Geometric Puzzles, Virtually

by Math Circle Network

During February’s Online Math Teacher Circle session, Henri Picciotto presented geometric puzzles that educators and students could attempt virtually using online manipulatives he created.


The session started with an explanation of Tangrams. The Tangram is a set of seven geometric shapes made up of five triangles, a square, and a parallelogram. In this activity students use the Virtual Tangrams to determine which shapes they can make with the seven pieces.

Henri used the above link to show how to play with tangrams virtually. He had the participants, in groups of four, complete a series of questions about arranging tangrams into various sized rectangles.

Screen Shot 2021-03-04 at 12.48.23 PM

In the above table participants logged which shapes were possible to build with the tangram pieces. For each shape, a green check was placed if the shape can be built with that number of tangram pieces (e.g., it is possible to build a square with four tangram pieces).


In the second half of the session Henri introduced the participants to pentominoes.

Pentominoes are shapes made with five squares. In this activity students will use the Virtual Pentominoes to try to answer and do the following:

  • Why do only some of the pentominoes have a “flip” option?
  • What size rectangles can be covered with pentominoes?
  • Make puzzles by doubling or tripling pentomino dimensions.

With the above link participants were able to take screen shots and upload their solutions:

How many holes can you make using the pentomino pieces?
What sort of rectangles can be made?
Multiple attempts to make 5 by 5 squares
Different ways to make the same shape but using different sets of pentominoes
Lastly, attendees made "blowups" of shapes, again using different sets of pentomo pieces.

Going Further

To learn more about tangrams and pentominoes, Henri Picciotto’s website offers many free activities to do with them both:

For more information and activities done by Henri, visit his website at

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