This activity provides a connection between geometry and algebra by looking at geometric concepts in a coordinate plane. In addition, it draws upon an ancient Chinese legend and culture to add interest to the context of the lesson.
As they construct the tangrams, students are required to graph points defined by ordered pairs in the four quadrants and write the ordered pair for a given point in any one of the four quadrants. They are also required to identify midpoints of line segments. Once the tans are constructed, students can explore a variety of other mathematical concepts related to geometry, measurement, and fractions (e.g., transformations in a plane and area of geometric shapes).
The main lesson itself provides meaningful learning opportunities, but the possible extensions enrich the depth of the mathematical learning by connecting the geometry to concepts of measurement, fractions, decimals, and percents.
3. Reason mathematically.
5. Make mathematical connections.
Invitation to Learn:
Share the story of the tangram. According to legend, the tangram
puzzle originated in China. The legend tells of Tan, a Chinese nobleman,
who wished to present the emperor with a gift of an exquisite square tile.
Unfortunately, he dropped the tile on his journey and broke it into pieces.
When he opened the bag he was carrying it in, he found that the tile
broke into exactly 7 pieces--5 right triangles (2 small, 2 large, and 1
medium), a square, and a parallelogram. Tan tried to put the pieces back
together to reconstruct the square tile, but he could not. What he found,
however, was that he could make many other shapes with the seven
pieces. He decided that the broken pieces made an even grander gift than
his original square tile.
Although it is not known exactly when tangrams came about, we know that they became quite popular in the United States and Europe during the nineteenth century and have remained popular among geometry enthusiasts today.
Instructional Procedures:
There is a wonderful book called Grandfather Tang's Story that tells about a man sharing a story of a variety of animals. As each animal is introduced, Grandfather Tang rearranges the tangram pieces to illustrate the next animal in the story.
The original activity can be done without using the coordinate plane.
Exploring the topic of tessellations in more detail would be a rich opportunity here. Students can look at tessellation concepts in art (e.g., MC Escher) as well as in the real world (e.g., honeycomb structures).
Observe as students work with the instructions for constructing the tangram. The completed tangram and completed worksheet can serve as formal assessment strategies. Students could create a kite design using reflection symmetry and record their design in a coordinate plane. Students could then construct their design, connecting it to art.