Illustrative Mathematics
Illustrative Mathematics: 8.ns Comparing Rational and Irrational Numbers
For this task, 8th graders are presented with pairs of rational or irrational numbers. They must state which number in the pair is higher and explain their thinking. Aligns with 8.NS.A.2.
Wolfram Research
Wolfram Math World: Irrational Numbers
This math site explains what it means for a number to be irrational and names various persons who have proven the irrationality of some numbers, the site also gives several numbers who are thought to be irrational yet have not been...
Illustrative Mathematics
Illustrative Mathematics: 8.ns Identifying Rational Numbers
For this task, 8th graders are presented with a mixed set of eight different numbers and must identify them as rational or irrational and explain how they know. Aligns with 8.NS.A.1.
CK-12 Foundation
Ck 12: Algebra: Properties of Rational Numbers
[Free Registration/Login may be required to access all resource tools.] Recognize and identify irrational numbers and the set of real numbers
CK-12 Foundation
Ck 12: Algebra: Irrational Square Roots
[Free Registration/Login may be required to access all resource tools.] Find approximate solutions to equations involving irrational numbers.
TED Talks
Ted: Ted Ed: The Psychology Behind Irrational Decisions
Often people make decisions that are not "rational" from a purely economical point of view. Sara Garofalo explains heuristics, problem-solving approaches based on previous experience and intuition rather than analysis. [4:39]
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
CK-12 Foundation
Ck 12: Arithmetic: Properties of Rational Numbers
[Free Registration/Login may be required to access all resource tools.] In this lesson students identify rational numbers as the ratio of two integers. Students examine guided notes, review guided practice, watch instructional videos and...
Free Math Help
Free Math Help: Algebra Lesson: Rational Numbers
Learners examine the set of real numbers. The resource includes detailed explanations about rational and irrational numbers. It provides example problems.
Math Open Reference
Math Open Reference: Irrational Number
Learn about irrational numbers with this easy reference guide. Provides a detailed definition and examples that enhance further explanation. Provides links to related topics.
ClassFlow
Class Flow: Rational and Irrational Numbers
[Free Registration/Login Required] By the end of the lesson, students will classify numbers into number families to help understand how to distinguish the difference between rational and irrational numbers. Students will demonstrate this...
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: About Rational Numbers
Math Forum response giving a rather thorough overview of rational and irrational numbers, with a brief look at the history of these and other number sets.
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.
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.
University of Saskatchewan (Canada)
University of Saskatchewan: Decimal Expansions
The University of Saskatchewan's Department of Mathematics and Statistics provides high school students with an online tutorial on decimal expansions. It begins with a focus on decimal representation of real numbers, followed by how this...
Texas A&M University
Wtamu Virtual Math Lab: Intermediate Algebra
This site is a tutorial for students in algebra 2 or for those who need a refresher. The site has explanations, definitions, examples, practice problems and practice tests are found covering topics such as linear equations, graphing,...
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...
Math Words
Math Words: Rational Numbers
Mathwords provides a brief description with an easy to read chart that includes all types of real numbers.
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.
Doina Popovici
Math Play: Rational and Irrational Numbers Game
An interactive game where students have to determine whether a number is a rational or a irrational number.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Irrational Powers
Math Forum response considering whether an irrational number taken to an irrational power yields a rational or irrational number. Responses include a method of generating irrational #s x & y such that x^y is rational.
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.
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