Pentomino Challenge

Primary/Junior (Age 6 – 12)

Curriculum Goal

Primary/Junior: Geometry and Spatial Reasoning

  • Describe and represent shape, location, and movement by applying geometric properties and spatial relationships in order to navigate the world around them.
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Appendix A
Jamboard Link

Context

  • Students can work individually or in pairs to perform the pentomino challenge.

Materials

In-person version

Online version

Challenge

  • Each student/pair will begin with 60 tiles or the Pentomino Jamboard (virtual).
  • Explain to the class that a pentomino is a geometric shape made by joining five equal squares edge to edge.
  • Ask your class: “Using sets of five tiles, how many unique pentomino configurations can you build?”
  • Explain that any rotation of the shape is a version of the same pentomino. Tell the students we will revisit this idea once we’ve had an opportunity to start creating pentomino shapes.
  • Explain that the configurations must join edge to edge, rather than at the vertices.
  • Let the students begin creating pentominoes, and after two minutes, do a quick check-in to
    make sure they all understand the activity. At this point, show an example of a pentomino and use it to demonstrate that different flips and rotations remain the same pentomino.
  • Now it’s time for the challenge. Provide students with ample time to create as many
    configurations as possible using their 60 tiles.
  • There will be much discussion between students. Listen to their conversations and provide support when needed.
  • Ask the students to discuss how many pentominoes they think there are. When appropriate, reveal that there are 12 possible pentomino shapes. Show them what those look like.
  • There are bonus challenges in the slides and in the Extensions section of this document.
  • The Pentomino Challenge Google Slides file has instructions in the presenters notes. The
    slideshow will be useful for both in-class and online instruction. An image of all the solutions can be found toward the end of the document.

Look Fors

  • Can students accurately configure different pentominoes (e.g., Using five tiles, aligning the tiles side by side)?
  • What spatial language are students using? Is it being communicated correctly?
  • Can students identify duplicate pentominoes that have different orientations?

Extension

  • Ask the students to try to come up with the letter codes of each pentomino (the letters of the alphabet that each shape resembles).
  • Challenge students to configure all 12 pentominoes into one big rectangle (See possible solutions in Pentomino Challenge PowerPoint).
  • Find the area and perimeter of each pentomino? What do students notice about the area?
  • Which pentominoes have rotational symmetry? Which pentominoes have reflection symmetry?
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Jamboard Link

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