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...
University of Utah
Rational and Irrational Numbers
Conquer any irrational fears you might have of irrational numbers. As class members investigate how to represent numbers geometrically, they learn about rational and irrational numbers, including approximating and ordering rational...
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 worksheet that is a handy tool for...
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.
Willow Tree
Rational vs. Irrational Numbers
Build an understanding of rational numbers and their counterpart irrational numbers. Lead learners through an explanation of rational numbers and the ways they can be expressed. Then introduce them to irrational numbers and make...
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...
Charleston School District
Identifying Irrational Numbers
These numbers have some personality! Are they rational or irrational? The lesson examines the definitions of rational and irrational numbers and shows examples of how to identify them.
EngageNY
The Decimal Expansion of Some Irrational Numbers
Develop a definition of irrational numbers through an exploration of square roots. The 11th instructional activity in this series of 25 asks scholars to estimate the value of a square root. Learners observe as the estimation extends...
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...
Curated OER
Rational and Irrational Numbers
Here is a rational and irrational numbers worksheet in which learners identify 10 different expressions related to various types of numbers. They determine whether each expression given is a rational or irrational number.
Illustrative Mathematics
Rational or Irrational?
Is 4 plus the square root of 2 rational or irrational? After your class has gained a basic grasp of rational and irrational numbers, use this worksheet to push them a little further in their understanding. Learners must identify sums and...
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...
Mathematics Vision Project
Module 4: Rational Functions
Time to study the most sensible function — rational functions! The seven-lesson unit develops the concept of a rational function through a connection to rational numbers and fractions. Scholars graph functions, solve equations, and...
Curated OER
Rational, Irrational and Square Roots
Students identify rational and irrational numbers and their use in mathematical functions. Through demonstration, students discover the difference between rational and irrational numbers and their use. Using estimation skills students...
EngageNY
Rational and Irrational Numbers
Back to the basics: learning how to add numbers. The 17th installment of a 35-part module first reviews addition techniques for rational numbers, such as graphical methods (number line) and numerical methods (standard algorithm). It goes...
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...
Curated OER
The Real Number System: Rational or Irrational
In this real numbers worksheet, learners determine if 14 expressions when simplified are rational or irrational. Students take the square and cube roots of numbers to determine if the result is rational or irrational.
Curated OER
The Irrational Numbers
In this algebra worksheet, students solve rational numbers using addition, subtraction and multiplication. They identify the rules of solving rational and irrational numbers. There are 50 questions on 6 pages.
Illustrative Mathematics
Operations with Rational and Irrational Numbers
Learners complete addition and multiplication tables that include rational and irrational numbers. They also answer a series of questions about the sums and products of irrational and rational numbers. One suggested modification would be...
Curated OER
Number Sense and Numeration
Students add and subtract integers. For this algebra lesson, students discuss number sense as they sort numbers in the correct order. They analyze and label numbers differentiating between rational and irrational numbers.
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.
CK-12 Foundation
The Real Numbers: Number System
Get real about learning the real number classification. Young mathematicians create a graphic organizer of the real number system using an interactive. They answer a set of challenge questions on the classifications of real numbers.
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
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...