Apply Translations, Reflections, and Rotations to Solve Spatial Puzzles: Tangram Transformations

Aligned to standards HSG-CO.A.3: Rigid Transformations of Polygons, HSG-CO.C.11: Theorems about Parallelograms, and HSG-CO.B.6: Transform Figures using Rigid Transformations.

A Tangram is a Chinese geometric puzzle consisting of a square cut into seven pieces that can be arranged to make various other shapes. We’ve put together a math mini-project that challenges students to apply reasoning about translations, reflections, and rotations to calculate the precise transformations made between Tangram figures of their own design.

The complete project plan is available here for download in Word or PDF format.
  • This project integrates conceptual, procedural, and strategic knowledge of congruence and transformations as applied to 2D geometric shapes.
  • Instead of simply creating a Tangram pattern, students rigorously describe the precise transformations of each individual shape (i.e. triangles, rectangles, and parallelograms) in order to generate their composite Tangram pattern.
  • Students also try to follow another student’s transformations and see if they arrive at the same pattern.

Here’s a quick look at what’s included in the downloadable project packet:

  • Tangram starting position
  • Printable Tangram shapes
  • A blank coordinate grid for students to use
  • Possible solutions/ideas for Tangram puzzles
The complete project plan is available here for download in Word or PDF format.