EngageNY
The Decimal Expansion of Some Irrational Numbers
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...
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...
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
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...
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...
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
Numbers Beyond Reason!
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.
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
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...
Curated OER
Rational, Irrational and Square Roots
Seventh graders identify rational and irrational numbers and then, estimate the square root of numbers that are not perfect squares. They then identify what the radical is and differentiate between that and a division symbol clearly....
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.
Curated OER
Numbers 1.1
In this numbers 1.1 worksheet, students solve 64 problems about all kinds of numbers: rational, irrational, prime, composite, square roots, fractions, decimals.
Curated OER
Whole Numbers
A game is a great way to learn. Study what makes an integers, their traits, and characteristics. This lesson includes 3 separate activities intended to promote an understanding of integers, whole numbers, and opposites. The class is...
Curated OER
Babylonian Mathematics I
Learners examine a Babylonian clay tablet and the mathematics found on it as a catalyst to investigate a variety of mathematical ideas. They work with prime numbers, classify numbers as whole, integer, rational, or irrational and use...
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
Simplify Radicals
Learners are introduced to the concept of radicals and how to use them in various situations. They review rational and irrational numbers while simplifying different number sentences. They also practice factoring perfect squares.
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.
EngageNY
Converting Repeating Decimals to Fractions
Develop a process with your classes for converting repeating decimals to fractions. Through this process, pupils understand that any repeating decimal can be written as a fraction. The 10th lesson in this 25-part module helps reinforce...
Curated OER
Order in the Classroom
First graders define and identify integers, rational, irrational, real, and complex numbers. They place number cards in ascending and descending order.
Curated OER
Numbers, Numbers Everywhere!
Explore properties of integers! For this algebra lesson, pupils add, subtract, divide and multiply using integers correctly. They differentiate between rational and irrational numbers.