Lesson plan

Lesson 1: Tessellations of the Plane

teaches Common Core State Standards 8.G.A http://www.corestandards.org/the-standards

Lesson 1: Tessellations of the Plane

This optional sequence of three lessons can be done any time after the first unit in the course. Students are introduced to tessellations of the plane. The activities in this lesson provide students a chance to go more deeply and apply grade 8 geometry concepts to a mathematical context. The activities in this sequence of three lessons build on each other, so should be done in order. It is not necessary to do all three lessons to get some benefit, although more connections are made the further one gets.

As students progress through the activities, they gain an intuition for the variety of ways some shapes can be put together to build a tessellation and the restrictions on how some shapes can be put together to build a tessellation. They start with general tessellations, and then look at regular tessellations. Finally in the third lesson, they examine tessellations using other regular polygons.

Throughout these lessons, students make use of structure when building their tessellations (MP7). They reason abstractly and quantitatively when deciding which polygons can be used in the different types of tessellations (MP2) and make viable arguments to convince each other that some polygons cannot be used to tessellate the plane.

Lesson overview

  • 1.1 Optional Activity: Notice and Wonder: Polygon Patterns (5 minutes)
  • 1.2 Optional Activity: Tessellations (20 minutes)
    • There is a digital applet in this activity. 
  • 1.3 Optional Activity: Describing a Tessellation (20 minutes)

Learning goals:

  • Create and describe patterns with specific polygons that fill the plane.

Learning goals (student facing):

  • Let’s explore geometric patterns!

Required materials:

  • pre-printed slips, cut from copies of the blackline master
  • tracing paper

Required preparation:

  • If using the print version of the materials, all students require tracing paper.
  • If using the applets in the digital version of the materials, students may not need tracing paper.
  • Prepare 1 pre-cut copy of the Describing a Tessellation blackline master for every 2 students.
  • Each student needs one of the two slips showing an individual tessellation.


  • tessellation - A tessellation of the plane is a regular repeating pattern of one or more shapes that covers the entire plane.

  • Access the complete Grade 8 glossary.


  • This lesson builds on the standard: CCSS.7.G.AMO.7.GM.A






IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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