Number and Number Sense, Computation and Estimation 

Measurement and Geometry 

Probability, Statistics, Patterns, Functions, and Algebra 

SOL Review Materials 




Number and Number Sense
Focus: Relationships within the Real Number System
The student will describe orally and in writing the relationships between the subsets of the real number system. 


Essential Knowledge and Skills 
 Describe orally and in writing the relationships among the sets of natural or counting numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
 Illustrate the relationships among the subsets of the real number system by using graphic organizers such as Venn diagrams. Subsets include rational numbers, irrational numbers, integers, whole numbers, and natural or counting numbers.
 Identify the subsets of the real number system to which a given number belongs.
 Determine whether a given number is a member of a particular subset of the real number system, and explain why.
 Describe each subset of the set of real numbers and include examples and nonexamples.
 Recognize that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.†Revised March 2011

Essential Understandings 
 How are the real numbers related? Some numbers can appear in more than one subset, e.g., 4 is an integer, a whole number, a counting or natural number and a rational number. The attributes of one subset can be contained in whole or in part in another subset.


Vertical Articulation 
 SOL 6.4  Represent multiplication and division of fractions

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Organizing Numbers (PDF)  Investigating the real number system (Word)
 Warmup: The Real Number System (doc)
 Notes/Practice: The Real Number System (doc)
 Notes: The Real Number System (ppt)
 Notes: The Real Number System (flipchart)
 Notes: The Real Number System #2 (flipchart)
 Notes: The Real Number System (pdf)
 Teacher Notes: The Real Number System (pdf)
 Project: Real Number Stories (doc)  Sample Student Artifacts (zip)
 Flowchart: Real Numbers (doc)
 Activity: Find Someone Who Can... (doc)
 VDOE Algebra Readiness Curriculum Companion: Working with Integers (pdf)

Real World Lessons 

Practice 
 Rational vs. Irrational  What is True? (doc)
 Real Numbers  Who Am I? (doc)
 Real Number Statements (flipchart)
 Real Numbers Practice #1 (doc)
 Real Numbers Practice #2 (doc)
 Quiz Review: The Real Number System (doc)
 Quiz: The Real Number System (doc)

SelfAssessments 
 SOL 8.2 MiniQuiz: Real Number System

Skills 

Videos 
 PH: Classifying real numbers and rational or irrational

Explore
Learning 

Websites 
 Song: Number Types (YouTube)
 Quiz: 10 question selfchecking quiz on identifying Real Numbers (studyzone.org)
 Nice short tutorial on the Real Number system with example problems (Univ. Iowa)
 Real Number flashcards  vocabulary words/definitions (quizlet.com)

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Working with Integers  The lessons in this section focus on comparing, adding, subtracting, multiplying, and dividing integers as
well as describing the subsets of the real number system. (pdf)

Common Core
Standards 
7.NS.2d 
8.EE.2 
8.NS.1 
8.NS.2 
8.EE.2 
NRN.3 

