise Seed Bead Necklace they learned. Artist unknown Artist unknown Glass and string Turquoise and horn clasp Extensions Provide opportunities for children Children work in teams to Host a bead market. Assign 20" 26" to make and read different kinds of create multiple bead strands. Begin monetary values to different bead Private Collection. Private Collection. patterns. Clap patterns for children by sketching a visual of multiples shapes or colors. Use algebraic to echo during transition times. patterns. See Skip Counting on equations to determine the price Gather items for children to sort Crayola.com. Use the number grid of each student love bead necklace. and arrange into patterns, such as and white Model Magic compound Repeat activity with different prices. crayons, recycled plastic containers, to create 100 small beads. Create Suggest that gifted students and natural objects such as shells. a color code for multiples of 2, 3, explore bead-making traditions from Some children with special needs 4, 5, 6, 7, 8, 9, and 10 (one color around the world. Use algebra skills might represent their bead patterns for each). Write numbers on beads. to represent different beading styles. with small table blocks or plastic Add dots or stripes of color to dem- Check out African Trade Beads beads first. onstrate multiples. Some beads will on Crayola.Com to find out how to have one color. Others may have make rolled-paper beads. See Merry Math Patterns on several (numeral 24). Prime numbers Crayola.com for a whole-class will have no color at all. patterning activity. Suggest children interview family members who may remember love Powder Glass beads. What stories can they share Beaded Necklace about the beads? Artist unknown Glass and cotton threads 30" Private Collection. Building fun and creativity into standards-based learning 20 Mathematics Mathematics 21 A Bountiful Table—Fair-Share Fractions

Objectives Multiple Intelligences Students create concrete, realistic, geometric drawings of Interpersonal Logical-mathematical food to use to explore the concept of equal or fair shares. Students use fractions to divide their art into sets to Intrapersonal Spatial demonstrate their understanding of fractions at a complexity Naturalist appropriate to their grade level.

National Standards Visual Arts Standard #5 Mathematics Standards Reflects upon and assesses Number and Operations the characteristics and Understand numbers, ways of representing numbers, relationships merits of their work and among numbers, and number systems the work of others Geometry Use visualization, spatial reasoning, and geometric modeling to solve problems Problem Solving Apply and adapt a variety of appropriate strategies to solve problems Representation Create and use representations to organize, record, and communicate mathematical ideas

Background Information Vocabulary List Everyday objects were often the subjects of Wayne Use this list to explore new vocabulary, Thiebaud’s still-life . His painterly depictions of create idea webs, or brainstorm cakes and pies are especially well known. Unlike much related subjects. 1960s Pop Art that satirically depicted consumerism in the United States, Thiebaud’s paintings seem to be nostalgic and Fairness Sevenths reverent. Thiebaud exploited the physical properties of paint. Fractions Shape He captured the look and feel of the substance depicted, Eighths Sharing such as icing on cakes, by applying thick layers. Thiebaud Fifths Sixths described this palpable, sensuous employment of paint as Half Texture “object transference.” Musical notes Thirds Time Foot Resources U.S. currency Yard Proportion Behind the Scenes Series: Vol. V, Wayne Thiebaud: Line. Quarter Hosted by Penn and Teller Liquid measures Delightful look at line with the help of illusionists Penn and Musical notes Teller. All ages enjoy watching the artist Wayne Thiebaud create a drawing of an ice cream cone using line. (DVD/VHS, U.S. currency distributed by GPN, 28:29 min.) Counting With Wayne Thiebaud by Susan Rubin Presents the concepts of counting and number with Thiebaud’s drawings, etchings, and paintings of multiple sweet treats. A perfect introduction to any early elementary lesson on art, fractions, and sharing. The National Gallery of Art: www.nga.gov (search the site for “Thiebaud”) Wayne Thiebaud: A Paintings Retrospective by Steven A. Nash with Adam Gopnik Artwork by students from Brings together 120 of Thiebaud’s paintings, , and Wood Creek Elementary School, watercolors. Full-color illustrations capture students of Farmington Hills, Michigan. all ages. Older students and adults will also learn much Teacher: Lynn Schatzel about Thiebaud’s impact on .

Building fun and creativity into standards-based learning 22 Mathematics Mathematics 23 A Bountiful Table—Fair-Share Fractions

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Ask students what sharing means to them. Discuss how an apple or a pizza could be shared. Offer example Process: Draw and divide foods into equivalent parts Preparation situations, such as eight people and one apple. Invite students to explain how they could divide the apple so Session 1 1. Suggest that students imagine they are looking down at the top of a table filled with foods. Fill drawing paper and every person gets a fair share. 20-30 min. with erasable crayon outlines of food as if seen from above. Use paper circles to demonstrate equivalent fractions. Brainstorm other foods or sets of items that could be Discussion Draw lines to divide foods so each person in the group can receive a fair share. divided fairly into parts (watermelon, loaf of bread, oranges). How would you divide each fairly for two people, 2. three, seven, or for the whole class? 3. Exchange drawings with classmates to check for dividing accuracy. Erase and redraw lines as needed to make For younger students and those with some types of learning disabilities, place a clear transparency over a large all shares equal. image of a food that could be divided, such as a loaf of bread. Invite students to use a Gel Marker as if it were a knife to “cut” the food into slices, fairly divided for a given number of people. Wipe off and repeat to “cut” a Process: Use oil pastels to decorate variety of different fractions. Session 2 4. Fill line drawings with oil colors. Encourage children to use color-blending techniques to achieve For older and more advanced students, reverse the process and estimate how many whole foods are needed to 20-30 min. realistic effects. divide to feed a large group of people. Chefs plan in advance how much food to prepare. 5. Decorate foods with designs, such as those found on fancy desserts or fun arrangements of pizza toppings. Display prints of cake paintings by Wayne Thiebaud. Describe the shape of these desserts, pizzas, and other favorite foods when looking down on them from above (circle, rectangle, square, oval). Process: Slice and “serve” equivalent fractional parts Session 3 6. Cut foods into fair-share fractions according to the number of children in the group. Place each piece on a paper Divide into groups of three or Divide into groups of four to Divide into large groups with 20-30 min. plate. Arrange plates of divided foods on a table or desks. four. Each student thinks of a seven. (Odd numbers are more eight or more. Each group will dessert or a healthier food. challenging.) create a buffet of “foods” to share. 7. Groups divide each other’s foods among their plates so everyone has an equal share. Talk about how it feels to have fair shares. Return foods to the original plates. Explain that foods will be divided Explain that each team will Challenge teams to create enough so that everyone in the group gets create oil pastel art to illustrate food so there are enough slices to 8. Divide food among plates so the shares are unfair. Ask students to talk about how they feel about unfair shares. a fair share of every one. a table filled with foods. Teams serve everyone multiple pieces. Have students switch plates with each other to see other points of view. How could the amount of food divide their foods into equivalent How many whole items are needed available be divided so that each person does get a fair share? fractional quantities so that there to feed the large group? 9. Identify the fractional parts with their correct names and symbols by writing on the back of each piece. are enough pieces to serve to everyone in their group. Assessment • Assess division of each student’s food into accurate, fair fractions. • Observe the process of determining fair and unfair shares in each group. Do students use mathematical reasoning ® Erasable Crayons Markers Oil Pastels Scissors Crayola • • • • to divide the foods fairly? How convincingly do they present their viewpoints? Supplies • Children write or orally describe their foods and the way they were divided into equivalent fractional quantities Other • Drawing paper • Paper plates • Paper towels using accurate names and symbols. Materials • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things they learned. Set-up/Tips • Erasable Crayons are recommended to create simple shapes that can be erased and redrawn as needed. Pencil sketches often lead to drawings with small details that are a challenge to fill in with oil pastels. Extensions Younger children and students Incorporate a gourmet chef In what other ways are foods with special needs might begin by contest into the lesson. Students represented in the arts? Consider • Demonstrate how to use a bit of paper towel or cotton swab to blend oil pastel colors. dividing actual foods so they have a create ballots and vote on criteria still-life paintings from various time • Show students how to gently brush pastel crumbs into the trash. relevant concrete experience before for their foods such as these. periods and parts of the world. What working with representations. • Drawing that has the most do those depictions reveal about the Hold an international foods buffet elaborately decorated foods. culture, setting, and artist? in which families share their favorite • Drawing that has the most unique Challenge gifted students to create ethnic dishes with small groups of way to divide the desserts equally. fraction games using the pieces children. Children determine when Find out about careers as food they created. objectives the foods are appropriately divided stylists, chefs, and restaurant could be to identify, compare, among participants. managers, for example. What add, subtract, multiply, or divide mathematical skills are necessary fractions. for these positions?

Division diagrams show Pizza pie that is cut into segments shows parts 1/2, 1/4, 1/8 and 1/16 of a whole. of a whole circle.

Division diagrams show 1/3, 1/5 and 1/7 of a whole circle.

Cakes cut into segments showing fraction cuts.

Building fun and creativity into standards-based learning 24 Mathematics 25 Whimsical Charting and Checking

Objectives Multiple Intelligences What Does It Mean? Students explain increasingly complex relationships between Curiosities: rare or novel Interpersonal visual arts, mathematics, and the cultures, times, and locations of objects or ideas Native American peoples. Logical-mathematical Whimsy: fanciful beaded Students create replicas of Native American handiwork that Spatial ornament created by they use to chart, estimate, check, and analyze colored bead data. Native American artists for souvenirs National Standards Visual Arts Standard #4 Mathematics Standards Understands the visual arts in relation to history Number and Operations and culture Compute fluently and make reasonable estimates Problem Solving Apply and adapt a variety of appropriate strategies to solve problems Representation Create and use representations to organize, record, and communicate mathematical ideas

Background Information Vocabulary List Native American women in many nations were skilled in Use this list to explore new vocabulary, create idea webs, beadwork. To economically survive in a changing world, or brainstorm related subjects. enterprising women of the Iroquois nation, particularly from • Data-recording techniques the Mohawk and Tuscarora tribes, designed and crafted beaded Charts & graphs Music items to sell to tourists in the late 1800s through early 1900s. Bar Notes These items, particularly pincushions, became quite popular Circle Staff as souvenirs at places such as Niagara Falls. Flow chart Tally marks Artwork by students from “Beaded whimsies,” as they are now often called, were Picture Sandy Plains Elementary School, made in shapes such as hearts, canoes, and fancy, high-top Checklists Baltimore, Maryland. shoes. Their stuffed fabric bases were embellished with seed Counting Teachers: Jen O’Flaherty, Rob Bartoch and bugle beads in a wide array of hues. Motifs included birds, flowers, leaves, and the U.S. flag. Sometimes they were emblazoned with dates and the names of travel destinations. • Native American art Very few of the designs were typical of the motifs used on Famous contemporary artists the Native Americans’ own beaded items. Instead they were Alan Houser shrewdly designed to specifically appeal to the gaudy tastes Clementine Hunter of Victorian tourists. Edmonia Lewis Jaune Quick-to-See Smith Traditional techniques Resources Beadwork Pottery Beaded Critters by Sonal Bhatt Tourist trade Inspiring how-to book for ages 9 and up. Photographs of Baskets colorful bead animal embellishments reminiscent of those Curiosities found on “beaded whimsies.” Toys Trading Identities by Ruth B. Phillips Whimsy Images and historical anecdotes introduce older students to art forms produced by Native Americans for tourists in northeastern United States.

Artwork created by students from St. Theresa School, Hellertown, Pennsylvania. “From Niagara Falls” Hanging Shoe “1905” Hanging Pincushion Whimsy Picture Frame Circa early 1900s Beaded Whimsy Glass beading on purple velvet field Circa early 1900s 7 1⁄2" x 6 1⁄4" x 2 1⁄4" High-relief glass beading on shocking pink cotton field Collection of Dr. Thomas Schantz. 10" x 6 1⁄4" Collection of Dr. Thomas Schantz. Building fun and creativity into standards-based learning 26 Mathematics Mathematics 27 Whimsical Charting and Checking

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Share information and pictures of Native American beadwork. Some created beaded pincushion whimsies to sell Process: Design cushion Design cushion Design cushion Preparation to tourists. Ask students to discuss how these crafters may have tracked the number of beads needed to plan for Session 1 1. Draw a simple geometric shape 1. Outline a shape (heart, star, 1. Outline an interesting shape and each design. 20-30 min. (circle, triangle, square) on a shell) on a 3- x 4-inch paper. (flower, bird, turtle) on 3- x Discussion Craft a sample relevant whimsy to inspire student creativity. 3- x 4-inch paper. 4-inch paper.

Show children the sample whimsy. Ask students to suggest ways to tally numerical data. If they were bead . Draw at least one more shape inside the original. Ask how they might record the artists, how might they record the number of beads it takes to cover a small number of beads of each color so bag? Explain how to create a chart to record estimates as well as actual . Show students how to create a beading pattern by filling the cushion with colored dots. Draw dots to they could make more identical number of beads used. Create personal charts to estimate and tally colors form patterns. whimsies. Together, chart the of beads used in their own artwork. Process: Make the whimsy number of beads of each color using Ask how they might calculate the total number of beads used by the entire tally marks or picture symbols. class, including how many of each color were used. Session 2 . Form a tennis-ball amount of Model Magic compound into the cushion. 40-60 min. . Cut 10-inch ribbons. ends. Poke one end of the loop into the top of the cushion. Glue in place. Each child makes a blank chart Create a class chart with one Students work together to Roll tiny Model Magic beads. Glue colored spheres to the cushion. Apply glitter glue for dramatic effects similar to the one created together. row for each student and columns determine and record the total 6. if desired. Air-dry whimsies 24 hours. Shade in or write names of colors labeled with colors to chart, estimate, number of beads the class used in as headings. Include spaces to and total beading whimsies. their combined projects as well as estimate, tally, and record the how many of each color they used. Process: Estimate, chart, and check Estimate, chart, and check number of beads of each color Brainstorm, define tasks, form teams, Session 3 . Children estimate the total . Students estimate the total number of beads and the number of beads and the total beads used. and create materials needed to 20-30 min. number of beads on their of each color in their designs. Record on individual charts. organize and record data. whimsies as well as the number of each color. Record on 8. Add individual estimates to class 8. Follow the plan for gathering Crayola® • Colored Pencils • Glitter Glue (optional) • Markers • Model Magic® • School Glue • Scissors individual charts. chart. Total estimates for all class estimation data. Supplies 8. Children count and record the beads and each color. number of beads of each color Other • Modeling tools • Ribbon, yarn, or string • Ruler • White paper on their whimsies. . Count the number of each . Gather class bead-usage data Materials color of beads used. Record on according to student plan. . Children count each other’s individual and class charts. beads to check accuracy. What Set-up/Tips • Add color to white Model Magic compound using washable markers. similarities and differences did 10. Students check each other’s data for accuracy. Analyze and • Use scissors to cut flattened Model Magic shapes. they notice? discuss findings. • Glue beads to the form. Glue ribbon to Model Magic whimsy. Assessment • How effectively did students in grades 5 and 6 contribute to creation of a class plan for tallying results? “Fox Box” With Lid and Handles Beaded Whimsy • Compare individual and group data charts with actual bead designs. Circa early 1900s • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things Glass beading on electric pink cotton field they learned. 7" x 5 1⁄2" x 8" including loops Collection of Dr. Thomas Schantz. Extensions Use finished whimsies to provide Students create plans for half-size Look for patterns in the data. additional practice in estimating, whimsy replicas. Use previous data Challenge students to compare counting, and recording data. Work to estimate the number of beads different designs and data patterns in pairs to estimate, check, and needed for these versions. Write to form hypotheses about the data. record data for several whimsies. directions, trade directions with Are there factors that lead one Younger students and those with classmates, and follow them to cre- whimsy to have a higher count of some types of learning disabilities ate replicas. Count and record actual beads than another? Identify those could use beads to work on sorting number of beads used. Compare factors and test hypotheses. and classification skills. actual numbers with estimates.

Encourage a simple, large design and the use of large beads rather than tiny ones for students whose fine-motor skills are not yet fully developed. Challenge advanced students with an interest in research to find out more about other forms of Native American beadwork and report their findings to the class.

Tri-lobe Heart Hanging Pincushion Whimsy Circa early 1900s Glass beading on pink field 8" x 8 1⁄4" x 3" Collection of Dr. Thomas Schantz. Building fun and creativity into standards-based learning 28 Mathematics Mathematics 29 Shaping Up With Shapes

Objectives Multiple Intelligences What Does It Mean? Students identify, compare, and contrast shapes, and shapes Color gradation: passing Logical-mathematical Linguistic within shapes, in artistic compositions. of one tint or shade of Students make and use shape stamps to create -like Spatial color to another by very compositions featuring overlapping images. Linguistic small (barely perceptible) Artwork by students from Students in grades K to 2 use spatial reasoning skills to count the degrees St. Theresa School, number of times each shape appears in their artistic compositions. Color value: relative Hellertown, Pennsylvania. Students in grades 3 and 4 use measuring tools to determine and lightness or darkness of chart the perimeters of shapes within their artistic compositions. a color Students in grades 5 and 6 use measuring tools and spatial reasoning skills to determine the total area covered by similar shapes within their artistic compositions.

National Standards Visual Arts Standard #1 Mathematics Standards Understands and applies Geometry media, techniques, and Use visualization, spatial reasoning, and geometric modeling to solve problems processes Reasoning Recognize reasoning and proof as fundamental aspects of mathematics Grades 3-6 Measurement Apply appropriate techniques, tools, and formulas to determine measurements

Background Information Vocabulary List During the 1920s, Swiss artist Paul Klee often spattered Use this list to explore new vocabulary, create idea webs, watercolor over stencils and netting. When Klee taught or brainstorm related subjects. at the Bauhaus (a famous German art school), he experimented with this technique. The effect is shown Area Line Rhythms in Glance of a Landscape. In this work, Klee applied Balance Linear figures Rotation Color Motion Shape brushstrokes of pale gray opaque watercolor on top of Color fields Movement Texture transparent watercolor that was spattered broadly to Composition Patten Transformations create trees. Klee usually mounted his drawings on Emphasis Perimeter Unity cardboard, which was where he wrote the title and Enlargements Proportion Value date for this composition. Form Reflections Variety Gradations Repetition Resources Dreaming Pictures: Paul Klee by Paul Klee Klee’s dream world is made accessible through this tour of his compelling artwork. Children’s comments and questions add to the enjoyment. Echoes for the Eye: Poems to Celebrate by Barbara Esbensen Compilation of poems and lovely watercolor illustrations. Draws attention to the repetition of shapes and patterns in the natural world. Shape Patterns by Marion Smoothey Investigates the world of shapes, then offers fun activities for drawing, measuring, and using them.

Building fun and creativity into standards-based learning 30 Mathematics Mathematics 31 Shaping Up With Shapes

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Create a wall poster depicting a square grid: 4 rows of 4 squares each. Process: Stamp shapes Preparation Invite children to search for and count all of the squares they see in the poster. Session 2 . Brush paint colors on flat side of a shape. Press stamp, paint side down, on paper. Lift stamp. Repeat using and 40-60 min. different paint colors. Flip or turn the shape so it appears in a variety of places and angles in the design. Discussion Ask a student volunteer to outline Challenge students to find more than 16 squares. Ask students to explain Observe color effects. each of the 16 small squares in how they can find more than 16 squares in the grid. Ask students why they the grid, writing a numeral inside think most people would see only 16 squares. . Exchange shapes with classmates. Repeat stamping. Overlap several different shapes and colors. Air-dry the paint. each square. Look for rectangles in much the same way. Challenge children to find other Challenge more advanced students with more complicated grids. Process: Outline shapes squares. Help children see the largest square (the entire grid) and Session 3 . Outline several shapes with glitter glue to enrich the surface design. Air-dry the glue. squares made of 4 and 9 smaller 10-15 min. squares. Outline those squares in another color. Process: Count shapes Count and chart shapes Session 4 6. Use the sample design to 6. Ask students to identify all of the shapes in their artwork. Display examples of art by Paul Klee and the sample design. Ask students to look at this artwork carefully to find 20-30 min. demonstrate how to count . Create charts to show the number of each shape in the compositions. shapes and patterns that others may not see. Look closely at colors to find gradations and compare color value. shapes. Remind students that Discuss how looking carefully sharpens thinking and can assist in solving problems. shapes may have been flipped 8. Use measuring tools to 8. Challenge students to determine Create sample shape stamps and a large sample design with overlapping shapes. or turned, but they still remain determine the perimeter of the area covered by each shape the same shape. each shape in the design. in their design. Add information ® ® Crayola • Glitter Glue • Model Magic • Paint Brushes • Scissors • Tempera Paint . Show children how to create Add information to chart. to chart. Supplies a simple chart to record the . Total the length of all perimeters. . Calculate the area covered by number of each shape in the overlapping shapes. Other • Drawing paper • Hand-held pencil sharpeners • Modeling tools (such as craft sticks, markers, and plastic knives) their artwork. Materials • Paper towels • Recycled newspaper • Water containers 8. Count and record the number of each shape on their own artwork. • Rulers Assessment • Exchange finished designs with a • Compare designs with a partner. • Students create charts with spaces Set-up/Tips • Cover painting surface with recycled newspaper. partner. Partners add up the total How are they similar and how are for recording total area covered number of shapes they see in the they different? Compare the types by each shape in their designs as Process: Create stamps finished art. Check to see if their and sizes of shapes that appear a “quiz” for a partner. Exchange Session 1 1. Flatten Model Magic compound with hands or roll with a marker barrel. Make it thick enough to pick up easily. counts match. in each design. Compare similar finished designs. Partners measure 5-10 min. shapes to see which is larger and and calculate the area covered . Children cut shapes (triangle, parallelogram, rhombus) appropriate to their geometric skills. Air-dry 24 hours. smaller. Compare colors in similar by each shape in the design. shapes. Estimate sizes, then mea- Compare results with the sure to check. Record comparison design’s creator. results on paper to display with both designs. Farmers Market Produce Photo by R. De Long • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things they learned. Extensions Repeat this technique using other Brainstorm real-life reasons to Combine stamps into a corporate shapes such as leaves, letters, or measure perimeter. Borrow a book . Students work together paper cut-out handprints. Flip, slide, of children’s wallpaper borders. to brainstorm, choose, and plan and turn stamps for different effects. Each student chooses a favorite. large shapes to cut from posterboard Make shape pattern puzzles Challenge the class to measure the and cover with stamps. Challenge on long strips of paper. Use the perimeters of the gym or cafeteria. students to do calculations in stamps to make repeating patterns How many feet of border are needed advance. for a partner to analyze and finish. to decorate the walls all the way Encourage gifted students to (Example: square, square, triangle, around? How many rolls are needed? measure and calculate areas of square…) Challenge students to measure the increasingly irregular shapes. perimeters of other shapes, includ- ing doorways, rugs, or furniture. See Metric Hugs on Crayola.com.

