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Area Art: Ethnomathematics For The Twenty-First Century

Overview | Activities

Introductory Activities:

1. Can you find basic shapes (triangle, rectangle, square) in each of the following figures?
Using the IT'S HIP TO BE SQUARE HANDOUT, identify as many combinations of basic shapes you can find inscribed within the borders of figures A through F. In some cases, you may choose to identify other polygons like trapezoids or parallelograms inscribed in the same figures. Name each of the more complex shapes.

2. What is Area?
Access the Standard Deviants School Geometry: Figuring Out Area, Segment 3 "Area of Combined Shapes & Review" video through EdVideo Online at http://www.thirteen.org/edonline/edvideo/index.html. Once downloaded, FAST FORWARD the video to the image of a young woman explaining the "Area of Polygons" (you will see a chalkboard in the background with white text; time = 2:55). PLAY the video which reviews ways to calculate the area of a square (time = 2:55-3:05), a rectangle (time = 3:06-3:08), a triangle (time = 3:09-3:10), a trapezoid (time = 3:11-3:16) and a circle (time = 3:17-3:22). Record the formulas necessary to calculate area for each of the figures.

Area of a square = s2 where s= the measure of the sides
Area of a rectangle = bh where b = the measure of the base and h= the measure of the height
Area of a triangle = 1/2 bh *Note: A right triangle is basically a square or rectangle divided in half.
Area of a trapezoid = 1/2(b1 + b2)h
Area of a circle = r2 where r = radius of the circle and is approximately equal to 3.14

Log onto the Area Explained Web site at http://www.mathleague.com/help/geometry/area.htm. For each of the shapes, make sure that you can follow the steps used to calculate area and perimeter. If necessary, take notes in a notebook or on a separate sheet of paper. The same formulas are available on the STANDARD DEVIANTS GEOMETRY 2 NOTE CARD HANDOUT.

Go to the Math Playground Web site at http://www.mathplayground.com/geometryMovie.html. Calculate the area and perimeter of at least four rectangles. Once you are satisfied that you have mastered these calculations, you are ready to consider more challenging questions.

3. How do you find the area of combined (compound) shapes? Look at the figures shown below.

A trapezoid may be conceptualized simply as a rectangle with two right triangles on the sides. The area of many combined shapes like those identified in the IT'S HIP TO BE SQUARE HANDOUT can be calculated simply by breaking the complex figures into smaller parts. PLAY the video segment used to answer "Introductory Activity Question 2: What is area?" from the beginning. The narrator explains how the shape of a typical mailbox found in the United States looks like the combination of a rectangle and a semicircle. Watch the segment to review strategies that can be used to calculate area of such figures.

Learning Activities:
Apply principles of geometry to other types of math problems

Try to solve the problem on the NCTM Weekly Problem Web site (http://www.nctm.org/high/asolutions.asp?ID=216). In the problem a rectangle inscribed within a quarter circle. Use your knowledge of the area of a circle and the area of a rectangle to finish the problem. Since you only have ¼ of the full circle, the shaded region is represented by the difference of the ¼-circle area and the rectangle. If you are stumped, the site provides a detailed explanation of the problem.

2. GED Practice
http://researchreply.inquisiteasp.com/cgi-bin/qWeb corporate.dll?PCMF7J Several good examples of questions on the GED Math test are available on this site. Complete the questions and get a summary of your performance. As you learn more about geometry, you should be able to complete all of the problems in the set. There are a few simple rules to remember: All of the interior angles of a triangle must add to 180 degrees and those of a circle, a square or rectangle will add to 360 degrees. These two facts will get you well on your way to answering the questions if you remember that in most regular shapes, you can find either a square, rectangle, triangle or circle hidden within its area.

Culminating Activities:
Identify geometry in art and culture

1. Islamic Art: Tiling and Geometric Patterns
Print out pages 22 and 24 of the GEOMETRIC PATTERNS HANDOUT (Available online at http://www.projects.ex.ac.uk/trol/trol/trolna.pdf). How do these patterns compare geometrically? (Answer: The patterns shown on page 22 radiate from the center of circles and polygons, while the patterns shown on page 24, commonly called knot patterns, are based on grids.)

