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Developing Geometry Understandings and Spatial Skills through Puzzlelike
Problems with Tangrams: Tangram Puzzles
Tangram Puzzles |
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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.
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?"
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Take
Time to Reflect
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- 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?
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Tangram Puzzles
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