To enable students with special needs to more readily see shapes within shapes, encourage them to outline each shape with a different color so the overlapping images can be seen more easily. Challenge students to find congruent parts within each other’s compositions. Chihuly Glass Shapes Photo by R. De Long

Building fun and creativity into standards-based learning 32 Mathematics Mathematics 33 Toying Around With Geometry

Objectives Multiple Intelligences What Does It Mean? Students create functional, wheeled 3-D toys reflecting spatial Corner: where three or Linguistic Spatial reasoning skills with geometric forms. more edges meet Students draw and label the pictures (K-2, 5-6) or write and Logical-mathematical Edge: location where two illustrate toy package inserts (3-4) describing geometric attributes Spatial plane figures meet “Andy Gump” Toy Circa 1930s of their structures to demonstrate their understanding of the way Plane figures: flat, 2-D parts were used in the invention process. Cast iron images of geometric shapes 7 1⁄4" x 3 3⁄4" x 6" Space figures: 3-D Collection geometric forms such as of Rudy Clark. spheres, cubes, and cones

National Standards Visual Arts Standard #2 Mathematics Standards Using knowledge of Connections Steam Powered Shovel Toy structures and functions Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Circa 1931 Geometry Fabricated tin and cotton cord Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop 20" x 7" x 14" mathematical arguments about geometric relationship Collection of Rudy Clark. Communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Measurement Apply appropriate techniques, tools, and formulas to determine measurements Problem Solving Solve problems that arise in mathematics and in other contexts Representation Artwork by students from Use representations to model and interpret physical, social, and mathematical phenomena John J. Jennings Elementary School, Bristol, Connecticut. Teacher: Barbara Grasso

Background Information Vocabulary List Toys are an important part of children’s lives because they Use this list to explore new vocabulary, create idea webs, stimulate young minds. Toys help children learn important or brainstorm related subjects. concepts, develop motor and thinking skills, and express their • Art terms Armature Original personalities. In many cultures, play is also viewed as a prepa- Form Shape ration for life. With Native American children, for example, Glaze Texture each traditional toy carries a unique legacy of history, tradi- Joining tion, design, and practical technique. Perhaps one of the first toys, dating back to 6000 BCE, was a game of chess, which • Favorite toys Analyze Compare/contrast evolved from an Indian game called Chaturanga. 3-D forms Hand-made toys In Europe during the 1300s to 1500s, many toys were Corners Manufactured items destroyed in an effort to eliminate the spread of the Bubonic Edges plague. Combined with the wear and tear of time, it is difficult Planes to find antique toys from periods before the 16th century. Construction methods Alexander Calder was fascinated by motion and created Mobile/stationary handcrafted toys early in his art career. He and other artists designed forms and shapes with moveable parts. Their art, • Package insert Name of toy Diagram including famous mobiles, considered fun by many, moves Geometric terms Draw and delights the eyes and minds of children of all ages. Alliteration Label Onomatopoeia

Resources • Simple machines Inclined planes Dolls and Toys of Native America—A Journey Through Levers Childhood by Don & Debra McQuiston Wheels/axles Beautiful full-color images with text describe how toys taught Native American children their life skills while bringing them • Space figures Cone delight and joy. Cube Cylinder Roarr: Calder’s Circus by Maira Kalman Pyramid An introduction to Alexander Calder and his tiny, playful Rectangular prism circus. Inspires children of all ages to be creative and have Sphere fun while using their problem-solving skills.

Building fun and creativity into standards-based learning 34 Mathematics Mathematics 35 Toying Around With Geometry

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Display 3-D figures (or images of them) including a sphere, pyramid, rectangular prism, cube, cone, and cylinder. Process: Add details Preparation Ask students to describe what they see. Lead children to discover that all 3-D (or space figures) combine flat 2-D Session 3 . Embellish the toy with ribbon, toothpicks, chenille stems, and other craft items. Attach with glue. Air-dry the glue. (or plane figures). A cube consists of six flat squares. The locations where two plane figures meet are called edges. and 20-30 min. 10. Decorate the toy using gel markers. Discussion Areas where three or more edges meet are called corners. Look for plane figures, edges, and corners in the displayed objects and other common items. Focus on using geometric vocabulary. 11. Mix a glaze of equal parts glue and water. Brush the glaze over the Model Magic. Air-dry the toy. Look at several samples of toy packages. Does what is displayed on the outside of the package always match what is inside? Share experiences with toys that need to be assembled. Process: Draw and label picture Write package inserts Draw detailed diagrams Analyze a moveable toy with axles, wheels, and a simple body. Ask children to figure out how the toy works and Session 4 1 2. Look carefully at the toy. Draw 12. List all of the 3-D forms and 12. Draw the toy and label the how the parts of the toy function to make it move. Count the wheels. Point out the axle(s) on which the wheels 30-40 min. all of the 3-D forms and 2-D planes used to construct the toy. diagram (including specific rotate. Ask children to identify the plane and space figures that make the toy’s body. If possible, take the toy apart planes used to construct the 1 3. Diagram and label all plane space and plane figures, edges, to demonstrate how the parts make up the whole toy. toy. and space figures used to and corners) in detail from at Challenge students to design an original, wheeled, moveable toy (for display only) that can be built with plane and 1 3. Draw a picture of the finished create the toy. least three different angles, space figures such as recycled materials and Model Magic®. Children decide how many wheels, axles, and other moving such as looking at figure from toy. Label the 2-D planes and 3- 1 4. Write step-by-step directions parts their inventions will have. This toy will be part of a “kit” for which they will also prepare a “package insert.” above, from below, head on, D forms. One method is to draw explaining how to construct an arrow to one part of the toy from the back, left side, right Ask children to identify what the toy as if it were a kit to be side, or underneath. and then draw the plane shape assembled. space figure/form a drinking straw to which the arrow points. represents (cylinder). What 2-D Older children also write geo- shape can be seen when looking at metric terms for the shapes and the end of a straw? (circle) Repeat forms. with other forms as needed to expand their geometry vocabulary. Assessment • Are the toys wheeled and movable? Crayola® • Gel Markers • Model Magic® • Paint Brushes • School Glue • Scissors • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things they learned. Supplies • How original are the toys? Did • Review both toy and package • Interview students about their Other • Chenille stems • Decorative craft items (such as toothpicks, buttons, feathers) • Dowel sticks (1/8-inch diameter) children creatively use the insert, informally interviewing toys, referring to drawings and Materials • Large paper clips • Modeling tools such as plastic dinner knives, craft sticks, and toothpicks armatures, modeling materials, children to assess their awareness labels, to determine their ability • Plastic drinking straws • Recycled plastic beverage bottles or other clean, found objects and embellishments to invent of space figures, plane figures, to identify plane and space figures their toys? and spatial reasoning. and their positions in space. • Recycled produce trays • Rulers • String, ribbon, or yarn • Water containers • White paper • Observe children’s abilities to • Is the package insert drawn • Are the three perspective Set-up/Tips • Ask students and their families to collect clean recycled items. communicate both verbally and on with detail? Are toy parts labeled drawings accurate and detailed? paper about the construction of correctly? • By its nature, wood is rough and may contain splinters. Ask parent volunteers to cut dowel sticks into their toys. varying lengths. • Are the assembly directions clear • Can children correctly name basic and in chronological order? • Remind children that the toys they create are for display only—they are not recommended for use. 2-D shapes and 3-D forms? • Encourage students to use their imaginations. Offer strategies, modeling techniques, and ideas to support student innovations. Extensions Younger children and those with Invite children to think of names How do the toys measure up? • Model Magic fresh from the pack sticks to itself. Use glue to strengthen Model Magic seams and joints. special needs might enjoy creating for their toys based on the toy’s Challenge gifted students to measure these toys with the assistance of geometric design. each toy’s height, weight, length, • Show children how to construct moveable axles by inserting a dowel stick into a straw. Push wheels on the family members, either in the Work in teams to create ad width, rolling speed from point to ends of the dowels. classroom or at home. campaigns for the toys. Write point, and other characteristics. Take toys “on the road” for a toy jingles, design print ads, and/or Create comparison lists, ranking toys Process: Create axles and wheels parade. Invite school staff, parents, produce radio and television ads. by various measures (tallest, widest, Session 1 1. Measure and cut straws into the desired lengths for axles. and other friends and relatives to the Set up a toy fair in the classroom heaviest, fastest). 20-30 min. . Choose dowel rods that are about 3 inches longer than the straws. Insert the dowels into the straws. classroom. Or visit other classrooms to display toys, inserts, and adver- Research inventions and inventors. to show student creations. Pair Find out how some inventions came . Roll and flatten Model Magic® compound into wheels. tisements. Invite children from each toy inventor with a visitor so neighboring classrooms to visit the about accidentally while others . Push wheels on the ends of dowels. Air-dry the wheels. the inventor can tell how he or she toy fair. Survey them as they leave have a history of effort behind them. made the toy. Ask visitors to share about which three toys they would Compile research into visual and Process: Build the body of the toy positive feedback about the toys most like to buy. Tally and talk written reports for an Invention Hall Session 2 . Choose an armature upon which to build the toy, such as a plastic bottle or cardboard box. with the inventors. about the results. of Fame. See Crayola.com for an Activity Page to start the research. 20-30 min. 6. Build up the body by attaching plane figures cut from recycled items to the armature with Model Magic slabs. Keep the toy factory rolling! See Find out about the creative inven- Overlap edges and glue sections to the bottle as needed for reinforcement. Add texture and decorative elements Crayola.com to make Hollyhock tions of Leonardo DaVinci. Let his with Model Magic bits and modeling tools. Dolls and Quack, Moo, and Oink creative ideas inspire more designs. Finger Puppets, for example. See the Recycle Inventions Lesson Attach axles to the body. One way to do this is to press strips of Model Magic over the straws onto the . Provide materials for children to Plan on Crayola.com for ideas. underside of the armature. independently invent their own 8. Tie string to one end of a paper clip. Glue the other end of the paper clip and embed it in Model Magic robots from recycled cereal boxes. compound on the front of the toy. Air-dry the construction for 24 hours. Check out the Accordion-Arm Robot on Crayola.com for inspiration. Building fun and creativity into standards-based learning 36 Mathematics Mathematics 37 Measure Twice, Create Once

Objectives Multiple Intelligences What Does It Mean? Students apply skill-level appropriate techniques and tools Cubit: principal unit of Bodily-kinesthetic Logical-mathematical to determine the real size of objects using standard and measurement in ancient nonstandard units of measure. Interpersonal Egypt, equal to 52.4 cm Students apply mathematics and problem-solving skills to Logical-mathematical Petroglyph: drawing or create scale drawings of objects. Spatial carving on rock created by prehistoric people Pictograph: artwork that National Standards shows people, places, and/ or things in pictures, signs, Visual Arts Standard #1 Mathematics Standards or symbols Understands and applies media, techniques, Measurement and processes Understand measurable attributes of objects and the units, systems, and processes of measurement Connections Recognize and apply mathematics in contexts outside of mathematics

Background Information Concept List The Ancient Egyptians incorporated a measurement system Use this list to explore new vocabulary, create idea webs, into all fundamental areas of their lives, including commerce, or brainstorm related subjects. Artwork by students from building, and art. St. Theresa School, • Nonstandard units of measure Hellertown, Pennsylvania. Using body parts with which to measure, the Egyptian Paper clips Index cards measurement system included units such as the cubit (the length of a man’s arm from elbow to tip of middle finger), • Terms palm (cross-wise width of hand), and span (the length of Height Length Width outstretched upper limbs). Graphic artists use the human head as the basic unit of • Units of measure – Length measurement for drawing the entire body in proportion. The Metric U.S. Customary Egyptian height of the head from the chin to the top of the head is the Centimeter Foot Cubit “ruler” by which vertical lines in a human form are measured. Kilometer Inch Palm Fine artists often consider that most people are 7.5 head Meter Mile Span lengths tall. Millimeter Yard One way archaeologists record prehistoric petroglyphs • Scale and pictographs is to carefully create a string grid over the Models Drawings petroglyphs or artifacts and then do a scaled-down sketch Cars Book illustrations Digs on paper of what they see in each square. Globes Maps Petroglyphs Trains Scientific illustrations Pictographs Artwork by students from Resources Spring Garden Elementary School, Bethlehem, Pennsylvania. Math Curse by Jon Scieszka & Lane Smith Teacher: Pat Check Humorous look at numbers in everyday life, including measurement, time, , and problem-solving. All ages. Picasso’s One-Liners by A collection of Picasso’s one-liners, drawings created in one movement, without lifting drawing tool from paper. All ages. The Painter by Peter Catalanotto A celebration of creativity in life and art. Cover illustration shows a father tracing his child’s body on large paper. Simple text and vivid watercolor illustrations appeal to young children.

Artwork by students from Spring Garden Elementary School, Bethlehem, Pennsylvania. Teacher: Pat Check Building fun and creativity into standards-based learning 38 Mathematics Mathematics 39 Measure Twice, Create Once

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Introduce use of hands and fingers Who has measured objects using ancient Egyptian units of measure? Process: Measure and draw larger, Measure and draw smaller, personal grids Preparation as units of measure. Demonstrate Talk about the Egyptian standards for length—the cubit, palm, and span— Session 2 personal grids 6. Using 12- x 18-inch construction paper, students each create an evenly how to determine the length of a and how long each might be. Use a yardstick or ruler to measure body parts and 30-40 min. 6. Create a grid of 2-inch squares spaced grid with the same number of rows, columns, and cells as on marker by counting fingertips set and shoe sizes, for example. Compare findings among students to see the the team grid. Lightly number each cell to match the larger grid. Discussion side by side along the barrel. Show variations. Talk about how that could be a challenge when building furniture on a full sheet of construc- how to measure the length of a desk or sewing clothes. tion paper. Follow steps from Reduce and redraw Session 1, mark papers every by counting palms set side by side. Brainstorm and list different measurement units suitable for the grade level . Show students how to draw the lines and curves that appear in the 2 inches. Number squares in Invite children to measure other and children’s skills including U.S. Customary, metric, and historic measures. larger squares of the team grid on the corresponding smaller squares this larger grid to match the objects and compare results. What Which units measure length and which measure area? of their personal grids to create a reduced version of the figure outlined smaller grid. do they notice? Why might two on the large craft paper. different children using the same Enlarge a hand body part to measure the same . Demonstrate how to copy the object obtain different results? lines and curves that appear in the squares of the smaller grid Crayola® • Construction Paper™ Crayons • Erasable Colored Pencils • Markers into the corresponding squares Supplies of the larger grid. • Paint Brushes • Tempera Paint Process: Add color and patterned designs to smaller grids Other • Construction paper • Rulers Session 3 8. Students fill all the shapes in their smaller grids with crayon color to enrich and personalize them. Materials 30-40 min. • Craft paper on a roll • Paper plates • Paper towels • Recycled newspapers • Water containers • Yardsticks Process: Paint large hand design Paint team grid Session 4 . Fill larger hand grids with colors . Fill the group grid with paint colors. Plan use of negative space to Set-up/Tips • Cover painting surface with recycled newspaper. 30-40 min. and patterns. highlight the outline if desired. • Mix paint colors on paper plates. Assessment • Assess student grids for precise measurements. Process: Measure and draw a grid Measure and draw a grid • Observe the drawing process. Did students use problem-solving strategies to redraw and scale figures? Session 1 1. Children measure and cut con- 1. Children divide into small groups of three to five. Cut craft paper • Students exchange drawings to check how well smaller drawings match larger drawings. 20-30 min. struction paper in half (4.5 x 6 large enough to contain a life-size contour drawing of one student in inches). Lay one piece flat, the group. • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things they learned. vertically. Place ruler along the . Students measure and mark 3- or 4-inch square grids, depending on left edge of the paper and mark their skills, of columns and rows of squares on craft paper. off inches starting at the top. Extensions Practice measuring desktops or Show children sports play books Research how archaeologists use Do the same on the right side. . Number the squares from left to right across each row. Observe other classroom items using a variety created by coaches. How is scale scale plans to show the locations of multiplication and other patterns in numbered cells at the ends of of units of measure such as crayons, used to create play books? How do discoveries and details of structures. . Use a ruler to connect the each row. paper clips, or yarn. Make and grid the drawings of various plays show See in Paint on Crayola. marks, making rows across scale drawings of the desktops to problem-solving strategies? com for an exploration of the Great the paper. Trace a body model represent the various units of Create scale drawings of favorite Pyramids. . Create 1-inch wide columns in . Each group chooses a model from the team to lie on the grid in an measure. sports fields. The On the Court Challenge students with strong a similar manner. unusual position. Simplify the grid-making part Lesson Plan found on Crayola.com mathematical aptitude to explore . Number squares consecutively . Team members trace around the model. of this lesson for young students offers a fun way to bring math, architectural blueprints (of the from left to right across the or those with special needs by science, art, and sports together in school if possible) and explain the rows, starting on the top row. providing cardboard “rulers” a big way. scale notations and other symbols marked off in inches. to classmates. Use problem-solving Trace a hand skills to determine the real sizes of . Children place an open hand the rooms and building. or simple shapes on a grid and Beside the Still Waters trace around them with crayon, 1984-2003 To demonstrate how mural artists use grids, each child selects a photograph of a simple object or photograph or draw a simple figure using Artist: Kendall Shaw depending on children’s abilities. Superimpose a grid over the picture. On mural paper create a larger, proportionate simple shapes on the paper. Acrylic and mirrors grid. Create a drawing of the object using skills learned during this lesson. on 60" x 60" Collection of the artist.

Sun Ship 1982 Artist: Kendall Shaw Acrylic and mirrors on canvas 4 panels, total 101" x 101" Collection of the artist.

Building fun and creativity into standards-based learning 40 Mathematics Mathematics 41 It’s About Time…Average Time!

Objectives Multiple Intelligences What Does It Mean? Students measure elapsed time to answer questions about Mean: a mathematical Bodily-kinesthetic average time needed to complete tasks. average Students collect, organize, analyze, and display relevant time Interpersonal Median: the middle point research data. Logical-mathematical in a series of values Students in grades K-2 sketch pictures of daily tasks and Naturalist Mode: the value that occurs record the time each task takes. the greatest number of Students in grades 3-6 draw in sketchbooks and record the times in a given series amount of elapsed time they draw each day. Students design color-coded bar graphs to show the results of their research and analyze their findings.

National Standards Visual Arts Standard #3 Mathematics Standards Chooses and evaluates a range of subject matter, symbols, Data Analysis and Probability and ideas Formulate questions that can be answered with data and collect, organize, and display relevant data to answer them Measurement Understand measurable attributes of objects and the units, systems, and processes of measurement

Background Information Vocabulary List Some art takes very little time to create and other art takes Use this list to explore new vocabulary, create idea webs, hours, weeks, and sometimes years. Graffiti typically takes or brainstorm related subjects. little time and little skill to generate and many believe it • Art terms Composition Mural creates a visual blight within cities. Some communities in Fine art Sketch the United States have found solutions that contribute visual Graffiti Sketchbook improvements and demonstrate that artwork, even graffiti, Mixed media Visual effects can take time. One example of this is The Philadelphia Mural Multi media Arts Program (MAP). This public art program works in partner- ship with community residents, grassroots organizations, • Calculating Approximate Median government agencies, educational institutions, corporations, Average Mode and philanthropic groups to design and create of Estimate Rounding Artwork by students enduring value while actively engaging youth in the process. Mean Total from Michael Jordan Those who participate in these efforts come to a clearer Community School, understanding of just how much time it takes to create art • Graphing Bar graph Statistic Chicago, Illinois. while working as a team. Data Table Teachers: Elyse Martin, Pictograph Trish Davlante

Resources • Telling time Century Duration All I See by Cynthia Rylant and Peter Catalanotto Day Elapsed time A young boy’s friendship with a painter inspires the way Decade Half hour he sees the world around him. For all ages. Half past Hour Counting on Frank by Rod Clement Minute Artwork by students from With the help of his dog, Frank, the narrator collects O’clock St. Theresa School, math-themed facts. Appealingly illustrated, for all ages. Second Hellertown, Pennsylvania. Year

Artwork by students from St. Theresa School, Hellertown, Pennsylvania.

Building fun and creativity into standards-based learning 42 Mathematics Mathematics 43 It’s About Time…Average Time!

