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This lesson provided by:
Author: Joyce Waid
System:Blount County
School:Locust Fork High School
Lesson Plan ID: 11762

The Real Number System


This lesson focuses on a clear understanding of the real number system by using a variety of teaching strategies. A graphic organizer on a slideshow illustrates how the classifications of numbers relate. A kinesthetic activity helps students compare the classifications.

Content Standard(s):
MA2013(8) 1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. [8-NS1]
Local/National Standards:  
Primary Learning Objective(s):

Students will classify numbers within the real number system. Students will identify numbers as rational or irrational. Students will classify rational numbers as integers, whole numbers, or natural numbers.

Additional Learning Objective(s):  
Approximate Duration of the Lesson: 31 to 60 Minutes
Materials and Equipment:

6 chairs, signs (Real, Rational, Irrational, Integer, Whole, Natural), container to draw numbers from, practice sheet for each student

Technology Resources Needed:

PowerPoint presentation (see attached), desktop publishing software such as MS Word or Publisher for making signs and numbers (or use the attached file)


This lesson may be used as an introductory lesson where students have limited knowledge of the vocabulary and the teacher defines the classifications. This lesson may also be used as reinforcement with students who have already defined the classifications.

1.)The teacher will need to define and describe each classification of the real number system. It is a good idea to illustrate the progression through time. For example, when students were in kindergarten they had only an understanding of numbers that they could count, hence the term counting numbers (or natural numbers). In first grade they understood zero and how it functioned as a placeholder. In seventh grade they learned to use integers. In Algebra II they will learn an entirely new number system, complex numbers.

2.)Use the diagrams in the attached slideshow presentation to further illustrate the attributes of each classification.

3.)Select six students to sit in chairs in the front of the room facing the class. The first round should probably be with students who have a good understanding of the concept.

4.)Give each student a sign to wear: (in this order) Real, Rational, Irrational, Integer, Whole, Natural.

5.)The remaining students will draw numbers from a container. As each student reads his/her number, the students in the front will stand if the number meets the constraints of their classification.

6.)Teacher observation and assessment will determine how many rounds are played. When the teacher feels the connections have been made, a discussion will evolve. Students will begin to see that Irrational and Rational never stand at the same time. They will also see that Real always stands. If Natural is standing, then Whole and Integer will also. Allow students to make these observations. Do not rush the process.

7.)Give the students the practice sheet for classwork or homework.

8.)Be sure to give enough guided practice before assigning independent work.

Attachments:**Some files will display in a new window. Others will prompt you to download. Numbers.doc
Practice Sheet - Real numbers.doc
The Real Number System 2.ppt
Assessment Strategies:

Re-teaching decisions will be made based on teacher observation of the kinesthetic activity and the follow-up practice. Students will also be assessed using a unit test.


The lesson could be expanded by adding the complex number system to the kinesthetic activity. Students could also be asked to place various numbers in the appropriate area on the diagram in the slideshow presentation.


Special needs students may need to complete the practice sheet with peer pairing. The teacher may also provide the students will teaching aids such as the diagram used on the slideshow or sets defining each number. classification.

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior

Be sure to check the student's IEP for specific accommodations.
Variations Submitted by ALEX Users:
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