Virginia SOL 8.NS.2.b
The Standard
Classify and explain why a given number is a member of a particular subset or subsets of the real number system.
Virginia Standards of Learning for Mathematics · The student will investigate and describe the relationship between the subsets of the real number system.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify every real number subset that contains a given number. They use a number’s form and properties to explain each classification.
What Mastery Looks Like
- Students classify numbers in fraction, decimal, integer, and radical form. They can explain, for example, why −5 is an integer, rational number, and real number, while √2 is irrational and real.
Common Misconceptions
- Students may name only the smallest subset instead of every subset that contains the number. They may assume every square root is irrational or that every nonterminating decimal is irrational. Some confuse negative integers with irrational numbers.
How to Assess It
- Give students −4, 0.75, √49, and √3. Ask them to list every applicable subset and justify each classification in one phrase.
Lesson moves
Ways to Teach It
Sort number cards into nested hoops labeled natural, whole, integer, rational, irrational, and real, then defend two placements.
Write a response to this claim: Every square root is irrational. Use two examples to prove or disprove it.
Play subset bingo by calling numbers such as −8, 2.5, √16, and π while students mark every matching category.
Classify numbers from a bank statement, measuring tape, and calculator display, then explain which real number subsets appear.
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Printable 8.NS.2.b Worksheet
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Related Standards
- 2.NS.2.g
Compare two whole numbers, each 999 or less, represented concretely, pictorially, or symbolically, using words (greater than, less than, or equal to) and symbol...
- 8.NS.2.a
Describe and illustrate the relationships among the subsets of the real number system by using representations (e.g., graphic organizers, number lines). Subsets...
- 8.NS.2
The student will investigate and describe the relationship between the subsets of the real number system.
- 8.NS.2.c
Describe each subset of the set of real numbers and include examples and non-examples.
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