Tangram Geometry
Michael Ilan Loeb, PS 89—The Cypress Hills Community School
| Grade: Third Content Area: Math
Time Frame of Unit: Five 1-hour lessons
Language(s) of Lessons: English
Unit Theme: Using the Chinese Tangram to deepen basic geometric
understandings
|
Standards to Be Addressed
National Council of Teachers of Mathematics Grade 3-5 Geometry
Standard
Analyzing characteristics and properties of two- and three-dimensional
geometric shapes and developing mathematical arguments about geometric
relationships.
- Students will demonstrate knowledge of how to classify two-
and three-dimensional shapes according to their properties and develop
definitions of classes of shapes such as triangles and pyramids.
- Students
will demonstrate knowledge of how to investigate, describe, and reason about
the results of subdividing, combining, and transforming shapes.
- Students
will explore congruence and similarity.
Applying transformations and using symmetry to analyze mathematical
situations.
- Students will demonstrate knowledge of how to predict and
describe the results of sliding, flipping, and turning two-dimensional
shapes
Using visualization, spatial reasoning, and geometric modeling to solve
problems.
- Students will demonstrate knowledge of how to build and draw
geometric objects and create and describe mental images of objects,
patterns, and paths
National Council of Teachers of English and the International Reading
Association Standards for the English Language Arts
- Standard 4: Students adjust their use of spoken, written, and visual
language (e.g., conventions, style, vocabulary) to communicate effectively
with a variety of audiences and for different purposes.
- Standard 12: Students use spoken, written, and visual language to
accomplish their own purposes (e.g., for learning, enjoyment, persuasion,
and the exchange of information).
Teachers of English to Speakers of Other Languages, ESL Standards for
Pre-K Students
Guiding Questions
- What are Tangrams?
- What are the geometric relationships among common shapes?
- What happens when shapes are flipped, slid, or rotated?
- What designs can be made using only the shapes of the Tangram?
- What kinds of new shapes can be formed by combining several Tangram shapes?
Big Ideas
- Listening closely is essential for following directions
- Shapes can be manipulated or transformed by flipping, sliding, or rotating
- Tangram pieces can be combined to create standard geometrical shapes or artistic
designs
- Geometric understanding is important for artistic expression
Background/Prior Knowledge to be Activated in the Unit
- Familiarity with basic polygons—isosceles triangle, square, parallelogram,
trapezoid
- Using visual information and manipulatives for mathematical problem-solving
- Following oral instructions to manipulate shapes
- Knowledge of Chinese culture and traditions
Objectives
Content Area Skills and Concepts
- Name and classify Tangram shapes
- Develop geometric understanding of shapes, angles, congruence, and
similarity
- Combine Tangram pieces to create new shapes
- Reproduce Tangram designs from drawings
- Create drawing from Tangram designs
- Learn how shapes can be manipulated by flipping, sliding, and rotating them
Language Skills
Vocabulary Related to Study Unit
- Tangram/Tan
- Triangle, square, rectangle, parallelogram, trapezoid
- Right angle
- Flip, slide, rotate
- Small, medium, large
- Fold, cut
- Pattern
- Clockwise, counterclockwise
- Congruent, similar
Listening
- Comprehending oral instructions
- Asking and answering questions
- Requesting information and assistance
Speaking
- Giving precise instructions using command form verbs and providing
clarification as needed
- Requesting clarification
- Participating in full class, group, and pair discussions
Teaching/Learning Activities
- Become familiar with Chinese Tangram pieces and puzzles by participating
in an interactive read aloud of Grandfather Tang’s Story.
- Make a 7-piece Tangram Set by following oral instructions.
- Reproduce and color Tangram designs of familiar figures and objects
using all 7 pieces by following solutions provided by teacher.
- Find and draw solutions for making a square, triangle, parallelogram,
rectangle, and trapezoid using 2, 3, 5, and all 7 Tangram pieces
- Create original artistic shapes using Tangram pieces
Materials/Resources
- Burns, M. (2000). About teaching mathematics: A K-8 resource. Sausalito:
Math Solutions.
- Tompert, A. (1990). Grandfather Tang’s Story: A Tale Told with Tangrams.
New York: Crown Publishers.
- Changram: Chinese Tangram Puzzle Game (magnetic pieces and game board
with 21 pages of suggested designs and solutions). Available from Selchow
and Righter.
- 6” card stock squares
- Plastic Tangrams Sets (one set for each student or for each partnership)
Assessment
Observe students as they cut Tangrams. Are they able to understand the instructions? Are they able to fold and cut with precision? Can they recover if they have missed a step, or do they become frustrated?
Examine finished sets for accuracy. Ensure that all 7 pieces have been created and that no edges were cut off.
Circulate while students work on shapes, paying close attention to the ability of individual students to flip, slide, and rotate pieces to make shapes. When they are stuck, can they follow peer instructions? Do they give instructions using precise mathematical language?
When working with and without a solution in front of them, can students mentally perform the rotations and flips necessary to recreate a design or must they physically move the Tans? Do they recognize shapes that merely need to be rotated or flipped? Can they recall previous solution strategies they have employed?
Save completed Tangram shapes
graphic organizer and student Tangram art for classroom display and inclusion in math portfolios.