Operation Rational Irrational Numbers

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SWBAT know when the sum or product of rational and irrational numbers is rational or irrational.

Big Idea

Real numbers are either rational or irrational. But do we know the nature of sums and products of these real numbers?

Accessing Prior Knowledge

20 minutes

At the start of class, I hand each student an Entrance_Card. I intend students to work independently on this task. When students are done, I go over the questions with them and then I allow the students to play an rational or irrational number game on the computer for a few minutes. After they have several minutes to play the game, I call on a student to explain the difference between a rational and an irrational number using examples.

Teacher Note about Entrance card question 1b: Students tend to define rational numbers as :”numbers that can be written as a fraction” The problem with this is that irrational numbers such as  the square root of 3 are also fractions. A better definition is that rational numbers are “numbers that can be written as a fraction of integers”.

Before moving on to the main activity for the day, I use the thumb rule to assess the students on their ability to identify rational and irrational numbers. The site below may help those students who need it the extra help.


Additional Resources:     



New Info/Application

40 minutes
NewInfo.docx page 1
NewInfo.docx page 2


15 minutes
Generalization.docx page 1