Project Title: Real World Geometry
The following is our "Cliff Note" version of the full project, meant to provide you with a quick overview of its main features and the standards and content it covers. The complete project specs and related resources are available at these websites:
http://stleos.pvt.k12.ca.us/StLeosSite/classes/Seventh/
PROJECT/geoindex.html
Created by: Thomas Pulchny, St. Leo the Great School, San Jose, CA
Grade Level: 7th Mathematics
Time Frame: 4 months
Description of Project:
- What geometric concepts are involved in the construction of angles, polygons, transformations, and bisectors?
- How is geometry used in the real world?
Content Areas
- mathematics (geometry concepts, use of formulas)
- language arts (expository writing, journal writing, oral presentation)
- social studies (research, history)
- technology
- art and design (shape, texture, line)
Goals
- Students will recognize and appreciate the many applications of geometry in the multicultural world around them.
- Students will view computer/information systems literacy and Internet/World Wide Web access as effective learning and research tools.
- Students will appreciate the colorful history of geometry
- Students will be able to collaborate effectively in small groups.
- Students will demonstrate understanding of geometric concepts and formulas
- To address a variety of learning styles (visual, tactile, auditory, kinesthetic) through geometry and multimedia use.
- To offer students real-world presentation experience.
- To enable students to effectively communicate essential aspects of ideas in a variety of modalities.
- To allow students to understand the importance of geometry in art design.
The Task:
Students in grade seven participated in collaborative teams that will enable them to an appreciation for the innumerable applications of geometry in the world around them. They gained an understanding of the history of geometry and came to appreciate the many professionals who employ geometry in their daily work. In cooperative groups researched one or more geometry topics and concepts and presented their ideas in a multimedia presentation . This unit is also being adapted for the fifth grade level by Diane Fahrner from St. Raymond's School in Menlo Park, California.
Big Ideas/Essential Learnings:
The project connected to the community and world of work:
"Geometry is used in science, art, construction, architecture, gardening, and traffic signs. Geometry surrounds students everywhere. Artists, builders, designers, masons, machinists, structural engineers, and writers all use geometry on the job." (Chapin et. al. 1995) Students are created this project for the education of each other and other students in the school, as well as their parents and the Internet community. The students recognized that this project is a different way of investigating math: it is not just numbers and facts, it is visual and creative. It is hoped that students developed an interest in professions which use geometry, such as landscape architecture, architecture, graphic design and others."
Assessment:
Geometry unit pre-testadministered during the first week and a post-test administered at the culmination of the unit
- Real World Geometry Project Evaluation Rubric
- Interactive geometry journal and journal assessment rubric.
- Teacher observation of students
- Ongoing reflection by teacher in a journal.
- Students will describe how teamwork was useful to the completion of this project.
- Students will describe how this project might have been different if completed independently.
- Each team's progress will be chronicled through the use of video, pictures, and rubrics.
- Completion of geometry learning activity to be shared with other teams
- Completion of a geometry art assignment
- Group and individual self assessment with the use of rubrics
- Each team will compose at least ten "Geoprady" questions for a class quiz game
- Geometry Quiz games
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Content/Standards
CA Content Standards Geometry and Measurement 2. Students compute the perimeter, area and volume of common geometric objects and use these to find measures of less common objects; they know how perimeter, area, and volume are affected under changes of scale. 2.1 routinely use formulas for finding the perimeter and areas of basic two-dimensional figures and for the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and circular cylinders 2.2 estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking them up into more basic geometric objects 2.3 compute the length of the perimeter, the surface area of the faces, and the volume of a 3-D object built from rectangular solids. They understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor 2.4 relate the changes in measurement under change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 12 square inches, 1 cubic inch = 2.54 cubic centimeters) 3. Students know the Pythagorean Theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures. 3.1 identify and construct basic elements of geometric figures, (e.g., altitudes, midpoints, diagonals, angle bisectors and perpendicular bisectors; and central angles, radii, diameters and chords of circles) using compass and straight-edge 3.2 understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections 3.3 know and understand the Pythagorean Theorem and use it to find the length of the missing side of a right triangle and lengths of other line segments, and, in some situations, empirically verify the Pythagorean Theorem by direct measurement 3.4 demonstrate an understanding of when two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures 3.5 construct two-dimensional patterns for three-dimensional models such as cylinders, prisms and cones 3.6 identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and how two or more objects are related in space (e.g., skew lines, the possible ways three planes could intersect)
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