Illuminations: Geometric Understanding Through Tangram Puzzles

Geometric Understanding Through Tangram Puzzles

Tangram Challenges

Describing figures and visualizing what they look like when they are transformed through rotations or flips or are put together or taken apart in different ways are important aspects of geometry in the lower grades. This two-part tangram example demonstrates the potential for high-quality experiences provided by computer "shape" environments for students as they learn concepts described in the Geometry Standard. Problem-solving tasks that involve physical manipulatives as well as virtual manipulatives afford many students an entry into mathematics that they might not otherwise experience. In Tangram Puzzles, students can choose a picture and use all seven pieces to fill in the outline. In this second part, Tangram Challenges, students can use tangram pieces to form given polygons.

Learning Objectives
 

Students will

  • use tangram pieces to form given polygons.

Materials
 
  • Computer and Internet connection

Instructional Plan

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]



[Stand-alone applet]

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 Options
 

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?

Teacher Reflection
 
  • 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?

NCTM Standards and Expectations
 
Geometry Pre-K-2
  1. Describe attributes and parts of two- and three-dimensional shapes
  2. Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.
  3. Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes .
  4. Create mental images of geometric shapes using spatial memory and spatial visualization.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
© 2000 National Council of Teachers of Mathematics
Use of this Web site constitutes acceptance of the Terms of Use

The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council.