Lesson H.1A.4
H,1A.4: Develop, identify, and/or justify equivalent algebraic expressions, equations, and
inequalities using the properties of exponents, equality and inequality, as well as the
commutative, associative, inverse, identity, and distributive properties. (Inequalities is
taught in the linear equations and inequalities and systems of equations unit. Properties of
exponents are taught in Chapter 7.)
Learning Target:
 Identify and use the commutative, associative, inverse, identity, and distributive
properties to solve and evaluate equations and expressions.
Topic: Commutative Property
Warm-up: True or false: 3 + 7 = 10 and 7 + 3 = 10? True or False: 6 + 4 = 4 + 6?
Teach:
 Changing the order of the numbers does not change the sum or product.
Active Engagement:
 Give students places cards with numbers and have them physically change the order
to prove that it does not affect the sum or product.
 Analogy of commuting to and from home to work. Any order is the same distance.
 Vocabulary notes with examples.
 Add to an Algebra Property Dictionary.
Topic:
Associative Property
Warm-up: True or false: 3 + (6 + 1) = 10 and (3 + 6) + 1 = 10? True or False:
(2  3)  5  2  (3  5) ?
Teach:
 Changing the grouping of the numbers does not change the sum or product.
Active Engagement:
 Analogy of commuting to and from home to work to mall. Any order is the same
distance.
 Vocabulary notes with examples.
 Add to an Algebra Property Dictionary.
Topic: Inverse Property
Warm-up: Fill in the blank to make each statement true:
a. -3 + __ = 0
b. 4 + __ = 0
c. 5  __  1
d.
1
 __  1
7
Teach:
 Additive Inverse what you can add to a number to make the sum 0.
 Multiplicative Inverse what you can multiply to a number to make the product 1.
Active Engagement:
 Vocabulary notes with examples.
 Add to an Algebra Property Dictionary.
Topic: Identity Property
Warm-up:
1. Fill in the blank to make each statement true:
a. 2 + 0 = __
b. 0 + -5 = __
c. 0 + __ = 7
-or2. Any number plus zero is the original number. Write three examples that prove that
statement is true.
Teach:
 Additive Identity is that any number plus zero equals the original number.
 Multiplicative Identity is that any number times one is the original number.
Active Engagement:
 Vocabulary notes with examples.
 Add to an Algebra Property Dictionary.
Topic: Combining Like Terms
Warm-up: If you have 5 semi-trucks and 3 kittens. How many semi-trucks do you have?
How many kittens do you have?
Teach:
 Combine like terms
 Important Vocabulary: Coefficient, constant, & term
Active Engagement:
 Vocabulary notes with examples.
 Add to an Algebra Property Dictionary.
Guided Practice (Work time):
 H.1A.4 Simplifying the Expressions WS (1 & 2)
Topic: Distributive Property
Warm-up: Use order of operation to compute:
a. 2(5) + 2 (-7)
b. 2(5-7)
Teach:
 Distributive property. Methods could include the mail-carrier, algebra tiles,
rainbow, etc.
Active Engagement:
 Vocabulary notes with examples.
 Add to an Algebra Property Dictionary.
Guided Practice (Work time):
 H.1A.4 Distributive Property Worksheet (1 & 2)
 H.1A.4 Guided Practice Associative/Commutative/Distributive/Identiy/Inverse
Properties Worksheet
Common Misconceptions:
 Commutative and Associative Properties do not work with subtraction or division.
 Inverse defined as opposite can confuse kids to change the sign of a number, it
might work better to define Inverse as the undoing.
 Students only distribute to the first number in the parenthesis.
 Students will try to simplify too much when combining like terms so there is only
one term left for an answer.