Making Tangrams User-Friendly
An Educator's Reference Desk Lesson Plan
OVERVIEW: Often when students are introduced to tangrams, they are asked to put
the pieces together to form a square. This is often a difficult and frustrating
task, because they have no background as to how the pieces fit together.
PURPOSE: To provide students with some insight as to how the tangram pieces fit
together, and to stimulate their interest in forming shapes and exploring
patterns using the tangram pieces.
OBJECTIVE(s): Students will:
1. construct the tangram pieces from a square paper by following directions to
fold and cut.
2. make observations on the pieces formed and compare how they are related to
each other.
3. explore patterns and shapes with the tangram pieces.
RESOURCES/MATERIALS:
• square sheet of paper (students can fold from 8.5" x 11" plain paper)
• plastic sets of tangram pieces
• overhead tangram set for demonstration
ACTIVITIES AND PROCEDURES:
Students will fold and cut a square piece of paper by following these
directions. Students should discuss and record observations in small groups
after each step.
1. Fold the square sheet in half along a diagonal, unfold and cut along the
crease. What observations can you make about the two pieces you have? How can
you "prove" that your observations are correct?
2. Take one of the halves, fold it in half and cut along the crease. Make more
observations and be able to support your statements.
3. Take the remaining half and lightly crease to find the midpoint of the
longest side. Fold so that the vertex of the right angle touches that midpoint
and cut along the crease. Continue with observations. Congruent and similar
triangles may be discussed, as well as trapezoid.
4. Take the trapezoid, fold it in half and cut. What shapes are formed? Students
may not realize that these shapes are trapezoids as well. What relationships do
the pieces cut have? Can you determine the measure of any of the angles?
5. Fold the acute base angle of one of the trapezoids to the adjacent right base
angle and cut on the crease. What shapes are formed? How are these pieces
related to the other pieces?
6. Fold the right base angle of the other trapezoid to the opposite obtuse
angle. Cut on the crease. You now should have the seven tangram pieces. Are
there any more observations you can make? Have the students mix up the pieces
and try to put the pieces together to form the square which was the shape of the
paper they originally started with. Students may be given plastic tangram pieces
to do the remaining activities.
7. Have students order the pieces from smallest to largest and explain what
criteria they used for their arrangement. Students should be able to verify
their arrangement. Focus on the arrangement of pieces based on area. Use the
small triangle as the basic unit of area. What are the areas of each of the
pieces in triangular units?
8. Create squares using different numbers of tangram pieces and find the area of
the squares in triangular units. For example, to form a square with one tangram
piece, students should identify the square piece which is 2 triangular units in
area. To form a square with two tangram pieces, students should use the two
small triangles (2 triangular units in area) or the two large triangles (8
triangular units in area). Students should continue to try to form squares with
3 pieces, 4 pieces, 5 pieces, 6 pieces and all 7 pieces. Are there multiple
solutions for any? Are there no solutions for any? Do you notice any patterns?
TYING IT ALL TOGETHER:
1. Have students turn in list(s) of observations from tangram folding. If the
length of a side of the original square is 2, what are the lengths of the sides
of each of the tangram pieces cut?
2. Have students make conjectures based on their findings from the making
squares activity. Students may observe that the areas of the squares appear to
be powers of 2 and that they are unable to make a 6-piece square. When all
combinations of 6-pieces are considered, the possible areas are not powers of 2.