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Assemble a sample sketchbook. Discuss the subject of graffiti. Have students share where they have seen Process: Sort and analyze data Sort, evaluate, and display data Preparation Display two clocks with movable graffiti. How long does it take to create graffiti? Explain that fine artists take Session 3 . Students review their sketch- . Students calculate the total time it took for each of them to create all and hour and minute hands, and sample time and practice drawing in sketchbooks to prepare for creating larger 20-30 min. books to find the tasks that took seven drawings. sketchbook. works such as mural paintings. Share examples of large outdoor murals the most and least time. List all Discussion such as those created by the Philadelphia Mural Arts Program. . Students divide the sum by seven to find the average (arithmetic mean) Show the clocks. Discuss how the tasks in order according time that drawings were made for one week. time is measured. How long is a With students, create sketchbooks. Sandwich seven sheets of white paper to times. second, minute, half hour, hour? inside folded drawing paper. Staple along spine. 6. Share drawings and findings. Compare and graph data, individually and . Share sketchbook drawings as a class. Analyze findings. Ask children to name activities that Ask students how long they think it will take them to create seven detailed and compare elapsed times take different amounts of time to do, drawings of the things they see around them (there is no rush)? What do for various students doing . Advanced students perform more sophisticated calculations with the such as brushing teeth or traveling they think will be the average time per drawing? Ask each student to record similar tasks. data, such as comparing the range of time differences or calculating to school. Use clocks to show start this estimate on the back cover of his/her sketchbook. the percentage of total time each drawing took. Use class time data to 6. Show students how to create and finish times for several typical Explain how to calculate an average. Tell students that, although each calculate mean, median, and mode. bar graphs using their data. activities. sketch will take a different amount of time, after they are finished they will Encourage them to use a 8. Challenge students to turn time calculated in minutes into fractional and Ask students how long they think be able to calculate the average time per sketch. Show how to calculate an different color for each activity. decimal expressions of parts of an hour. Then calculate averages using it will take them to carefully create average by asking how many days last week each student brought lunch or these figures. similar sketchbooks (this is not a did some other similar, variable task. Tally the results; divide the total by the race). Record estimates. Set a number of students in the class. Assessment • Review student sketchbooks to • Students work in pairs to check each other’s calculations with a calculator. clock at the start time. Create Create a bar graph poster to illustrate how students will chart their check for accurate recording of • Compare and discuss bar graphs. sketchbooks: Demonstrate how drawing times. tasks and time measurements. to sandwich seven sheets of copy paper inside folded drawing paper. • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things Staple along spine. Set a second they learned. clock to show the finish time. Together calculate how long it took. Extensions Create a time survey with children Investigate how things change Students with strong mathemati- Compare actual time to estimates. to find out how families enjoy time over hours, days, and months. cal backgrounds define and explain together and how much time they Document changes with drawings the terms median and mode to Crayola® • Colored Pencils • Crayons • Markers spend doing their favorite activi- and mathematical data in layered the class. Work together in small Supplies ties. Have children generate survey tab books. See the How Time Flies groups to have students determine questions and record data at home. Lesson Plan on Crayola.com for the median and mode for the data Other • Calculators • Clock(s) • Copy paper • Staplers and staples • Stopwatch(es) (optional) Create dioramas showing how each directions. collected on the sketchbook project. Materials • White drawing paper (12- x 18-inch) family spends time together. See Hold elapsed time showdowns! Discuss results. Family Food Favorites on Crayola. Students create clocks with move- Challenge small groups of students Process: Design cover Design cover com for creative inspiration. able hands. One partner’s clock is to create elapsed-time game shows. Younger children and those who labeled “start time;” the other is “end Students identify problems related Session 1 1. Children write the word “TIME” 1. Students draw decorative letters to create titles for their sketchbooks. need more practice make paper time.” Each clock can indicate a.m. to calculating time, elapsed time, 20-30 min. on the covers of their sketch- Add interest by including increasingly more elaborate shapes, colors, plate clocks that have moveable or p.m. Partners stand back-to-back and average time as brainteasers for books. Decorate the covers with and patterns. hands attached with brass paper and record times on their clocks. contestants. Hold a game show day. shapes and patterns around the . Explain to students that they will create detailed drawings of objects fasteners. Children use them to Call out “showdown.” Students turn letters. they see. They are to record the time in minutes that it takes to do each solve relevant time story problems. to their partners and calculate the . Explain that each day students daily drawing in small data blocks in one corner of each of seven pages: elapsed time between the clocks. will complete a different task at “START,” “FINISH,” and “ELAPSED TIME.” Students calculate elapsed home or school. Children draw time daily or at the end of their research. Children make a chart of their daily activities. Set the hands on a paper Hold an obstacle course rally, a picture of each task in their clock to indicate when they do these activities (wake up, go to school, eat much like a car rally. Students time sketchbooks and write how lunch). Children draw pictures to illustrate the different activities. each other in a series of challenges many minutes each task took. that they invent. Record individual data for each event. Total times to Process: Collect data over 7 days Collect data over 7 days determine elapsed times for each Sessions 2 . Each day children measure how . Review the assignment each day. student. Use data to calculate 20-30 min. long it takes to do activities Students share their sketches with averages, means, modes, and such as watch ice cream melt, classmates. Talk about how long medians for each event and the walk around the entire school it took to create each one. entire rally. together, or draw a detailed self- portrait. They record an estimate before actually timing each task. Evaluate estimates. Swiss Clock Photo by R. De Long

Czech Clock Photo by R. De Long

Building fun and creativity into standards-based learning 44 Mathematics Mathematics 45 Purchasing Flower Power!

Objectives Multiple Intelligences Students assess the characteristics of their flower creations and Interpersonal Naturalist those of their classmates as they recognize the artistic merits of creating individual flowers by hand and combining them into Logical-mathematical bouquets. Naturalist Students use place value and estimation to read, write, compare, and order decimals involving money, using play money to practice purchasing flowers within a budget. Artwork by students from Students create flowers using a multi-step -like technique. PS 132K, Brooklyn, New York. Teacher: Charlotte Ka National Standards Visual Arts Standard #5 Mathematics Standard Reflects upon and assesses Grades K-2 the characteristics and Algebra merits of their work and Use mathematical modes to represent and understand quantitative the work of others relationships Grades K-6 Number and Operations Compute fluently and make reasonable estimates Problem Solving Solve problems that arise in mathematics and in other contexts

Background Information Concept List Most flowers and plants sold in the United States are grown Use this list to explore new vocabulary, locally. Some, however, come from great distances. Florists create idea webs, or brainstorm related subjects. get a variety of plant materials from wholesalers, who obtain 10% off Production costs them from huge international auctions. The largest flower 25% reduction Radial design auction in the world is held in Aalsmeer, Holland. Imagine 30% less Repetition, rhythm, an auction building that covers 160 acres with complex, Auctioneer & pattern computerized moving and tracking systems for their fragile Banker Retailer wares. About 14 million flowers are auctioned every day in Botanist Rose windows Aalsmeer—that’s 3 billion flowers a year! Blooms include Bouquets Seasonal colorful carnations, chrysanthemums, freesia, lilacs, and roses. Careers Stock broker Most of these flowers are shipped to other countries. Discount calculations Vendor Your favorite, fragrant flower in a Mother’s Day bouquet Financial planner or wedding arrangement may have been grown in Bulgaria, Florist auctioned in Holland, flown by jet across the ocean, and then Horticulturist trucked to your hometown. Imported Individual items Local Resources Mandalas Manufacturer Flowers by David Burnie Marketer/advertiser Bright illustrations and photographs with detailed text. Multiples Presents botany in a fun framework. Older students are intrigued by information, while younger students are inspired by colorful images. The Reason for a Flower by Ruth Heller Rich illustrations present the many functions of flowers. Text is just right for lessons on basic botany. Excellent resource for all grade levels.

Flower Market Arles, France Photo by J. McCracken

Artwork by students from The Creation, Rose Window Trinity Kids Club, Washington National Cathedral Trinity Wesleyan Church, Radial design Washington, D.C. Allentown, Pennsylvania. in a tile design. Photo by J. McCracken Teacher: Alison Panik Building fun and creativity into standards-based learning 46 Mathematics Mathematics 47 Purchasing Flower Power!

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Display pictures of flower arrangements that contain more than three flowers. Display other artifacts that illustrate Process: Create stems Preparation radial design, such as photographs of rose window and mandala designs and close-up views of flowers. Session 4 8. Gather the finished blossom into a cone. Press the pointed end flat against the top of a barrel. Discuss how flowers are bought and sold. Talk about how flowers could be purchased by the stem or in bouquets. and 30-40 min. 9. Wrap floral tape around the point of the filter and over the pencil to attach blossom to pencil (see diagram). Discussion Ask children what they know about how flowers are grown, priced, shipped, and sold. Ask students whether they think it is more expensive to purchase a whole bouquet or to buy individual stems to make your own bouquet. Make price tags Find out! 10. Cut 1- x 2-inch rectangles of oak tag to create price tags. Punch a hole in one end of tag and insert ribbon Create some unusual blossoms following the steps here to use in display, discussions, and demonstrations. or yarn. 11. Provide ability-appropriate direction to students regarding pricing. (For example, younger students might price Look closely at illustrations and Lead children to develop a plan to research and compare the real costs flowers in 5¢ increments—5¢, 10¢—while older students use larger dollar and cent amounts.) Students decide photographs of flowers that clearly of creating a bouquet within a budget. Where could they go to find out? on the price of each of their flower stems and write the prices on the tags using decimal dollar notation ($.79) demonstrate radial design. Ask With student assistance, create simple paper money—$1, $5, $10, and on one side and cents notation (79¢) on the other. Encourage children to take into account the work that went children what shapes they notice. $20 bills as well as coins. into creating each individual flower and the uniqueness of each bloom. Place strings across the photo to Identify samples of radial design found in nature and art. show the symmetry of the flower 1 2. Create decorative borders on both sides of the price tags. Tie price tags to flower stems. in each “pie slice.” Assessment • Arrange flowers in containers to • Set a predetermined budget. • Arrange flowers in a flower Explain that students will “manufacture and sell” flowers within a budget. After creating several single-stem create a flower market display. Teams of students calculate the market display. Students work flowers that will demonstrate radial design, they price their flower stems individually. With those flowers, they Children sort flowers according to cost of buying several flowers in pairs to choose, calculate, and will put together beautiful bouquets, but the cost of the entire bouquet may not exceed the assigned budget! a variety of physical characteristics. while staying within their budget. “purchase” different combinations Provide plastic coins for children How many combinations can of flowers, using bills and coins. ® • Crayola • Colored Pencils • Fabric Crayons • Glitter Glue • Scissors • Washable Markers to use to “purchase” single stems they create within their budget? Observe students’ abilities to Supplies and different combinations of • Set up a flower market and calculate cost, count money, two or more stems. Observe provide play money for students give change, and use problem- Other • Coffee filters • Green floral tape • Hole punch • Iron (adult use only) • Oak tag • Paper towels children’s abilities to calculate to use to “pay” for different solving skills to exchange one flower for another to get the Materials • Recycled newspaper • Ribbon or yarn • Sealable plastic bags • White paper and count coins. bouquets. Observe calculation and problem-solving skills. most for their budgets. Set-up/Tips • Use play money coins. Or ask parents to provide real coins in • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things sealable plastic bags labeled with they learned. each child’s name. Extensions Very young children and those Depending on the time of year, Research plant breeding. Explore • Cover art surfaces with newspaper. with some disabilities may be most take the artistic flower experiences different kinds of cut flowers to see • Place newspaper under coffee filters for better control during coloring and ironing. Show children how to apply successful in decorating blossoms into the real world. In winter, force variations in color, size, fragrance, firm pressure when coloring coffee filters with fabric crayons to achieve the best color results. only with washable markers and blooms from dormant flowering and petal shape. Discuss why then spritzing them with water. trees and shrubs (such as azaleas floriculturists and geneticists might • Store each child’s coffee filter flowers in a large sealable plastic bag labeled with the child’s name between sessions. They may also need assistance and dogwoods). In spring, plant and want to create new and different • Enlist parent volunteers to iron coffee filters. with wrapping the floral tape. grow marigolds from seeds. In fall, kinds of flowers. At the end of the unit, create extract natural dyes from colorful Talk about intellectual property Process: Create flower blossom radial designs vases to display flowers in the flowers and leaves. Place fabric over and the breeder’s bill of rights. Session 1 1. Demonstrate how to fold a coffee filter in halves, quarters, and then in eighths by folding in half again, again, school. See Very Versatile Vases on flowers and leaves and pound with Why does the price of flowers 30-45 min. and again. Crayola.com for a unique technique. a mallet. vary so much? Gifted students Tip: Place a rock at the bottom to (plus 2. Unfold and press the coffee filter flat. Draw radial designs on several coffee filters with fabric crayons, adding could investigate the cost of seeds/ prevent toppling. ironing) similar lines, shapes, and colors in each section. Leave some sections plain. cuttings, greenhouse/field environ- Grow flowers from seeds. Price ments, growing seasons, shipping, 3. AN ADULT heat-sets the crayon. Place plain paper on newspaper. Lay filter on the paper. Cover with a second and sell them at a school event. and various other factors that play sheet of paper. AN ADULT irons the filter with a hot iron in a well-ventilated area. Press the design with slow a role in the price of flowers. steady pressure, moving from area to area slowly for 1 to 2 minutes. Colors will “bleed” a bit like batik. Cool. Process: Add marker colors Session 2 4. Fold the ironed coffee filters several times. How to fasten paper blossom 20-30 min. 5. Press washable marker nibs against the folded filter and hold in position so the filter absorbs color through all layers. Unfold. to pencil stem 6. Dampen paper towels. Gently press on coffee filters to dampen them, diffusing marker color for added effects. Air-dry filters. Gather filters Tightly wrap floral Wrap until blossom together and tape to join blossom is secure on stem. Process: Add glitter glue pinch/twist at to pencil stem. Session 3 7. Decorate blossom centers and edges with glitter glue. Outline interesting parts to make them stand out. center point. 15-20 min. Air-dry the filters.

Radial design in a hibiscus flower. Building fun and creativity into standards-based learning 48 Mathematics Mathematics 49 Personal Math Motto Banners

Objectives Multiple Intelligences What Does It Mean? Students write algebraic equations to show how lines are used Contour drawing: Intrapersonal Logical-mathematical to create plane figures, and how plane figures are used to create drawing that focuses the illusion of three-dimensional space figures. Linguistic Naturaliston edges and three- Students connect similarities and differences between visual Logical-mathematical dimensional outlines Artwork by students arts and mathematics by analyzing and applying the equations Spatial of objects, folds, or from CS 102, in 2-D and 3-D figures. patterns using line Bronx, New York. Students develop an appropriate problem-solving plan, and without shading Teacher: Neila Steiner then draw pictures to arrange lines, shapes, colors, and textures Trompe l’Oeil: artwork to create 3-D illusions on banners. that is portrayed realisti- Students identify mottos that relate to mathematical problem cally so that people solving or geometric proofs. think they are looking at something real; visual illusion such that 2-D National Standards paintings appear to be 3-D Visual Arts Standard #6 Mathematics Standards Makes connections between visual arts and Algebra other disciplines Represent and analyze mathematical situations and structures using algebraic symbols Reasoning and Proof Select and use various types of reasoning and methods of proof

Background Information Vocabulary List Some artists are so skillful at creating illusions that they fool Use this list to explore new vocabulary, create idea webs, the viewer into thinking they see three-dimensional objects in or brainstorm related subjects. real space even though the art is only two-dimensional. One • Algebra terms Equation method of illusion painting is called Trompe l’Oeil, which Unknown means “fool the eye.” Because these kinds of paintings are Variable on flat (two-dimensional) surfaces, it takes much observation, planning, and even mathematical skill to create these illusions. • Design with shapes Inversions/ mirror images Throughout history, artists have used various devices to help Patterns them duplicate the look of three-dimensional objects, or to Symmetry create the illusion that one object is close and another very far away. • Illusions Optical After-images Resources Pictographic ambiguity A Trick of the Eye: Trompe l’Oeil Masterpieces by Eckhard Famous artists Hollman and Jurgen Tesch Josef Albers Explores five centuries of Trompe l’Oeil: , M.C. Escher hyperrealism, and visual puns. Identifies tricks artists use to manipulate visual . Something for all ages. Magic Grandfather Tang’s Story by Ann Tompert Ages 6 through 9 enjoy this tale of two shape changers told • Mottos Guiding principal, goal, or ideal Japanese Textile by a Chinese grandfather. He illustrates the story by shifting Sentence, phrase, or word Banner tangrams into different shapes. Includes a tangram pattern. Spirit, character, or purpose of a 2001 person or group Seeing Double by J. Richard Block Unknown artisan Use age-appropriate examples from this collection of more Paint on dyed silk • Three-dimensional (3-D) art Contour drawings than 200 illustrations to demonstrate how shapes can be 15" x 31" Depth arranged to give impressions of more than one idea. Kyoto, Japan Form Private Collection. Shadow Volume

Building fun and creativity into standards-based learning 50 Mathematics Mathematics 51 Personal Math Motto Banners

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Post several quotations related to mathematics or problem solving, such as Carl Sandburg’s “Arithmetic is where Process: Sketch 2-D and 3-D designs Preparation numbers fly like pigeons in and out of your head.” Read the quotations aloud and ask students to explain what they Session 1 1. On paper, students plan their own personal illusion illustrations, one with plane figures and one with and think they mean. 20-30 min. space figures. The student art samples pictured were made with two large squares, one above the other. Place Discussion Display pictures of quilt designs that create 3-D illusions through the juxtaposition of simple light- and dark- 2-D plane figures in the top and 3-D figures in the bottom square. colored shapes. Process: Create fabric designs Create a bulletin board showing Start a bulletin board showing the equation: Session 2 the “recipe” or equation for a shape. . Use fabric crayons or fabric markers to draw the planned illustrations on fabric. Be sure to leave a 1 1/2-inch (A+B)+(A+B)=C 30-40 min. border at the top for hanging and a 3-inch space to separate the shapes. Demonstrate how two horizontal (horizontal line + vertical line) + (horizontal line + vertical line) = square. lines and two vertical lines combine Invite students to create several more equation “recipes” for a variety of Process: Choose mottos Research mottos to create a square. regular plane figures (rectangle, triangle, hexagon). More advanced students Session 3 . Brainstorm encouraging and/or . Children research pertinent quotations about math and problem-solving With students, make a matching add irregular figures. 20-30 min. humorous words, phrases, and or geometric proofs. Or they create their own inspirational math mottos. game using recycled household With students, create a poster with line drawings illustrating 3-D figures: items shaped as a cone, cube, sentences about problem . Write chosen mottos on banners. cone, cube, cylinder, pyramid, egg form, sphere, and rectangular prism. solving and math. cylinder, pyramid, plastic egg, Write names of forms on separate pieces of paper. Children match names sphere, and rectangular prism. of figures to forms. Expand the activity to include a set of small cards with . Children choose mottos that Write the names of the shapes on names of plane figures and a set of small number cards. Challenge students stand out for them. Write cards to match the objects. to identify the plane figures required to create each space figure and how mottos on banners. many of each are needed to make the figures. Process: Embellish designs Children use colored craft sticks, yarn, and rubber bands to analyze how lines are used to create plane figures Session 4 . If the designs are to be heat set, an adult does this before proceeding. (squares, circles, rectangles, triangles). Ask children to explain what kinds of lines are needed to create each shape. 15-20 min. 6. Embellish designs with glitter glue. Air-dry the glue. Use paper shapes to analyze how plane figures are used to create 3-D space figures. Explore how tangrams can be arranged to create the illusion of 3-D figures on a flat surface. Discuss how combined shapes create identifiable Process: Prepare banner for display objects such as figures, animals, and plants. Session 5 . Roll construction paper. Glue the end to form a cylinder. Hold in place until air-dry. Look at examples of Trompe l’Oeil, optical illusions, and geometric art. Invite students to think about 10-15 min. combinations of lines that create shapes. 8. Apply glue to back of top 1-inch border of fabric. Place paper cylinder onto the glued border and roll. Air-dry the glue. Crayola® • Colored Pencils • Fabric Crayons • Fabric Markers • Glitter Glue • School Glue • Scissors . Cut ribbon or yarn into 3-foot length. Thread through the cylinder and tie closed to hang. Supplies Assessment • On index cards, children write • Students write equations for the lines needed to create each plane figure, Other • Construction paper • Fine-grade sandpaper sheets (optional) • Freezer paper (optional) equations for some of the shapes the shapes needed to create each space figure, and the figures needed Materials they created in their designs. to create illusions in their designs. Ask students to exchange papers to • Iron (for adult use only, optional) • Newsprint • White cotton fabric • White paper • Yarn or ribbon Talk with students about the check equations. designs and their equations to Set-up/Tips • Ask parent volunteers to measure and cut a clean, white cotton sheet into 18- x 24-inch pieces, one for each child. • Do the images on the students’ banners show an understanding of how assess learning. lines and colors can be manipulated to create visual illusions? • Cover drawing surface with plain newsprint. • Do banners include a variety • For more intense fabric crayon colors, place fabric of shapes? on top of a very fine grade of sandpaper before decorating. Hold in place with masking tape as Japanese Textile Banner • Are the mottos chosen for the banners pertinent and spelled properly? needed. Press hard and lay down a thick layer of 2001 Unknown artisan • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things crayon. Fabric crayon colors look much brighter they learned. Write or print statements on labels to attach to the back of each student’s banner. when they are heat set. Paint on silk brocade 15" x 39 1⁄4" • To stabilize fabric for decorating with either Kyoto, Japan Extensions Print out the Eye Illusions activity Challenge students to invent new optical illusions, adding movement markers or crayons, ask adult volunteers to iron Private Collection. page from Crayola.com. Discuss each to the equation. Provide a variety of art materials, such as acetate sheets, freezer paper on the back. illusion, then challenge children to recycled file folders, straws, and brass fasteners for students to experiment • Adults heat-set the fabric crayon or marker create their own. with spinning, flipping, and bending images. Encourage students to think of color designs according to package directions Cut tangram pieces from recycled their own ideas and go to Crayola.com for inspirational crafts, such as Flash (optional). file folders for younger children and a Neon Mini-Sign, Geometric Optic Spinner, and Optical Delusion. those with some learning disabilities Student research groups investigate the work of famous illusionists and to manipulate into animal shapes. explain special techniques they used to create their illusions. After shapes are defined, students Invite an ophthalmologist to speak to the class about how movies create add texture and color to clarify an illusion of movement. the image. Challenge students with strong spatial awareness to create tessellations. Share the book Hello, Red Fox by Eric Carle with the class. Japanese Textile Banner Talk about how illusions can 2001 be created through the use of Unknown artisan complementary colors. Paint on silk brocade 15" x 25 1⁄2" Kyoto, Japan Building fun and creativity into standards-based learning Private Collection. 52 Mathematics Mathematics 53 Animals: A Brood, a Clutter, a Drift, and More!

