Illuminations: Geometric Understanding Through Tangram Puzzles

Geometric Understanding Through Tangram Puzzles

Tangram Puzzles

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 this part, Tangram Puzzles, students can choose a picture and use all seven pieces to fill in the outline. In the second part, Tangram Challenges, students can use tangram pieces to form given polygons.

Learning Objectives
 

Students will

  • choose a picture and use all seven pieces to fill in the outline.

Materials
 
  • Computer and Internet connection

Instructional Plan

Task

Choose a picture and use all seven pieces to fill in the outline. Use the "Hint" button if you need help.

[How to Use the Interactive Figure]

[Stand-alone applet]

Getting Started

Young students' experiences with puzzles provide a background for undertaking this activity. Because similar puzzles are available for use with plastic or paper tangrams, students can move back and forth between concrete materials and the computer environment. After the students have had time to work with the outlines, teachers might ask them questions such as the following, which challenge them to try different solutions or to reflect on the strategies they used to solve the puzzles:

  • Can you fill the outlines in another way?
  • How many different ways are there to fill in this shape?
  • What do you do when you cannot figure out a puzzle?
  • Can some tangram pieces substitute for others?

What Students Learn

Whereas completing the same or similar puzzles with both physical and computer manipulatives may help students generalize their experiences, the computer environment is likely to encourage them to think about how they need to manipulate the tangram pieces rather than approach the task mainly by trial and error. Working with a partner at the computer to complete puzzles also encourages students to become more precise in their use of vocabulary about space. Teachers can enrich students' vocabulary in class discussions by these comments on students' actions, such as "I see you are rotating the parallelogram " or "What difference would flipping make?"

Teacher Reflection
 
  • How can teachers provide time for all students to interact with the virtual tangrams?
  • What discussions about the students' work with the tangram puzzles could teachers plan that would enrich students' understandings of shape and movement in space?

NCTM Standards and Expectations
 
Geometry Pre-K-2
  1. Describe, name, and interpret relative positions in space and apply ideas about relative position.
  2. Create mental images of geometric shapes using spatial memory and spatial visualization.
  3. Recognize and apply slides, flips, and turns.
  
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
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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.