The Real Number System

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Students will be able to classify numbers in the real number system.

Big Idea

This lesson relates the real number system to its historical perspective.

Warm up and Homework Review

5 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. This lesson’s Warm Up- Real Number System is meant to access prior knowledge on number systems.  We will use this as a spring board for the day's lesson.  

Introduction to Number Systems

17 minutes

This lesson is a foundation topic meant to prepare students to enter the complex number system. The real number system was addressed in prior years but I feel that it is important enough to look at again to ensure that all students will be coming into the next couple of lessons from the right place.  

My hook for this activity is a video from teacher tube on the history of numbers.  It is about 7 minutes and provides a nice survey of the development of numbers into our current number systems.

Next, we build a diagram that shows the connections between the different sets of numbers.  As we build this diagram, we relate the numbers back to the historical perspectives in the video as well as the students' experiences learning numbers as they grew up.  

Classifying Numbers Activity

20 minutes

Each pair receive a set of cards with the names of each number system: natural, whole, integer, rational, irrational, and real; each of which have been printed on separate colored paper.  As I pull up the numbers on the PowerPoint, the pairs will hold up the number systems that apply to that number (Math Practice 2).  I will then call on a student to explain a portion of their solution.  For example, if the number is 12/4, I may ask a student why they chose to put this in natural numbers.    Please watch the Video Narrative for additional thoughts on this activity.

An alternate method is to make this a race where the first 3 or 5 groups get a point for holding up the correct systems.

Exit Ticket

3 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

Today's lesson asks students to determine a number that is a rational number but not an integer.


Today’s homework allows the students to reaffirm their knowledge of the separate number systems within Real Numbers.  The first problem gives them several numbers to categorize within the number systems.  The remainder of the problems asks the students to come up with numbers that fit into certain systems but not others (Math Practice 1).