Explain operations on rational and irrational numbers

Start lessonBegins with Rational irrational operations · Slides

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Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

HSN.RN.B.3

**HSN.RN.B.3**: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

HSN.RN.B.3: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

What you'll learn

Explain why the sum or product of two rational numbers is always rational, using a general algebraic argument (not just examples)
Explain why the sum of a rational number and an irrational number is always irrational, using proof by contradiction
Explain why the product of a nonzero rational number and an irrational number is always irrational, using proof by contradiction
Identify the key role of the "nonzero" condition: explain why 0 times an irrational number is rational, and why the general product rule requires the rational factor to be nonzero
Classify expressions like 3 + √2, (1/2) · √5, or 7 + √9 as rational or irrational and justify the classification using the learned arguments

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Rational irrational operations

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Exercise

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