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...
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.
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.
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...
EngageNY
Irrational Exponents—What are 2^√2 and 2^π?
Extend the concept of exponents to irrational numbers. In the fifth installment of a 35-part module, individuals use calculators and rational exponents to estimate the values of 2^(sqrt(2)) and 2^(pi). The final goal is to show that the...
Curated OER
Radicals and the Irrational Numbers
In this Integrated Algebra worksheet, learners differentiate between rational and irrational numbers and locate irrational numbers on a number line. The one page worksheet contains six problems. Answers are provided.
Curated OER
Rational and Irrational Numbers 1
You'll need scissors, glue sticks, and mini whiteboards for this activity on rational and irrational numbers. Learners work in groups to classify a variety of expressions as rational or irrational. They are also given a mock discussion...
Curated OER
Rational and Irrational Numbers 2
Is the circumference of a circle always, sometimes, or never rational? Learners answer questions individually and also work in groups to look at sums and products of rational and irrational numbers. They must also be able to use the...
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.
Charleston School District
Comparing and Ordering Irrational Numbers on a Number Line
Estimating the value of numbers is much harder than it sounds! Scholars compare and order the value of numbers presented in different forms including fractions, decimals, roots, integers, and pi. This builds on the previous lessons in...
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 Irrational Numbers
In this Algebra I/Algebra II instructional activity, students identify rational and irrational numbers. The one page instructional activity contains a combination of ten multiple choice and free response questions. The answers are...
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...
CK-12 Foundation
Simplification of Radical Expressions: Irrational Garden Plot
All is not simple in the garden of rationals and irrationals. Learners use a context of a garden to practice simplifying irrational numbers involving radicals. They also find areas of garden with irrational side lengths.
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
Algebra 1: Simplifying Radicals
After discussing the difference between rational and irrational numbers, the class pratices simplifying, adding, and subtracting radical expressions. They play a game which involves passing around cards until they have matching hands of...
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
The Rational Number System
In this rational number system worksheet, students identify rational and irrational numbers. They use a Venn Diagram to place numbers in their correct number set. This five-page worksheet contains approximately 10 problems. Answers are...
Charleston School District
Evaluation of Roots
You mean the square root of five and five don't have the same value? Learners estimate the value of irrational roots. As they practice estimating the value, they increase their understanding of roots. The lesson is the fourth in a series...
Alabama Learning Exchange
Classifying Complex Numbers
Imaginary numbers are a real thing. Scholars learn about complex numbers, real numbers, and imaginary numbers. They classify given numbers as strictly complex, strictly real, or strictly imaginary in an individual or group activity.
Charleston School District
Pre-Test Unit 7: Real Numbers
Don't be irrational! Use this pre-test to assess your classes' ability to work with all types of real numbers. The lesson asks learners to estimate value, evaluate roots, and order numbers. This begins a series of lessons on the real...
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.