9th Grade Unit 2 Lesson 1 Day 1
9th Grade Math Class; Lesson Number 1 Day 1 Properties of Equality
Key Standards addressed in this Lesson:
MCC9‐12.A.REI.1 Explain each step in solving a simple equation as following
from the equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution. Construct a viable argument
to justify a solution method.
Time allotted for this Lesson: 1 Day
Materials Needed:
Key Concepts in Standards:
Students should focus on and master linear equations and be able to extend and apply their reasoning to other types
of equations in future courses. Students will solve exponential equations with logarithms in future courses.
Properties of operations can be used to change expressions on either side of the equation to equivalent expressions.
In addition, adding the same term to both sides of an equation or multiplying both sides by a non-zero constant
produces an equation with the same solutions. Other operations, such as squaring both sides, may produce equations
that have extraneous solutions.
Example: Explain why the equation
that
+
+
= 5 has the same solutions as the equation 3x + 14 = 30. Does this mean
is equal to 3x + 14?
Essential Question:
How do you identify and apply the properties of equality?
Vocabulary:
Tier 1: already knows
Tier 1
Property
Order of Operations
Variable
Equality
Equation
Coefficient
Tier 2: needs review
Tier 3: New Vocabulary
Tier 2
Tier 3
Associative Property
Justify
Commutative Property
Prove
Identity Property
Inverse Property
Distributive Property
Reflexive Property
Symmetric Property
Transitive Property
Properties of Equality
Concepts/Skills to Maintain: Refer to TE
 Using inverse operations to isolate variables and solve equations
 Maintaining order of operations
 Understanding and use properties of exponents
Opening:
Opening Activity: Unscrambling Vocabulary Words (Attached)
9th Grade Unit 2 Lesson 1 Day 1
Work Session:
Teacher Notes on Properties of Operations and Equality (attached)
Students fill-in the guided notes.
Closing:
Ticket out the door:
Justify each step using the appropriate property:
3x -2(3y - 2x + 8) - 3
3x + - 6y + 4x + -16 - 3
3x + 4x + - 6y + -16- 3
(3x + 4x) + 6y + (-16 – 3)
7x + 6y + -19
Corresponding Task(s) (if not in work session – there may be several tasks that
fit) –
****All Tasks can be found at www.georgiastandards.org****
Highlight the Mathematical Practices that this lesson incorporates:
Make
sense of
problems
and
persevere
in solving
them
Reason
abstractly
and
quantitatively
Construct
viable
arguments
and
critique
the
reasoning
of others
Model with
mathematics
Use
appropriate
tools
strategically
Attend to
precision
Look for
and make
sure of
structure
Look for
and
express
regularity
in
repeated
reasoning
9th Grade Unit 2 Lesson 1 Day 1
Opening Activity
Unscramble these letters to form mathematical words.
COTMMUATIVE
ACISASETIVO
DEINTITY
NE I V RS E
DUSTIRIVBITE
Now arrange the circled letters to form a mathematical word that is related to the
above terms.
P
P
9th Grade Unit 2 Lesson 1 Day 1
Teacher’s Notes
The Properties of Operations
Here a, b and c stand for arbitrary numbers in a given number system. The properties of
operations apply to the rational number system, the real number system, and the complex number
system.
Associative property of addition
Commutative property of addition
Additive identity property of 0
Existence of additive inverses
Associative property of multiplication
Commutative property of multiplication
Multiplicative identity property of 1
Existence of multiplicative inverses
Distributive property of multiplication over addition
(a + b) + c = a + (b + c)
a+b=b+a
a+0=0+a=a
For every a there exists –a so that a + (–a) = (–a) + a = 0.
(a × b) × c = a × (b × c)
a×b=b×a
a×1=1×a=a
For every a ≠ 0 there exists 1/a so that a × 1/a = 1/a × a = 1.
a × (b + c) = a × b + a × c
The Properties of Equality
Here a, b and c stand for arbitrary numbers in the rational, real, or complex number systems.
