This lesson allows students to examine tessellations and their geometric properties. The activity
and discussion may be used to develop students' understanding of lines, planes, angles, and
polygons.

Objectives

Upon completion of this lesson, students will:

have been introduced to tessellations

have learned about lines, planes, angles and polygons

have experimented with the area and perimeter of polygons

Standards Addressed:

Grade 10

Geometry

The student demonstrates an understanding of geometric relationships.

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 3

Geometry

The student demonstrates an understanding of geometric relationships.

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

Grade 4

Geometry

The student demonstrates an understanding of geometric relationships.

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

Grade 5

Geometry

The student demonstrates an understanding of geometric relationships.

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

Grade 6

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

Grade 7

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

Grade 8

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

Grade 9

Geometry

The student demonstrates an understanding of geometric relationships.

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

The student demonstrates a conceptual understanding of geometric drawings or constructions.

Geometry

Congruence

Experiment with transformations in the plane

Understand congruence in terms of rigid motions

Third Grade

Geometry

Reason with shapes and their attributes.

Grades 6-8

Geometry

Use visualization, spatial reasoning, and geometric modeling to solve problems

Grades 9-12

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

Use visualization, spatial reasoning, and geometric modeling to solve problems

Geometry

Data Analysis and Probability

Competency Goal 3: The learner will transform geometric figures in the coordinate plane algebraically.

Geometry and Measurement

Competency Goal 2: The learner will use geometric and algebraic properties of figures to solve problems and write proofs.

Grade 8

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 3: The learner will understand and use properties and relationships in geometry.

Integrated Mathematics III

Geometry and Measurement

Competency Goal 2: The learner will use properties of geometric figures to solve problems.

Introductory Mathematics

Data Analysis and Probability

COMPETENCY GOAL 3: The learner will understand and use properties and relationships in geometry.

Geometry and Measurement

COMPETENCY GOAL 2: The learner will use properties and relationships in geometry and measurement concepts to solve problems.

Technical Mathematics I

Geometry and Measurement

Competency Goal 2: The learner will measure and apply geometric concepts to solve problems.

Technical Mathematics II

Geometry and Measurement

Competency Goal 1: The learner will use properties of geometric figures to solve problems.

7th Grade

Geometry

The student will demonstrate through the mathematical processes an understanding of proportional reasoning, tessellations, the use of geometric properties to make deductive arguments. the results of the intersection of geometric shapes in a plane, and the relationships among angles formed when a transversal intersects two parallel lines.

The student will demonstrate through the mathematical processes an understanding of proportional reasoning, tessellations, the use of geometric properties to make deductive arguments. the results of the intersection of geometric shapes in a plane, and the

Geometry

Geometry

Standard G-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

Reason for Alignment: The Geometry in Tessellations lesson is another look at the properties of tessellating polygons. This one is fun for the students as well as a quick way of investigating these figures.

Student Prerequisites

Arithmetic: Student must be able to:

identify polygons

measure angles

understand congruent figures

Technological: Students must be able to:

perform basic mouse manipulations such as point, click and drag.

use a browser for experimenting with the activities.

Teacher Preparation

Access to a browser

pencil and paper

Copies of supplemental materials for the activities:

A closed plane figure formed by three or more line segments that do not cross over each other

regular polygon

A polygon whose side lengths are all the same and whose interior angle measures are all the same

tessellation

A tessellation is a repeated geometric design that covers a plane without gaps or overlaps

Lesson Outline

Focus and Review

Remind students what has been learned in previous lessons that will be pertinent to this lesson
and/or have them begin to think about the words and ideas of this lesson:

Ask students if they remember what polygons are, and what makes regular polygons unique.

Let the students know what they will be doing and learning today. Say something like this:

Today, class, we will be talking more about the geometry involved in tessellations, and we
will discover which types of polygons tessellate a plane.

Teacher Input

Explain to the students how to do the assignment. You should model or demonstrate it for the
students, especially if they are not familiar with how to use our computer applets.

Open your browser to the
Tessellate! page in order to demonstrate this activity to the students.

Show students how to select one of the regular polygon shapes and click the "tessellate"
button to see it displayed.

Ask students to count the number of sides of the polygon.

Record the number of sides in the
data table , and help students complete the rest of the information for the shape you have chosen.

Guided Practice

Try another shape, letting the students take the lead in completing the data table for this new
shape.

Encourage students to determine a pattern among the regular polygons that they work with. Ask
the students to predict which regular polygons will and will not tessellate and why.

Select the third regular polygon, observe what it looks like in the Tessellate activity, and
then complete the data table for this shape.

Ask students what the data table would look like for 5, 7 and 8-sided polygons.

Help students analyze the data and draw a conclusion about which shapes will tessellate
the plane and why.

Alternatively, have the students complete a similar
exercise on the computer using the Tessellate activity, a screen capture utility and a drawing
program.

Closure

You may wish to bring the class back together for a discussion of the findings. Once the students
have been allowed to share what they found, summarize the results of the lesson.

Alternate Outline

This lesson can be rearranged in several ways if there is only one available computer:

You can model all the parts of the lesson for the students, asking them to complete the data
table with you as a class.

Model the
connect the dots activity to the whole class on the computer using the Tessellate activity, a screen capture
utility and a drawing program, but then distribute the
Tessellations on Paper Worksheet to each student to complete individually.