Objectives Multiple Intelligences Students recognize various materials, techniques and pro- Interpersonal Naturalist cesses, and can describe and use these to communicate ideas, experiences, and number stories to elicit viewer response. Linguistic Spatial Students (K-2) count with understanding, recognize “how Logical-mathematical many” in sets of objects, and compare sizes of those sets. Students (3-4) identify and build three-dimensional objects from two-dimensional representations of that object. Students (5-6) use geometric models to represent and explain algebraic relationships among the sets depicted.

National Standards Visual Arts Standard #3 Mathematics Standards Chooses and evaluates a Number and Operations range of subject matter, Understand numbers, ways of representing numbers, relationships symbol, and ideas among numbers, and number systems Problem Solving Build new mathematical knowledge through problem solving Connections Recognize and apply mathematics in contexts outside of mathematics

Background Information Vocabulary List Why are groups of animals called different names? Some Use this list to explore new vocabulary, choices seem obvious, such as a colony of bats or ants, or a create idea webs, or brainstorm related subjects. herd of deer or cattle. Other group names may be romantic or Band (gorillas) even mysterious, such as these unusual animal group names: Litter (kittens, pigs) Bed (clams, oysters) Murder (crows) • a dole of doves Brace (ducks) Muster (peacocks) • a business of ferrets Brood (chicks, hens) Pack (hounds, wolves) • a knot of frogs Cast (hawks) Pod (seals, whales) Clutter (cats) • a horde of hamsters Pride (lions) Colony (ants) School (fish) • a charm of hummingbirds Company (parrots) Skulk (foxes) • a parliament of owls Drift (hogs) Sleuth (bears) • a gang of weasels Flock (birds, sheep) Swarm (bees) Gaggle (geese) • a murder of crows Team (horses) Gang (elk) Troop (kangaroos) A group of birds of any species is usually called a flock. Herd (cattle, elephants) Crows, with their sinister associations, may have earned their Knot (toads) group name by their association with melodrama, such as the work of Edgar Allen Poe. Lexicographers suggest that group names of animals have their roots in animal behaviors. Names such as a pride of Artwork by students from lions or a gaggle of geese seem to support that theory. Mountain Plains School, But what about hamsters and ferrets? Morris Plains, New Jersey. Teacher: Val Negra Resources A Crash of Rhinos, a Party of Jays: The Wacky Ways We Name Animal Groups by Diane Swanson and Mariko Ando Spencer A whimsical introduction to animal groups appropriate for all ages. Comic illustrations for each animal and group name. Counting opportunity for early elementary classes. Animals: Pictures and Words by Carolyn Jackson More than 175 different animals featured in color photo- graphs and illustrations that attract students of all ages. Older elementary children will be intrigued with facts Artwork by students from about animal behavior. Mountain Plains School, Morris Plains, New Jersey. Teacher: Val Negra Building fun and creativity into standards-based learning 54 Mathematics Mathematics 55 Animals: A Brood, a Clutter, a Drift, and More!

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Display age-appropriate books and other pictures of groups of animals. With students, label them. Process: Create 3-D animal sets Preparation Make a three-dimensional model depicting a set of one kind of animal. Session 2 . Use a tennis ball amount of Model Magic compound to mold an animal body form. Use geometric forms and 45-50 min. such as spheres, cubes, cylinders, and rectangular prisms. Model, pinch and pull animal legs, necks, heads, Discussion tails, or other animal features to make a realistic animal. . Create a set of the same kind of animal. Use modeling tools to add texture and details. Make both adults ® Crayola • Colored Pencils • Crayons • Model Magic® • School Glue • Scissors and young. Supplies 6. Arrange animals on a Model Magic base representing their natural habitats. Air-dry models for 24 hours. Other • Drawing paper • Modeling tools such as plastic dinner knives, craft sticks, and toothpicks Process: Embellish animal sets Materials ® • Velcro tape • White paper Session 3 . Decorate dried models with markers and/or watercolor. Air-dry paint. 10-15 min. • Poster board Process: Count and compare set sizes Compare 3-D with 2-D sets Identify algebraic relationships Set-up/Tips • Work on a clean, dry surface. Session 4 8. Label each set with the type of 8. Study the animal set models. 8. Study the dioramas and • Model Magic® compound fresh from the package sticks to itself. If the modeling material has dried, use glue to 20-30 min. animal depicted. Compare them with dioramas. animal models. attach pieces. . Study all the model animal sets. Discuss correlations among 3-D . Identify algebraic relationships forms and 2-D shapes. Process: Choose and research an Research animal groups Research animal groups Count how many animals are among the animal models, such in each set. . Calculate the number of geo- as 1 (brood of 6) + 4 (brace of Session 1 animal group 1. Students research facts about 1. Teams of three or four students metric forms that were used 5) = 20 birds 20-30 min. one type of animal. work together to select 10. Identify sets that are equal 1. Students each choose an animal in number. Compare sizes to create the animal models. 10. Students explain their math from the photos displayed. . Students write a paragraph that research facts about three or Which sets used the most four different types of animals. of sets using terminology proofs to other teams. . Students identify the animals’ includes facts they discovered. such as equal, less than, and different forms? group names. . Title the writing with the . Compile a chart with columns more than. for each animal. Title each . Students list facts they know name that is given to the animal group. column with the group name Assessment • Did each student depict one • Are the features of the animals • Teams check each other’s sets about the animal selected, that corresponds to the animals. including habitat. type of animal, show an accurate created in dioramas and sculpted and math proofs. Do algebraic . List animal facts about each habitat, and label the set with its sets accurate based on student relationships compare groups, animal in each column. correct name? research? such as birds, four-legged animals, • How accurately did students • How descriptive were compari- or water animals? . Create a diorama that includes 2-D drawings of the animal(s) researched. count and compare the number sons between 2-D and 3-D Draw animal features to accurately represent research facts. Depict the of animals in each set? representations? animal’s natural habitat. • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things they learned. Extensions Challenge students to compare and contrast the behaviors of animals. Students write descriptive para- How do various animals relate to each other in terms of survival? Identify graphs to explain how they arrived Berks County cows animals in the models that might have a predator-prey relationship. at their mathematical calculations. Photo by R. De Long Younger children and those with learning challenges may benefit from Challenge students to explore using common manipulatives such as table blocks to represent sets of the real relationships among animal animals before they create their own animal set models. groups in different habitats. Examine Write a step-by-step sequence of how to create a Model Magic animal set. how the survival of each animal group depends on the survival of another. Gifted students invent new species of animals by combining features from two or more animal species.

Sheep hand-colored photo Image Artist: Wallace Nutting

Zebra-head lamps Photo by R. De Long

Building fun and creativity into standards-based learning 56 Mathematics Mathematics 57 Keeping Track of Time

Objectives Multiple Intelligences Students create a replica timepiece that reflects understanding Interpersonal Logical-mathematical of how a clock is heavily influenced by the visual arts in its design, while serving as a mathematical tool. Logical-mathematical Students (K-2) develop a common referent to understand and Spatial practice how time is measured. Students (3-4) select and apply appropriate standard units to estimate, measure, and compare the time it takes to conduct simple activities. Students (5-6) recognize international time zones and the relationships among time units as they are converted from one to another within the system.

National Standards Visual Arts Standard #1 Mathematics Standards Understands and applies Data Analysis and Probability media, techniques, and Formulate questions that can be addressed with data and collect, organize, and display relevant data to processes answer them Visual Arts Standard #4 Measurement Understands the visual arts Understand measurable attributes of objects and the units, systems, and processes of measurement in relation to history and Problem Solving cultures Apply and adapt a variety of appropriate strategies to solve problems Representation Create and use representations to organize, record, and communicate mathematical ideas

Background Information Telling Time: How to Tell Time on Digital and Analog Clocks! People have come up with methods for measuring time by Jules Older & Megan Halsey apparently as long as history has been recorded. Ancient Clearly explains concepts of time, including the measurement sundials were round disks marked with hours much like of when something happens as well as how long something today’s clocks. An upright structure cast a shadow on the takes place. Good choice to introduce time and review concepts. disk on sunny days. While sundials were relatively efficient The Story of Clocks & Calendars by Betsy & Giulio Maestro and evolved over several thousand years, they had limited use Details about the history of timekeeping complete with color in cloudy weather. photos and illustrations. For students in grade 3 and above. The hourglass was invented to solve this challenge. An hourglass is formed by two round glass bulbs, one above the other, connected by a short, narrow neck. When the Vocabulary List hourglass is turned over, sand flows slowly from the upper Use this list to explore new vocabulary, create idea webs, glass bulb into the lower one. The amount of sand, and the or brainstorm related subjects. width of the neck, determine how long it takes for the sand • Measuring time to completely empty into the lower bulb. Units Tools Components of In the 1300s, the first mechanical clocks were invented. Century Alarm clock an analog clock Some were wound by springs, while swinging pendulums Day Analog clock Bells drove others. Inventors continued working to create clocks Decade Atomic clock Case that were more and more accurate, with innovations including Hour Calendar Chimes gears and wheels. By the early 1800s, mass-production of Minute Cuckoo clock Face identical clock parts made it possible for almost everyone Second Digital clock Gears to own a timepiece. Week Egg timer Hour hand Year Hourglass Minute hand Artwork created by students from Clock innovations continue. Digital and wireless clocks, Pendulum Numerals St. Theresa School, such those that pick up radio to assure the correct (grandfather) Pendulums Hellertown, Pennsylvania. time, are common. Chemistry contributed to the invention of clock Second hand the atomic clock, which tells time to almost perfect accuracy Pocket watch Springs using a specific atom. Stopwatch Sundial Artwork created by students from Wristwatch Resources Mount Propsect Elementary School, Basking Ridge, New Jersey. Clocks & More Clocks by Pat Hutchins • Art elements and principles Teacher: Susan Bivona A fun introduction to telling time for younger students. Balance Pattern Texture Also offers a problem-solving situation for older students Crayon resist Proportion Unity exploring the measurement of time. Line Shape

Building fun and creativity into standards-based learning 58 Mathematics Mathematics 59 Keeping Track of Time

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Display images and examples of different types of clocks. Talk about similarities and differences between historic Process: Assemble clocks Preparation and contemporary clocks. Discuss how time keeping changed over the years. Session 3 6. Glue clock faces on the cases or background. Design an unusual, even humorous, timepiece to inspire student creativity. Note art elements used on the different and 20-30 min. . Attach any hands with a brad in the center of the face. Assemble other moving parts as needed. Discussion clocks on display. Challenge students to invent their own clocks using these elements. Introduce and reinforce time-telling skills on different types of clocks. Read books about time and its passage. Process: Tell time Estimate, measure, and Use an international Discuss recipes that include With students, chart times from Session 4 8. Pair students to play telling compare times time-keeping system cooking times (such as “Bake for at least three different time zones Grades K-2 time games appropriate to their 8. Estimate the time it takes to 8. Teams of students research 45 minutes”). based on Coordinated Universal 20-30 min. abilities.. For example, role play do several simple tasks such world time zones. Each student “What am I doing when the Read time schedules for public Time (UTC) also known as as sharpen a pencil, read a selects a city and positions the clock shows…?” Set clock to a transportation. Invent and solve Greenwich Mean Time (GMT)/Zulu. Grades 3-6 recipe, or do homework. clock to match that city’s time. time. Give one hint. Using the problems using these charts. 45-50 min. hint and time of day, students . Make a chart with three . Calculate time differences or more write or illustrate the activity. columns. Title the columns, (forward and backward) Crayola® • Colored Pencils • Crayons • Glue Sticks • Markers • Paint Brushes • Scissors • Watercolors Activity, Estimate, and Actual. between the cities identified Supplies 10. Note the time on the chart by members of the team. and the clock and then do 10. Chart class information to show Other • Brads • Compasses (optional) • Construction paper • Paper towels • Recycled file folders the activity. city name, country, and time Materials • Recycled newspaper • Water containers • White paper 11. Move the hands on the clock to zones represented. note the time when the activity Set-up/Tips • Provide tools for drawing round faces such as compasses, clean plastic lids, recycled CDs, or paper plates. was completed. Demonstrate their use as needed. 1 2. Calculate the amount of time • Demonstrate how to press hard with crayons for best results with crayon resist. it took to do the activity. How • Cover painting area with newspaper. close was the estimate to the actual time? Process: Draw a clock case Session 1 1. Students plan their clocks. Choose the size and shape of the clock box. Decide whether the clock will have Assessment • Are numerals correctly arranged • Observe students as they solve • Check to see if students correctly 45-50 min. hands, be digital, or use some other way to show time. Students must be able to change minutes and hours. on clock faces? problems and figure out design calculate the differences in time • Assess students’ abilities to read challenges while creating their between two cities. . Draw imaginative clock cases using 2-D art elements (line, shape, color, texture). Glue paper together for clocks. large clocks, such as grandfather clocks. and show times on clocks. • Evaluate completeness and • Determine student abilities to • Assess student ability to read accuracy of chart. Process: Make a clock face Create the clock display relate times to everyday activities. recipes and/or schedules and show times on the clocks they Session 2 . Trace circles on file folders . Design and decorate colorful crayon clocks on file folders or poster created. 45-50 min. or poster board. With crayon, board. Be creative with the design of clock hands, numeral fonts, and mark 12 hours with numerals, other elements. • Review calculations of elapsed time for correctness. Roman numerals, or even . Draw and color hour, minute, and second hands or other devices for symbols! Decorate clock face tracking the passage of time. Cut them out as needed. with a unified, balanced design. • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things Leave some areas plain. they learned. . Draw and color hour and Extensions Involve several classes or even the whole school in this project! Encourage students to bring clocks from home minute hands. Cut them out. (with parental permission) for a short-term display. Tally how many are collected per class, per grade, per type of clock, and other factors. Have each grade level create and display their clocks. Lead a variety of comparison activities . Paint the clock faces. Wax in the crayon resists the watercolor using different categories at each grade level. paint so the crayon color pops through. Air-dry the paint. Create colorful clocks for extra Find out more about the kinds Research big clocks, such as practice using Crayola erasable of clocks used to tell time around Big Ben in London and the large products! See Clock Hands That the world. Create a display of clocks clock on Parliament Hill in Ottawa. Town clock in Bern, Erase, a Lesson Plan on Crayola.com. with a map indicating the regions Find out how these clocks work, Switzerland Students use erasable markers to of origin. Go to Crayola.com to how they are set, and how math Photo by R. De Long draw simple digital clocks on slick, see how to create a Floral Cuckoo contributed to building these small paper plates or individual Clock. landmarks. Check out the Canada white boards. Play matching games Parliament Hill coloring page on with digital and analog (face) clocks. Crayola.com for an introduction.

Challenge gifted students to create their own elapsed-time board games.

Sundial South of France Photo by J. McCracken

Building fun and creativity into standards-based learning 60 Mathematics Mathematics 61 Spin a Radial Design

Objectives Multiple Intelligences What Does It Mean? Students (K-2) name, classify, draw, compare, describe attributes, Motif: a distinctive and Bodily-kinesthetic Spatial and investigate two-dimensional shapes in radial symmetry. recurring form, shape, Students (3-4) precisely describe, classify, and understand Logical-mathematical figure, or other feature relationships among radial designs. Spatial in a design Students (5-6) make and test conjectures about geometric Radial symmetry: when properties and relationships and develop logical arguments to objects or sections fan out justify conclusions about spinners they make that include in a regular pattern form radial designs. a central point Students use radial design motifs as the basis for creating working spinners.

National Standards Visual Arts Standard #3 Mathematics Standards Chooses and evaluates a Geometry range of subject matter, Specify locations and describe spatial relationships using coordinate symbols, and ideas geometry and other representational systems Visual Arts Standard #6 Communication Makes connections between Use the language of mathematics to express mathematical ideas visual arts and other precisely disciplines Connections Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Representation Create and use representations to organize, record, and communicate mathematical ideas

Background Information Vocabulary List Invention of the kaleidoscope has been traced to a Scottish Use this list to explore new vocabulary, create idea webs, scientist, Sir David Brewster, who patented it in 1817. In the or brainstorm related subjects. 1870s Charles Bush, from the United States, made improve- ments to the original design of the kaleidoscope and started • Terms a fad! Axis Line Reflective The word kaleidoscope is based on three Greek roots— Balance Midpoint Shape Circular Mirror-image Similar kalos (beautiful), eidos (form), and scope (to see). Intersecting Color Motif Symmetry mirrors inside a kaleidoscope reflect beautiful repeated Fraction Pattern patterns formed by small objects such as pieces of colorful Identical Radial glass that rotate around a central point. • Examples of radial symmetry Resources Anemone Grapefruit half Rose windows Coral Hex sign Rosette designs Hex Signs: Pennsylvania Dutch Barn Symbols & Their Flower Hub cap Starfish Meaning by Don Yoder & Thomas E. Graves Jellyfish Color photographs display the use of radial symmetry in the folk Kaleidoscope art of hex signs. Useful for identifying line, shape, and colors seen in each repeated section of hex designs. Information Artwork created by students from about the meaning of each symbol. For students of all ages. St. Theresa Elementary School, Kids Book of Kaleidoscopes by Carolyn Bennett & Jack Romig Hellertown, Pennsylvania. Demonstrates how to build a simple kaleidoscope. For grades 3 and up. Illustrations and text explain light refraction and reflective symmetry concepts in a fun and friendly presentation. Black Color Explosion Created by a kaleidoscope designer. radial design Artist: Betsy Moerder Starfish by Lloyd G. Douglas Introduce the concept of radial symmetry to younger students using the full color photographs of starfish. Close-up views of the detailed patterns on starfish arms will inspire identification of line, shape, and color that can carry over to children’s designs.

Radial designs in motion Building fun and creativity into standards-based learning 62 Mathematics Mathematics 63 Spin a Radial Design

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Display a variety of manufactured and natural objects that illustrate radial designs, such as clocks, flower blossoms, Process: Decorate spinners Preparation decorative plates, hubcaps, and kaleidoscopes. Introduce radial art from other cultures, such as Pennsylvania German Session 3 . Trace around paper plates on recycled file folders. Cut out circles. Save scraps. hex signs, Aztec calendars, and Tibetan mandalas. and 45-60 min. . Use a ruler to divide the file folder circles into six sections the same size as the pie-shaped motif plan. Discussion Examine the symmetry in the objects. Calculate a symmetrical division of sections within each design. How many times is a motif in the symmetry repeated? Identify the shapes, lines, and colors in the repeated motif in each design. 6. Follow the motif plan to decorate all six sections of the spinner. Photocopy a picture of a radial motif. Study the repeated motif. Cut apart the sections. Challenge students to reassemble the pieces. Process: Assemble spinners Create a sample spinner. Show students how to create and use the spinner. Session 4 . Measure two 24-inch pieces of yarn. 20-30 min. 8. Poke a hole in the center of the spinner with a pencil. Push about an inch of the yarn through the hole. ® Colored Pencils Markers School Glue Scissors Crayola • • • • . Put a dot of glue on a small folder scrap. Press it over the end of the yarn on the back of the spinner. Supplies Air-dry the glue. Other • Paper plates (small) • Recycled file folders • Rulers • White paper • Yard sticks or measuring tapes Process: Spin designs Materials • Yarn or string Session 5 10. Work in pairs to spin designs. One partner holds the top end of the yarn. The other partner turns the spinner 15-20 min. round and round to twist the yarn. Let go to see the design spin! Process: Classify radial designs Identify motifs Predict radial design attributes Session 1 1. Students classify several samples 1. Students select motifs for their 1. Students list factors that they Analyze radial designs 20-30 min. of radial designs by line, shape, radial designs. Motifs must think will prove that a design 11. Students review their lists of and color. include lines, shapes, and colors. can be both radial and sym- factors that could prove that a metrical while in motion. design can be both radial and symmetrical while in motion. Process: Design motifs How many of these predictions Session 2 . Trace around paper plates on paper to create circles. Cut out circles. Fold them into six equal pie-shaped are evident in the working 20-30 min. sections. Cut along fold lines. spinners? . Sketch a motif in one section. Combine shapes, lines, and colors. Try different motifs in other sections. Choose a motif that is pleasing. Assessment • Students (K-2) accurately classify elements of symmetrical radial designs. Students (3-4) choose radial designs that include line, shape, and color. Students (5-6) orally justify their arguments that designs can be both radial and symmetrical when in motion. • Observe that spinners are assembled correctly and work properly. • Children describe their designs using math and art vocabulary (symmetry, balance, shapes, lines, and colors).

