CCSS.Math.Content.HSN-RN.B

MathGrades 9–12The Real Number System

The standard

Use properties of rational and irrational numbers.

Common Core State Standards for Mathematics

What this standard means

Students need to predict and explain what kind of number results when they add, subtract, multiply, or divide rational and irrational numbers. They should use examples and properties, not just decimal guesses.

Mastery looks like saying why 3 + √2 is irrational, why 5√2 is irrational, and why √2 · √2 is rational. Students often overgeneralize, thinking any expression with a radical is irrational, or trust rounded calculator decimals too much.

Ways to teach it

  • Hands-on activity: give students number cards like 4, 1/2, √3, and √12, then sort operation results into rational or irrational piles.
  • Discussion prompt: ask, “Can two irrational numbers ever make a rational number?” and require one example and one non-example.
  • Quick assessment: students complete four blanks, rational plus irrational, irrational times irrational, rational divided by irrational, and explain one answer.
  • Real-world connection: compare exact diagonal lengths of square tiles, like √2 feet, with rounded calculator measurements used for cutting materials.

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Related standards

Standard text verified against corestandards.org on July 10, 2026.

Page updated July 10, 2026.

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