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Teaching Irrational Numbers – Middle School Math and Science

Teaching Irrational numbers can be difficult for students to understand. Students learn about rational numbers throughout elementary and early middle school. Irrational numbers are usually taught in 8th grade.

What is an Irrational Number?

Irrational means not rational.

Remember the definition of a rational number. A rational number is a number that can be written as a fraction.

Since irrational means not rational that means the definition of an irrational number is a number that cannot be written as a fraction.

Understanding Irrational Numbers

To help students understand the definition of irrational numbers, review writing decimal numbers as fractions. Put a decimal value on the board and have students help you write the decimal as a fraction. Emphasize that we always look for the last place and use that value for the denominator.  After you have reviewed writing decimals as fractions discuss what would make it impossible to write a decimal as a fraction. Students usually realize that it would be a number that never ends and never repeats because you need the last place for the denominator. The numbers are irrational numbers.

Introduction to Irrational Numbers Activity

After you have helped your students understand what an irrational number is, try this activity. The Understanding Irrational Numbers activity is best done after defining irrational numbers and before estimating irrational numbers. This activity has students finding sides lengths of squares when given the area. The first square has an area that is a perfect square and students should have no trouble finding the side length of the square.

The second square has an area that is not a perfect square. Students use a calculator (not the square root key) to find the side length. Students use number sense to pick a side length to start with. They square the number (or multiply it by itself) and try to get closer and closer to the area. Students get excited as they get closer. Make it a competition and see who can get the closest. Students start to realize they will never get the exact area. They just get closer because the side length of the square is an irrational number.  They also see the importance of estimating this number to understand it. This activity is a free download.


I hope you will try this activity with your students if you are looking for a way to help them understand what an irrational number is. My students enjoy competing and seeing who can get the closest to the area of 35. Throughout the year I will ask them the names of numbers we are working on reiterate the concept. 

Read the blog Teaching Rational Numbers for teaching ideas for helping students understand rational numbers.

Check out this ready-made unit on Number Systems for more activities on irrational numbers. Each of the lessons has an editable PowerPoint, guided notes, activity and practice sheet. You and your students will love it!

Rizwan Ahmed
Rizwan Ahmed
AuditStudent.com, founded by Rizwan Ahmed, is an educational platform dedicated to empowering students and professionals in the all fields of life. Discover comprehensive resources and expert guidance to excel in the dynamic education industry.


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