7.02: Tangrams

Tangrams are a seven-piece geometric puzzle that dates back at least to the Song Dynasty in China (about 1100 AD). Below^[1] you will find the seven puzzle pieces. Make a careful copy (a photocopy or printout is best), cut out the puzzle pieces, and then use them to solve the problems in this section.

Whenever you solve a tangram puzzle, your job is to use all seven pieces to form the shape. They should fit together like puzzle pieces, sitting flat on the table; no overlapping of the pieces is allowed.

You can trace around your solutions to remember what you have done and to have a record of your work.

Problem 1

Use your tangram pieces to build the following designs^[2]. How many can you make?

(These are all separate challenges. Each one requires all seven pieces. Once you solve one, trace your solution. Then try to solve another one.)

Problem 2

Use your tangram pieces to build the following designs^[3]. How many can you make?

(These are all separate challenges. Each one requires all seven pieces. Once you solve one, trace your solution. Then try to solve another one.)

Think / Pair / Share

• Which tangram problems were easier and which were harder: making “real life” objects like cats and people, or purely mathematical objects like the rectangle?
• What do you think made one kind of problem easier or harder?

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1. Image of tangram puzzle from Wikimedia Commons, public domain. ↵
2. Tangram puzzles from Wikimedia Commons, public domain. ↵
3. Tangram puzzles from pixababy.com,CC0 Creative Commons. ↵