4th Grade Unit: A Tale Told with Tangrams
by Zania

RATIONALE

A Tale Told with Tangrams is a unit created for a fourth grade mathematics classroom, with the purpose of working across content areas. This unit combines math with language arts and technology, demonstrating how language arts and technology can be used to enhance a math curriculum. This unit lasts for fiftteen days and is designed based on an eighty minute block for math. During the course of this unit students will combine their knowledge of geometry and narrative writing to create a stop motion animation video.

The unit is based on the book, Grandfather Tang’s Story: A Tale Told with Tangrams by Ann Tompert. In the story, Grandfather Tang tells his granddaughter about two shape shifting fox fairies whose friendly game leads to severe consequences. Tangrams are used in the telling of the story. The storyteller arranges the tans to show the shape of the character or object represented in the story.

A tangram is a Chinese puzzle that begins as a square, which is then divided into seven standard geometric figures: five right triangles, one square, and one parallelogram, of different sizes. Each piece is called a tan. All seven of the tans must be used when creating a figure. They can touch but not overlap. The mathematical purpose of this lesson is for students to (a) become familiar with geometric shapes, (b) learn how to create Power Polygons, the combination of more than on polygon (c) learn and apply slides, turns, and flips. Since tangrams are geometric figures that have to be manipulated with slides, turns, and flips to create characters that are power polygons, they are the perfect fit for a geometry unit. The ability to take tangrams and use them to create a digital narrative using stop motion animation, allow students to “build on the foundation of traditional literacy, research skills, technical skills, and critical-analysis taught in the classroom” (Jenkins, 2009, p.29). Stop motion animation makes it possible for students to both manipulate figures into motion and then see the figures in motion once the video is complete.

Stop motion animation requires the producer to manipulate a model to “create an illusion of movement when the film is shown in sequence” (Knobel& Lankshear, Eds., 2010, p.161). In geometry students build visual and spatial skills as they investigate shape, size, relative position of figures and the properties of space. Figures are moved with a slide, turn, or flip. These visual and spatial skills that students build within a geometry unit enables them to embark on the task of creating a stop motion animation video.

Stop motion animation is a form of story-telling. Knobel and Lankshear (2010) state that “creating a narrative, developing characters, and finding visual aesthetic in which to place them are essential and central values at the art of all filmmaking” (p.162). Using digital story telling in a geometry unit “provides students the opportunities for them to be apprenticed in the kind of high-end digital multimedia authoring skills which would serve them well for the future” (p.180).

During this unit, students are allowed to work in groups. Through class and group discussions, posting helpful links to the class wiki, and giving movie reviews of their classmates finished project, students can draw on different sets of expertise and collaborate to solve problems (Jenkins, 2009). According to Jenkins (2009) “children often feel locked out of the worlds described in their textbooks through the depersonalized and abstract prose used to describe them (p.38). This unit tries to prevent that feeling by taking a geometry unit that students have to learn (Figures in Motion) and turning it into an engaging one that gives students ownership of learning, identifying and applying of that skill.

The student has to move the tans with a slide, turn, or flip. The student has to create super polygons in order to make the tangrams into a figure. The student has to create a narrative using the tangram figures. And the student has to move each tan in order to create the stop motion animation video. Jenkins acknowledged that “educators have always known that students learn more through direct observation and experimentation than from reading about something in a textbook or listening to a lecture” (p.42). Therefore what better way for students to learn about figures in motion than through stop motion animation.


At the end of this unit, students will have an understanding of how to move figures, create tangram characters, build their spatial memory and visualization skills, and create a stop motion animation video.

Below follows the unit detailing how students can accomplish all of these objectives.

STANDARDS

Geometry 4.G
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.


Language Arts:
Reading Standards for Literature K-5: Integration of Knowledge and Ideas

7. Make connections between the text of a story or drama and a visual or oral presentation of the text, identifying where each version reflects specific descriptions and directions in the text
Reading Standards for Informal Text K-5: Integration of Knowledge and Ideas

7. Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears.
Writing Standards K-5

3. Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.
  1. Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally.
  2. Use dialogue and description to develop experiences and events or show the responses of characters to situations.
  3. Use a variety of transitional words and phrases to manage the sequence of events.
  4. Use concrete words and phrases and sensory details to convey experiences and events precisely.
  5. Provide a conclusion that follows from the narrated experiences or events.

