Illustrative Mathematics
Identifying Rational Numbers
Eight different numbers are listed for mathematics masters to analyze. They simply tell if each number is rational or irrational. They can also explain their reasoning. A simple and straightforward activity that is a handy tool for...
Illustrative Mathematics
Converting Decimal Representations of Rational Numbers to Fraction Representations
A rational number is a ratio of two integers. Discuss with your class how to convert the rational numbers of repeating decimals to fractions. A good commentary on letting x equal the repeating decimal and multiplying each side of...
Illustrative Mathematics
Comparing Rational and Irrational Number
Algebra learners must know how to use rational numbers to approximate irrationals. This resource asks participants to decide which number is larger without using a calculator. It makes a great exercise to use as a five-minute transition...
Illustrative Mathematics
Irrational Numbers on the Number Line
There are four irrational numbers that participants need to graph. Pi(π), -(½ x π), and √17 are easy to approximate with common rational numbers. On the other hand, the commentary describing the irrational number 2√2 is not...
Illustrative Mathematics
Calculating and Rounding Numbers
Mathematicians need to know that not all numbers are rational. We approximate irrational number with rational numbers. That is why a calculator may be misleading. This task give learners an opportunity to see how rounding a number and...
Education Development Center
Sum of Rational and Irrational is Irrational
Sometimes the indirect path is best. Scholars determine whether the sum of a rational number and an irrational number is irrational. Reading a transcript of a conversation between classmates leads to an indirect proof of this concept.
Illustrative Mathematics
Placing a Square Root on the Number Line
There are many ways to approach finding the rational approximation of an unknown square root. Here is a problem that will help math learners make a connection between square roots and their order on a number line. As usual, determine two...
Oregon Department of Education
Building Number Sense
It's never too early to begin a child's math education. This collection of fun hands-on activities engage youngsters in building their number sense as they learn how to count objects, identify numerals, compare amounts, and much more.
5280 Math
Pythagorean Triples
From Pythagorean triples to the unit circle. Learners use the Pythagorean Theorem to find Pythagorean triples and then relate their work to the unit circle in a fun algebra project. Their discovery that x^2+y^2 is always equal to one on...
Cut the Knot
What's a Rational Number?
This question is answered by discussing and comparing rational and irrational numbers. For more advanced levels of Algebra, there are sections that discuss different lemmas of rational numbers and give their proofs.
Lawrence Hall of Science
The Math Page: Topics in Pre Calculus: Rational and Irrational Numbers
Here is a site that clearly and thoroughly explains rational and irrational numbers as subsets of the real number system. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point...
Texas Instruments
Texas Instruments: Real Numbers
Students learn to identify real numbers as rational numbers and irrational numbers. They review rational numbers as repeating decimals, and irrational numbers as non-repeating decimals. They also review commutative, associative,...
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.
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....
J Coffman
Joseph Coffman's Lecture Notes: Properties of Numbers
The lesson examines properties of real numbers. Students learn about rational numbers, properties of real numbers, and irrational numbers. Examples and an assessment are included.
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.
Integrated Publishing
Integrated Publishing: The Discriminant
A thorough investigation of what the discriminant is and how it is used. Contains examples and exercises, with answers on the page.