NY Next Generation Math AI-N.RN.3
The Standard
Use properties and operations to understand the different forms of rational and irrational numbers.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
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
Ways to Teach It
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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Printable AI-N.RN.3 Worksheet
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