Common Core Math - HS Number and Quantity
Lesson Plan
Explain operations on rational and irrational numbers
Goals / Objectives
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
Standards
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.
Academic Vocabulary
Not in our source material
Remediation
This lesson’s brief has no prerequisite standards
Enrichment
Accommodations
Not in our source material