6. With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting.
Language Standards K-5

3. Use knowledge of language and its conventions when writing, speaking, reading, or listening.
a. Choose words and phrases to convey ideas precisely.*
b. Choose punctuation for effect.*
c. Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion).


PREREQUISITE KNOWLEDGE
Prior to this lesson, students have (a) used wiki pages (b) used iMovie to make videos from flip camera footage and photos (c) learned the geometric names of polygons with 3-12 sides (d) used Power Polygons

KEYWORDS
Grandfather Tang’s Story, stop motion animation, Tangrams, flip, slide, turn, Power Polygon, characters, setting, plot, solution

GOALS
Classroom:
  1. Students will be able to understand how tangram story telling can be used to demonstrate and understand figures in motion.
  2. Students will be able to understand that sliding, turning, and flipping an object repeatedly can create continuous motion as demonstrated in the creation of their stop motion animation videos.
Beyond the Classroom
  1. I want students to develop a “passion for being imaginative, creative, and expressing their identities—even changing their identities—through finding new ways to create and share their [work] within supportive communities of learners” (Knobel & Lankshear, Eds., 2010, p.180)
OBJECTIVES
Math:
  • Students will be able to identify the polygons within the tangram and use them to create Power Polygons
  • Students will be able to apply flips (reflections), slides (translations), and/or turns (rotations) to each tan in order to create a tangram figure.
  • Students will be able to use spatial memory and spatial visualization skills in order to solve tangram puzzles and create the movement in their video.
Language Arts
  • Collaborate in groups on specific artistic elements to develop a stop animation video using tangrams.
  • Create an original tangram stop animation video that will demonstrate figures in motion via slide, turn, or flip, and include the narrative story elements of characters, setting, plot, and solution.
  • Evaluate and provide feedback on video production.

UNIT DESCRIPTION
This project allows students to combine language arts, math and technology. Students learn and apply how to put geometric figures in motion by sliding, turning, and flipping tans to create tangram figures. Each tan slide, turn, and flip is captured with a digital camera. Then the images are uploaded in sequence to iMovie to create a stop motion animation video. The video also needs to incorporate the four basic elements of a written narrative, characters, setting, plot, solution, but represented visually.
In this unit students will be read the story Grandfather Tang’s Story: A Tale Told with Tangrams and will engage in several activities. First students will slide, turn, and flip their tans both physically and digitally to create tangram images. They will also view and discuss stop animation videos created with the manipulation of tangrams. Students will learn how to make a stop motion video using iMovie and work cooperatively in groups to create an original stop motion video using tangrams. Students will blog about their process, post information/questions/comments to the class wiki, and present their final videos to their peers. After videos are viewed, students will post constructive comments about two other groups videos on the class wiki.
TECHNOLOGY
  • internet
  • wiki
  • digital camera
  • computer (Mac)
  • video editing software (iMovie)

MATERIALS

  • Set of large Tangrams (magnetic tangrams are best for board modeling)
  • Class set of tangrams
  • Grandfather Tang’s Story: A Tale Told with Tangrams by Ann Tompert
  • Teacher created sample of stop animation based on a segment of Tompert’s book
  • Story board planner

SUPPLEMENTARY RESOURCES

Tangram Websites:
National Library of Virtual Manipulatives: Interactive Tangram Puzzles
PBS Kids game: Cyberchase and Sagwa
Digital Tangram Video

Stop Animation Tutorial Video:
How To Video

Sample Tangram Stop Animation Videos:
Tangram Love
Tangram

Books
Grandfather Tang’s Story: A Tale Told with Tangrams by Ann Tompert
Tangram Magician by Lisa Campbell Ernst
The Tangram ABC Book by T. Foster
Then and Now on Old MacDonald's Farm by T. Foster

ACTIVITIES
Days 1-2
Display a set of magnetic tangrams for students to view on the board. Ask students if they can name the polygons, using their geometric name (five right triangles, one square, and one parallelogram). Then arrange tangrams into an animal and ask students what they think the figure represents. Explain to students that this set of polygons is called a tangram. Each shape is called a tan. A tangram is made up of seven tans. Inform them that you will be reading them a story called Grandfather Tang’s Story by Ann Tompert. During the reading of the story, teacher arranges the tans to show the shape of the characters. Lead students in a discussion of how the actual changing of the tangrams influenced how they received the story and if it changed their level of engagement. Then show the digital story of Grandfather Tang’s Story by Ann Tompert that you created. (The sample video came be a scene taken from the book and not the entire book.) Divide students into groups of four or five to compare the reading of the story and the manual changing of the tangrams with the digital story. Have students share their groups' views with the whole class.

