Lesson 1: Rational Numbers
Duration of Days: 3
Lesson Objective
Students will be able to identify and classify rational and irrational numbers as part of working with square roots.
What is the difference between a rational and an irrational number?
How can we estimate the value of a square root for a non-perfect square?
Why is understanding the number system essential for solving problems involving right triangles?
Square Root
Radical
Rational Number
Irrational Number
8.NS.A: Know that there are numbers that are not rational, and approximate them by rational numbers.
1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
Target H: While this target broadly covers understanding and applying the Pythagorean Theorem, it specifically includes the prerequisite skill of identifying and classifying rational and irrational numbers when working with square roots.
Description: This lesson serves as the foundational introduction to the Pythagorean Theorem unit by exploring the number system, specifically focusing on perfect squares, non-perfect squares, and the distinction between rational and irrational numbers.
Purpose: To provide the necessary numerical background for calculating side lengths of right triangles.
DOK Level: Level 2 (Skill/Concept) – Classifying and estimating square roots.
Architectural Measurements: Using square roots to determine the diagonal dimensions of building materials or spaces
Perfect Squares Only: Students may believe only perfect squares have square roots.
Rational/Irrational Confusion: Students often mistake repeating decimals as irrational rather than rational.
Visual Aids: interactive concept visualization
Guided Practice: Provide structured notes for students
IAB: The Number System
Performance Tasks