This activity provides step-by-step directions for making tangram pieces.
- One sheet of
construction paper per
- Grandfather Tang's Story, by Ann Tompert; ISBN 0517885581
Background for Teachers
Acute—an angle that is smaller than a right angle (i.e., measures
less than 90 degrees)
Congruent—figures, segments, or angles that have the same size
Obtuse—an angle that is greater than a right angle (i.e., measures
more than 90 degrees)
Parallel—lines that do not intersect
Parallelogram—a quadrilateral with two pairs of parallel sides
Trapezoid—a quadrilateral with exactly one pair of parallel sides
Intended Learning Outcomes
1. Demonstrate a positive learning attitude toward mathematics.
2. Become mathematical problem solvers.
3. Reason mathematically.
4. Communicate mathematically.
Invitation to Learn
Tell or read Grandfather Tang's Story.
Use the following step-by-step directions (word for word if you
choose) to direct this activity. [In brackets are discussion suggestions
that emphasize geometric concepts.] At each step along the way, it's
helpful if you fold and tear a large piece of paper as a demonstration.
By the way, instead of cutting, fold back and forth, then lick, fold,
and tear! It works!
- First we need to make a square piece of paper. Fold your sheet so
that a shorter side coincides with a longer side. Tear (or cut) off
the excess strip of paper. Unfold the remaining paper.
[Discuss the original shape (rectangle), and the shape you now
Note: After each of the following steps, have students reassemble
the torn pieces into a square before going on.
- Fold along the diagonal in the square. Tear along the fold.
[Discuss the two shapes. The two triangles are alike or
congruent; each has one square corner called a right angle.]
- Fold each triangle in half. Unfold each. Tear one triangle along
the fold to make the first two tangram pieces. Set them aside.
[Discuss the shapes. All are right triangles; the two small
triangles are alike or congruent; the small triangles are the same
shape or similar to the large triangle.]
- Take the large triangle and fold its square corner (right angle) to
the middle of the opposite side (hypotenuse). Tear along the new
fold to make the third piece.
Set this triangle aside.
[Discuss the resulting shapes and angles. A trapezoid is a foursided
figure with one pair of opposite sides parallel; in this case,
the triangle has a right angle but the trapezoid does not; two
angles in the triangle are congruent to two angles in the
- Hold the figure (trapezoid) with the longest side toward you.
Notice the fold line down the middle. Fold the lower left corner
(acute angle) to the middle of the bottom side. Unfold it. Tear
along the two fold lines to make the fourth and fifth pieces
(triangle and square).
[Discuss the shapes. The triangle is similar but not congruent to
the other triangles; the square is similar but not congruent to the
original square; the trapezoid has two right angles.]
- Hold the figure (trapezoid) with the longest side toward you and
right angles to the left. Fold the top right corner (obtuse angle) to
the opposite corner (right angle) so that the top side now
coincides with the left side. Unfold it. Tear along the fold to
make the sixth and seventh pieces.
[Discuss these last two shapes. The triangle is congruent to the
other small triangles; the parallelogram, a four-sided figure with
opposite side parallel, has two angles congruent to the smaller
angles in the triangles.]