Patterns, Functions, and Algebra
Focus: Linear Equations
The student will apply the following properties of operations with real numbers:
a) the commutative and associative properties for addition and multiplication;
b) the distributive property;
c) the additive and multiplicative identity properties;
d) the additive and multiplicative inverse properties; and
e) the multiplicative property of zero. 


Essential Knowledge and Skills 
 Identify properties of operations used in simplifying expressions.
 Apply the properties of operations to simplify expressions.

Essential Understandings 
 Why is it important to apply properties of operations when simplifying expressions?
Using the properties of operations with real numbers helps with understanding mathematical relationships.


Vertical Articulation 
 SOL 5.19  distributive property of mult
over addition
 SOL 6.19abc  a) investigate/recognize
identity properties for add/mult; b)
multiplicative property of zero; c)
inverse preperty for mult
 SOL 8.15c  identify properties of operations
used to solve equations
 SOL A.2abc  perform operations on
polynomials  a) apply laws of
exponents to perform operationss on
expressions; b)
add/subtract/multiply/divide
polynomials; c) factor first and
second degree binomials/trinomials
(1 or 2 variables)

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Properties (PDF)  Identifying and applying properties (Word)
 Notes: Properties of Real Numbers (ppt)
 Notes: Properties of Real Numbers (flipchart)
 Notes: Properties of Real Numbers #2 (flipchart)
 Notes: Properties with Caddies (ppt)
 Activity: Properties Cut & Paste (doc)
 Activity: Properties Foldable (doc)
 Game: Properties Concentration (flipchart)
 Notes: Property Pictures (doc)
 VDOE Algebra Readiness Curriculum Companion: Using Order of Operations and Exploring Properties (pdf)

Real World Lessons 

Practice 
 Worksheet: Properties (doc)
 Worksheet: Properties #2 (doc)
 Worksheet: Identifying Properties (pdf)
 Puzzle: Properties (pdf)
 Quiz: Properties (doc)
 Properties of Real Numbers (flipchart)
 Worksheet: Properties Matching (doc)

SOL Mini Quiz 
 SOL 7.16 Mini Quiz: Properties (pdf)  (doc)

Skills 

Videos 
 Additive Inverse Property (mp4)
 Associative Property (mp4)
 Identity Properties (mp4)
 Multiplicative Inverse Property (mp4)
 Multiplicative Property of Zero (mp4)
 Properties Rap (mp4)

Explore
Learning 
 Chocomatic (Multiplication, Arrays, and Area): Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar.

Websites 
 Regents Prep: Properties Practice
 Regents Prep: Properties Practice #2
 ClassZone: Commutative, Associative, and Distributive
 Brainpop: Commutative Property
 Brainpop: Associative Properties
 Brainpop: Distributive Property
 Quia: Rags to Riches Property Review
 Quia: Property Review
 Quia: Associative Property Battleship
 Quia: Properties Battleship

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Using Order of Operations and Exploring Properties  The lessons focus on order of operations and evaluating numerical expressions. Students
will also investigate and recognize properties of real numbers used to solve an equation. (pdf)

Common Core
Standards 
6.NS.4 
6.EE.3 
7.NS.1a 
7.NS.1b 
7.NS.1c 
7.NS.1d 
7.NS.2a 
7.NS.2c 