Red Steel Tractor Wheels • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things Lancaster, Pennsylvania they learned. Photo by J. McCracken Extensions Use the spinner plans to learn Find out more about mandalas Gifted students research the more about fractions. Cut each and the significance of symbols history and science of kaleido- circle into sections. Place them on and objects that appear in them. scopes. Find out how math is vital paper plates. Work in pairs to com- Print mandala coloring pages from to their function. pare, add, and subtract fractions. Crayola.com. Build kaleidoscopes to experiment Print Writing Fractions activity pages Students construct mandalas to with visual perception. See the from Crayola.com for more practice. reflect their personalities and life Color Kaleidoscopes lesson plan Experiment with how different experiences. See Cool Kaleidoscope on Crayola.com. shapes and designs have different Sun Catcher on Crayola.com for a Measure the angles of each lines of symmetry. Use unbreakable unique way to bring light to these section radiating from the center mirrors to produce multiple images. personal expressions. of the spinner design. Experiment Hold a symmetry search! with designs using larger and smaller Challenge students to identify angles, keeping balance and radial objects that exhibit different kinds symmetry in mind. of symmetry: reflective (mirror) symmetry, radial (rotational) symmetry, translation (sliding) symmetry, and gliding reflective (footprint) symmetry.

Interior of , El Capitolio de Puerto Rico Parasailing Over the Caribbean San Juan, Puerto Rico Palm Beach, Aruba Photo by Erica Simon-Brown Photo by J. McCracken

Building fun and creativity into standards-based learning 64 Mathematics Mathematics 65 Balls: Classify, Roll, and Bounce

Objectives Multiple Intelligences Students (K-2) recognize, compare, sort, and classify balls Bodily-kinesthetic Logical-mathematical according to attributes such as size, volume, weight, and decoration. Interpersonal Spatial Students (3-4) use United States customary and metric units Logical-mathematical of measure as they experiment with, measure, and chart the Spatial distances that balls roll. Students (5-6) select, and use United States customary and metric units to measure bounce height, bounce range, and graph data according to bounce characteristics.

National Standards Visual Arts Standard #1 Mathematics Standards Understands and applies Measurement media, techniques, and Understand measurable attributes of objects and the units, systems, processes and processes of measurement Apply appropriate techniques, tools, and formulas to determine measurements Connections Recognize and apply mathematics in contexts outside of mathematics

Science Standards Grades K-4 Properties of objects and materials Position and motion of objects Grades 5-6 Motions and forces Transfer of energy Artwork created by students from Freeman Elementary School, Phillipsburg, New Jersey. Background Information How Big Is a Foot? by Rolf Myller Teacher: Kathy Prichard When a ball is dropped, gravity pulls it toward the ground. A different approach to measuring puts the spotlight on The ball gains energy from its downward motion. When the uniform units of measure. Just right for younger students. ball reaches the ground, that energy goes into changing the Also presents compelling questions for older children. shape of the ball. Depending on how the ball is constructed— Joey and Jet by James Yang what material is used and other characteristics—the ball may Younger students enjoy the adventures of a bouncing ball, flatten to the floor or bounce back up in the air. a boy, and his dog. The surface also affects how a ball bounces. A ball’s speed is reduced significantly by its interaction with the ground. Two things affect the speed of the ball: the coefficient of Vocabulary List restitution (COR) and the coefficient of (COF). Use this list to explore new vocabulary, create idea webs, or brainstorm related subjects. • How high a ball will bounce if dropped from a given height is the COR. A high COR surface gives a ball a Acceleration Potential energy higher bounce (the ball bounces off the surface almost Ball Predict as fast as it traveled to the surface). A low COR surface Bounce Shape gives a ball a lower bounce (the ball bounces off the Compare Speed surface quite a bit slower than it traveled to the surface). Energy Sphere Evaluate Surface • The COF is the measurement of the frictional force of Experiment Texture the ground surface on a ball. Friction slows down a ball. Form Velocity A high value of COF indicates a high frictional force on a Fraction ball—meaning that a ball’s motion is stopped or slowed Friction by material on the surface, such as fibers. Graph Gravity Height Resources Kinetic energy Counting on Frank by Rod Clement Mass Get kids excited about calculating and measuring! Fun story Material about a boy and his dog, appropriate for all ages. Measure

Building fun and creativity into standards-based learning 66 Mathematics Mathematics 67 Balls: Classify, Roll, and Bounce

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Ask children to name spherical objects. What is the difference between a sphere and a circle? What happens Process: Create team charts Create rolling course and Create bounce boxes and Preparation when you view a sphere from different directions? What stays the same? Session 3 4. In teams, create a chart on result charts measure charts Display balls and spheres in a variety of sizes, materials, textures, and weights, such as those shown here. and 30-50 min. which to record ball attributes. 4. On craft paper, teams create 4. In teams, create bounce boxes Create several Model Magic® ball examples. Encourage children to handle and (if possible) roll and bounce them. Discussion Choose a team recorder. courses for measuring the and measurement charts (see Observe closely. 5. Write headings in block letters lengths their balls roll. pictures for ideas). Decorate Classifying, rolling, and bouncing balls can be fun and exciting! Provide time and space (preferably outdoors or and decorate the chart. 5. Teams make Rolling Experiment them with paint and/or markers. in a gym) to safely compare, roll, and bounce sports balls (inflated and flat), as well as balls of yarn, snowballs, and Air-dry the paint. other nontraditional spheres. Experience firsthand the physics of rolling, bouncing, and kinetic energy! Charts with two columns. Title one column prediction and the Demonstrate sculpting techniques such as these: second column actual. • Add washable marker color to white Model Magic compound. Blend for a marbleized effect. Knead more to Students predict how far they create a solid color. 6. think each ball will roll. Record • Wrap the compound around an object, such as a small rubber ball or bead. Roll between palms to smooth. predictions. • Poke indentations into the ball with a finger or modeling tool. • Wrap thin Model Magic rolls around a rubber ball or other object. Process: Classify balls Measure rolling distances Predict and measure Provide opportunities for students to use standard and nonstandard measuring tools. Session 4 6. In teams, closely observe each 7. Students take turns gently roll- bounce heights 30-50 min. ball made by team members. ing the balls along the measure Position the bounce box on the ® 5. Crayola • Markers • Model Magic® • Scissors Identify attributes of each one. sheet. Try to use equal force. floor against a wall. Tape the Supplies Mark classifications on chart. 8. Measure the distance each measure chart to a wall next to • Paint Brushes • Tempera Paint 7. Count, summarize, and analyze ball rolls. Record actual roll the bounce box. the results. distance. Create a chart on which Other • Craft paper • Measuring tools (U.S. customary and metric) 6. 9. Summarize and evaluate to record bounce height Materials • Modeling tools such as plastic dinner knives, craft sticks, and toothpicks • Paper roll • Recycled boxes the results. predictions and actual results • White paper • Optional for ball construction: beads, bells, buttons, foil, Silly Putty®, small balls of the experiment. 7. Bounce balls inside the box. • Masking tape Record, compare, and evaluate • Optional for bounce chambers: the results. cork sheets, felt, hard tiles, metal buckets, plastic containers Revise predictions and repeat experiment to verify results. • Recycled boxes Assessment • Observe students as they classify, measure, and record data. How well do they work together? Are their findings • Recycled newspaper accurately observed, measured, and recorded? • Ask children to think of and undertake new experiments, such as rolling balls on inclines, counting the number Set-up/Tips • Ask families to help gather beads, ribbon, string, and other items that can be used to create unique Model Magic of bounces on different surfaces, and predicting the height a ball will reach rolling down one side of a concave balls and boxes that can be used as bounce chambers. slope and up the other (like a skateboarder’s half-pipe). Use measuring skills to record results. • To increase bounce-ability variables, choose different surfaces for the bottom of bounce chambers such as hard • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things plastic mats or soft bubble wrap or packing foam. they learned. Process: Create balls Extensions For very young students and those Work together using Crayola Combine results from small groups Session 1 1. Encourage students to use their imaginations to make various size balls. Make each ball unique by embedding with special needs, invite family outdoor products, such as Sidewalk to form a class graph of results. 30-50 min. assorted materials into the Model Magic compound. Air-dry the balls for at least 24 hours. members to join in the project. Chalk and Sidewalk Paint. Create Use Crayola Sidewalk Chalk and Create ball games using measur- courts and play areas on the play- Sidewalk Paint to create a court Process: Observe ball attributes Select units of measure Select units of measure ing skills, such as the Catch-the-Ball ground. See directions for Four for the Bottle Tag lesson plan on Session 2 2. Students observe all of the balls 2. Review U.S. customary and 2. Review U.S. customary and Game on Crayola.com. Students Squares, Bounce Between Colors Crayola.com. 30-min. they created. metric units of measure. metric units of measure. play the game and record data on on Crayola.com to measure and Challenge gifted students to how many times they attempt and paint a Four Square court. Play this 3. Children identify and orally 3. In teams of three of four, 3. In teams of three of four, vote experiment more with bouncing succeed at getting the ball in the precision bouncing game as a class. describe ball attributes such as vote on which unit of measure on which unit of measure to use balls. Investigate the mathematics of hole. Hold a tournament and diagram Hold a tournament. Diagram the color, size, shape, decoration, to use for the “rolling balls” for the bounce experiments. physics by exploring the formulas the results of the competition. results of the competition. and weight. experiment. for determining potential energy and kinetic energy.

Variety of decorative spheres Artist unknown Private Collection. Building fun and creativity into standards-based learning 68 Mathematics Mathematics 69 Secret Castles: Solve the Number Mysteries!

Objectives Multiple Intelligences Students identify the elements of architecture through the Interpersonal Spatial study of castles and design elements of castle construction. Students work in small groups using mathematical problem- Logical-mathematical Artwork created by students from solving skills to create castles that have numerated features. St. Theresa School, Hellertown, Pennsylvania. Spatial National Standards Visual Arts Standard #4 Mathematics Standards Understands the visual arts in relation to history Number and Operations and cultures Understand numbers, ways of representing numbers, relationships among numbers, and number systems Problem Solving Apply and adapt a variety of appropriate strategies to solve problems

Background Information Vocabulary List A castle is a large, fortified residence, usually surrounded by Use this list to explore new vocabulary, create idea webs, thick walls. Traditionally, castles have high windows and or brainstorm related subjects. towers with numerous features designed to keep the place • Castle functions Defense Residence secure. Size, shape, building materials, and number and History Social structure orientation of buildings may differ among castles, but they Power Wealth all typically look ornate and stately. Some walled fortifications date as far back as the walls of • Castle features Arches Moat Babylon (1600 BCE) and the Qiang Castle in southwest China Arrow loops Towers (111 BCE). The majority of castles in Europe were built during Construction materials Walls the (1000 to 1500). Doors Windows The difference between castles and other buildings, such Drawbridge as cathedrals and manors, is that castles served many purposes. Flags Most castles served to defend against invaders, to provide a residence to the powerful lord of the region and his family, • Examples of castles Edinburgh and as a symbol of that lord’s power over the social structure Matsumoto of the surrounding villages and countryside. Neuschwanstein Palace of Versailles Prague Resources Windsor A Medieval Castle by Fiona MacDonald Cut-away view of the inside of a medieval castle. Makes learning about castle elements fun. Older students find plenty of richly detailed information in texts and captions. Castle by David Macauley Explore the process of constructing a castle, including tools, workers, and materials. Detailed and ink illustrations and a compelling storyline. For grades 3 and up. What Were Castles For? from Usborne Starting Point History Simple text in a fun presentation of facts about everyday life in a castle. For all ages.

Artwork created by students Artwork created by students from Triangle Elementary School, from Triangle Elementary School, Hillsborough, New Jersey. Hillsborough, New Jersey. Teacher: Nancy Knutsen Teacher: Nancy Knutsen Building fun and creativity into standards-based learning 70 Mathematics Mathematics 71 Secret Castles: Solve the Number Mysteries!

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Ask students to describe the buildings they live in. How do you think the builders decided on the number of doors, Process: Paint castles Preparation windows, and floors in the building? Have children count different architectural elements in their homes, school, and Session 3 . Use Tempera Mixing Mediums to give each castle a unique look. Pearl It! gives the castle a pearly sheen. and other public buildings. 20-30 min. Glitter It! adds sparkle. Texture It! makes rough, realistic textured walls. Air-dry the paint. Discussion Arrange for tables in an open gallery to display finished castles. Create a few Model Magic® castle features for display. Process: Emphasize features Add details Session 4 8. Outline features of castles 8. Emphasize features on castles with markers and glitter glue. Add more Display photographs and illustra- With students, display books, posters, prints, and other resources about 20-30 min. with markers and glitter glue. details, such as statues in niches and balustrades. Air-dry. tions of castles. Read nonfiction castles. Clearly label photos to identify location and time period, as well Air-dry the glue. books about castles as well as folk as castle elements. Keep a world map nearby to reference. Read historical and fairy tales set in castles. fiction related to castles and castle-living. Process: Solve the number mysteries Create an idea web around the Look at the display of castle photographs. What decisions did castle build- Session 5 . Students name and label their castles. concept of castles. Brainstorm what ers make? What factors influenced their choices? What are some common 20-30 min. children know about castles, how features in castle construction? What function do you think each feature 10. For each castle, students number a paper from 1 to 10 or 20 as appropriate. Label papers with castle names. they are built, and what they look played in castle life? What 3-D forms can you identify in castle structures? Find the secret numbers hidden in each castles’ features. Write the feature next to each numeral. like. Ask children about who lives in Students work in small groups to find out how castle features were built, 11. Castle builders reveal their secret numbers so students can check their lists. a castle and what happens there. such as… Students form groups of 3 or 4. • shapes, sizes, and mechanics of doors Assessment • Observe students as they brainstorm and collect information about castle features. Note children’s use of resources to learn about castle construction and correct castle terminology. Explain that each team will work • height and shape of the keep together to build a unique castle. • location and design of steps, bridges, and towers • Assess problem-solving skills, teamwork, and use of tools during the planning and construction process. Ask students to explain their team’s construction process. • gate house design and location Teams brainstorm and sketch features to include in the castles they are • Evaluate student identification and counting of features, both on their own castles and on castles built by going to construct. other teams. • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things Crayola® • Colored Pencils • Glitter Glue • Markers • Model Magic® • Paint • Paint Brushes • School Glue they learned. Supplies • Scissors • Tempera Mixing Mediums Extensions Plan the activity to suit young Research peasant life. Construct Research castle floor plans. children and those with disabilities. villages outside the castle walls. Find out what each room and Other • Craft paper • Index cards • Modeling tools such as plastic dinner knives, craft sticks, and toothpicks For example, limit the number of Challenge students to create their space was used for. Materials • Paper plates • Paper towels • Recycled boxes and cardboard • Recycled cardboard tubes features to 5. Or have two piles own individual cottages and With exceptional students, • Recycled newspaper • Ruler • Water containers • White paper of cards, one with numerals and manors. Check out the Thatched introduce the concept of scale another with features. Children Roof Cottage on Crayola.com drawing. To what scale are Set-up/Tips • Demonstrate how to cover boxes or other armatures with Model Magic slabs. Show how to press the compound draw a card from each pile to give for inspiration. different floor plans drawn? with a craft stick to make it look like stone. Glue any dry pieces together. more structure to the activity. Read the Sir Circumference books Each student creates a floor plan Hold a Builders’ Day. Ask parents by Cindy Neuschwander. Use each • Cover the painting area with newspaper. for the inside of the team castle. to donate clean recycled containers topic to spur an investigation of a Take into account where doors, • Use paper plates as palettes to combine mixing mediums with tempera paint. Mixing mediums can also be applied and other items. Set up stations math process using the castles. For windows, and towers are located. before painting and on top of dry paint. around the classroom with different example, use string to measure the Challenge students to measure materials to build a variety of differ- circumference of the castle towers and use scale. Process: Plan team castles Plan team castles Plan team castles ent dwellings. Display constructions after reading Sir Circumference and Session 1 1. Ask a volunteer to write numer- 1. On paper, each team writes a 1. On paper, each team writes a with child-created labels in a gallery. the First Round Table. 30-40 min. als 1 through 20 on individual list of numerals from 1 to 10. list of numerals from 1 to 20. index cards. Turn them over. Each group selects a card in turn until all are taken.

. Teams use the number cards to . Ask teams to plan their castles to have one of an architectural feature, plan how many of each feature two of another feature, three of something else, and so on. The secret will be on their castle—doors, to each castle will be to discover how the other teams used number in windows, flags, towers, and their designs—so remind teams to keep their lists hidden! other architectural elements. . Teams work together to sketch their castle plans from different angles . Teams sketch a plan of what (front, back, sides, and from above), paying attention to the 3-D forms their castle will look like. that make up the castle structure. Castle Along the Rhine . Teams create lists of steps to construct their castles, materials needed, and who will do what. River Germany Photo by J. McCracken Process: Construct castles Session 2 . Students follow their plans to construct their castles with recycled materials and Model Magic® compound. 30-60 min. Suggest that they use their imaginations and problem-solving skills to improve their plans as they work together. Ashford Castle (may be County Mayo, Ireland 6. Remind teams to measure and use tools to be sure everything on their lists fits together. Prompt students to Circa 1228 AD repeated) count each feature to make sure they stick to their plans. Air-dry castles for 24 hours. Photo by J. McCracken Building fun and creativity into standards-based learning 72 Mathematics Mathematics 73 Mazes and Labyrinths: Design Your Pathway

Objectives Multiple Intelligences What Does It Mean? Students recognize, identify, and navigate through patterns Labyrinth: a winding path Logical-mathematical Spatial of angles and lines forming the geometric pathways of mazes resembling a , with Artwork by students from and labryinths. Spatial one entry and one exit, Mount Prospect Elementary School, Students (K-2) create simple maze designs on graph paper Spatial that circles inward to a Basking Ridge, New Jersey. demonstrating pencil control skills and a basic understanding central point and then out Teacher: Susan Bivona of lines and right angles. to the exit Students (grades 3-4) use geometric drawing tools and graph Maze: a complex series paper to demonstrate their understanding of various lines of paths offering various and angles as they create increasingly sophisticated maze or choices, only one of which labyrinth designs appropriate to their ages and ability levels. eventually leads from one Student (grades 5-6) research, design, and create a school or more starting points labyrinth. to the exit

National Standards Visual Arts Standard #1 Mathematics Standards Understands and applies media, techniques, Geometry and processes Specify locations and describe spatial relation- ships using coordinate geometry and other representational systems Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics

Background Information Resources Although the terms maze and labyrinth are often used In Search of Knossos: The Quest for the Minotaur’s interchangeably, a labyrinth is actually a winding path that Labyrinth by Giovanni Caselli resembles a spiral and circles inward to a central point. Travel back in time with an archaeologist to explore There is only one entrance and one exit in a labyrinth. archaeological digs, architectural finds, and other evidence A maze is usually formed by lines and angles. It often has of the Minoan civilization that lived on Crete. For older several possible starting points and multiple paths from elementary students. which to choose, although only one path leads to the exit. King Arthur by Marc Brown Labyrinths have been found in many ancient cultures and An early elementary read-aloud or middle elementary almost always had spiritual significance. In medieval times chapter book. Introduces students to Merlin’s maze. they were often laid on the floors of cathedrals where they were used as a sort of miniature pilgrimage. Today, some The Amazing Book of Mazes by Adrian Fisher alternative medicine practices use labyrinths as part of the Extensive history of mazes with many photographs and healing environment. Many people fined that labyrinth diagrams to share with children. walking gives them focus, a sense of inner peace, and has Z Goes Home by Jon Agee spiritual significance. Follow the predictable alphabet pattern with unexpected Mazes, which are a type of puzzle, have offered fascinating results on every page. Younger children enjoy the story, challenges to people for centuries. During the , particular the letter Z’s trip into a labyrinth. Older students are gardeners often created 3-D vertical mazes by planting hedges intrigued by the use of hard angles and lines in the illustrations. to create complex paths that were difficult to navigate after the shrubs grew above eye level. England’s Hampton Court Palace has one such maze for visitors to attempt. Today corn- Vocabulary List fields are often planted as challenging mazes. Interestingly, Use this list to explore new vocabulary, create idea webs, corn has been a staple food in Central and South America or brainstorm related subjects. for centuries, and its name, influenced by Spanish, is maize. Some parks even use mirror mazes to confuse • Geometric terms Acute angle Parallel and entertain visitors. 2-D paper mazes are enjoyed in many Angle Pattern forms by children as well as adults. Circle Pentagon Curve Perpendicular Hexagon Rectangle Line Right angle Obtuse angle Square Octagon Triangle

• Mazes and labyrinths Corridor Mouth Entrance/Entry Network Exit Passage Labyrinth Path Building fun and creativity into standards-based learning 74 Mathematics Maze Mathematics 75 Mazes and Labyrinths: Design Your Pathway

