Tracy Rains
Material Type:
Lesson Plan
Middle School, High School
  • Decimals
  • Exploring Real Numbers
  • Integers
  • Ratio
    Creative Commons Attribution Non-Commercial
    Media Formats:
    Downloadable docs, Interactive, Text/HTML, Video

    Rational & Irrational Number

    Rational & Irrational Number


    In this seminar you will explore different types of numbers in math. You will learn to classify numbers into the categories of natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. You will see how some numbers can be classified in a few of these categories. Some important things to consider will be whether or not a decimal number terminates or repeats.



    Apply properties of rational and irrational numbers to solve real world or mathematical problems.



    Introductory warm-up activity.

    Does the diagram below look familiar? See if you can label each circle with the types of numbers listed.

    *Remember that a circle inside of a circle means that it includes that type of number inside of it as well. For example, the largest red circle would include all types of numbers that fall inside of it.

    Struggling?  No worries - this is just to get the wheels turning - we will review as we move forward!



    Read or watch the resources to learn about this concept, then do the practice activity.




    Now that you are thinking about number types and how they are related, click this link to review:  Number Types This link, Irrational Numbers, has plenty of examples of each type of number as well as the opportunity to begin classifying numbers at the very bottom. Be sure to list each type of number in your math notebook, as well an example for each.  You will want to include the diagram as well - so you remember how they are all related.

    Take some time to watch this video on types of numbers: Irrational numbers, Rational Numbers: With Real World Examples.  It shows not only why these numbers apply to math class, but also gives real world examples of these numbers as well. In your math notebook please list each type of number, a short definition, and an example of each.

    This video, Classifying Numbers: Rational & Irrational will give you practice in doing just that.  Please hit “pause” to attempt to classify the numbers yourself and then “play” to see if you are correct. If needed, watch the video once and then go back and try it on your own the second time through. How did you do?

    To practice classifying rational & irrational numbers please click here.   

    While rational and irrational number classifications are the two you see most often in math, it is still good to practice classifying all types of number.  Click here and here for practice in doing just that.  



    Discuss your ideas / opinions / understandings.

    Get with a partner and take a look at the list of numbers below & then discuss:

    .33333………,  ¼ , 1, , 1.11

    • Which numbers are rational?

    • Which numbers are irrational?

    • What is the difference between these 2 types of numbers?

    • Which numbers could also be classified as: natural, whole, integer, or real numbers?

    Finally, take some time to put the numbers in order from smallest to largest. Try to do this individually and then compare your orders. How did you each go about putting them in order?  Take time to explain the process used to each other.


    Now it is time to self-check how much you have learned about this topic.  If you do not know as much as you thought, go back to the “Explore” section of this seminar and reread, rewatch, or redo the activities listed.  See your facilitator if you have questions.

    Click here to take the quiz online. You do not have to log into the quiz site in order to take this quiz. If a window pops up asking you to sign up for the quiz site, just close the sign-up window and start your quiz.


    This is a task or project where you can show what you know.

    Create a chart (copy and paste the one below) displaying each of these types of numbers: Natural Number, Whole Number, Integer, Rational Number, Irrational Number, and Real Number.  Use your own words (does not need to be a formal definition) to describe this type of number. Then create a third column where you list at least 3 numbers that are examples.

    Each column of this chart should be filled in to show full completion of this task.

    Once you have finished your chart, pick one number from each row in the “examples” column.  Take some time to try to put these numbers in order. This shows that not only can you classify numbers, but you also can compare them as well.



    Complete this wrap-up activity where you reflect on your learning.  

    Name one thing that was new to you in this lesson.  How does it relate to what you already knew about numbers?  What are you still struggling with? What can you do to overcome this struggle?