Explain to students that the video you created was made using stop motion animation and that stop motion animation is a two step process. First, it requires the producer to take a series of still images of an object as it is moved, with a slide, turn, or flip, in small increments. Then those images are then placed in sequential order and played as a film, creating the illusion that the object is moving on its own.

Next, play the You Tube movie Tangram Love by Laura Ferla and Liakatas Dimitrios to show an example of a stop motion animation tangram story that does not include dialogue or text. Ask students to discuss in groups if they could identify the characters, setting, plot, and a solution within the video. Have students share their ideas with the whole class as the teacher records responses on the board.

Sample student answers: The setting is outside because I see a tree, grass, and a rock. The characters are a boy and a girl. The plot is that the boy likes the girl and he is waiting for her to come and doesn’t know if she is going to show up. At the end of the story the girl shows up and they hug and kiss.

Have students explain how the authors of the video were able to create the four elements of a story (characters, setting, plot, solution) without using dialogue. Define how figures are put in to motion: slide/translation (moves a figure in a straight direction), flip/reflection (gives the mirror image of a figure) and turn/rotation (moves a figure about a point). Demonstrate each motion using a tan. Replay segments of the video pausing it at different intervals as the tans change or move. Have students identify how the authors of the video put the tans in motion (slide, flip, turn) in order to create movement. Explain to students that they are going to work in groups to create an original digital tangram story, like the sample videos, using stop motion animation. The stop motion animation will require students to create a narrative and put their tans in to motion using the three types of movements.
Day 3-4
On day three, review the definitions for slide/translation (moves a figure in a straight direction), flip/reflection (gives the mirror image of a figure) and turn/rotation (moves a figure about a point) collectively. Explain to students that in order to create tangram images they will need to utilize these three motions. Divide students into pairs to work on the computer. On the computer students will choose a link from the list of tangram interactive sites located on the class wiki site. These sites, such as National Library of Virtual Manipulatives (1999-2010), allow students to create tangram pictures by sliding, flipping, and turning each tan until all seven tans fit into the image outline. This is an engaging way to allow students to practice making tangram images reinforcing the three ways that figures can be put into motion. It also enables them to work on their spatial memory and visualization skills.

On day four, allow students to form into groups of four or five. Then pass out a set of tangrams and story board worksheets to each group. Replay and review the stop motion animation videos from days one and two to remind students how they can portray the elements of a narrative (characters, setting, plot, and solution) into a digital storyline. Groups are in charge of all creative decisions, including if they are going to use narration, text, music, and how they will relate their setting to the audience. Students will be able to browse websites, like to find tangram templates of animals and other figures that they can use in their stories as well as revisit the interactive tangram sites they used the day before for character ideas and formations.
Day 5
On day five, students will have the opportunity to play and get familiar with the technology that they will use to create their stop motion animation videos. First, students will watch a youtube tutorial on how to create a stop motion video using a camera and iMovie software. Next, students will take one of their tangram pieces and take pictures of it turning 360 degrees with their digital cameras or flipping or sliding it across the desk. Students will then practice importing, editing, and publishing their images following the directions given in the tutorial video.
Days 6-13
On days 6 through 9, students will work in groups, equipped with digital cameras, tangrams, computers and material to make any other props they need for their movie (construction paper, marker, crayons, etc). For example if the setting of the video is outside, students could take construction paper and draw trees, grass, flowers in the background. Then when the tangrams are laid on top of the paper it becomes the setting of the story.

