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MATH IN ART by taoyni


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


 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 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
                 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

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               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:
   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

      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

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      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
      Perspective – a technique for representing three-dimensional space on a flat
          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
      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
   Rulers
   Glue
   Tape
   12x18 construction paper
   colored pencils, markers, crayons
   compasses - SAFE-T finger compass

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Resources (always check websites for safe content)
      National Council of Teachers of Mathematics
      Virtual Manipulation: Tessellations @
      Tessellations Theme Page @
      Symmetry and Tessellations Activities Links @
      Pattern Blocks Exploring Fractions with Shapes and
      The Early Greeks Contribution to Geometry

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.

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

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

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Grade Subject              # and description
K-4        Social          7a. Knowledge of the use of tools of social science inquiry
           Studies         (such 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
           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
                           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

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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
                     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

           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

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