Lesson 1Tessellations of the Plane

Learning Goal

Let’s explore geometric patterns!

Activity 1: Notice and Wonder: Polygon Patterns

Problem 1

What do you notice? What do you wonder?

Six tessellations.

Activity 2: Tessellations

Problem 1

With your partner, choose one of the six shapes in the toolbar that you will both use.

  • Select the shape tool by clicking on it. Create copies of your shape by clicking in the work space.

  • When you have enough to work with, click on the Move tool (the arrow) to drag or turn them.

  • If you have trouble aligning the shapes, right click to turn on the grid.

  • When you are finished making your tessellation, you can hide the points.

open applet in presentation mode

  1. Compare your tessellation to your partner’s. How are they similar? How are they different?

  2. If possible, make a third tessellation of the plane with your shape (different from the ones you and your partner already created). If not possible, explain why it is not possible.

Print Version

With your partner, choose one of the six shapes that you will both use to create a tessellation.

Six polygons. A parallelogram, an equilateral triangle, a square, a hexagon, a rhombus, and a trapezoid.

  1. Compare your tessellation to your partner’s. How are they similar? How are they different?

  2. If possible, make a third tessellation of the plane with your shape (different from the ones you and your partner already created). If not possible, explain why it is not possible.

Activity 3: Describing a Tessellation

Problem 1

Pick one of the figures and describe the tessellation. Your partner will identify which tessellation you are describing. Then trade roles so your partner describes the tessellation and you identify the figure.

This should not be a alt text description. Tactile is needed.....Four tessellations.One tessellation has groups repeating rows of two rectangles. The first row has yellow and green alternating rectangles and the second row has blue and red alternating rectangles. Another tessellation has alternating blue and red alternating rectangles slanted upward and to the right. Below the red and blue rectangles are alternating yellow and green rectangles. A third tessellation has groups of three rectangles next to one another, sharing the long sides: the long sides are vertical. In addition to these groups of three rectangles, there are single rectangles with the long side lying horizontally. A fourth tessellation has alternating rectangles placed horizontally then vertically.

Problem 2

You and your partner each have a card with a tessellation.

  1. Describe what is on your card so that your partner can produce the tessellation (this should be done so that you cannot see your partner’s work until it is complete).

  2. Check together to see if your partner’s tessellation agrees with your card and discuss any differences.

  3. Change roles so your partner describes a tessellation, which you attempt to produce.

  4. Check the accuracy of your construction and discuss any discrepancies.