Abstract
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 3
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Geometry
- The student solves problems using perimeter or area.
Grade 4
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Geometry
- The student solves problems using perimeter or area.
Grade 5
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Geometry
- The student solves problems (including real-world situations) using perimeter or area.
Grade 6
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Geometry
- The student solves problems (including real-world situations) using perimeter, area, or volume.
Grade 7
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Geometry
- The student solves problems (including real-world situations).
Grade 8
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Geometry
- The student solves problems (including real-world situations).
Grade 9
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Geometry
- The student solves problems (including real-world situations).
Grade 10
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Geometry
- The student solves problems (including real-world situations).
Third Grade
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Geometry
- Reason with shapes and their attributes.
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Measurement and Data
- Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Grades 9-12
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Measurement
- Apply appropriate techniques, tools, and formulas to determine measurements
6th Grade
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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
- 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.
7th Grade
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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
- 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.
8th Grade
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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
- 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.
Geometry
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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.
7th Grade
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Measurement
- 7.7 The student, given appropriate dimensions, will
- 7.7a The student, given appropriate dimensions, will estimate and find the area of polygons by subdividing them into rectangles and right triangles
4th Grade
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Measurement
- 4.13.b
- 4.13.b The student will use measuring devices to find perimeter in both standard and nonstandard units of measure.
5th Grade
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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.
Student Prerequisites
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Arithmetic:
Students must be able to:
- add, count
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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
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Copies of supplemental materials for the activities:
- Worksheet To Accompany the Perimeter Lesson
Key Terms
perimeter
The sum of the lengths of all the sides of a polygon
Lesson Outline
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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!
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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.
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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.
- If you choose to, you may pass out the Worksheet to Accompany The "Perimeter" Applet
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Guided Practice
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?
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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.
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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.)