mathematics excursion is a brief mathematics activity. To maximize
student learning, certain prerequisites are necessary to use this
activity. Thus, it would be appropriate to include this activity as
part of a more fully developed Standards-based lesson, but it should
not be used as a complete stand-alone lesson.
Initiating the Excursion
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 could move back and forth
between concrete materials and the computer environment. To facilitate
this, you could have each student cut out the tangram pieces from the
second page of the Slide, Flip, Turn Activity Sheet.
Slide, Flip, Turn Activity Sheet
Then, before going online, place a triangle, square,
and parallelogram on an overhead projector. Ask student volunteers to
demonstrate the three transformations that will be used in this
activity (flips, turns, and slides) as preparation for solving the tangram puzzles. Engage students in a brief discussion about each of
the three transformations. Discuss the effect that each of these
transformations has on the shapes.
Developing the Excursion
Group students into teams of two or three. Give each group a copy of the Slide, Flip, and Turn Activity Sheet.
Students should go to the Tangram Puzzles E‑Example to complete the following activity.
Tangram Puzzles E-Example (Java)
a newer, Flash version is available here:
Tangram Puzzles E-Example (Flash)
Have partners work together to solve four different tangram
puzzles. For example, one can give directions as the other "drives the
mouse." Encourage the students to think about how they need to
manipulate the tangram pieces before they begin moving the pieces.
Encourage them to make a plan about how to move the pieces, rather than
using trial‑and‑error as their strategy. Discuss with students the
plans they develop. Ask them to defend their reasoning. This will
elicit use of accurate mathematical vocabulary and associate it with
the appropriate transformation.
Teams should record their solutions on the activity sheet. Partners should switch roles until all four puzzles are completed.
The closing should be structured so that students can review and
pull together what they have learned. Include questions or tasks that
encourage students to reflect on their work, particularly as related to
the specific stated Learning Objectives. For example, after students
complete the activity, you could have them consider questions similar
to the guiding questions below. In so doing, they will consolidate what
they have learned. Furthermore, this will provide an opportunity for
you and your students to assess what they have learned and what they
still want or need to understand. This will help you plan for further
When the four puzzles are completed, ask students to review their
solutions. Help them do this by asking questions like the following:
- Show me where you used a flip, a turn, and a slide in solving a puzzle.
- Look at this figure [put a tangram piece or other geometric
shape on the overhead], draw what it will look like when it is flipped
[or rotated or slid].
- Look around the classroom for examples of transformed shapes. Describe the transformation.
- Were any of the puzzles more challenging than the others? Why?
- Go back and review the solution of each puzzle. How were the solutions alike? How were the solutions different?
- Compare your solutions with some other students' solutions. How were the solutions alike? How were the solutions different?