Prepare sets of tangrams for your students ahead of time.  You should make 2 sets for each student.  Explain a little of the history of tangrams and show your students some of the many pictures that can be made.
 Challenge your students to create their own designs with their tangrams.  Can they make a fish?  A cat?  A strange-looking plant?  When students have had opportunity to explore and create, have them create their favorite design and then glue the arrangement onto construction paper.  Later, when the glue has dried, use these designs as a classroom set of puzzles.  Hand out the designs and new sets of tangrams and have students try to recreate their classmates’ designs.  With younger students, the designs may be recreated by matching the pieces directly on top of the puzzles.  After the activity, use the puzzles to decorate your classroom.

Folding Tangrams (3-8)

Creating a set of tangrams from written instructions is a great exercise in geometry vocabulary and following directions.  You can do this to have your students make tangrams and use them with some of the other activities.  Here’s the instructions I use with my students.  With younger students, you’ll want to lead the class in this construction; with older students, you may wish to supply written instructions and have them work on the construction in groups.

1.  Start with a square piece of construction paper.
2.  Fold in half along the diagonal and cut along the resulting crease.
3.  Fold one of the resultant triangles in half and cut.  Set these two pieces aside (1 & 2).
4.  Find the midpoint of the hypotenuse of the remaining large triangle by folding and lightly creasing.
5.  Fold the triangle so that the vertex of the right angle touches the midpoint of the hypotenuse.  Cut along the resulting crease, and set aside the small triangle (3).
6.  Fold the remaining trapezoid in half along its line of symmetry and cut into two smaller trapezoids.
7.  Fold one trapezoid so that the vertices at the ends of the longest edge meet.  Cut along the crease to make a small triangle and a square (4 & 5).
8.  Fold the other trapezoid so that the obtuse angle meets the right angle at the opposite vertex.  Cut along the crease to make another small triangle and a parallelogram (6 & 7).

Grandfather Tang (3-4)

Read your class the book “Grandfather Tang’s Story” (by Ann Tompert, published by Dragonfly Books).  Divide your students into 11 groups and give each group a picture of one of the animals from the story.  Each student should try to make their group’s assigned animal and then glue the pieces to construction paper.  Retell the story using the students’ pictures.

Tangram Challenges 1 (3-5)

Use these tangram math puzzles to help your students get acquainted with how the pieces fit together.

1.  How many shapes can be made using just the two large triangles, placing them edge to edge?  (answer:  There are three).
2.  Make a square using three triangles.
3.  Make a polygon with the least number of sides possible (answer: a right triangle is possible).
4.  Make a polygon with the maximum number of sides (answer: by offsetting the pieces slightly, irregular polygons with 23 sides are possible!)
5.  What fraction of the original square does each of the tangram pieces represent?  How can you tell?

Tangram Challenges 2 (6-8)

1.  Construct squares using 1 piece, 2 pieces, 3 pieces, etc., all the way up to 7 pieces.  Sketch you solutions.  One arrangement is not possible - which is it?  (answer:  6 pieces is not possible).
2.  If the original square has an edge length of 2, what are the edge lengths of each piece?  (hint:  the diagonal of a square has length square root of 2 times the edge length.)
3.  Construct a convex hexagon.  There are only 13 possible convex shapes - how many can you find?

Shape Race (3-8)

Copy six to eight tangram designs onto one piece of paper.  Make photocopies, one for each pair of students, and cut apart the designs to make small “packs of cards.” Each pair of students should receive on pack of designs.  Your students should choose one of these pictures and either race or work cooperatively to recreate the design.  This activity builds spatial reasoning and visualization and is a favorite with my students.
 You can download a page of designs ready to print by clicking HERE.