The Challenge: Get yourself a square of paper (or something else?) and cut yourself a set of tangrams. Then create away!

Materials Needed: Scissors, paper Math conceptsyou could explore with this challenge: angles, geometry, lines, polygons, proportions/ratios, symmetry, tessellations

The Background: Tangrams have a bit of a muddled history – they’re definitely Chinese in origin, but I’ve found accounts of them existing as early as 1796, some argue 1815, and of course, there was a European guy who made up The Eighth Book of Tan, which has been proven a complete hoax.

There are OOOOODLES of tangram “puzzles” out there, but I’d argue you may have more fun with students just creating their own creations, and THEN you introduce the “tangram paradoxes”. For example, the three shapes below appear to have the same outlines, and yet definitely not the same. Subtle changes in how they’re arranged definitely encourage students to start wondering and noticing and calculating areas.

There are, of course ways to just play with shape. You can make cats, or the middle shape here is fun because it looks to me right now like a bird, yet if you rotate it, I start seeing flowers or snakes. The last shape invites me to start considering area and proportion among the triangles shown.

Reflection questions:

Which of the shapes are most alike or most different?

Can you create other “paradoxes”?

Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

2.) Reason abstractly and quantitatively. How might you describe the “size” of each shape? How do the areas of the shapes compare?

7.) Look for and make use of structure. How many equal edges are available? How about edge combinations?