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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 in this series of 25 asks scholars to estimate the value of a square root. Learners observe as the estimation extends further and further...
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Workbook
1
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
EngageNY

Comparing Irrational Numbers

For Students 8th Standards
Build on your classes' understanding of irrational numbers by comparing their values. The 13th lesson in the 25-part module has individuals estimate values of both perfect and non-perfect roots. They finish by graphing these numbers on a...
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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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Interactive
CK-12 Foundation

Square Roots and Irrational Numbers: Estimating Radicals

For Students 8th - 10th
Try out a resource using triangles to estimate radicals. An interactive app allows learners to approximate some irrational numbers involving square roots. They find the two consecutive numbers that an irrational number lies between by...
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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

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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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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Worksheet
Curated OER

The Irrational Numbers

For Students 9th - 11th
In this algebra worksheet, learners 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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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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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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Worksheet
Curated OER

Radicals and the Irrational Numbers

For Students 9th - 10th
In this Integrated Algebra worksheet, students differentiate between rational and irrational numbers and locate irrational numbers on a number line.  The one page worksheet contains six problems.  Answers are provided. 
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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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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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Lesson Plan
Curated OER

Real Numbers

For Teachers 8th - 10th Standards
Young mathematicians examine and discuss the concepts of integers, rational numbers, irrational numbers, and real numbers. They list examples of each term and order numerical examples.
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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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Handout
Charleston School District

Comparing and Ordering Irrational Numbers on a Number Line

For Students 8th - 9th Standards
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...
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Assessment
Charleston School District

Review Unit 7: Real Numbers

For Students 8th Standards
Provide pupils with problems to check their understanding of the concepts within the unit. The seven-part series of lessons covers concepts related to irrational numbers. Learners convert between fractions and decimals, estimate the...
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Lesson Plan
Illustrative Mathematics

Calculating and Rounding Numbers

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

The Irrational Numbers

For Students 9th - 11th
In this Algebra I/Algebra II worksheet, learners identify rational and irrational numbers.  The one page worksheet contains a combination of ten multiple choice and free response questions.  The answers are included. 
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Lesson Plan
Curated OER

Numbers Beyond Reason!

For Teachers 4th
Fourth graders use the story of the discovery of irrational numbers to explore the different classes of numbers, the different ways in which numbers may be represented, and how to classify different numbers into their particular class.
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Lesson Plan
Curated OER

Add Positive And Negative Numbers

For Teachers 6th - 8th
Scholars investigate the concept of adding positive and negative numbers. They practice adding using the number line for scaffolding. This can be done as a game for younger learners, but may also be helpful for engaging the older pupils.
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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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