Program Background
Cypress Hills Program Features
Program Model: 50/50
Languages: Spanish and English
Language of Initial Literacy Instruction: All students are taught in the partner language and English simultaneously
Student Background Within the Dual Language Program
Linguistic Profile: Of 246 students enrolled in 2004, roughly one third spoke predominantly English at home, one third spoke predominantly Spanish, and one third spoke both languages.
Ethnic Profile: Most students (71%) are Latino, with families from the Dominican Republic, Puerto Rico, Mexico, Ecuador, El Salvador, Honduras, Colombia, and other Latin American and Caribbean countries. African American students, many with family ties to the English-speaking Caribbean, account for 27% of the student body. Asian and White students make up the remaining 2%.
Percent of students in the program qualifying for free/reduced price lunch: 85.4%
Unit Plan
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
- Goal 2: To use English to achieve academically in the content areas
Standard 1: Students will use English to interact in the classroom
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.
Lesson Plan
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 develop mathematical arguments about geometric relationships.
- 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
Teachers of English to Speakers of Other Languages, ESL Standards for Pre-K Students
- Goal 2: To use English to achieve academically in the content areas
Standard 1: Students will use English to interact in the classroom
Guiding Questions
- What are Tangrams?
- What are the geometric relationships among common shapes?
- What happens when shapes are flipped, slid, or rotated a shape?
- What designs can be made using only the shapes of the Tangram?
Motivation (15-20 minutes)
Whole Group Activity
Read aloud Grandfather Tang’s Story: A Tale Told with Tangrams. Discuss the 7 pieces of the Tangram introduced in the story and point out their origins in China. Preview the idea that a wide variety of animals and figures can be made with the Tans.
Assessment
Observe students as they work in pairs to complete their designs. Are they able to work together using precise mathematical language?
Examine finished sets for accuracy. 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 students give each other instructions using precise mathematical language? Do students work together using the appropriate content and functional language structures to guide their interactions and complete their activity?
Extension
The unit on Tangrams can be the basis for future activities in math, art, and writing. Students can write a story similar to Grandfather Tang’s Story that uses Tangram designs as illustrations or use Tangram figures to complete mathematical problems, such as finding the area of a square or other geometrical shape. Students can work on Tangram puzzles during center time, recreating designs from books or creating their own designs and recording them on paper.
Objectives
Content Area Skills and Concepts
- Name and classify Tangram shapes
- Learn how shapes can be manipulated by flipping, sliding, and rotating them, and how they can be combined to create new shapes or designs
Language Skills
Math Vocabulary
- Tangram/ Tan (each of the 7 individual pieces)
- Square
- Flip, slide, rotate
- Small, medium, large
- Fold, cut
- Congruent
- Similar
Listening
- Comprehending oral instructions
Speaking
- Giving precise instructions using command form verbs and providing clarification as needed.
Examples:
“Pick up the small/medium/large _______.”
“Put the small/medium/large ________ next to/below/above the_____.”
“Rotate the small/medium/large _______ clockwise/counterclockwise.”
- Requesting clarification
Examples:
“Could you repeat that, please?”
“Where should I put the ______?”
Thinking/Study Skills
- Following oral instructions
Materials/Resources
- Copy of Grandfather Tang’s Story: A Tale Told with Tangrams.
- Magnetic set of Tangrams or prearranged sets of Tangrams to demonstrate the transformations at the heart of Grandfather Tang’s Story
- Teacher-made recording of oral instructions on how to make a Tangram from card stock cut into 6” squares
Teaching/Learning Activities (30-45 minutes)
Whole Group Activity
Demonstrate how the 7 Tangram Tans can be flipped, rotated, and rearranged to produce different designs, referring to Grandfather Tang’s Story.
Use overhead, poster, or magnetic Tangram pieces to identify and label all 7 Tangram pieces. Briefly discuss the fact that some of the pieces are the same size (congruent) and some are the same shape but not the same size (similar).
Pair Activity
Pair students with their math partners and distribute Tangram kits and a template with the outline of a design that the students will make. Students work in pairs to use the Tans to complete the design. Students should be encouraged to use the precise math vocabulary and language structures noted above. Teacher will circulate providing hints as needed.
Whole Group Activity
Meet back as a whole class to have students share their experiences in creating their designs, review the names of the seven Tans, review the concepts of similar and congruent, and set the stage for the subsequent lessons which will focus on more complex designs.
Teaching the Lesson
This unit on Tangram geometry was originally created as an extension of a 2-D geometry unit in Everyday Math and as part of an ongoing social studies unit on Asia. It also has ties to visual arts and language arts. The book Grandfather Tang’s Story: A Tale Told with Tangrams introduces the interdisciplinary unit. It is an engaging tale of friendly competition that encourages students to make predictions. It introduces the 7 pieces of the Tangram, addresses their origins in China, and most importantly, shows a wide variety of animals and figures that can be made with the Tans. This last aspect of the book is particularly important when working with second language learners, because it provides a visual preview for the activity that will follow. This book is especially useful as motivation for the lesson by bringing together the artistic expression demonstrated in the illustrations, the use of Tangrams as a basis for writing, and the explicit connections made between Tangram geometry and Chinese culture.
Trying to make basic shapes or copy Tangram designs without a model that shows how to arrange pieces is frustrating. Students may not remember to rotate or flip shapes. There are many things that the teacher can do to help reduce the cognitive demands of this task. First, by preparing different versions of the same outline with varying numbers of clues, the teacher will be able to help students achieve the content objectives. Second, by providing students with the vocabulary and the language structures that go with them, and by modeling the use of these language forms, the teacher will help ensure that the students meet the language objectives for the lesson. These types of visual and linguistic scaffolds are particularly essential in TWI classrooms because of the varying levels of language proficiency in the class.