Virginia SOL 8.NS.2.c
The Standard
Describe each subset of the set of real numbers and include examples and non-examples.
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 describe natural, whole, integer, rational, irrational, and real numbers in their own words. They sort numbers into every set that applies and give examples and non-examples for each set.
What Mastery Looks Like
- A student places -4 in the integer, rational, and real sets, and places √2 in the irrational and real sets. They justify each choice from a definition and give a valid example and non-example for every set.
Common Misconceptions
- Students often think every decimal is irrational or that every square root is irrational. They may assign a number to only one set, or place zero among natural numbers while excluding it from whole numbers.
How to Assess It
- Exit ticket: Complete six rows for natural, whole, integer, rational, irrational, and real numbers, giving a definition, example, and non-example for each.
Lesson moves
Ways to Teach It
Place number cards into nested hoops labeled natural, whole, integer, rational, and real, with a separate irrational region inside real.
Write an explanation of why -3 belongs to several sets while √3 belongs only to the irrational and real sets.
Play Name Every Set by revealing number cards and awarding points only when teams list every correct set membership.
Classify a temperature of -5°C, a $12 price, and a √2-meter diagonal, then explain which number sets model each.
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Related Standards
- 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.1.c
Use multiple strategies (e.g., benchmarks, number line, equivalency) to compare and order no more than five real numbers expressed as integers, fractions (prope...
- 8.NS.2.b
Classify and explain why a given number is a member of a particular subset or subsets of the real number system.
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