Rational vs Irrational Numbers Explained
Grade 9 Algebra 1 90-minute lesson IB Mathematics Framework
Learning Objectives
Understand definitions and properties of rational and irrational numbers Classify different numbers as rational or irrational with justification Represent numbers visually on number lines and with models Communicate mathematical reasoning clearly
Warm-up Poll
Write down any number on your paper Is your number rational or irrational? Be ready to explain your thinking!
What Are Rational Numbers?
Can be expressed as a fraction a/b where b ≠ 0 Includes whole numbers, integers, and fractions Decimal form: terminates or repeats Examples: 1/2, -3, 0.75, 0.333...
What Are Irrational Numbers?
CANNOT be expressed as a fraction of integers Decimal form: non-terminating and non-repeating Goes on forever without a pattern Examples: √2, π, √3, e
Rational vs Irrational Comparison
{"left":"Can be written as a/b fraction\nDecimals terminate or repeat\nExamples: 1/3, 0.25, -7\nIncludes all integers","right":"Cannot be written as fraction\nDecimals never end, never repeat\nExamples: √2, π, √5\nInfinite non-repeating decimals"}
Group Classification Challenge
Form groups of 5 students each Classify the numbers on your cards Prepare to justify ONE classification Use calculators and visual models
Common Misconceptions
'All decimals are irrational' - FALSE 0.333... is rational (equals 1/3) 'Square roots are always irrational' - FALSE √4 = 2, which is rational
Number Detective Worksheet
Individual assessment task Classify given numbers with justification Show your work clearly Sketch numbers on number line
Reflection Question
Why is it important to distinguish between rational and irrational numbers? How might this knowledge help in future math courses? Share one insight from today's lesson
Key Takeaways & Next Steps
Rational numbers can be written as fractions Irrational numbers have non-repeating, non-terminating decimals Both types fill the real number line Next: Operations with irrational numbers
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