This lesson is designed to examine the mathematical concept of perimeter. These activities and
discussions may be used to develop students' understanding of this mathematical concept.

Objectives

Upon completion of this lesson, students will:

be able to calculate the perimeter of a random shape on a grid

Standards Addressed:

Grade 10

Geometry

The student solves problems (including real-world situations).

Grade 3

Geometry

The student solves problems using perimeter or area.

Grade 4

Geometry

The student solves problems using perimeter or area.

Grade 5

Geometry

The student solves problems (including real-world situations) using perimeter or area.

Grade 6

Geometry

The student solves problems (including real-world situations) using perimeter, area, or volume.

Grade 7

Geometry

The student solves problems (including real-world situations).

Grade 8

Geometry

The student solves problems (including real-world situations).

Grade 9

Geometry

The student solves problems (including real-world situations).

Third Grade

Geometry

Reason with shapes and their attributes.

Measurement and Data

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Grades 9-12

Measurement

Apply appropriate techniques, tools, and formulas to determine measurements

6th Grade

Measurement

The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine unit rates; and the use of scale to determine distance.

The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine

7th Grade

Measurement

The student will demonstrate through the mathematical processes an understanding of how to use ratio and proportion to solve problems involving scale factors and rates and how to use one-step unit analysis to convert between and within the U.S. Customary System and the metric system.

The student will demonstrate through the mathematical processes an understanding of how to use ratio and proportion to solve problems involving scale factors and rates and how to use one-step unit analysis to convert between and within the U.S. Customary

8th grade

Measurement

The student will demonstrate through the mathematical processes an understanding of the proportionality of similar figures; the necessary levels of accuracy and precision in measurement; the use of formulas to determine circumference, perimeter, area, and volume; and the use of conversions within and between the U.S. Customary System and the metric system.

The student will demonstrate through the mathematical processes an understanding of the proportionality of similar figures; the necessary levels of accuracy and precision in measurement; the use of formulas to determine circumference, perimeter, area, and

Geometry

Geometry

Standard G-3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles.

4th Grade

Measurement

4.13.b The student will use measuring devices to find perimeter in both standard and nonstandard units of
measure.

4.13.b

5th Grade

Measurement

5.10 The student will differentiate between perimeter, area, and volume and identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation.

7th Grade

Measurement

7.7a The student, given appropriate dimensions, will estimate and find the area of polygons by subdividing them into rectangles and
right triangles

7.7 The student, given appropriate dimensions, will

Student Prerequisites

Arithmetic: Student must be able to:

add, count

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:

The sum of the lengths of all the sides of a polygon

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 to recall information about polygons

You might ask students to consider how they might trace the perimeter of a polygon that is
drawn on the board, or you may begin the day by running the perimeter of the school!

Objectives

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

Today, class, we will be talking more about the perimeter of polygons. We will learn exactly
what this term means, and we will learn how to calculate the perimeter of random shapes on a
grid.

We are going to use the computers to learn about perimeter, but please do not turn your
computers on or go to this page until I ask you to. I want to show you a little about the
Perimeter Explorer applet first.

Teacher Input

You may choose to lead the students in a short
discussion (see also:
Perimeter Algorithm Discussion) about how to find the perimeter for random shapes. 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
Perimeter Explorer in order to demonstrate this activity to the students

Perimeter is the total length around the object. So imagine the grid lines are equal to one
step. And imagine the outside edges of the figure are tight ropes. You want to see how many
steps it will take you to get all the way around the edge. The number of steps would be the
perimeter.

Once we have calculated the perimeter we will put our answer in the perimeter input box and
click the check answer button. For now, ignore the area input box.

Try another example, letting the students direct your moves. Or, you may simply ask, "Can anyone
describe the steps to use this activity?"

If your class seems to understand the process for doing this assignment, simply ask, "Can
anyone tell me what you will do now?"

If your class seems to be having a little trouble with this process, do another example
together, but let the students direct your actions: Can someone describe how I would find the
perimeter of this shape?

Independent Practice

Allow the students to work on their own and to complete the
worksheet, should you choose to provide one. Monitor the room for questions and to be sure that the
students are on the correct web site.

Closure

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.

You may wish to collect data from the students to demonstrate that there are even more than
five possibilities for each of the areas.

Alternate Outline

If there is only one computer available have all students pull out a sheet of graph paper and
give them each of the 5 areas. See how many different shapes they can generate at the given
areas on their papers. Collect different ideas on the board for the conclusion.

You may wish to use one or more of the data collection tools in the conclusion of the lesson:
Boxplot or
Simple plot to graph the data. (Be sure to read the "how" pages on each of these activities for
instructions on plotting more than one data set for each of the set areas.)