Lesson 1Tiling the Plane

Learning Goal

Let’s look at tiling patterns and think about area.

Learning Targets

  • I can explain the meaning of area.

Lesson Terms

  • area
  • region

Warm Up: Which One Doesn’t Belong: Tilings

Problem 1

Which pattern doesn’t belong?

  1. blue pattern tile
  2. yellow pattern tile
  3. combination of blue and yellow pattern tile
  4. combination of blue tiles, yellow tiles, and blank spaces pattern tile

Activity 1: More Red, Green, or Blue?

Problem 1

Your teacher will assign you to look at Pattern A or B.

In your pattern, which shapes cover more of the plane: blue rhombuses, red trapezoids, or green triangles? Explain how you know.

Pattern A

A plane composed of a series of pattern blocks: blue rhombuses, red triangles, and green trapezoid.

Pattern B

A plane composed of a series of pattern blocks: blue rhombuses, red triangles, and green trapezoid.

You may use this applet to help. Explore what you can see or hide, and what you can move or turn.

open applet in presentation mode
Print Version

Your teacher will assign you to look at Pattern A or Pattern B.

In your pattern, which shape covers more of the plane: blue rhombuses, red trapezoids, or green triangles? Explain how you know.

Pattern A

A plane composed of a series of pattern blocks: blue rhombuses, red triangles, and green trapezoid.

Pattern B

A plane composed of a series of pattern blocks: blue rhombuses, red triangles, and green trapezoid.

Are you ready for more?

Problem 1

On graph paper, create a tiling pattern so that:

  • The pattern has at least two different shapes.

  • The same amount of the plane is covered by each type of shape.

Lesson Summary

In this lesson, we learned about tiling the plane, which means covering a two-dimensional region with copies of the same shape or shapes such that there are no gaps or overlaps.

Then, we compared tiling patterns and the shapes in them. In thinking about which patterns and shapes cover more of the plane, we have started to reason about area.

We will continue this work, and to learn how to use mathematical tools strategically to help us do mathematics.