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Display reproductions of labyrinths and mazes. Discuss similarities and differences. Ask students if they have ever Process: Reproduce and solve mazes Create labyrinth Preparation walked through a maze or labyrinth. Talk about their feelings in trying to find their way. Session 2 . Tape plain paper on top of the maze template. . Find a safe, large area on a play- and Provide sample paper mazes for students to trace with their fingers. Use masking tape to outline a maze or 30-40 min. ground to create a labyrinth. labryinth on the floor for students to walk. 6. Remove a crayon wrapper. Rub the crayon barrel over the paper to Discussion reveal a colored print of the maze or labyrinth. Make several copies. 6. Use a yardstick and a ball of Share information about life-size Search for specific geometric features in sample mazes and labyrinths: . Choose a captivating theme for each maze. Embellish the mazes with string to measure and mark mazes and labyrinths from both parallel and perpendicular lines; right, acute, and obtuse angles; and drawings and words to illustrate the themes. lines from point to point so the ancient and modern times. geometric shapes formed by the lines, angles, and curves. lines of the labyrinth correlate 8. Trade designs with a partner. Trace pathways from start to finish, to the plan. Share an age-appropriate story Ask students to research and share information about the history of first with a finger, then with an erasable colored pencil. about a maze or labyrinth. mazes and labyrinths. Read the Greek myth of Theseus or some other age- . After the correct path has been identified, overline it with glitter glue. appropriate story. Air-dry. Demonstrate how to draw a geometric maze on graph paper. Include starting and end points as well as some dead ends in the design. Show an example of a template made from glue and how it is used to make crayon rubbings of Assessment • Students review each other’s • Students check that one navigable • Check that the final labyrinth the maze. designs to be sure all include path exists among several mislead- design is scaled to match the plan. one navigable path. ing choices. Does the path extend • How cooperatively did students from a starting point on one side Crayola® • Erasable Colored Pencils • Do the tracings of graph paper work with their partners to create lines show evidence of steady of the maze to an exit on the the large labyrinth? Supplies opposite side? How original is • Crayons • Glitter Glue • School Glue • Sidewalk Chalk pencil control? the maze theme? Is the maze • Ask questions about student decorated to reflect the theme? Other • Graph paper • Straight edges • Triangle templates • White paper designs. What patterns can they Materials identify? What do they notice • Are students able to identify lines, • Cardboard • Construction paper • Masking tape • String • Yardsticks about the lines and shapes? Do angles, and curves in the designs the designs match the chosen using correct geometric terms? Do Set-up/Tips • Ask K-4 parents and volunteers to collect heavy cardboard for templates. themes? the mazes include several types of angles and/or curved lines? • Practice creating glue designs on recycled paper before beginning a larger, more complex maze. • Place masking tape loops between the rubbing paper and the template to hold them in place for rubbing. • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things they learned. Process: Design simple mazes Design complex mazes Design a school labyrinth Session 1 1. On 1-inch graph paper, use a 1. Draw practice mazes using 1. Research the history and Extensions Challenge children to work Set up a Meticulous Mazes learn- Create indoor labyrinths with 30-45 min. red erasable colored pencil to erasable colored pencils on functions of labyrinths. together to create life-size mazes in ing station with markers and paper. masking tape. mark an S (Start) on the left graph paper. Advanced students the classroom using carpet squares Print directions for Meticulous Turn 2-dimensional line and angle . In pairs, create labyrinth laid end to end. Walk the mazes. Mazes from Crayola.com to post at edge and an F (Finish) on the include more than one start sketches on graph paper. mazes into 3-D designs using Crayola right edge. point. Use rulers and triangles Print and share the Johnny the station. Students create line and Model Magic compound. Crayola. to create acute, obtuse, and . Choose a design to reproduce Appleseed Maze activity page angle mazes. com shows how to make a Maze in . Draw a simple zigzag path using in large scale outdoors. lines and right angles from S to right angles in the patterns. on Crayola.com. Challenge students to create a Box Top. F, following lines on the graph Include curved paths as well. . Create a scaled-up plan of the Incorporate popular story lift-a-flap mazes with dead-end Work in teams to invent and paper. Erase as needed to adjust Erase as needed. Make sure chosen design(s) to reproduce characters into maze designs. squares that flip up to display math create labyrinth games. See the the path. This is the “solution” there is a path in and out of to scale on a playground or questions that must be answered Magnetic Mazes lesson plan on to the maze puzzle. the designs! another safe location. correctly to pass. Crayola.com. . Use contrasting colors to create . Choose one challenging design Challenge advanced students a tangle of alternate but dead-end to reproduce. to construct replicas of famous paths around the red one. Add . Transfer the maze design to labyrinths. rounded as well as zigzag paths. sturdy cardboard. Children with special needs will benefit from the kinesthetic experience of solving 3-D mazes. If possible, arrange . Transfer the maze design to . Over-line the design with glue a visit to a local corn or hay bale maze; or with parent volunteers, set up something similar on school grounds. sturdy cardboard. Over-line all to make a template. Air-dry the Encourage inquisitive students to research famous mazes such as the one at England’s Hampton Court Palace maze lines with glue to make glue overnight. and report their findings to the class. Older students with an interest in the spiritual or therapeutic significance of a template. Air-dry the glue labyrinths research and report on those topics. overnight.

Man in the Maze Pendant Covenant Presbyterian Circa 1900s Church Labryinth Artist: Marvin Lucas Napa, California 2 1/2" x 1/4" with 24" chain Photo by R. De Long Silver Private Collection.

Building fun and creativity into standards-based learning 76 Mathematics Mathematics 77 The Math of Maps

Objectives Multiple Intelligences What Does It Mean? Students (K-2) survey a room, create a map of the room, and Bird’s-eye view: a view Bodily-kinesthetic Spatial then describe the relative spatial relationships of the shapes from above, as if one were on the map that represent the objects in the room. Interpersonal flying over the object Students (3-4) create a room or school map that visually Logical-mathematical Cartography: the art of describes coordinates within the room that specify measured Naturalist creating maps distances between coordinates and indicates directions for Spatial Scale: accurate propor- moving from one location to another using the map. tions when drawing two Students (5-6) visualize an area in their community from a or more objects bird’s-eye perspective and compare and contrast the relative proportions of the area. Students create a two-dimensional treasure hunt map of a three-dimensional area containing distances between one point and another point to find hidden treasures.

National Standards Visual Arts Standard #5 Mathematics Standards Reflects upon and assesses the characteristics and merits of own Geometry work and the work of others Specify locations and describe spatial relationships using coordinate geometry and other representational systems Measurement Apply appropriate techniques, tools, and formulas to determine measurements

Artwork by students from Background Information Vocabulary List Fredon Township School, Maps use points, lines, and areas to represent specific spaces. Use this list to explore new vocabulary, Newtown, New Jersey. Size, shape, color, orientation, and pattern all help to visually create idea webs, or brainstorm related subjects. Teacher: Beth Delaney communicate information about a location or how things are Areas Large scale Points distributed over an area. Often points and areas are defined by Cartographer Latitude Ratio position with reference to a coordinate system. Cartography Legend Represent Some of the oldest known maps are preserved on Babylonian Color Lines Scale clay tablets from as far back as 2300 BCE, which is about the Coordinate Longitude Shape same time as the start of Chinese mapmaking. In the first century Distance Map Size BCE, the Roman emperor ordered a project to map Roman Fraction Measurement Small scale roads. It took almost 20 years to map 50,000 miles! Pre- Key Orientation Symbol Columbian maps in Mexico used footprints to represent roads. Pattern Texture Modern careers in surveying and mapping involve measuring, Value locating, and establishing lines, angles, elevations, and features— both manufactured and natural—to determine the facts, sizes, K-2 3-4 5-6 and shapes of real locations. Today’s cartographers (map-makers) Determine safe indoor and/or outdoor environments for this map-making project. Choose a start location for all often use multiple computer-driven data sources and design Suggested Preparation treasure hunters. Invite adult volunteers to assist children in navigating the environment during data-collection and software to create custom maps. Mapmakers also use the math treasure map assessment. concepts of scale, projection, and a variety of numeric methods and to represent locations, including basic coordinate systems. Discussion Ask younger students to describe how to get from the front door of the school to the classroom. What directional words and phrases are helpful? Prompt students to use increasingly precise vocabulary to indicate the directions. If there were a treasure hidden on the school campus, how might a map help them find it? Resources Display a variety of maps. Include an imaginary pirate’s treasure map if possible. Examine the sample maps. What Career Ideas for Kids Who Like Math by Diane Lindsey Reeves visual elements are effective? How are lines used? What kinds of data are shown? How are specific points marked? Good resource for upper elementary and middle school How are landmarks indicated? How is distance represented? How do coordinates help indicate locations? students interested in math careers. Shows how adults in Create a sample map for all students, several treasures, and a decorated box to inspire children’s creativity and everyday life apply math. better understand the construction process. How Maps Are Made by Martyn Bramwell Demonstrate techniques for shaping air-dry clay by pinching, poking, rolling, or coiling it. Use modeling tools to Interesting history of early maps. Explains many modern carve or etch into the clay. Show how to join pieces or smooth edges by dampening the area with a wet finger. mapmaking techniques. Good introduction to cartography Score wide surfaces with a toothpick and press them together. careers for older children. Set up a table of “treasures” for students to handle. What makes an object a treasure? Mapping Penny’s World by Loreen Leedy Younger students enjoy this story of a little girl who creates Artwork by students from maps to help her dog find his hidden toys. Fredon Township School, Newtown, New Jersey. Teacher: Beth Delaney Building fun and creativity into standards-based learning 78 Mathematics Mathematics 79 The Math of Maps

K-2 3-4 5-6 K-2 3-4 5-6 Crayola® • Air-Dry Clay • Colored Pencils • Crayons • Glitter Glue • Paint Brushes • School Glue Process: Create maps Create maps Supplies • Scissors • Watercolors Session 4 . Use measurement data to . Use the map sketches and measurement data to draw treasure maps 30-45 min. create final maps using small to scale. Other • Measuring tools (U.S. customary and metric) • Modeling tools or more items (such as erasers or beads) 10. Include a compass rose on maps as well as a legend indicating the to indicate nonstandard mea- Materials • Non-standard measuring tools (blocks, boxes, dowel sticks, shoes) • Paper plates • Paper towels scale and meaning of symbolic lines, images, and colors. surement units. Mark the start, • Recycled boxes • Recycled newspapers • Water containers • White paper finish, and major landmarks on the maps. Set-up/Tips • Paper plates make convenient, portable sculpting surfaces. 10. Demonstrate how to draw • Cover the painting area with newspaper. symbols to show the map scale. • Ask families to donate clean, recycled boxes. Process: Decorate treasures Process: Survey a space Calculate coordinates within Visualize relative distances Session 5 11. Paint treasures. Use just a little water and add layers of paint for more intense colors. Air-dry the paint. Session 1 1. In pairs, students sketch a space between areas 30 min. or 1 2. Add sparkle and emphasize details with glitter glue. Air-dry the glue. 30-min. the space in the classroom. 1. Students measure, record, and 1. Students identify the relative more Pay attention to the relative compare relative lengths of distance between their homes placement of doors, windows, features in the classroom such to another point, such as a Process: Hold a treasure hunt closets, shelves, furniture, and as the length of the walls, the friend’s home or to a play- Session 6 1 3. Place finished treasures in boxes, adding packing material to protect them. other features. width of the doors, and the ground. How do the sizes of 45 min. or 1 4. Create a label to fit on the lid to identify the creator of the treasure. Older students write their names very small . Offer advanced students the linear length of the windows. the land areas compare? more and decorate the label. Glue labels on boxes. option to consider another . Consider other school features . Visualize the distance between room for this project. 1 5. Take turns secretly hiding the treasures. This may need to be coordinated and done in small groups in confined such hallways, common spaces, areas. Consider features that areas to prevent prematurely finding another child’s treasure. cafeterias, and offices. appear between locations such as streets, stores, or community 16. Students trade maps to find each other’s treasures. structures. Assessment • Check that each pair of students • Check student maps to see • Check to see if students visualized Process: Sculpt treasures completed an accurate survey of that they focus on, and visually and created a map reflective of a Session 2 a room, created a map of it, and describe, coordinates within a community area from a bird’s-eye . Students sketch ideas for one or more small, three-dimensional treasures to sculpt from Air-Dry Clay. Urge older then described the relative spatial room that specify measured dis- perspective. 30-45 min. students to make intricate, detailed . Students choose small boxes in which their treasure(s) will fit. relationships of the shapes on the tances between coordinates and or more . Students make the treasures they sketched. Air-dry projects for at least 3 days. map that represent the objects in directions for moving from one the room. location to another using the map. Process: Gather map data Session 3 . Escort students around the area selected for the treasure hunt, perhaps as a school field experience. Ask them • Check maps for accurate scale and use of lines, points, and coordinate 60-90 min. to view the area as mapmakers. What are the outer boundaries? How could certain objects in the area be grids to represent the area. indicated as landmarks on a map? Students secretly choose where they will hide their small boxes containing their treasures. • Ask students to provide feedback to each other about the accuracy of their maps. Students might offer “two stars and a wish” to each other. Each star is a compliment. The wish is a way to provide constructive feedback: “I wish 6. Students consider ways to 6. Students consider how the treasure hunt area looks from above (bird’s- your map were more clear about…/had more information about….” indicate distances between eye view). Use metric tools to measure distances between points. • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things objects and/or boundaries. . Remind students about various approaches to map making. Urge older they learned. . Talk about ways to measure with students to use more sophisticated techniques. They might draw lines a large, actual unit and then from place to place to create an easy map, or plot map points to search Extensions Young children and those with Students create coordinate maps of imaginary towns. Include parallel and how to indicate that distance for, or make a coordinate grid and provide a series of coordinates for special needs may benefit from perpendicular streets as well as buildings in a variety of geometric shapes. on a map using a smaller unit. the treasure seeker to follow. practice with basic directional terms Students draw 1-inch square coordinate grids over their maps and prepare Measure several distances with before making their treasure maps. a blank coordinate grid. Form partnerships. Without showing their original 8. Provide metric measuring tools for map making. Students mark the Play a game like Simon Says to move maps to their partners, students describe their maps using coordinates and both standard and nonstandard start, finish, and major landmarks. Use tools to measure true distances measuring tools. around the room following specific correct geometric terms. Partners listen and follow directions to duplicate between points along the path to the treasure. Record measurement directions using terms such as left, the imaginary town map on a blank grid. Compare maps. Are they identical? 8. Note measurements on the data on map sketches. right, 10 steps forward, or west. If not, decide what the listener and/or speaker could have done differently. map sketches. Use new mapmaking skills to draw Encourage students with an interest in research to find out more about neighborhood maps, local maps, and the history of mapmaking including challenges faced by early cartographers maps of other pertinent curriculum from various civilizations. How did early Egyptians make their own paper? General Map of the Discoveries content. See Egyptian Papyrus Paper on Crayola.com for directions and make your of Admiral de Fonte showing the Use math and mapping words as own paper for a new treasure map. high possibility of a passage to new vocabulary and spelling words. Explore the math of projection mapping. How do cartographers create flat the Northwest, 1772 maps of a round planet? Artist: Thomas Jefferys 27 cm x 34 cm Paris, France Collection of Barry Goldin.

Building fun and creativity into standards-based learning 80 Mathematics Mathematics 81 Estimate a Pot’s Capacity

Objectives Multiple Intelligences What Does It Mean? Students create decorative pots reflective of various cultures. Capacity: the amount of liquid or other Logical-mathematical Linguistic Students explore how the same amount of modeling measurable material a vessel can hold compound (measured by volume) can be used to create Spatial Coil: sculpting technique using long coils pots with different capacities. Linguistic (“”) of compound. Coils are wrapped Students (K-2) identify each pot’s capacity and then order around an armature or held in place to form their pots according to capacity. an empty vessel Students (grades 3-4) select and apply appropriate standard Pinch: technique to sculpt a pot from a lump of units of measure to determine the capacity of their pots. compound by pressing into the middle with the Students (grades 5-6) select and apply the conversion of thumbs and rotating to hollow out the interior appropriate customary systems of measure to metric units Slab technique: modeling compound is rolled of measure to determine the capacity of their pots. or pressed flat, then cut into shapes and sealed together to form the bottom and sides of a vessel. Edges are smoothed to complete the National Standards sculpture Visual Arts Standard #2 Mathematics Standards Volume: measure, in cubic units, of the amount Using knowledge of structures and functions Measurement of space a 3-D object occupies Visual Arts Standard #4 Understand measurable attributes of objects and Understands the visual arts in relation to history the units, systems, and processes of measurement and culture Connection Recognize and apply mathematics in contexts outside of mathematics

Background Information Vocabulary List American Indian Vessel Clay has been used by many cultures throughout history to cre- Use this list to explore new vocabulary, Mound builder culture ate dishware, cooking pots, storage utensils, vases, and other create idea webs, or brainstorm related subjects. Artist unknown objects. Because clay is inexpensive and easy to find, many of • Pottery process Clay Seal Carved Stone these objects were used and thrown away, but some very old Coil Shape 4" x 5" examples have survived. Their form and design make it pos- Firing Slab Collection of Kevin Zelienka. sible to conclude something about their function as well as the Glaze Slip culture that produced them. Often these vessels held liquids Join Vessel such as oil or water. Others were used to store grain for the Kiln Wheel next planting season. Some pots were very large while others Pinch were very small. Artists often use unique shapes and surface designs that • Exterior decoration Burnishing Punctuation make it possible to recognize the cultural origins. Decorations Embossing Stamping and patterns carved or painted onto ancient clay vessels often Incision depict the folk stories, history, or beliefs of the culture. Figures from mythology appear on many vases, while • Archaeology of pottery Date Technological many Native American tribes decorated their vessels with dis- Form innovation tinctive geometric designs. Function Themes Artwork by students from Level of Trade pattern Hiller Elementary School, stratification Madison Heights, Michigan. Resources Teacher: Craig Hinshaw A Single Shard by Linda Sue Park Set in a 12th-century Korean village known for its pottery. Novel invites readers to join a 13-year-old as he learns the potter’s craft from a master. Newbury Award winner inspires Acoma Polychrome Pottery Santa Clara, San Ildefonso Pot discussion. Artist: Lucy Lewis Artist unknown Clay and paint Carved, burnished clay Ceramics by Ruth Kassinger 6" x 4 1/2" 6" x 3 1/2" Science and history of pottery as well as the cultural myths Private Collection. Private Collection. associated with many works. Intrigues older readers. Colorful illustrations inspire all ages. The Pot That Juan Built by Nancy Andrews-Goebel Playful, rhyming, informative text. Introduces readers to Juan Quezada, a noted Mexican potter. Information about both the art and science of pottery appeals to a wide audience. Bright, colorful illustrations. Artwork by students from Hiller Elementary School, Madison Heights, Michigan. Building fun and creativity into standards-based learning Teacher: Craig Hinshaw 82 Mathematics Mathematics 83 Estimate a Pot’s Capacity

