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Exploring Geometry with Tangrams
Subject Area:
Math
Grade Level(s):
7
Duration of Activity:
5-8 class periods
Description of Activity:
Students will explore properties and relationships of geometric shapes through the use of tangrams.
Objectives: Students will
- identify and classify polygons by properties and relationships.
- create an example of symmetry using tangram pieces.
- list properties and give examples of similar and congruent polygons.
- find the area and perimeter of polygons.
- perform transformations on geometric figures.
- use the World Wide Web to investigate tangrams.
- create a Microsoft PowerPoint presentation as a terminal project to demonstrate understanding of the geometry objectives listed above.
Materials/Equipment:
- Grandfather Tang’s Story by Ann Tompert [ISBN 0-517-57487-X]
- Construction paper cut in 4-inch squares
- Scissors
- Computers with Internet access
- Microsoft PowerPoint or other presentation software
- Diskettes containing tangram template
- Handout 1: Tangram Pattern
- Handout 2: Directions for Folding and Cutting a Tangram
- Handout 3: Discussion—Exploring Geometric Shapes (handout for teachers’ use)
- Handout 4: Discovering Attributes of Polygons
- Handout 5: Exploring Congruence, Similarity, Symmetry, and Reflection of Polygons
- Handout 6: Area of Tangrams
- Handout 7: Directions and Rubric for Tangram Presentation
- Handout 8: Grandfather Tang’s Story Microsoft PowerPoint Presentation (for teachers’ use)
Prerequisites (skills or background needed):
- Basic word-processing skills and use of features such as drag and drop and copy and paste
- Basic knowledge of creating a slide in Microsoft PowerPoint
Procedure
Teacher Component: The teacher will
- read Grandfather Tang’s Story to students while they view Handout 8: Grandfather Tang’s Story Microsoft PowerPoint Presentation. Please note that this presentation was created using Microsoft Office XP. If other versions of the software are used, the presentation will have to be modified. Some animation features will not be available in Microsoft Office 2000 or earlier versions.
- guide students in the creation of their own set of tangram pieces by giving verbal directions to accompany the written and graphic directions described on Tom Scavo’s Web site, A Math Forum Web Unit: Constructing Your Own Set of Tangrams/ http://mathforum.org/trscavo/tangrams/construct.html. Use Handouts 2 and 3 for this part of the lesson.
Handout 2: Directions for Folding and Cutting a Tangram contains the verbal directions for this activity. As students fold and cut their tangrams, teacher and students will discuss the polygons formed and their attributes.
Handout 3: Discussion—Exploring Geometric Shapes contains specific questions for students and teachers to discuss.
- distribute construction paper, scissors, and Handout 4: Discovering Attributes of Polygons, Handout 5: Exploring Congruence, Similarity, Symmetry, and Reflection of Polygons, and Handout 6: Area of Tangrams
- guide students in the creation of their Microsoft PowerPoint presentations.
Student Activities: The student will
- listen as the teacher reads Grandfather Tang’s Story.
- create a set of tangram pieces by following the directions on Constructing Your Own Set of Tangrams / http://mathforum.org/trscavo/tangrams/construct.html or from the directions in Handout 2: Directions for Folding and Cutting a Tangram.
- participate in the class discussion of the polygons formed using Handout 3: Discussion—Exploring Geometric Shapes.
- complete Handout 4: Discovering Attributes of Polygons, Handout 5: Exploring Congruence, Similarity, Symmetry, and Reflection of Polygons, and Handout 6: Area of Tangrams using the tangram template and/or the student’s own tangram to manipulate and explore the tangram polygons in order to discover attributes, symmetry, similarity, area, and perimeter of those polygons.
- create a Microsoft PowerPoint presentation to illustrate and explain polygons and their attributes, symmetry, similar polygons, congruent polygons, area and perimeter.
Accommodations:
- An overhead projector could be used to show tile arrangements used in the story.
- Tangram pieces can be made larger or of materials such as plastic, felt, and so forth for easier use by students with special needs.
Extension Activities:
Integration:
- Career Discovery: As part of the child care unit, students will read Grandfather Tang’s Story, including some of the class additions, to a group of pre-school children.
- Social Studies: Students may include the information they gathered about the history of tangrams in reports and projects about China.
- Language Arts: Language Arts and Math teachers may team to complete the writing activity.
Assessments:
- Student presentations will be assessed using Handout 7: Project Description and Rubric for Final Assessment Project.
URLs:
Curriculum Frameworks
Mississippi:
Seventh Grade
- Use concepts of geometry in angles and polygons and extend the concepts of perimeter and area. (P, G, M, N)
- Identify polygons to twelve sides.
- Classify and compare the properties of quadrilaterals.
- Classify triangles by sides and angles.
- Identify congruent segments, angles, and polygons.
- Perform transformations (rotations, reflections, translations) on plane figures using physical models.
- Investigate symmetry of polygons.
National Educational Technology Standards (NETS):
- Apply productivity/multimedia tools and peripherals to support personal productivity, group collaboration, and learning throughout the curriculum. (3, 6)
- Design, develop, publish, and present products (e.g., Web pages, videotapes) using technology resources that demonstrate and communicate curriculum concepts to audiences inside and outside the classroom. (4, 5, 6)
- Select and use appropriate tools and technology resources to accomplish a variety of tasks and solve problems. (5, 6)
TerraNova:
13 Measurement (Level 10-21/22)
Demonstrate an understanding of measurement systems, units, and tools by describing, calculating, or estimating size, location, and time; by using the concepts of perimeter, area, volume, capacity, weight, and mass; and by identifying appropriate degrees of accuracy.
Solve problems involving principles of measurement, rate, and scale.
Use manipulatives to explore shapes, area, and perimeter; and to model and represent measurement problems.
Describe measurement processes, compare techniques, estimate, and communicate estimation strategies.
14 Geometry and Spatial Sense (Level 10-21/22)
Demonstrate spatial sense and an understanding of geometry by visualizing and identifying two- and three-dimensional objects, classifying shapes, recognizing symmetry, using transformations, applying geometric formulas, and evaluating properties of geometric figures.
Use manipulative shapes to explore spatial relationships, patterns, and model geometric problems.
Link and Feedback to Author(s):
Sarah Fleeman, South Delta Middle School, Anguilla, MS
fleeman@dixieconnect.com
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