National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Square Roots and Irrational Numbers
Math Forum response to whether square roots of all non-perfect squares are irrational. Contains a proof showing that such cases are, indeed, irrational.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Irrational Numbers; Rational Square Roots
Dr. Math responds to how one can tell whether a number is rational or irrational. A proof is discussed in the response.
Wikimedia
Wikipedia: Irrational Number
At this site from Wikipedia you can learn the definition of an irrational number, then look at examples and explanations of why some numbers are irrational and others are not.
Lawrence Hall of Science
The Math Page: Skill in Algebra: Radicals: Rationals & Irrationals
Here is a site that clearly and thoroughly explains many topics related to radicals. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point this site out to students who have...
Common Core Sheets
Common Core Sheets: The Number System 8.ns.1 Worksheets
Print or create worksheets to assess students' understanding of rational and irrational numbers.
CK-12 Foundation
Ck 12: Arithmetic: Comparison of Rational Numbers
[Free Registration/Login may be required to access all resource tools.] Compare and order rational numbers on a number line and by using inequality symbols
Other
Platonic Realms: Conic Sections
A proof to show that the square root of two is an irrational number, followed by a shorter and even more beautiful proof.
Alabama Learning Exchange
Alex: Calm and Erratic!
During this lesson, students will learn why numbers are rational or irrational. Rational numbers are numbers that can be written in the form a/b. Irrational numbers cannot be expressed in the form a/b, where a and b are integers.
National Institute of Educational Technologies and Teacher Training (Spain)
Ministerio De Educacion: Los Numerous Reales
In this module you will learn about rational and irrational numbers.
Common Core Sheets
Common Core Sheets: The Number System 8.ns.2 Worksheets
Print or create worksheets to assess students' understanding of radicals, square roots, and irrational numbers.
Alabama Learning Exchange
Alex: Those Number Aren't Just Moody.
Rational numbers can sometimes cause problems when they're converted to repeating decimals. That, we can handle. But, what about those irrational numbers that can only be "sort of, like approximated"? How can we expect middle schoolers...
Purple Math
Purplemath: Number Types
This site explores the different types of numbers: natural numbers, whole numbers, integers, and rational and irrational numbers. Content includes some practice questions.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Rational and Irrational Number
Math Forum response to the size of the set of rational numbers. Responses investigate the countability of sets and basic set theory.
Other
The Prime Glossary: Rational Numbers
This site gives a definition of what a rational number is. Gives examples and formulas. Very helpful.
CK-12 Foundation
Ck 12: Algebra: Sets and Symbols
[Free Registration/Login may be required to access all resource tools.] Classify real numbers as rational numbers, whole numbers, integers, and irrational numbers.
Help Algebra
Help algebra.com: The Real Number System
Natural numbers, whole numbers, integers and rational numbers begin this lesson on the real number system. You can also learn more about the number line and absolute value. Examples and diagrams are included to enhance understanding.
Texas Instruments
Texas Instruments: Number Sets
When you start this activity, students receive a Venn diagram of real number sets (natural, whole, integer, rational, irrational)on their calculator. This same diagram is projected on the Activity Center screen at the front of the room....
Math Open Reference
Math Open Reference: Number
Resource defines numbers into two main categories, counting numbers and scalars. It also gives examples of number notation.
Alabama Learning Exchange
Alex: The Real Number System
This instructional activity 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...
Curated OER
Math Words: Rational Numbers
Mathwords provides a brief description with an easy to read chart that includes all types of real numbers.
CK-12 Foundation
Ck 12: Arithmetic: Conversion of Decimals, Fractions, and Percent
[Free Registration/Login may be required to access all resource tools.] Understand, identify and find equivalent forms of rational numbers
Washington State University
Washington State University: Sets & Other Basic Concepts
Washington State University provides an introduction to sets and subsets and the symbols used to represent them.
Khan Academy
Khan Academy: Approximating Square Roots
Practice finding the approximate value of square roots by thinking about perfect squares. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video, or receive hints.
CK-12 Foundation
Ck 12: Algebra: Pythagorean Theorem and Its Converse
[Free Registration/Login may be required to access all resource tools.] Recognize and use the Pythagorean Theorem