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Display examples of pottery in a variety of styles from different eras and cultures. Invite children to describe what Process: Determine pot capacity Measure pot capacity Measure and convert Preparation they see. Draw conclusions about how the pottery may have been used and who created it. Through creation of Session 4 6. Explain that marbles will 6. Create a chart with two col- pot capacity and their own pottery, students will demonstrate an understanding of how form and function are interrelated and the 30-45 min. be used as units of capacity. umns: U.S. Customary Estimate, role culture plays in the . 6. Create a chart with four Discussion Students estimate how many and U.S. Customary. columns: U.S. Customary marbles it will take to fill Ask children questions such as: Review the concept of capacity Consider how pottery has changed . Estimate the capacity of pots in Estimate, U.S. customary, their pots. Record estimates How do people use ceramics today? by experimenting with how differ- over the ages. Examine several U.S. customary (fluid ounces) Metric Estimate, and Metric. on a chart. What are some of the items you use ent sized containers hold varying ceramic styles. Discuss what each units. Record estimates on . Students estimate the capacity that are made from clay? amounts of water and nonstandard can reveal about the society and . Students fill their pots to the the chart. of their pots in both metric Show how to estimate and units of measure such as marbles. time period from which it comes. rim with marbles, counting as 8. Fill pots with aquarium gravel. (milliliter) and U.S. customary measure the liquid capacity of Explore how two vessels with Research the history of pottery, they do so. Record how many Empty gravel into measuring (fluid ounces) units. Record different vessels. Experiment with different shapes may hold equal including the science of clay and marbles each pot holds on cups to determine the approxi- estimates on the chart. the chart. nonstandard measures such as amounts of water. Show how one ceramics. mate capacity of each vessel. 8. Students fill their pots with marbles or aquarium gravel. vessel may have a capacity equal Research and identify the differ- 8. Arrange pots in order from Record U.S. customary aquarium gravel. Empty the to two other vessels (i.e., 2 cups ences between the U.S. customary highest capacity to lowest measures on the chart. gravel into measuring cups to equals 1 pint). system of measure and the metric capacity. What are the factors determine the approximate system of measure. that determine how much a capacity of each vessel. Record vessel will hold? Does the shape research findings on the chart. Measure the volume of blocks and boxes of different sizes using measuring tools, units, and calculators if necessary of the pot matter? What about to compute length x width x height. Younger students might measure cubic inch cubes and then build structures the thickness of the pot walls? with them, counting the cubes to measure the volume of the structures. Discuss and demonstrate basic modeling techniques such as how to pinch clay into shapes to make pinch pots, Assessment • Each child uses the demonstrated • Students successfully use basic • Students successfully create a how to roll it to create coils and slabs, and how to join pieces by adding a bit of water and scoring with a tool. hand-building techniques to create hand-building techniques to create pot using one of the three hand- a vessel. pottery. building pottery techniques. Demonstrate pottery-decorating techniques using tools to create indentations, imprints, and lines on the pot’s surface. • Students estimate the capacity of • Students check the accuracy of • Students check one another’s their vessels using marbles as units U.S. customary measures for one measurements and conversions Crayola® • Air-Dry Clay or Model Magic® • Markers • Paint Brushes of measure. another’s pots. for accuracy. Supplies • Tempera Mixing Mediums: Pearl It!, Glitter It!, Texture It! • Watercolors • Children measure actual capacity using marbles, counting correctly. Other • Chart paper • Modeling tools (plastic dinner knives, craft sticks, toothpicks) • Paper plates Materials • Students correctly record and thoughtfully analyze their research findings. Students draw conclusions about how • Recycled newspaper • Water containers the structures of pots affect their capacity. • Marbles • Aquarium gravel • Measuring cups • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things they learned. Set-up/Tips • Cover work surface with recycled newspaper. Sculpt, air-dry, and paint modeling compound on paper plates. Extensions Try Pinch a Pot of Petals on Explore the treasure of Chinese Advanced students research • Add drops of water to Air-Dry Clay if it starts to dry while sculpting. Crayola.com to make pinch pots. porcelain, using the Pretend Porcelain pottery from various cultures and • Air-dry the pottery completely before experimenting with capacity. Estimate and measure capacities lesson plan on Crayola.com. present their findings to the class. • Glaze painted pottery with a glaze of equal parts of school glue and water or with mixing mediums for added of these new vessels. Create Measure Up! Capacity Classmates form small groups surface strength. Ask parents to donate a variety Charts to visualize how the units representing different cultures to of clean, recycled containers for measure up. See this Lesson Plan on create replicas of their pottery for • Pots are for decorative use only. They are not intended to hold or store liquids. students to use to practice their Crayola.com. Ask parents to donate display. Include colorful maps and estimation and measuring skills. safe, clean, recycled, cylindrical information boards. Process: Sculpt and embellish pots Use different materials to measure containers, such as snack and film Session 1 1. Form a tennis-ball size lump of either Air-Dry Clay or Model Magic compound into cubes. Measure cubes (length capacity of containers. Provide canisters. Children fill cylinders with 30-45 min. x width x height). Adjust cube sizes so all are approximately the same volume of modeling compound. measuring cups. water to measure the capacity of . Form vessels with the compound. Use pinch, coil, and/or slab techniques to build the pottery form. What those of different widths and heights. variations in pot structures might affect capacities? Explore the concept of volume and capacity with younger students and those with special needs by conducting . With modeling tools, decorate the surface. Children’s decorative styles should be increasingly elaborate as the following experiment: Students drop golf balls or other similar items, one at a time, into an unbreakable their skills mature. Air-dry Model Magic for 24 hours. Air-dry clay pots for 3 days. container half filled with water. What happens? What conclusions can they draw? Can students suggest a way of measuring exactly 1 cup of peanut butter, margarine, or a similar product making use of the water-displacement Process: Decorate pots theory demonstrated? Session 2 . Decorate the surface of the pot with watercolors. Older children’s decorations should be more detailed and Mathematically talented students research the work of , especially his water-displacement theory. 30-45 min. sophisticated. Air-dry the paint. Share findings with the class including the story of his bathtub discovery. Is this story fact or fiction? Process: Add finishing touches Session 3 . Paint at least one coat of a Crayola Mixing Medium or a glaze of glue on the pot if desired. Air-dry the coating. 20 min.

Building fun and creativity into standards-based learning 84 Mathematics Mathematics 85 What Are the Chances?

Objectives Multiple Intelligences What Does It Mean? Artwork by students from Students predict the probability of how many times a Benday screening: Oakhurst Elementary School Logical-mathematical Linguistic Fort Worth, Texas. particular number will appear in a random sequence and silkscreen printing Teacher: Amanda Warner Grantz record the results. Spatial process using a pattern Grade 3-6 students observe how artists from the Pop-Art of dots to create images movement used line and color to define space. Pop Art: Students initiate a grid of random shapes, randomly select of the 1950s and 60s colors to fill the shapes, and count the results. in which artists were Students compare their predictions with their results. inspired by images from mass media Grade 3-6 students express their data in mathematical terms and graph the results.

National Standards Visual Arts Standard #3 Mathematics Standards Chooses and evaluates a range of subject matter, Data Analysis and Probability symbols, and ideas Understand and apply basic concepts of probability Grades 5-6 Representation Create and use representations to organize, record, and communicate mathematical ideas

Background Information Probably Pistachio by Stuart J. Murphy Want to win a lottery? Or predict the weather? The study Playful introduction to probability for all ages. Older students of probability helps people figure out the likelihood of may enjoy calculating the probability of events in the book something happening. If you are using a spinner or rolling happening to them! a number cube, you might want to know how likely you Uncle Andy’s by Jamie Warhol are to get a certain number. A warm, personal, child’s eye view of Pop artist Andy Warhol If there are five different numbers on a spinner (1, 2, 3, 4, on a visit to his New York City apartment. Children in grades 5), you have a one in five chance of spinning any one of the 1-4 will learn about the creative process as they observe numbers. The probability (or chance) of spinning any one of Warhol through the eyes of his young nephew. these 5 numbers can be expressed by a fraction (1/5) or a decimal (0.20), in a range from 0 to 1. Events that are very likely to happen would have a probability near 1, such as Vocabulary List spinning a number (the pointer might land on a dividing line). Use this list to explore new vocabulary, create idea webs, or brainstorm related subjects. Events that are unlikely to happen would have a probability Artwork by students from near 0, such as the spinner stopping on a line. Probability • Mathematical terms St. Theresa School, can also be expressed by a percentage (such as a 20% chance Certain Likely Outcome Hellertown, Pennsylvania. of spinning a 4 when there are 5 numbers on the spinner). Chance Lines Predict When figuring out the probability of an event happening, Decimal Diagonal Percentage it is important to first identify all of the outcomes that could Even chance Intersecting Probability possibly occur (the sample space). For example, when predict- Event Parallel Random K-2 3-4 5-6 Fraction Perpendicular Sequence ing the weather, consider the possibility of all different kinds Introduce the concept of prob- Review the concept of probability. Students brainstorm examples of Graph Occurrence Sample space Suggested of weather first. Then look at other factors to determine the Preparation ability by creating a spinner with where probability is used in daily life (weather predictions, lottery results, likelihood of each type of weather event. When considering Impossible Odds Unlikely and numerals 1, 2, and 3 on it. Each batting averages). the probability of a weather event for a particular day, the child divides paper or a white board • Art terms Discussion Look at work by Roy Lichtenstein, , and/or Joan Miro. Note National Weather Service looks at all other days in their histor- into three columns and writes a 1, how their compositions fill the space on a page. Show students how these ical database that have the same weather characteristics (such Benday screening Cartoon 2, or 3 at the top of each column. artists use lines and color to define space. as temperature, pressure, humidity) and may determine, for Color Random number Children take turns spinning. All example, that on 70% of similar days in the past, it rained. With students, develop and post a list of ways surface space can be divided Comic strip generators and container children tally how many times each using mathematical terms such as intersecting lines, circles, and triangles. Pattern Artist unknown number is spun. Add the tally marks Resources Pop Art Private Collection. for each number. Talk about the Popular culture results. Discuss the meaning of the Getting to Know the World’s Greatest Artists: Roy Primary colors word random. Explain that the Lichtenstein by Mike Venezia Space chance of a number being spun Introduces students to Roy Lichtenstein’s Pop Art and his use is called the probability. of flat colors and trademark Benday dots. Bright reproductions Read Probably Pistachio to and easily understood text will inspire students of all ages. the class. Brainstorm familiar games that

involve probability (such as BINGO). Building fun and creativity into standards-based learning 86 Mathematics Mathematics 87 What Are the Chances?

K-2 3-4 5-6 K-2 3-4 5-6 Crayola® • Colored Pencils • Crayons • Markers Process: Reflect on results Express probabilities and graph results Supplies Session 4 10. Talk about the results of ran- 10. Students calculate the probability of each number being generated 15-20 min. domly generating numbers and based on the actual data. Other • Drawing paper • Random number selectors (such as number cubes or spinners) • Rulers • White paper associated colors. Were any Materials colors used more than the • Colored counters (optional) others? Did any colors appear significantly fewer times? Process: Create color grids Create grids Compare results among teams. Session 1 1. In small groups, students take 1. In small groups, students work together to create a grid by filling 15-20 min. turns folding drawing paper drawing paper with lines and shapes using colored pencils. Make 11. Students express results as 11. Students express the actual until it has several crisscrossing sure sections are neither extremely large nor extremely small. fractions, with the numerator results as decimals and percent- lines. Unfold the paper. indicating how many times ages. Compare actual results to 2. Trace lines with a black marker. each number was rolled and the predictions. Draw conclusions. 2. Children trace over fold lines 3. Count the number of spaces. denominator indicating how 1 2. Use the information on the with a black marker to make many total rolls were made. a grid-like design of random chart to graph the data using shapes. 1 2. Students graph the results of a computer. their experiments using the 3. Teams count the number of data in the chart. spaces in their designs. Suggest that students lightly mark each Assessment • Observe children at each step of • Compare predictions, calculations, graphs, and artwork. Discuss observa- space as it is counted or place a the process, asking questions to tions. Use appropriate math vocabulary to describe designs. colored counter in the space as assess understanding of probability. they count it. • Review records of predictions and results for accuracy. Process: Predict and choose color codes Predict probabilities Session 2 4. To determine how to color each 4. To determine how to color each space of the design, students choose • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things 20-30 min. space of the design, students colors at random using a number generator (such as a number cube or they learned. choose colors at random using a spinner) and a color code. Each group chooses and/or creates a random For younger students, first create Challenge students to create their Generate a list of questions, number cube and a color code. number generator and then compiles a chart that lists the possible Extensions colorful spinners to explore the own probability games with Heads predict the probability of different On a chart (see sample), teams numbers that could be selected (see sample). Teams create their own probability of an event occurring ‘n Tails™ Colored Pencils. See Flip answers, and then poll a group. choose a color code to match color codes for every possible outcome (such as 1 = red, 2 = yellow). when there are 2, 3, 4, and 5 pos- Coins for Fun: A Tossing Game on See Slanted Surveys and every possible outcome on the 5. Teams work together to predict and record on the chart how often each sible outcomes. Show students how Crayola.com. on Crayola.com for a lesson plan number cube (such as 1 = red, number will be generated, given the total number of spaces on the grid. to record the results in columns on to explore how statistics can be 2 = yellow). Create individual Pop Art draw- 6. Students evaluate their predictions to discuss the probability of each the graph paper and then tally the ings in the styles of Lichtenstein misleading. 5. Teams predict how many times number/color being rolled. Use terms with a range such as impossible results. and Warhol. Fill spaces with colors Encourage students with a strong they think each number will – unlikely – even chance – likely – certain to express the probability Students with special needs may determined by chance. interest in art history or research to be rolled, taking into account of each prediction. find it less confusing to use random study the works of artists associated the total number of spaces on color selectors (a spinner with with Pop Art. Share findings with the grids. colors) rather than random number the class. Discuss messages they feel 6. Children arrange colored coun- selectors. the artists were trying to convey. ters to show their predictions for each number and after they have reached agreement, they record these predictions on Sample Chart Using a Six-Sided Random Number Generator the chart. Number of spaces on the grid: ______

7. Students take turns generating random numbers. Write each number generated in a separate space in the color Number Color choice Predictions Probability Results Actual probability grid until all spaces are filled. for the number (How many times will the (Grades 3-6) (How many times WAS (expressed as a fraction— number be rolled?) impossible – unlikely the number rolled?) grades 3-4; in decimals 8. When all sections are numbered, students count how many times each number was randomly chosen. How do – even chance – likely and percentages— the actual results compare with the team’s original predictions? – certain grades 5-6) 1 Process: Add colors and patterns 2 Session 3 9. Color each space of the design according to their selected color codes. Use solid colors or patterns, but only 3 20-30 min. one color in each space. Show work by Roy Lichtenstein as an example. 4 5 6

Building fun and creativity into standards-based learning 88 Mathematics Mathematics 89 Symmetrical Starburst

Objectives Multiple Intelligences What Does It Mean? Students (K-2) recognize, name, and draw kite shapes, Congruent: shapes coincide Interpersonal Spatial examples of radial symmetry, and assess how various viewers’ exactly when superimposed Artwork by students from Oakhurst Elementary School, responses differ to the work. Linguistic Kite folds: paper-folding Fort Worth, Texas. Logical-mathematical Students (grades 3-4) investigate, describe, and reason about method that results in a Teacher: Amanda Warner Grantz the results of subdividing, combining, and transforming shapes. Naturalist sled-kite shape (see diagram) Students (grades 5-6) examine the congruence, similarity, Spatial Radial symmetry: when and line or of a paper object using objects or sections fan out transformations. in a regular pattern from a Students describe their radial designs using geometry central point vocabulary that address grade-level standards.

National Standards Visual Arts Standard #5 Mathematics Standards Reflects upon and assesses the characteristics Communication and merits of own work and the work of others Communicate their mathematical thinking coher- ently and clearly to peers, teachers, and others Geometry Apply transformations and use symmetry to analyze mathematical solutions Use visualization, spatial reasoning, and geometric modeling to solve problems

Background Information Vocabulary List Radial symmetry is evident when regularly arranged objects or Use this list to explore new vocabulary, create idea webs, sections radiate from a central point or axis. Examples of radial or brainstorm related subjects. symmetry can be found in both nature and in human-made Angles Congruence Radial objects. Spider webs and cacti often display radial symmetry. Acute angle Fraction Reflective In the sea, five-rayed radial body symmetry is characteristic of Obtuse angle Line Rotation echinoderms such as feather stars, sea stars, and sea urchins. Right angle Midpoint Shape Radial symmetry is a feature seen in some works of Op Art, Axis Mirror-image Similar in rosette windows, and also in a relatively new craft form, tea Balance Motif Symmetry bag folding. Begun several years ago in Holland, this new art Circular Op-Art form developed by chance as a Dutch woman named Tiny van Color Pattern der Plas as she was sipping tea. She folded and arranged the decorative envelopes that come wrapped around European tea bags. Using some basic techniques similar to Japanese , this art also involves careful arrangement of folded paper in a kaleidoscope fashion, demonstrating radial symmetry.

Resources Starfish, Urchins, and Other Echinoderms by Daniel Gilpin Colorful photos of radial symmetry in nature. Sure to inspire all ages. Teatime With Emma Buttersnap by Lindsey Tate Discover the origins of tea, teatime, and customs surrounding the consumption of the beverage. Introduces the art of tea-bag folding.

Mola radial design Artist unknown 12" x 10" Cotton, cotton thread Private Collection. Building fun and creativity into standards-based learning 90 Mathematics Mathematics 91 Symmetrical Starburst

K-2 3-4 5-6 K-2 3-4 5-6 Suggested Display books, photographs, and art samples of radial symmetry. Include photographs of spider webs and sea Process: Embellish designs Preparation animals, from artists like M.C. Escher, and examples of tea-bag folding. Session 3 8. Embellish symmetrical shapes with patterns that support the radial symmetry of the design, such as: outline and In a circle of students, pass around one display item. Ask each child to look at it and think of one word that comes 15-20 min. shapes in a similar way around the design; add dots, dashes, or lines of colors similar to kites; and add shapes Discussion to mind. Ask students to share their words. Talk about how different students saw different things in the item. Repeat around the design on the background paper. activity with other items. Create examples of folded-paper shapes and final artwork. Demonstrate paper folding and other steps as needed. Assessment • Observe students for accuracy and ability to follow directions as they measure papers, fold kites, measure to find the midpoint, and experiment with radial designs. Look at a folded-paper kite. Students describe the geometry of • Students assemble kite shapes into • Students exchange work and • Examine art for congruent the kite as viewed from the folded a circular symmetrical design. check each other’s art for results sections that are similar and are side and unfolded side. Identify that illustrate an understanding of transformed into a starburst. shapes and angles. accurate subdivision and combing of shapes that transforms sections Crayola® • Colored Pencils • Glue • Markers • Scissors • Slick Stix™ Crayons into a symmetrical, radial design. Supplies • Display finished art. Students observe and reflect on what they see. Discuss impressions, comparisons, unique Other • Construction paper • Rulers arrangements, embellishment ideas, and use of colors. Identify elements that contribute to radial symmetry. Materials Locate and identify different kinds of angles and shapes in the designs. • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things Process: Fold kite shapes Fold kite shapes they learned. Session 1 1. Children each measure and cut 1. Measure and cut colored paper into 2-, 3-, and 4-inch squares. Make 30-45 min. drawing paper into a 12-inch eight squares in each size. Kite-fold all squares. Encourage students to Extensions Experiment with arranging and Be geometry detectives! Use Gather decorative papers. Cut or more square. Encourage students to help each other. layering tangram shapes around a paper-folding skills to create them into different-size squares. central point. another 3-dimensional work of art Create half kites (kite folded in half, help each other. . Cut a 12-inch square of colored paper. Use a ruler to find and mark Make paper kites to decorate the with lots of angles to measure and joining side tips) and pentagon kites . Hold the paper square in a the midpoint. identify. See the Tin Foil Twinkles (lower corner folded up to meet diamond formation with corners classroom. See Easy Breezy Kite on . Hold a small paper square in a diamond formation with corners Crayola.com for decorating ideas. lesson plan on Crayola.com for upper corner). Challenge students pointing up, down, and to the pointing up, down, and to the sides. See the diagram for folding Set up a kite-folding activity complete directions. to create unique radial designs. sides. See the diagram for directions. folding directions. center. Show children how to The craft of tea-bag folding has Measure the lines and angles . Repeat folds with all small squares so that the subdivision and fold kites in half for another shape grown beyond tea bag envelopes. of the radial designs. Repeat the . Figure out how many kite combining of sections will transform the shapes and create a option. Fold, arrange, and decorate Crafters often create decorative shapes, lines, and angles with 2- sections are needed to create starburst design. radial designs with any number papers to fold and arrange. Lead dimensional art materials on paper. a circular radial design. of kites. children to design their own deco- Explore more color, line, space, and . Cut that many more squares rative paper with radial symmetry, angles with the Shapes and Angles and fold them. using only a black outline of the lesson plan on Crayola.com. design. Copy designs to color. Use Process Form the radial design Transform shapes into a Create symmetrical designed paper to create kites to Session 2 . Assemble kites into a simple symmetrical design congruent shapes arrange in new radial designs. 30-45 min. circular, radial design. . Experiment with symmetrical . Experiment with different ways Make detailed colored pencil drawings of symmetry in nature, such as spider webs, flowers, or cacti. or more 6. Glue them to construction patterns. One way is to arrange folded papers can be arranged paper. Air-dry the glue. the one size of kite around the around the midpoint to make a . Color the faces of both the midpoint. Repeat the experi- balanced radial design, such as: folded sections and the inside ment with the other two sizes. • Side-by-side, fold down How to make kite folds of the folds. Make sure that the 6. Choose which size to arrange • Side-by-side, fold up drawings reflect symmetry in first. Glue kites around the mid- • Smaller kites arranged with Step 1. Step 2. Step 3. color, shape, and pattern. point in a symmetrical pattern. tips nested in larger kites, fold Fold one corner to Bring bottom left Bring top left edge . Tuck another size of kites into down or up opposite corner edge up to meet down to meet

the attached kites to form a • Folded arms of different colors of square. the crease. the crease. Unfold. second layer. Glue them in and sizes linked place on construction paper. 6. Think of unique arrangements. Repeat with the remaining Share ideas for other arrange- kites. Air-dry glue. ments that show balanced radial symmetry using only the kites made. . Glue final designs on Berks County Barn Hex Sign construction paper so they Photo by R. De Long are congruent. Air-dry glue.

Building fun and creativity into standards-based learning 92 Mathematics Mathematics 93 Stock-Smart Art

Objectives Multiple Intelligences What Does It Mean? Students increase their vocabulary and understanding of basic Scripophily: the hobby Interpersonal business investment terminology. of collecting stock and Students examine sample stock certificates and then create Logical-mathematical bond certificates for imaginary certificate designs for modern businesses. Spatial their artistic and historic Students in grades K-2 use the value of various coins to Naturalist value rather than their calculate imaginary stock values and write algebraic equations financial value using those values. Students in grades 3-6 identify how investments benefit individual investors as well as businesses.

