NY Next Generation Math AI-N.RN.3

MathGrades 9–12Use properties of rational and irrational numbers.

Standard Cluster

Use properties and operations to understand the different forms of rational and irrational numbers.

New York State Next Generation Mathematics Learning Standards

Cluster contents

AI-N.RN.3 is a cluster heading. These are the individual standards under it.

AI-N.RN.3.aPerform all four arithmetic operations and apply properties to generate equivalent forms of rational numbers and square roots.
AI-N.RN.3.bCategorize the sum or product of rational or irrational numbers.- The sum and product of two rational numbers is rational.- The sum of a rational number and an irrational number is irrational.- The product of a nonzero rational number and an irrational number is irrational.- The sum and product of two irrational numbers could be either rational or irrational.

Teacher's field guide

What Students Need to Do: Students use properties and operations in Algebra I to understand equivalent forms of rational and irrational numbers. They reason about whether sums and products remain rational or become irrational.
What Mastery Looks Like: The student classifies numbers, rewrites them accurately, and justifies outcomes using number properties rather than decimal appearance alone. Counterexamples are used when a claim is not always true.
Common Misconceptions: Students may call every nonterminating decimal irrational or assume the sum of two irrational numbers must be irrational. They may treat an approximation as an exact form.
How to Assess It: Ask students to classify and justify three claims: rational plus rational, rational plus irrational, and irrational plus irrational, using examples or counterexamples.

Lesson moves

Sort exact number cards into rational and irrational groups, then combine selected pairs with operation cards.
Ask students whether two irrational numbers can have a rational sum and require a counterexample.
Play always, sometimes, or never with claims about sums and products of rational and irrational numbers.
Distinguish exact and approximate forms when using irrational measurements in geometry or science.

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