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## 4.4.2 Tangram Challenges

 Tangram Challenges (applet)Students can use tangram pieces to form given polygons.

Task

Is it possible to complete all these tasks? Try these tangram challenges with the virtual tangrams:

• Make a square using only one tangram piece.
• Make a square using two tangram pieces.
• Make a square using three tangram pieces.
• Make a square using four tangram pieces.
• Make a square using five tangram pieces.
• Make a square using six tangram pieces.
• Make a square using all seven tangram pieces.

Which of these figures can you make using all seven tangram pieces?

• A trapezoid
• A rectangle that is not a square
• A parallelogram that is not a square
• A triangle

How to Use the Interactive Figure

Work on a challenge using the number of pieces required. To move a tangram piece, click on the piece and drag it to the desired location. To rotate a piece, drag it by a vertex. To select a tangram piece, click on it. To color a selected piece, click on a colored button on the right. Other features can be accessed from the following buttons:

 Flips the tangram piece that is selected Resets the work space

Working with Tangram Challenges in the Classroom

Many students will find these tasks very interesting but challenging. Young students are learning about position in space, new vocabulary, and properties of figures all at the same time. The computer tangrams may help them become more aware of the properties of figures and the processes they use in manipulating shapes because they must plan the moves they need to make. Teachers can encourage students to become more deliberate in their planning by having them work with a partner to talk about the actions they need to take. For example, students have to figure out explicitly how to place the tangram pieces in relation to one another in activities such as these, where there are no outlines. The built-in rotation and flip tools are also a good way to help students see the transformation motions.

These tangram challenges may be made easier by giving students outlines to use at their desks so they can experiment with fitting the seven tangram pieces into the outlines.

Assessment through Observations and Conversations

Activities such as Tangram Puzzles and Tangram Challenges can serve as vehicles for assessing students' thinking. In observing and talking with students, teachers might consider questions such as these:

How easily do students manipulate the shapes?

• What mathematical vocabulary are students using as they talk with one another?
• Do students recognize congruence and relationships among combinations of shapes?
• Do students appear to use what they have learned in earlier tasks in solving new problems

Take Time to Reflect

• How might work with computer manipulatives facilitate the learning of many children with special needs?
• What additional challenges might teachers create that would focus students' attention on the relationships among the tangram pieces?

Also see:

• 4.4  Developing Geometry Understandings and Spatial Skills through Puzzlelike Problems with Tangrams

• 4.4.1  Tangram Puzzles

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