Understanding Real Numbers: A Journey Through Rational and Irrational Values
In this learning module, we will explore the fascinating world of real numbers. We will begin by defining the set of real numbers, which includes both rational numbers and irrational numbers . You’ll learn how to classify these numbers, recognize their unique properties, and see how they form the foundation of much of the math you’ll use in your studies and in the real world.
Next, we will delve into square roots and cube roots, essential tools for working with real numbers. You’ll discover how these operations are the inverse of squaring and cubing, and how they can be used to solve equations. These skills will prepare you for understanding and applying the Pythagorean Theorem in a future learning module.
Finally, we’ll focus on practical techniques for estimating square roots and working with repeating decimals. Instead of relying on a calculator, you’ll learn how to estimate square roots by placing them on a number line, which will help you visualize and approximate their values. Additionally, you will explore how to convert repeating decimals into fractions, a useful skill for simplifying and handling numbers that cannot be expressed as finite decimals.
By the end of this module, you’ll have a solid understanding of real numbers, square roots, and decimals, giving you the tools to solve a wide variety of mathematical problems.
Classifying Real Numbers Lesson
Lesson Objective: By the end of the lesson, students will be able to classify numbers as real, rational, irrational, integers, or whole numbers, and understand that irrational numbers cannot be expressed as fractions.
Essential Question: What characteristics should you look for to classify a real number as irrational or rational?
Check for Understanding: Test your understanding with these end-of-lesson practice problems to reinforce your skills and master the concept!
Square Roots Lesson
Lesson Objective: By the end of the lesson, students will be able to valuate expressions involving square roots and use square roots to solve equations.
Essential Question: How can you use what you know about exponents to evaluate square roots?
Cube Roots Lesson
Lesson Objective: By the end of the lesson, students will be able to find cube roots of perfect cubes, evaluate expressions involving cube roots, and use cube roots to solve equations.
Essential Question: How are square roots and cube roots different?
Edpuzzle interactive student lesson. (FREE)
Check for Understanding: Test your understanding with these end-of-lesson practice problems to reinforce your skills and master the concept!
Edpuzzle interactive student practice. (FREE)
Edpuzzle interactive student practice. (FREE)
Edpuzzle interactive student practice. (FREE)
Edpuzzle interactive student practice. (FREE)
Estimating Square Roots Lesson
Lesson Objective: By the end of the lesson, students will be able to identify non-perfect squares, use a number line to determine the integer values a non-perfect square lies between, and approximate the square root of a non-perfect square to the nearest hundredth.
Essential Question: What is the difference between a perfect square and a non-perfect square?
Edpuzzle interactive student lesson. (FREE)
Check for Understanding: Test your understanding with these end-of-lesson practice problems to reinforce your skills and master the concept!
Edpuzzle interactive student practice. (FREE)
Edpuzzle interactive student practice. (FREE)
Edpuzzle interactive student practice. (FREE)
Edpuzzle interactive student practice. (FREE)
Edpuzzle interactive student practice. (FREE)
Writing Terminating & Repeating Decimals as Fractions Lesson
Lesson Objective: By the end of the lesson, students will be able to write terminating decimals as fractions and write repeating decimals as fractions.
Essential Question: How are terminating and repeating decimals different?
Edpuzzle interactive student lesson. (FREE)
Check for Understanding: Test your understanding with these end-of-lesson practice problems to reinforce your skills and master the concept!