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...
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 such...
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...
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 instructional activity that is a handy...
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 clear. It...
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...
Curated OER
Make a Math Mascot
Create a math mascot by identifying irrational and rational numbers. Learners will also solve linear equations.
Curated OER
Lesson 2 Ordering Numbers
Math wizards begin the lesson by comparing and ordering rational numbers. Using a number line, they discover the relationship between the numbers and practice ordering them in the correct way. They also review proper techniques for...
Curated OER
Algebra Worksheet: Number systems
This worksheet was originally created for a college level algebra class. It does contain some interesting questions about number and quantity that are important for algebra learners to understand. Natural numbers, integers, rational,...
Curated OER
The Real Number System
Learners analyze the real number system. They discuss real numbers, rational and irrational numbers, integers, whole numbers, natural numbers and more of the real number in the system. They differentiate between all these numbers.
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...
Other
Dan's Math: Basic Skills Topics
College professor Dan Bach offers a review of various basic topics in arithmetic, pre-algebra, and algebra. Order of operations, exponents, square roots, variables, and combining terms are just a few of the many topics covered.
TeachEngineering
Teach Engineering: Let's Take a Slice of Pi
Working as a team, students discover that the value of pi (3.1415926) is a constant and applies to all different sized circles. The team builds a basic robot and programs it to travel in a circular motion. A marker attached to the robot...
Math.com
Math.com: The Language of Algebra: Definitions
The resource investigates the algebra vocabulary. Detailed definitions, examples, and practice problems are included.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Numbers
Math Forum response to request for information on various number sets. Also defined and discussed are integers, natural numbers, whole numbers, irrational numbers, transcendental numbers, and algebraic 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.
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: Arithmetic:
[Free Registration/Login may be required to access all resource tools.] Learn how to add integers.
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
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: Algebra: Irrational Square Roots
[Free Registration/Login may be required to access all resource tools.] Find approximate solutions to equations involving irrational numbers.
Math Is Fun
Math Is Fun: E (Euler's Number)
Explains what Euler's Number is, its significance, and the formula used to calculate this irrational number. Gives memory tricks for remembering the value of e to 10 or 15 decimal places. Looks at some interesting properties of e and how...
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 learn to simplify and order rational numbers. Students examine guided notes, review guided practice, watch instructional videos and attempt...
Illustrative Mathematics
Illustrative Mathematics: N Rn and 8 Ns: Calculating the Square Root of 2
Jessica evaluates $\sqrt{2}$ on her calculator which shows a value of $$ 1.4142136. $$ She then writes $$ \sqrt{2} = 1.4142136. $$ Aligns with 8.NS.A.