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Workbook
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1
University of Utah

Rational and Irrational Numbers

For Students 8th Standards
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...
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Lesson Plan
Curated OER

Rational and Irrational Numbers 1

For Teachers 8th - 10th Standards
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...
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Lesson Plan
Curated OER

Rational and Irrational Numbers 2

For Teachers 9th - 12th Standards
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...
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Lesson Plan
Illustrative Mathematics

Comparing Rational and Irrational Number

For Teachers 7th - 9th Standards
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...
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Worksheet
Curated OER

myTestBook.com Rational and Irrational Numbers

For Students 7th - 9th
In this rational and irrational numbers worksheet, students answer multiple choice questions about rational and irrational numbers. Students complete 20 questions.
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Lesson Plan
Willow Tree

Rational vs. Irrational Numbers

For Students 7th - 10th Standards
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...
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Lesson Plan
EngageNY

The Decimal Expansion of Some Irrational Numbers

For Students 8th Standards
Develop a definition of irrational numbers through an exploration of square roots. The 11th lesson plan in this series of 25 asks scholars to estimate the value of a square root. Learners observe as the estimation extends further and...
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Handout
Charleston School District

Identifying Irrational Numbers

For Students 8th - 9th Standards
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. 
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Activity
Illustrative Mathematics

Identifying Rational Numbers

For Teachers 7th - 9th Standards
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...
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Activity
2
2
Illustrative Mathematics

Rational or Irrational?

For Teachers 9th - 12th Standards
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...
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Lesson Plan
Curated OER

Rational, Irrational and Square Roots

For Teachers 7th - 8th
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...
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Activity
Education Development Center

Sum of Rational and Irrational is Irrational

For Teachers 8th - 9th Standards
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.
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Lesson Plan
EngageNY

Rational and Irrational Numbers

For Teachers 10th - 12th Standards
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...
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Worksheet
Curated OER

Rational and Irrational Numbers

For Students 8th - 9th
Here is a rational and irrational numbers learning exercise 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.
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Worksheet
Curated OER

The Real Number System: Rational or Irrational

For Students 9th - 12th
In this real numbers worksheet, students 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.
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Worksheet
Curated OER

The Irrational Numbers

For Students 9th - 11th
In this algebra learning exercise, 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.
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Assessment
3
3
Illustrative Mathematics

Operations with Rational and Irrational Numbers

For Teachers 9th - 12th Standards
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...
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Assessment
EngageNY

Mid-Module Assessment Task: Grade 8 Module 7

For Students 8th Standards
Assess pupil understanding of rational and irrational numbers with a mid-module assessment that is the 15th lesson in the 25-part series. The questions represent the objectives in the first half of the series. Topics include decimal...
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Lesson Plan
Illustrative Mathematics

Converting Decimal Representations of Rational Numbers to Fraction Representations

For Teachers 7th - 9th Standards
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...
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Interactive
CK-12 Foundation

Simplification of Radical Expressions: Irrational Garden Plot

For Students 8th - 10th
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.
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Lesson Plan
Illustrative Mathematics

Irrational Numbers on the Number Line

For Teachers 7th - 9th Standards
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...
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Worksheet
Curated OER

My Test Book: Rational and Irrational Numbers

For Students 6th - 8th
In this online interactive math skills worksheet, students solve 10 multiple choice math problems regarding rational and irrational numbers. Students may submit their answers to be scored.
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Unit Plan
Mathematics Vision Project

Module 4: Rational Functions

For Students 9th - 12th Standards
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...
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Lesson Plan
EngageNY

Irrational Exponents—What are 2^√2 and 2^π?

For Teachers 9th - 12th Standards
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...

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