Days 10 through 13 students should begin editing and polishing their videos if they have not already started. At this stage students should decide if they are adding a voice over, text narration, music, or a combination of all three. Videos should be between one to two minutes in length and portray characters, settings, plot, solution and demonstrate figures in motion.
Homework consists of students (a) adding links to the wiki that they find useful and interesting (b) blogging about the stop animation process (c) responding to student blogs (d) students working on whatever they need in preparation of the next day (e) commenting on students finished video on the wiki site “movie reviews”
Days 14-15
By day 14, students will upload their finished movie to the class wiki page. The teacher can showcase students’ videos at the “Tangram Film Festival.” The Tangram Film Festival can be held in the classroom or if possible in the media center or auditorium. The audience can consist of just the class or oher invited guests. During the festival each groups’ video is played in front of the audience.

Day 15: Students are required to post comments on the wiki for two other groups videos. Students will write about what they enjoyed most about the video, and what, if anything they would have liked to see more of in a specific video. They also need to identify a sequence of tan moves within at least one videos that demonstrates each types of motion: flip, slide, turn.


ACCOMMODATIONS
1. Second language learners are able to benefit greatly through the use of tangrams because they are a hands on activity. Students will be able to turn, slide, and flip objects physically and digitally. They will get to see how their small manipulations create larger movements when they complete their video.
2. For students that are struggling in math, class discussions, wiki links, group members, and teacher prompting can provide the support needed to reinforce the concepts taught. How to videos and sample projects can also help students who have difficulty grasping what the end result should look like.

APPENDIX

Name _ Date _
Story Board Planner: Use the lines provided to plan out the narrative part of your story and the open space to plan out your tangram formations.
_
_
_
_
_
_
_

_
_
_
_
_
_
_










ASSESSMENT

Approaches (1)
Meets (2)
Exceeds (3)
Common Core Standards
Vision and evidence
(The movement of the Tans have to be related to the content of the story. Tans should be manipulated using all three motions: slide, turn, flip.)
Tangrams were not used for the main characters. Tan movements where arbitrary in facilitating the movements of the character(s) in the story.
Tans were only moved by one motion.
Tangrams were used for the main characters and tan movements where deliberate and logical in facilitating the movements of the character(s) in the story. Tans were moved by two motions.
Tangrams were used for the main characters and tan movements where deliberate and logical in facilitating the movements of the character(s) in the story. Tans were moved by all three motions. The plot was unique and creative.
Language Arts Standard 7
Mathematics Standard 4.G
Group collaboration
(teacher can judge each student’s involvement through in class observations and discussions with group)
Most members of the group did not participate in the final project
Most/all members of the group did participate and contribute to the final project
All members of the group did participate and contribute to the final project. They created a group environment in which each member felt valued and everyone’s ideas were part of the final outcome.
Language Standard 3
Execution
(Manipulations of the tans via slide, turn, or flip have to be in small enough increments that when played in sequence it creates movement)
The movements of the tans captured on the still frames are not are not small enough to create the illusion that the pieces are moving in a continuous sequence. Movements appear to be disconnected.
The movements of the tans captured on the still frames create the illusion that the pieces are moving in a continuous sequence.
The movements of the tans captured on the still frames create the illusion that the pieces are moving in a continuous sequence. Tans appear to move on their own.
Language Arts Standard 7
Mathematics Standard 4.G
Narrative components
(characters, setting, plot, solution)
Out of the four narrative requirements, only 1-2 are demonstrated and the plot is unclear.
Out of the four narrative requirements, all 4 are demonstrated and the plot is clear.
Out of the four narrative requirements, all 4 are demonstrated. The plot is clear and complex.
Writing Standard 3

REFERENCES

Jenkins, H., with Purushotma, R., Clinton, K., Weigel, M., & Robison, A. (2009).Confronting the Challenges of Participatory Culture: Media Education for the 21stCentury. Occasional Paper. Boston, MA: MIT/MacArthur Foundation.

Knobel, M. and Lankshear, C. (eds.) (2010). DIY media: Sharing, creating and learningwith new media. New York: Peter Lang.

Shamburg, C. (2008). English Language Arts: Units for Grades 9-12. Washington, DC: International Society for Technology in Education.

New Jersey National Core Curriculum Standards K-12

http://www.corestandards.org/Standards/K12/