Virginia SOL 8.NS.2
SOL Standard (Knowledge and Skills Cluster)
The student will investigate and describe the relationship between the subsets of the real number system.
Virginia Standards of Learning for Mathematics
Cluster contents
Knowledge and Skills in This Standard
8.NS.2 is a Standards of Learning standard. These are the knowledge and skills expectations under it.
- 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.b
Classify and explain why a given number is a member of a particular subset or 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.
Teacher's field guide
What This Cluster Means
What Students Need to Do
- Students identify how natural, whole, integer, rational, and irrational numbers fit within the real number system. They classify numbers into every subset that applies and support each choice with an example, definition, diagram, or number line.
What Mastery Looks Like
- Students correctly classify natural, whole, integer, rational, and irrational numbers using a nested diagram or number line. They explain classifications using properties such as terminating or repeating decimals and perfect-square roots.
Common Misconceptions
- Students often place a number in only one subset instead of all subsets that contain it. They may think every square root is irrational, or that repeating decimals, negative fractions, and zero are irrational.
How to Assess It
- Give students the numbers −4, 0, 3/5, √16, √7, and 0.333.... Ask them to name every subset for each number and justify two choices.
Lesson moves
Ways to Teach It
Give pairs a set of number cards to sort into nested hoops labeled natural, whole, integer, rational, irrational, and real.
Ask students to explain why −3 belongs to several subsets while √3 belongs to only irrational and real numbers.
Play a classification relay where teams place number cards on a nested subset chart and earn a point for each correct explanation.
Have students classify numbers from temperatures, bank balances, measurements, and calculator displays, then explain which subsets fit each value.
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Printable 8.NS.2 Worksheet
A ready-to-print activity worksheet aligned to 8.NS.2, with an answer key for the teacher on its own page. No account needed.
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