CCSS.Math.Content.HSN-RN.B

MathGrades 9–12The Real Number System

Standard Cluster

Use properties of rational and irrational numbers.

Common Core State Standards for Mathematics

Cluster contents

CCSS.Math.Content.HSN-RN.B is a cluster heading. These are the individual standards under it.

Teacher's field guide

What Students Need to Do: Students determine whether sums and products involving rational and irrational numbers are rational or irrational. They explain which results are guaranteed and use counterexamples when no single result is guaranteed.
What Mastery Looks Like: Students correctly predict when a sum or product must be rational or irrational. They support each claim with number properties, algebra, or a counterexample.
Common Misconceptions: Students may think combining two irrational numbers always gives an irrational result. They may also label every nonterminating decimal irrational, forgetting that repeating decimals are rational.
How to Assess It: Use an exit ticket: classify and justify the results of 3 + √2, √2 + (−√2), 5√3, and √3 × √3.

Lesson moves

Give pairs of rational and irrational number cards, then have students combine, calculate, classify, and explain each result.
Ask students to explain why rational plus irrational must be irrational, then find two irrational numbers with a rational sum.
Play a claim challenge where teams prove a statement about sums or products, or defeat it with a counterexample.
Compare exact and decimal forms of a square's diagonal length, then classify each measurement and explain why rounding changes its number type.

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