Log onto the Islamic Art Web site at http://www.maths2art.co.uk/islamicart.htm to examine patterns common in Islamic art forms. Click on the link to "Area and Perimeter" to get additional practice calculating these properties of two-dimensional shapes. Click on the "Construction" link to practice drawing some of these patterns on your own using GRAPH PAPER, a ruler and a compass.

2. Quilting: World influences and American traditions
Log onto Quilted Math at http://www.riverdeep.net/current/2001/11/112601_quiltedmath.jhtml. Look at the intricate "Heart and Gizzards" pattern; try to answer some of the questions provided on the site. An interesting problem is posed under the "Irish Chain Pattern": If the dimensions of this quilt are 60 in x 72 in, and 60 equal blocks were used to make the quilt, what were the dimensions of each block? (Answer: 1 in. x 1.2 in; Divide 60 in. by 60, and 72 in. by 60).

What is the area of a quilt with these dimensions? (Answer 4320 in2; Multiply 60 in. by 72 in.)

3. Geometric Patterns: Create your own virtual quilt
For those of us who like the idea of creating a virtual quilt, log onto the Anna Grossnickle Hines Quilting Page at http://www.aghines.com/Quilt/interactive/grid/grid.htm. Try making different designs using the various colored triangles-recreate the virtual quilt on GRAPH PAPER. If you are up to the challenge, create an actual quilt square out of fabric shapes.

Extension Activities:
Make more life connections between math, art and culture

Art
Identify various shapes in buildings by exploring images available online at sites like http://stockphotography.smugmug.com/gallery/710985/1/31039469; you could also try a more specific math connection using tangrams.

Check out the tangram exercises available at http://www.projects.ex.ac.uk/trol/trol/trolxk.pdf to see how fast you can create the various figures using different parallelograms.

Community Connection
World Aids Day is Friday, December 1st. Gather a group of friends or family and commit to each creating at least one square for an AIDS memorial quilt. Combine your pieces with squares of other members of your community and donate your shapes or your quilt to a quilting group working on a larger project or an organization sponsoring programs to raise funds and awareness of the worldwide AIDS crisis.

Home Construction
Homeowners and homebuyers sometimes have questions about the square footage (area) of their property. In most cases, homes and construction lots are not perfectly rectangular or triangular (1/2 of a quadrilateral); because of this, the calculations are much more involved than simply adding the areas of various familiar shapes. In this lesson, we used triangles and quadrilaterals that all had 90 degree angles. In real life, that is most often not the case. Check out the Math Forum's (http://mathforum.org/library/drmath/sets/select/dm_area_irreg.html) responses to several real-life questions involving area and perimeter of some "not so regular" spaces. For a less complicated (more interactive) view of the same kind of activity, complete the "Plot Plans & Silhouettes" activities available through Annenberg/CPB Math and Science Project at http://www.learner.org/teacherslab/math/geometry/space/plotplan/index.html.

Math
For more practice with trapezoids, visit the Open Reference Web site at http://www.mathopenref.com/trapezoidarea.html. Visit the Illuminations Web sites (For circles http://illuminations.nctm.org/ActivityDetail.aspx?ID=87 and for angle sums http://illuminations.nctm.org/ActivityDetail.aspx?ID=9) to learn more about circumference and interior angle sums of various regular and irregular polygons.

Math Education
Math concepts can often be traced to cultural roots. Did you know African cornrow curves are related to fractal geometry and that graffiti art is often reproduced using principles of coordinate geometry? Teaching math through culture is just one way of potentially meeting the needs of a multicultural, multiethnic, multilingual society. Visit any of the Web sites linked on the Culturally situated design tools Web site at http://www.rpi.edu/~eglash/csdt.html to find new ways of engaging students using the texts of the real world.

Social Studies
Islam originated in the 7th century in the Middle East (http://worldatlas.com/Web image/countrys/me.htm). Islamic art and architecture has been influential in Europe, Asia and the United States for hundreds of years. Visit the Antiques Roadshow "Tips of the Trade" Web site (http://www.pbs.org/wgbh/pages/roadshow/tips/tiles/tiles.html) to learn about the global influence of Islamic tiles.