Math in Art

MATH IN ART? ABSOLUTELY! A Survey of Patterns and Relationships Museum of Art and Archaeology - University of Missouri-Columbia Angela Lawler, Associate Museum Educator

Title: MATH IN ART? ABSOLUTELY!

The connections between art and math are strong and frequent, yet few students are aware of them. This program is integrated with history and art to engage even the most math-resistant of your students and to enlighten everyone about Greek geometric design, concentric circular art from Cyprus and other cultures, 1-point perspective, and M. C. Escher's work in tessellations.

Assessment and Instructional Plan: Assessment: Assessment occurs informally through shared dialogue about connections between Math and art during the tour at the Museum of Art and Archaeology.

Instructional Plan 1. Welcome the group to the Museum of Art and Archaeology at the University of Missouri-Columbia. Share what we’ll look for and how we’ll look (rules of museum behavior, overview of today’s museum tour). 2. While in the the lobby of the Museum of Art and Archaeology, introduce today’s activity with a discussion of an informal definition of Math. (Guide the discussion to defining Math as the study of attributes, traits, properties (numbers, shapes, patterns), and the relationship of these features.) 3. Attribute identification practice – line a few participants in such a way that a pattern is evident and ask the group to identify the pattern. Discuss multiple possibilities. Some examples: shoes, sandals, shoes, sandals … Short hair, long hair, short hair, long hair … Dark shirt, light shirt, dark shirt, light shirt … 4. Discuss how artists manipulate compositional elements, such as line, shape, color, balance, symmetry, and repetition, to create meaning in a work of art. 5. Proceed to the upstairs galleries to visit some or all of the following: A. Weinberg Gallery – i. Egyptian textiles – patterns and repetition, symmetry ii. Idi – Ka statue – canonical proportion, symmetry iii. Egyptian Tomb Relief – canonical proportion, asymmetry

May 2006 1 iv. Cyprus: Oinochoe or Jug (61.33) – patterns and repetition v. Cylindrical, Lidded Pyxis (64.69.1) – geometric patterns vi. Small Krater (90.109) - concentric circles vii. Amphoras (91.255, 58.3) - geometric patterns, figure proportion viii. Horse Pyxis (92.1) - geometric patterns B. European and American Gallery i. Madonna and Child – predella – 1-point perspective ii. Church – 1-point perspective C. Barton Gallery i. Chihuly’s Lime Persian Single (94.1) – concentric circles ii. Vasarely’s Uzok (81.54) – puzzle-like pattern iii. Kiss I (97.17) - repetition D. Carlebach Gallery i. Embroidered Textile (74.215) – pattern and repetition 4. Invite kids to share observations of artwork; its attributes, noticable patterns, knowledge of tools needed to create the artwork. Group management tip: Be sure to invite kids in the back to come to the front so they can view artifacts in cases. 5. Conclude the tour. Invite kids to share aloud or with a neighbor the artwork that was most interesting/memorable. 6. Follow-up with hands-on activities: a. Circle art – use with compass b. Drawing in 1-point perspective c. Tiling/tessellations

Student Prior Knowledge: Vocabulary . Polygon – closed figure formed by straight line segments (poly=many [Greek]; gon=angle [Greek]) . Pattern – a repeating arrangement of colors, shapes, and figures.

Vocabulary introduced/reinforced during activity . Quadrilaterals – four-sided polygon (square or rectangle)

. Hexagons - six-sided polygon

. Congruent – same size and same shape

. Plane - a two-dimensional, flat surface

May 2006 2 . Tessellation – any repeating pattern of interlocking shapes. Tessellations are also sometimes known as “tilings,” the repeated use of polygons and other curved figures to completely fill a plane without gaps or overlapping . Symmetrical - having both sides of a central dividing line correspond or be identical to each other . Asymmetrical - not arranged in a symmetrical way

. Geometric - relating to a period of ancient Greek culture, between 900 and 700 bc, noted for its decorative use of simple lines and shapes, especially on pottery - using straight lines and simple shapes, for example, circles or squares . Perspective – a technique for representing three-dimensional space on a flat surface. o One-point perspective – objects are seen face on and are drawn to a single vanishing point o Two-point perspective – objects are seen at an angle using two vanishing points . Concentric - circles of different sizes with the same middle point

Estimated Classroom Instructional Time (Hours): 30-40 minutes gallery visit, 40-60 minutes artistic creation time

Lesson Objective: Students will

. View and construct meaning from primary resources . demonstrate effective listening to learn, process and analyze information . discuss how artists manipulate compositional elements, such as line, shape, color, balance, symmetry, and repetition, to create meaning in a work of art . identify geometric design, patterns and repetition in art and artifacts . illustrate comprehension of mathematical knowledge through creation of various forms of art.

