Patterns, Functions, and Algebra
Focus: Variable Equations and Properties
The student will investigate and recognize
a) the identity properties for addition and multiplication;
b) the multiplicative property of zero; and
c) the inverse property for multiplication. 


Essential Knowledge and Skills 
 Identify a real number equation that represents each property of operations with real numbers, when given several real number equations.
 Test the validity of properties by using examples of the properties of operations on real numbers.
 Identify the property of operations with real numbers that is illustrated by a real number equation.
NOTE: The commutative, associative and distributive properties are taught in previous grades.

Essential Understandings 
 How are the identity properties for multiplication and addition the same? Different? For each operation the identity elements are numbers that combine with other numbers without changing the value of the other numbers. The additive identity is zero (0). The multiplicative identity is one (1).
 What is the result of multiplying any real number by zero? The product is always zero.
 Do all real numbers have a multiplicative inverse? No. Zero has no multiplicative inverse because there is no real number that can be multiplied by zero resulting in a product of one.


Vertical Articulation 
 SOL 4.16b  investigate/ describe
associative property for add/mult
 SOL 5.19  distributive property of mult
over addition
 SOL 7.16abcde  a) apply properties w/ real
numbers: commutative and
associative properties for add/mult;
b) distributive property; c) additive/multiplicative identity properties; d)
additive/ multiplicative inverse
properties; e) multiplicative property
of zero
 SOL 8.15c  identify properties of operations
used to solve equations

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Pick and Choose (PDF)  Exploring properties of real numbers (Word)
 Notes: Properties of Real Numbers (ppt)  explanation of each property
 Notes: Properties Speed Drill (flipchart)  20 practice problems using pictures to represent the properties
 Guided Notes and Practice: Properties of Real Numbers (doc)  6 pages includes notes, a fill in chart, practice problems and activities
 Activity: Number Properties Sort  Associative, Commutative, Identity (pdf)  30 questions to sort the properties into their respective category
 Activity: Properties Matching (doc)
 Graphic Organizer: Properties Flowchart (pdf)  helps students to know how to identify the different properties
 Selfpaced Properties ActivEngage (flipchart)  22 matching and multiple choice questions using ActivEngage.
 Game: Property Dominos (xls)
 Game: Name that Property! (ppt)  practice problems for students to practice identifying different properties
 Game: Number Property Matching (ppt)  practice questions to match with correct property
 Game: Properties: Last Man Standing (flipchart)  practice questions identifying different properties
 VDOE Algebra Readiness Curriculum Companion: Using Order of Operations and Exploring Properties (pdf)

Real World Lessons 

Practice 
 Worksheet: Identifying Properties of Multiplication (pdf)  12 multiple choice questions
 Worksheet: Properties  Inverse, Identity, Mult. Property of Zero (doc)  15 questions matching and creating properties
 Worksheet: Properties Multiple Choice (pdf)  20 multiple choice questions
 Worksheet: Properties Matching and Multiple Choice (doc)  30 practice problems including matching and multiple choice
 Quiz: Properties (doc)  10 question practice quiz

SOL Mini Quiz 
 SOL 6.19 Mini Quiz: Properties (pdf)

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 
 AAAMath: Properties of Multiplication
 AAAMath: Properties of Addition
 SoftSchools: Addition and Mulitplication Properties Quiz
 Edubakery: Math Properties Bingo Cards

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 