Reflexive property of equality
Symmetric property of equality
Transitive property of equality
Addition property of equality
Subtraction property of equality
Multiplication property of equality
Division property of equality
Substitution property of equality
a=a
If a = b, then b = a.
If a = b and b = c, then a = c.
If a = b, then a + c = b + c.
If a = b, then a – c = b – c.
If a = b, then a × c = b × c.
If a = b and c ≠ 0, then a ÷ c = b ÷ c.
If a = b, then b may be substituted for a in any expression containing a.
9th Grade Unit 2 Lesson 1 Day 1
9th Grade Unit 2 Lesson 1 Day 1
9th Grade Unit 2 Lesson 1 Day 1
9th Grade Unit 2 Lesson 1 Day 1
9th Grade Unit 2 Lesson 1 Day 1
Name:____________________________
Date:_____________
Guided Notes
The Properties of Operations
Here a, b and c stand for arbitrary numbers in a given number system. The properties of
operations apply to the rational number system, the real number system, and the complex number
system.
Associative property of addition
Commutative property of addition
Additive identity property of 0
Existence of additive inverses
Associative property of multiplication
Commutative property of multiplication
Multiplicative identity property of 1
Existence of multiplicative inverses
Distributive property of multiplication over addition
(a + b) + c = a + (b + c)
a+b=b+a
a+0=0+a=a
For every a there exists –a so that a + (–a) = (–a) + a = 0.
(a × b) × c = a × (b × c)
a×b=b×a
a×1=1×a=a
For every a ≠ 0 there exists 1/a so that a × 1/a = 1/a × a = 1.
a × (b + c) = a × b + a × c
The Properties of Equality
Here a, b and c stand for arbitrary numbers in the rational, real, or complex number systems.
Reflexive property of equality
Symmetric property of equality
Transitive property of equality
Addition property of equality
Subtraction property of equality
Multiplication property of equality
Division property of equality
Substitution property of equality
a=a
If a = b, then b = a.
If a = b and b = c, then a = c.
If a = b, then a + c = b + c.
If a = b, then a – c = b – c.
If a = b, then a × c = b × c.
If a = b and c ≠ 0, then a ÷ c = b ÷ c.
If a = b, then b may be substituted for a in any expression containing a.
9th Grade Unit 2 Lesson 1 Day 1
9th Grade Unit 2 Lesson 1 Day 1
9th Grade Unit 2 Lesson 1 Day 1
9th Grade Unit 2 Lesson 1 Day 1
9th Grade Unit 2 Lesson 1 Day 1
Identifying and Applying Properties Practice
Name the property shown by each statement.
1.
7 ● (-2) = (-2) ● 7
2.
-19 + 19 = 0
3.
12 + [(– 3) + 29] = [12 + (-3)] + 29
4.
15 + [8 + (-4)] = [8 + (-4)] + 15
5.
(2 ● 3) ● (-9) = 2 ● [3 ● (-9)]
6.
1● (-37) = -37
7.
(6 + 0) – 7 = 6 – 7
8.
1
●7= 1
7
9.
13 (2 – 6) = 13 (2) – 13(6)
10.
(-4 + 3)(5 + 6) = (-4 + 3)(5) + (-4 + 3)(6)
11.
4 + (9 + 6) = (4 + 9) + 6
12.
3(x + 5) = 3 • x + 3 • 5
13.
(3 + y) + 0 = 3 + y
14.
x•
15.
14xy = 14yx
16.
(3 • 9) • 1 = 3 • 9
17.
7 + (-7) = 0
18.
6 • (8 + c) = (8 + c) • 6
19.
x + 12 = 12 + x
20.
(x + y) • 5 = (y + x) • 5
21.
Why is it true that 3(4 + x) = 3(x + 4)?
22.
Why is 3(4x) = (3●4)x?
23.
Why is 12 – 3x = 3(4 – x)?
1
=1
x
Simplify the expression. Justify your steps.
24.
3b+ (4b - 6b + 2) –b
25.
2(6x – 5) – 3(5x + 4)