Material and Resources: Materials list  Scrap paper  Tag board, recycled manila folders, or other cardboard sheets  Pencils  Scissors

May 2006 3  Rulers  Glue  Tape  12x18 construction paper  colored pencils, markers, crayons  compasses - SAFE-T finger compass

Resources (always check websites for safe content)

 National Council of Teachers of Mathematics

 Virtual Manipulation: Tessellations @ http://nlvm.usu.edu/en/nav/frames_asid_163_g_2_t_3.html?open=activities

 Tessellations Theme Page @ http://www.cln.org/themes/tessellations.html

 Symmetry and Tessellations Activities Links @ http://britton.disted.camosun.bc.ca/jbsymteslk.htm

 Pattern Blocks Exploring Fractions with Shapes http://www.arcytech.org/java/patterns/patterns_j.shtml and http://mason.gmu.edu/~mmankus/Handson/manipulatives.htm

 The Early Greeks Contribution to Geometry http://www.cis.yale.edu/ynhti/curriculum/units/1984/2/

 http://www.sanford-artedventures.com/teach/teach.html

Classroom Organization: (large group, small group, pair etc…) Groups of 4-10

Student Work Product(s): Students will increases their senses of spatial relationships by . creating and manipulating tessellating tiles to create patterns and designs that will completely cover a plane leaving no spaces, gaps or overlaps . creating illustrations using 1-point perspective . experimenting with circular art using a compass

Strategies for Learner Engagement: Reciprical dialogue. Observe body language showing evidence children are engaged in the topic.

May 2006 4 Homework / Parent Communication: Parents/group leaders assist in chaperoning the group to the Museum, modeling behavior that encourages and invites all to be engaged in the topic.

What We Are Learning: Object-based learning in a museum Appropriate behaviors in a museum Critical thinking skills Observation skills Listening skills Relevant Missouri Grade Level Expectations: Grade Subject # and description Math Algebraic Relations 1. Understand patterns, relations and functions K-5 a) Recognize and extend patterns K-12 b) Create and analyze patterns K-2, 6-12 c) Classify objects and representations Math Geometric and Spatial Relationships 1. Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships K-12 a) Describe and use geometric relationships K-12 Math Geometric and Spatial Relationships 2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems Math Geometric and Spatial Relationships 3. Apply transformations and use symmetry to analyze mathematical situations 1-8 a) Use transformations on objects 2-8 c) Use symmetry Math Geometric and Spatial Relationships 4. Use visualization, spatial reasoning and geometric modeling to solve problems K-2 a) Recognize and draw three-dimensional representations Math Measurement 1. Understand measurable attributes of objects and the units, systems and processes of measurement K-2 a) Determine unit of measurement

May 2006 5 Math Measurement 2. Apply appropriate techniques, tools and formulas to determine measurements K-2 a) Use standard or non-standard measurement

Grade Subject # and description K-4 Social 7a. Knowledge of the use of tools of social science inquiry (such Studies as surveys, statistics, maps and documents) (1) Identify, select, use and create appropriate resources for social science inquiry Identify and use primary and secondary sources (diaries, letters, people, interviews, journals and photos) 5-8 Social 7a. Knowledge of the use of tools of social science inquiry Studies (such as surveys, statistics, maps and documents) (1) Using primary and secondary sources Select, investigate, and present a topic using primary and secondary resources, such as oral interviews, artifacts, journals, documents, photos and letters 9-12 Social 7b. Knowledge of the use of tools of social science inquiry Studies (such as surveys, statistics, maps and documents) (2) Selecting and analyzing primary/secondary sources

Grade Subject # and description Communication Reading K-12 Arts 1. Develop and apply skills and strategies to the reading process Communication Reading K-12 Arts 3. Develop and apply skills and strategies to comprehend, analyze and evaluate nonfiction (such as biographies, newspapers, technical manuals) from a variety of cultures and

May 2006 6 times a) Text Features c) Text Elements d) Understanding Directions Communication Listening and Speaking K-12 Arts 1. Develop and apply effective listening skills and strategies Communication Listening and Speaking K-12 Arts 2. Develop and apply effective speaking skills and strategies for various audiences and purposes a) Discussion and Presentation Communication Information Literacy K-12 Arts 2. Develop and apply effective skills and strategies to analyze and evaluate oral and visual media

Grade Subject # and description Science Strand 7: Scientific Inquiry K-12 1. Science understanding is developed through the use of science process skills, scientific knowledge, scientific investigation, reasoning, and critical thinking a) Scientific inquiry includes the ability of students to formulate a testable question and explanation, and to select appropriate investigative methods in order to obtain evidence relevant to the explanation b) Scientific inquiry relies upon gathering evidence from qualitative and quantitative observations c) Evidence is used to formulate explanations d) Scientific inquiry includes evaluation of explanations (hypotheses, laws, theories) in light of scientific principles (understandings) e) The nature of science relies upon communication of results and justification of explanations

Science Strand 8: Impact of Science, Technology and Human Activity 1. The nature of technology can advance, and is advanced by, science as it seeks to apply scientific knowledge in ways that K-8 meet human needs a) Designed objects are used to do things better or more easily and to do some things that could not otherwise be done at all

May 2006 7 Science Strand 8: Impact of Science, Technology and Human Activity 3-11 2. Historical and cultural perspectives of scientific explanations help to improve understanding of the nature of science and how science knowledge and technology evolve over time a) People of different gender and ethnicity have contributed to scientific discoveries and the invention of technological innovations

May 2006 8