National Standards Visual Arts Standard #4 Mathematics Standards Understanding the visual arts in relation to history and culture Number and Operations Compute fluently and make reasonable estimates Problem-Solving Solve problems that arise in mathematics and other contexts Artwork created by students Representation and teacher from Princeton Create and use representations to organize, record, and North Elementary School, communicate mathematical ideas Princeton, Minnesota. Teacher: Tom Tschumper

Background Information Money Sense for Kids by Hollis Page Harman Business organizations that are formed to manufacture goods, Older students learn about saving, spending, and investing develop new technology, or deliver products and services are money. Comprehensive, yet enjoyable, book about the basics most commonly formed as corporations. Often, groups of of economics. people share in the ownership of a corporation. Each unit of The Art of the Market: Two Centuries of American Business ownership is called a share. Shares (also called stocks) can be as Seen Through Its Stock Certificates by Bob Tamarkin purchased by individuals or groups. A corporation uses money A look at stock certificates and their value in the worlds of from investors to build its business. A stock certificate is a both art and American economic history. Students of all ages paper document reflecting legal ownership of a specific enjoy decorative elements in the certificates illustrated. number of shares in a corporation. Ups And Downs: A Book About the Stock Market by Stock certificates are one way to grasp a visual picture of the Nancy Lowwen and Brian Jensen K-2 3-4 5-6 historic development of industrial growth in the United States. An introduction to corporations, shares, stocks, and how These documents meld art and economics. For example, investment can benefit both businesses and individuals. Suggested Review concepts of money. Review concepts of money and investments. Some people collect old 19th-century railroad corporations stamped locomotives on Preparation Display real bills and coins to stock certificates as a hobby. This is called scripophily. their certificates, and early automobile companies incorporated identify. Talk about their design. popular Art Deco motifs. Today’s media giants use sleek, Vocabulary List and Ask students to display copies of stock market reports from newspapers Ask children how people earn, or Web sites. As a class, select several stocks. Track them over a period of modern graphics. Use this list to explore new vocabulary, create idea webs, Discussion spend, and save money. Talk about time and chart the rise and/or fall of their values. Calculate percentage of or brainstorm related subjects. Vintage certificates included lively text offering historic banks and their role in helping change in value. Students in grades 5 and 6 also determine median, mode, background on companies. Many older certificates printed • Business terms Asset Money people manage their money. and range. Discuss how changes in the stock market affect individual in several colors and featuring fine embellished engravings Business Ownership Ask children to name some investors and companies. are treated as rare, numbered, limited edition prints. These Buy Payout historic certificates are often framed and hung on office walls. familiar toy companies, stores, or Invite families who own stock to visit the classroom to show their Cash Profit restaurants. Explain that one way certificates and talk about stocks they own. The act of collecting stock certificates is known as Claim Reinvest people make money is by buying Consider inviting an investment broker to speak with the class. scripophily. Particularly valuable to collectors are those Corporation Save a share of a company. When the Dividend Sell signed by the historically important industrialists who owned company makes money it shares Earnings Share the companies, such as John D. Rockefeller, who started the that money, called profits, with Standard Oil Company of Ohio in 1862. A very rare stock Gain Shareholder Growth Spend shareholders. Often when people certificate from the late 18th-century Philadelphia and buy shares (or stock), they get a Lancaster Turnpike is printed on sheepskin. Investment Stock Loss Stock certificate special paper from the company Today, paper stock certificates are becoming rare and often Market called a stock certificate. people who want them must pay more. • Art terms Art Deco Pattern Show examples of actual or reproduction stock certificates. Encourage students to examine borders, logos, illustrations, signatures, and texts. Resources Border Style Design Texture Redesign a familiar, publicly held company’s stock certificate and show the new version to students to inspire Alexander, Who Used to Be Rich Last Sunday by Judith Viorst Embellish Vintage their creativity. Connects younger students’ experiences with money. Graphics Visual Alexander is a familiar character in children’s literature. Image

Building fun and creativity into standards-based learning 94 Mathematics Mathematics 95 Stock-Smart Art

K-2 3-4 5-6 K-2 3-4 5-6 Crayola® • Crayons • Colored Pencils Assessment • Are crayon rubbings clear and • Do border designs show attention to line, shape, color, texture, Supplies precise and are border designs and pattern? • Glitter Glue • Watercolor Paint • Paint Brushes enhanced with colorful lines, • Do certificates include the company name, a symbol reflecting the shapes, and patterns? company’s product, and signatures of important company leaders, as Other • Coins • Does the monetary value printed well as decorative border designs? Materials on the certificates equal the total • Paper towels • Recycled newspaper • Water containers • White paper • Are students able to read stock market charts, identify values, and value of the coins pictured in the compute the number of shares that can be purchased for a given border designs? Set-up/Tips • Cover art surface with recycled newspaper. amount of money? • Do students accurately compare • Demonstrate how to make crayon rubbings and do watercolor resist. • Students write a short paragraph describing how investments can the values of the certificates made benefit both stockholders and business. • Students can hold papers for each other while they do rubbings. Or tape coins to a table surface to hold them in by classmates? place before rubbing. Sharper images will result. • Does text provide information about the company? Process: Design a make-believe stock Redesign stock certificates Session 1 certificate 1. Select a publicly held company. Research its history and products. • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things 30-45 min. 1. Students each select a favorite . Using this information, use crayon to design a new certificate for the they learned. company for which to design a company’s stockholders. new stock certificate. Extensions Talk about why companies cre- Introduce students to a stock market game such as Pit and provide time . Include a company name, decorative border, a sign or symbol in a ate ads. Invite students to pretend for playing. Make border designs by placing . style that reflects the company’s product, space for signatures of they have been asked to make up a Ask students who are interested in product research to trace a specific coins under paper and rubbing company leaders, and other decorative features. Consider line, shape, name for a new product. What are product from its origin to its final destination. Who was involved in product over them with crayons. color, texture, and pattern in the design. some of their ideas? See the New design? What raw materials are used? How, where, and by what company . Embellish the certificates with Names lesson plan on Crayola.com. is it manufactured? How was it transported? Consider the Trucks at Work colorful words, lines, shapes, Invite a representative from a lesson plan found on Crayola.com as an example. and patterns. local bank to talk to the class about the value of saving money. See . With watercolors, emphasize specific parts of the stock certificate designs. Air-dry the paint. how to make a Bits and Pieces Bird Bank on Crayola.com. Process: Determine the “value” of the Add details to stock certificates Session 2 stock certificates . Choose an imaginary amount of money to invest in stocks. Research Young children and those with learning differences might benefit from a hands-on business project such as a class booth at a school carnival to sell bookmarks, gift bags, or other craft projects. Ask families to “invest” 30-45 min. . Add the value of all the coins current stock market reports to find the cost of one share of stock for the company portrayed on the stock certificate. quarters. Children determine how many raw materials can be purchased for the amount invested and how much depicted in the border to find they will charge for the products. How will the business be promoted? How many sales staff are needed at what the total value of the certificate. 6. Students calculate how many shares they could purchase with the times? Students keep track of sales and add up total income. How will they divide the money among investors? 6. In crayon, write that value in amount of money they chose. Record that information as an equation. Will everyone get back their original investment? Will they make a profit? large numbers on the certificate. . Students research who in their chosen corporations might sign the . Imagine that the coin value stock certificates. Or students invent names as representatives of the represents the actual value of companies. Add detailed text, embellishments, and imaginary signatures each stock. Compare stocks. to stock certificates. Artwork created by students from Which is most valuable? Which Princeton North Elementary School, is least expensive? Princeton, Minnesota. Teacher: Tom Tschumper 8. Use glitter glue to add sparkle to certificates. Air-dry. Process: Identify stock value Track stock values Analyze investments Session 3 . Form small groups. Write equa- . Track the value of the publicly . Track two publicly traded 30-45 min. tions to reflect the value of the traded stock for at least a stocks and compare which group’s stock. If the group were month. Graph its daily value. stock makes more money over to sell the stock, what could the course of at least a month. they buy with its value? Repeat Make line graphs to show their several times. relative daily values. At the end of the time periods, analyze which one would have been New York Stock Exchange the better investment. What Certificate of Listing trends are evident? Binney & Smith Inc.

Building fun and creativity into standards-based learning 96 Mathematics Mathematics 97 Geometric Weaving

Objectives Multiple Intelligences What Does It Mean? Students (K-2) observe and duplicate patterns, relations, Warp: the threads that run Bodily-kinesthetic Linguistic and functions of two-dimensional design in weaving. lengthwise on a loom Students (3-4) investigate and note how a change in one Interpersonal Weft: the threads that are variable relates to a change in a second variable as it applies Logical-mathematical woven over and under the to parallel and perpendicular lines and two-dimensional Spatial warp threads congruent figures in weaving. Students (5-6) represent, analyze, and generalize a variety of weaving patterns as they work in pairs to create paper with balanced designs.

National Standards Visual Arts Standard #6 Mathematics Standards Makes connections between visual arts and other disciplines Geometry Specify locations and describe spatial relationships using coordinate geometry and other representational systems Algebra Understand patterns, relations, and functions

Artwork by students from Background Information Vocabulary List Jordan Community School, Weaving, , and appliqué have long been vital Use this list to explore new vocabulary, Chicago, Illinois. elements of African artistry. The Kuba who live in the Kasai create idea webs, or brainstorm related subjects. Teacher: Elyse Martin river region of the Democratic Republic of Congo are known • Math terms Angle Perpendicular for their beautiful raffia cloth weavings. Axis Quadrant Kuba cloth is woven from the fiber of the raphia vinifera Balance Right angle palm. Production of these textiles is a multiple-stage process, Congruent Shape involving the men, women, and children of a clan. The process Line X-axis K-2 3-4 5-6 includes gathering and preparing the raffia fibers, weaving the Parallel Y-axis Suggested Show examples of pairs of lines Introduce/review the geometric concept of perpendicular and parallel cloth, dyeing the embroidery fibers, and embellishing the cloth Preparation that are parallel and pairs of lines lines. Ask students to use math terminology to describe the angle formed with embroidery, appliqué, patchwork, and dye. • Art terms Design Warp and that are perpendicular. Ask each by two perpendicular lines. Observe that at the intersection of two Historically, Kuba cloths have been buried with kings or Mirror Weaving student to use colored pencils to perpendicular lines, there is a 90° angle, like the corner of a square. those fortunate enough to own them as a sign of status. The Tandem Weft Discussion demonstrate their understanding of geometric patterns also have inspired modern artists such as Texture these concepts. Explore the algebraic concept Review/introduce basic algebraic Picasso and Klee. Today these cloths are traded to surrounding of number lines. Ask students concepts. Discuss the use of an areas and are occasionally used for ceremonial dress and where they have seen lines like axis as a line used to locate points. to cover royal stools. these (maps, graphs). Introduce Introduce the concept of a perpen- the concept of using coordinates to dicular axis used to locate points in plan points and shapes in a design a two-dimensional space or plane. Resources using a number grid to indicate the Draw an x –axis and y-axis on a Abuela’s Weave by Omar S. Castaneda placement of lines, corners, and grid to demonstrate how points All ages. Story of a Guatemalan weaver and her granddaughter. other features. can be placed in each quadrant. Contrasts the value of hand weaving with mass-manufactured Demonstrate how points are named . Introduce the concept of mirror images. Have students share examples. and how to balance points on Draw a vertical line on a white board. Ask one student to draw a large dot opposing sides of each axis. Draw Kuba by Rebecca Luechak (point) on the left side of the line. Ask another student to draw the mirror simple shapes using points in Details about the society, history, and art of the Kuba people image of that point on the other side of the line. Continue this activity each quadrant. of central Africa. Color illustrations appeal to students of with lines and shapes to practice creating a balanced design. Repeat with a all ages. horizontal line. Older students might repeat the activity with both horizontal Master Weaver From Ghana by Gilbert Ahiagble and and vertical lines at the same time, intersecting perpendicularly. Louise Meyer For older students. Visit a West African family and community Display samples of weaving, both actual and in photographs. Introduce terms such as line and shape, warp and where the kente cloth weaving trade is a group effort. weft, and over and under as students look at the samples. Draw attention to samples where the weaving lines (warps and wefts) are perpendicular to each other. Provide paper for students to create small, simple tabby weavings. Use art and math terminology to describe the weaving process and result. Create a paper weaving that illustrates a simple tabby weave—over and under with a warp and weft.

Artwork by students from Gayman Elementary School, Plumstead, Pennsylvania. Teacher: Cara Lucente Building fun and creativity into standards-based learning 98 Mathematics Mathematics 99 Geometric Weaving

K-2 3-4 5-6 K-2 3-4 5-6 Crayola® • Colored Pencils • Glitter Glue • School Glue • Scissors • Washable Markers Assessment • Check that students included line, • Students achieved a watercolor • Talk with partners as they work. Supplies shape, color, and pattern in their effect with their designs. Assess use of proper math and • Paint Brushes paper designs. • Students successfully weave art terminology as students • Students successfully complete the their strips. describe what they are drawing. Other • Brown grocery bags • Craft paper roll • Rulers • White drawing paper simple tabby weave process. Reinforce learning by using proper Materials terminology in response to their comments. Check accuracy of • Paper towels designs created by partners. • Recycled newspaper • Observe cooperative efforts to measure and weave in pairs. • Water containers • Display and discuss finished weavings. Assess use of proper terminology as students offer observations on each Set-up/Tips • Cover art area with newspaper. other’s work. Process: Design paper Design patterned paper Design complex patterns • Ask students to reflect on this lesson and write a DREAM statement to summarize the most important things they learned. Session 1 1. Decorate two papers with lines, 1. Decorate two papers with on paper 20-30 min. colors, shapes, and patterns patterns using washable 1. Challenge student pairs to Extensions Introduce children to wiggly weav- Challenge students to design Show students how to plot using washable markers. markers and colored pencils. create complex designs on two ing. See Crayola.com for a Wiggly weaving sheets that demonstrate ordered pairs on the coordinate . Use wet brushes on marker papers by drawing shapes. Weaving craft idea for inspiration. mirror images using all four quad- plane of a paper weaving. Create designs for a watercolor effect. . Fill in shapes with solid colors Create and use number lines when rants of an x- and y-axis. Measure, paper weavings using equal-width, Air-dry. or patterns so they mirror reading stories with students to rule out, and cut weft strips of their straight strips. Draw a four-quadrant each other. begin to formulate the concept of designs. Create a twill weave, with x- and y-axis on the weaving and x-axis as a progression of value or weft strips going over two warps number each line (+ going up and Process: Cut one design sheet into weft strips (in stories) of time. and then under one or two warps. to the right, - going down and to Session 2 Students add illustrations to class See the Rainbow in a Rug lesson the left). Model how to plot (x, y) . Use a ruler and colored pencils to measure, mark, and cut strips of paper from one of the decorated sheets. coordinates. Plot coordinates as 20-30 min. Measure strips as follows: timelines to demonstrate events plan on Crayola.com to create a rep- occurring over time. lica of Navajo weaving. Make Fiesta simple points or small shapes and K-2: 1-inch strips symbols on their weavings. Grades 3-4: 3/4-inch strips Mats for a Mexican culture celebra- Grades 5-6: Graduate the width of the strips so that each measures 1/2 inch at one end and a full inch at the other tion and create West African kente cloth with Crayola Overwriters®. . Add glitter glue to the warp sheet and weft strips. Air-dry glue. Young children and students Encourage gifted students to find out more about weavings created Process: Create the warp strips and weave whose manual dexterity is not fully by other cultures and report their findings to the class. Some might also Session 3 . Show students how to fold down an inch at the top of the second decorated sheet. Demonstrate how to developed may have better success enjoy researching artists who have created the illusion of weaving in their 30-40 min. measure and mark lines to create warp strips. working with lightweight poster paintings such as Paul Klee, Piet Mondrian, and Picasso. Students in K to 2 measure 1-inch vertical strips. board rather than drawing paper. Students in grades 3 to 6 measure 1/2-inch vertical strips. (Grades 5-6 do NOT graduate width of warp strips.) Provide help with cutting if Cut along drawn lines to create strips, stopping at the top fold, so the strips remain connected. necessary. Rapid I Movement 6. With a partner, create a simple tabby weave by weaving each weft strip over and under the warp strips. Artist: Barbara Schulman Tightly tuck the first strip under the top fold. 33" x 23" Acrylic, canvas, . Show students how to alternate brass grommets which end of the weft strip Private Collection. leads through the warp so that the graduated widths compli- ment each other. Demonstrate what happens if they are not alternated. 8. For added effects, cut thinner strips of colored paper and interweave them over and under the tabby weave pattern.

8. Alternate the over-under pattern with each weft. Tightly tuck all strips close to the previous weft until all strips are used. Process: Secure weavings to backings Kente Cloth Session 4 . Cut apart brown paper grocery bags and spread flat. Glue weavings to the plain sides of the bags so they do Artist unknown 30-40 min. not unravel. 3' x 2' 10. Glue all weavings together on craft paper to create a mural reflecting African Kuba textiles. Dyed cotton Private Collection.

Building fun and creativity into standards-based learning 100 Mathematics Mathematics 101 Choosing Crayola Art Supplies

The lessons in this guide suggest types of art materials. This chart outlines the specific characteristics of different Crayola art materials. Use it to choose which variation best meets your needs and those of your students.

CRAYONS/OIL PASTELS CHARACTERISTICS MARKERS CHARACTERISTICS Regular Crayons (3-5/8" x 5/16") • Brilliant colors; smooth, even color lay down. Regular Markers • Bright, brilliant, transparent colors. • Conical tip draws thick and thin lines. Large Size Crayons (4" x 7/16") • Brilliant colors; smooth, even color lay down. • Fine tip draws thin lines and detail. • Larger size for younger child palm grip. Washable Markers • Washability you can trust™–superior washability from hands and most clothing. Triangular Crayons • Brilliant colors; smooth, even color lay down. • Bright, brilliant, transparent colors. • Triangular shape helps guide correct pincer grip. • Conical tip draws thick and thin lines. • Anti-roll. • Fine tip draws thin lines and detail. Washable Crayons • Brilliant colors; smooth, even color lay down. • Wedge tip provides ease in broad strokes and vertical applications. • Available in regular, large, and triangular sizes. Gel Markers • Bright, opaque colors that deliver bold marks on black and dark papers. • Superior washability from walls, tables, and most surfaces. • World’s most washable marker with superior washability from hands and Construction Paper™ Crayons • Brilliant colors; smooth, even color lay down. most clothing. • Color shows on dark paper, brown craft paper, and similar surfaces. • Writes on glass, foil, glossy, and other non-porous surfaces. Fabric Crayons • Permanent when drawing is heat transferred to synthetic fabric. • Conical tip draws thick and thin lines. Overwriters® Markers Twistables® Crayons • Brilliant colors; smooth, even color lay down. • Bright “overcolors” magically color over darker “undercolors” for exciting and • Durable plastic barrel. dramatic effects. • No sharpening with easy twist-up action. Color Changeables™ Markers • Students have fun seeing colors magically “pop out” over each other for new Twistables Erasable Crayons • Complete erasability of marks. creative expression possibilities. • Brilliant colors; smooth, even color lay down. • Increased color variety as “wand” changes 7 colors to 7 new colors. • Durable plastic barrel. Twistables Markers • No lost caps! • No sharpening with easy twist-up action. • Bright, brilliant, transparent colors. • Eraser on each crayon. Fabric Markers • Permanent bright color on cotton or cotton blends when heat set. Twistables Slick Stix™ Crayons • Super-smooth color glides on paper. • Bullet tip for medium and fine detail. • Water soluble upon application. Dry-Erase Markers • Low odor, bold color that can be viewed from a distance. • Dries quickly with no smearing. • Chisel and bullet tips. • Durable plastic barrel. • Great for older student crayon techniques. • Appropriate for students with special needs due to ease of color lay down. COLORED PENCILS CHARACTERISTICS Oil Pastels • Opaque colors blend easily. • Good color lay down. Colored Pencils • Bright, vivid colors with opaque lay down. • Hexagonal shape prevents rolling. • Good blending. • Thick 3 mm lead; made from reforested wood. Portfolio® Series Oil Pastels • Opaque colors blend and layer well, with velvety lay down. • Unique water solubility allows watercolor washes. Watercolor Colored Pencils • Water soluble for watercolor and drawing effects. • Bright, vivid colors with opaque lay down. • Good blending. • Thick 3 mm lead; made from reforested wood. Erasable Colored Pencils • Complete erasability of pencil marks. • Bright colors with opaque lay down. • Good blending. • Eraser on each pencil. • Thick 3 mm lead; made from reforested wood. Twistables Colored Pencils • Bright colors; smooth, even color lay down. • Durable plastic barrel. • No sharpening with easy twist-up action. Twistables Erasable Colored Pencils • Complete erasability of pencil marks. • Bright colors; smooth, even color lay down. • Durable plastic barrel. • No sharpening with easy twist-up action. • Eraser on each pencil. Write Start® Colored Pencils • Thick 5.3 mm lead and large hexagonal barrel is great for young students. • Bright, vivid colors with opaque lay down. • Anti-roll. • Made from reforested wood.

Building fun and creativity into standards-based learning 102 Mathematics Mathematics 103 MODELING COMPOUNDS CHARACTERISTICS Air-Dry Clay • No firing, air-dry clay. • Good for high-detail projects. • Natural clay body to create solid, durable forms. • Suitable for all clay techniques. • White color suitable for all color/surface decoration. • Air-dries hard. Model Magic® • Soft, easy-to-manipulate compound. • Good for low-detail projects. • Good for young students and those who are developing manual dexterity. • Air-dries to consistency of a foam cup. Modeling Clay • Traditional oil-based clay. • Non-hardening and reusable.

Paints CHARACTERISTICS Premier™ Tempera • Ultimate opacity and coverage. • Creamy consistency flows smoothly and will not crack or flake. • Intense, true hues for accurate color mixing. Artista II® value-priced Tempera • Fine-quality colors with good opacity. • Creamy consistency flows smoothly and will not crack or flake. • Good hue positions for excellent color mixtures. • Washable from skin and fabrics. Washable Paint • Washability you can trust–superior washability from skin and fabrics. • Bright, clean colors for consistent color mixing. • Smooth-flowing formula will not crack or flake. • Pigment-rich colors are intense even when diluted; achieve accurate color mixes. • Thick, tube-like viscosity, for a variety of techniques from air-brushing to impasto. • Permanent, water resistant, and flexible when dry. Washable Finger Paint • Bright colors, thick consistency. • Washable from skin and fabrics. Watercolors • Bright, intense, transparent colors. • True hues for accurate color mixing. • Ideal for opaque and transparent techniques. Washable Watercolors • Washability you can trust–superior washability from skin and fabrics. • Bright, intense, transparent colors.

104 Mathematics