# Lesson 1

Tessellations of the Plane

### Lesson Narrative

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.

### Learning Goals

Teacher Facing

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

### Student Facing

Let’s explore geometric patterns!

### 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.

Building On