Identifying perfect numbers
Updated: January 19, 2007
Lesson planIn this lesson, students learn the definition of a perfect number and use various methods for determining what numbers are perfect.
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Lesson plan information
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Instructional level | |
School level | | • | High school (14-18 years) |
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Curriculum areas | |
Class time | |
Academic standards | | • | Math: Numbers and operations, reasoning and proof |
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ISTE NETS Standards | | • | Students use technology tools to enhance learning, increase productivity, and promote creativity. |
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Software required | | • | Microsoft Internet Explorer | | • | Microsoft Office Word |
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Teacher guide
Objectives
| • | Students will be able to define a perfect number. |
| • | Students will be able to determine whether a number is a perfect number. |
| • | Students will experience three methods for determining perfect numbers. |
Prerequisite skills
| • | Knowledge of the following vocabulary: factors, prime numbers, divisibility rules, and powers |
| • | Basic skills using Microsoft Internet Explorer |
| • | Basic skills using Microsoft Office Word |
How to begin
1. | Save the document Student directions to your classroom computers. Adjust the directions as needed for your lesson. When presenting your lesson to the students, have them use the student directions sheet as a jump point into the activity. |
2. | On the overhead projector or whiteboard, write down the first perfect number (six). Ask students to brainstorm why six is considered a perfect number. After they have provided several ideas, share with the students that six is considered a perfect number because it is the sum of all of its positive factors (excluding itself). |
3. | Tell the students that they will be working on defining and determining perfect numbers through this activity. |
Resources and Web links
Student activity
Description
In this activity you will learn about perfect numbers and practice three methods for determining whether a given number is a perfect number. You will summarize your learning in a Microsoft Office Word document you will hand in to your teacher.
| • | Software: Microsoft Internet Explorer, Microsoft Office Word |
| • | What to do Learn about perfect numbers and write a report 1. | Visit the perfect numbers Web site. | 2. | Read through the explanation of perfect numbers, and work through Exercise 1. | 3. | Open a new Word document and define―in your own words—a perfect number. | 4. | Read Exercise 2. | 5. | Copy the table in Exercise 2 into your Word document. | 6. | Complete the table. You must name three more perfect numbers beyond the Web site answers. | 7. | Summarize the three methods to find perfect numbers. | 8. | Comment on which of the three methods you prefer. | 9. | Proofread and save your work. |
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Ways to extend the student activity
Have students find additional perfect numbers using their preferred method.
Assessments
You can assess the following elements of the Word document the student submits:
| • | Definition of perfect numbers |
| • | Completed table with three new perfect numbers |
| • | Summary of the three methods to find perfect numbers |
| • | Comment on their preferred method to find perfect numbers |
Innovative teaching
