Lesson 1: Rational & Irrational Numbers
Duration of Days: 3
Lesson Objective
Students will understand that every number has a decimal expansion.
Students will distinguish between rational numbers (which terminate or repeat) and irrational numbers (which do not).
Students will convert repeating decimals into fractions and approximate irrational numbers on a number line.
What is the difference between a rational and an irrational number?
How can we use a number line to show the approximate value of an irrational number?
How do we turn a repeating decimal into a fraction?
Rational Number, Irrational Number, Decimal Expansion, Repeating Decimal, Terminating Decimal, Approximation, Number Line, Integers
8.NS.A.1: Know that numbers that are not rational are called irrational. Understand that every number has a decimal expansion.
8.NS.A.2: Use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line diagram.
Purpose: To expand the student’s understanding of the number system beyond integers and simple fractions, preparing them for higher-level operations with square roots.
DOK Level: 2 (Skill/Concept).
Students may think that all decimals are rational.
Students may struggle to realize that a number like p never ends and never repeats.
Confusion between a "very long" terminating decimal and a non-terminating irrational number.
Provide a graphic organizer for classifying numbers (Rational vs. Irrational).
Use color-coded number lines for plotting approximations.
Provide a step-by-step "cheat sheet" for the algebraic process of converting repeating decimals to fractions.
Exit Ticket