SOL Objective(s):
7.16 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.
8.1 The student will
a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with
real numbers.
8.15 The student will
c) identify properties of operations used to solve an equation.
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.
8.1 The student will
a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with
real numbers.
8.15 The student will
c) identify properties of operations used to solve an equation.
Previous and Related SOL Objectives:
3.20 The student will
a) investigate the identity and the commutative properties for addition and multiplication; and b) identify examples of the identity and commutative properties for addition and multiplication 4.16 The student will b) investigate and describe the associative property for addition and multiplication 5.19 The student will investigate and recognize the distributive property of multiplication over addition 6.19 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. 
Prerequisite Skills:

Khan Skill Phrases: 
The Basics and Background Information
• The commutative property for addition states that changing the order of the addends does not change the sum (e.g., 5 + 4 = 4 + 5).
• The commutative property for multiplication states that changing the order of the factors does not change the product (e.g., 5 · 4 = 4 · 5).
• The associative property of addition states that regrouping the addends does not change the sum [e.g., 5 + (4 + 3) = (5 + 4) + 3].
• The associative property of multiplication states that regrouping the factors does not change the product [e.g., 5 · (4 · 3) = (5 · 4) · 3].
• Subtraction and division are neither commutative nor associative.
• The distributive property states that the product of a number and the sum (or difference) of two other numbers equals the sum (or difference) of the products of the number and each other number [e.g., 5 · (3 + 7) = (5 · 3) + (5 · 7), or 5 · (3 – 7) = (5 · 3) – (5 · 7)].
• Identity elements are numbers that combine with other numbers without changing the other numbers. The additive identity is zero (0). The multiplicative identity is one (1). There are no identity elements for subtraction and division.
• The additive identity property states that the sum of any real number and zero is equal to the given real number (e.g., 5 + 0 = 5).
• The multiplicative identity property states that the product of any real number and one is equal to the given real number (e.g., 8 · 1 = 8).
• Inverses are numbers that combine with other numbers and result in identity elements [e.g., 5 + (–5) = 0; 15 · 5 = 1].
• The additive inverse property states that the sum of a number and its additive inverse always equals zero [e.g., 5 + (–5) = 0].
• The multiplicative inverse property states that the product of a number and its multiplicative inverse (or reciprocal) always equals one (e.g., 4 · 14 = 1).
• Zero has no multiplicative inverse.
• The multiplicative property of zero states that the product of any real number and zero is zero.
• Division by zero is not a possible arithmetic operation. Division by zero is undefined.
• Expressions are simplified using the order of operations and the properties for operations with real numbers, i.e., associative, commutative, and distributive and inverse properties.
• The commutative property for multiplication states that changing the order of the factors does not change the product (e.g., 5 · 4 = 4 · 5).
• The associative property of addition states that regrouping the addends does not change the sum [e.g., 5 + (4 + 3) = (5 + 4) + 3].
• The associative property of multiplication states that regrouping the factors does not change the product [e.g., 5 · (4 · 3) = (5 · 4) · 3].
• Subtraction and division are neither commutative nor associative.
• The distributive property states that the product of a number and the sum (or difference) of two other numbers equals the sum (or difference) of the products of the number and each other number [e.g., 5 · (3 + 7) = (5 · 3) + (5 · 7), or 5 · (3 – 7) = (5 · 3) – (5 · 7)].
• Identity elements are numbers that combine with other numbers without changing the other numbers. The additive identity is zero (0). The multiplicative identity is one (1). There are no identity elements for subtraction and division.
• The additive identity property states that the sum of any real number and zero is equal to the given real number (e.g., 5 + 0 = 5).
• The multiplicative identity property states that the product of any real number and one is equal to the given real number (e.g., 8 · 1 = 8).
• Inverses are numbers that combine with other numbers and result in identity elements [e.g., 5 + (–5) = 0; 15 · 5 = 1].
• The additive inverse property states that the sum of a number and its additive inverse always equals zero [e.g., 5 + (–5) = 0].
• The multiplicative inverse property states that the product of a number and its multiplicative inverse (or reciprocal) always equals one (e.g., 4 · 14 = 1).
• Zero has no multiplicative inverse.
• The multiplicative property of zero states that the product of any real number and zero is zero.
• Division by zero is not a possible arithmetic operation. Division by zero is undefined.
• Expressions are simplified using the order of operations and the properties for operations with real numbers, i.e., associative, commutative, and distributive and inverse properties.
Essential Knowledge and Skills
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to...
• Identify properties of operations used in simplifying expressions.
• Apply the properties of operations to simplify expressions.
• Identify properties of operations used to solve an equation from among:
 the commutative properties of addition and multiplication;
 the associative properties of addition and multiplication;
 the distributive property;
 the identity properties of addition and multiplication;
 the zero property of multiplication;
 the additive inverse property; and
 the multiplicative inverse property.
• Identify properties of operations used in simplifying expressions.
• Apply the properties of operations to simplify expressions.
• Identify properties of operations used to solve an equation from among:
 the commutative properties of addition and multiplication;
 the associative properties of addition and multiplication;
 the distributive property;
 the identity properties of addition and multiplication;
 the zero property of multiplication;
 the additive inverse property; and
 the multiplicative inverse property.
Vocabulary and Things to Know:commutative property
associative property distributive property identity property zero property inverse property properties can be phrased differently: zero property of multiplication or multiplicative property of zero 
Be Able To:define properties
identify properties from step to step in equations 
The topic: What is it and what will we learn?
Properties are the logical and mathematical reasons for why we can do what we do with regard to operations, simplifying, and solving equations/inequalities. IE: fancy words/phrases for things you knew when you were younger or could figure out.
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