Learning Objective
Name _______________________
We will evaluate1 expressions by using the order of operations.
1
simplify
CFU
What are we going to learn?
What does evaluate mean? Evaluate means __________________.
Activate (or provide) Prior Knowledge
Substitution means to replace a variable with a number.
Evaluate each expression below using substitution.
1. If x = 4, then what is
the value of x2?
42 = 4 • 4
= 16
2. If x = 3, then what is
the value of x2?
32 = 3 • 3
=9
CFU
Students, you already know how to substitute a number for a variable. We are going to use substitution to evaluate expressions by
using the order of operations.
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Concept Development
The order of operations shows the sequence that operations need to be performed.
• To evaluate an expression, substitute the given value of the variable2 and then perform the order of operations until no
more operations can be performed.
2
letter that represents an unknown amount
If x = 4, then 5 + (x - 2)2 • 7
Order
1st
2nd
3rd
4th
Operation
(Parentheses) or
[brackets]
Exponents
Multiplication or
Division
Addition or
Subtraction
Final Value
Example A
Example B
5 + (4 - 2)2 • 7
5 + 22 • 7
27 ÷ 4 • 3
5 + 4• 7
If both operations are present, work left to right.
5 + 28
28 – 4 – 10 + 5 – 3
If both operations are present, work left to right.
33
CFU
6 • (5 – 7)2 + 2 which operation would you perform first? How do you know?
A 6•5
B 5–7
C 7²
For the problem: 11 + 7 – 6 + 2 which operation would you perform first? How do you know?
A 11 + 7
B 7–6
C 6+2
For the problem:
In your own words, what does the order of operations show us? The order of operations show us _______.
Flashcards: First Operation
to Perform First
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice
The order of operations shows the sequence that operations need to be performed.
Evaluate expressions by using the order of operations.
(Parentheses) or [brackets]
Exponents
Multiplication or Division (left to right)
Addition or Subtraction (left to right)
Step #1: Substitute the given value of each variable into the expression. (write)
Step #2: Evaluate the expression.
a. Determine3 which operation to perform first. Hint: Use PEMDAS.
b. Repeat the order of operations until no more operations can be performed.
Step #3: Compute4 the final value.
Step #4: Interpret5 your answer. “The expression has a value of ___________.”
3 figure
out
solve mathematically
5 explain (synonym)
4
1. Evaluate:
2. Evaluate:
3. Evaluate:
If x = 9, then
(6x – 21) + (11 + x)2
If x = 6, then
(3x – 10) + (3 + x)2
(6 • 9 – 21) + (11 + 9)2
(54 – 21) + (11 + 9)2
(3 • 6 – 10) + (3 + 6)2
(18 – 10) + (3 + 6)2
(2 • -3 – 1)2 + 3 • 4
(-6 – 1)2 + 3 • 4
8 + (3 + 6)2
8 + 92
8 + 81
89
(-7)2 + 3 • 4
49 + 3 • 4
49 + 12
61
33 + (11 + 9)2
33 + 202
33 + 400
433
If x = -3 and y = 4, then
(2x – 1)2 + 3y
4. Evaluate:
If x = -2 and y = 5, then
(3x – 4)2 + 6y
(3 • -2 – 4)2 + 6 • 5
(-6 – 4)2 + 6 • 5
(-10)2 + 6 • 5
100 + 6 • 5
100 + 30
130
CFU
(#2a) How did I/you determine which operation to perform first?
(#2b) How did I/you know to repeat the order of operations?
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Relevance
The order of operations shows the sequence that operations need to be performed.
• To evaluate an expression, substitute the given value of the variable and then perform the order of operations until no
more operations can be performed.
1. Evaluating expressions by using the order of
operations will help you create tables of x- and
y-values that can be used when graphing
complex functions.
2. Evaluating expressions by using the
order of operations will help you do
well on tests.
Evaluate:
f(x) = (x – 1)² – 6
x
y
-2
3
-1
-2
0
-5
1
-6
2
-5
CFU
Does anyone else have another reason why it is relevant to evaluate expressions by using the order of operations? (pair-share) Why is
it relevant to evaluate expressions by using the order of operations? You may give me one of my reasons or one of your own. Which
reason is more relevant to you? Why?
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
(Parentheses) or [brackets]
Exponents
Multiplication or Division (left to right)
Addition or Subtraction (left to right)
The order of operations shows the sequence that operations need to be performed.
Skill Closure
Evaluate expressions by using the order of operations.
Step #1: Substitute the given value of each variable into the expression. (write)
Step #2: Evaluate the expression.
a. Determine which operation to perform first. Hint: Use PEMDAS.
b. Repeat the order of operations until no more operations can be performed.
Step #3: Compute the final value.
Step #4: Interpret your answer. “The expression has a value of ___________.”
1. Evaluate:
If x = 3, then (7x + 6) + 4x
2. Evaluate:
If c = 8 and w = −2, then (−c + 6)2 + 7w
(-1 • 8 + 6)2 + 7 • -2
(-8 + 6)2 + 7 • -2
(7 • 3 + 6) + 4 • 3
(21 + 6) + 4 • 3
(-2)2 + 7 • -2
4 + 7 • -2
4 + -14
-10
27 + 4 • 3
27 + 12
39
Constructed Response Closure
Maria’s answer:
Maria did not evaluate the expression below correctly. Her final
value was 144. What did she do wrong? Explain.
If x = 2
5 + (3x + 2)2
Summary Closure
5 + (3 • 2 + 2)2
5 + (3 • 4)2
5 + 122
5 + 144
144
What did you learn today about evaluating expressions by using order of operations?
Day 1 ___________________________________________________________________________________________________
Day 2 ___________________________________________________________________________________________________
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Independent Practice
Name _______________________
The order of operations shows the sequence that operations need to be performed.
Evaluate expressions by using the order of operations.
Step #1: Substitute the given value of each variable into the expression. (write)
Step #2: Evaluate the expression.
a. Determine which operation to perform first. Hint: Use PEMDAS.
b. Repeat the order of operations until no more operations can be performed.
Step #3: Compute the final value.
Step #4: Interpret your answer. “The expression has a value of ___________.”
1. Evaluate:
If b = 5, then
+ 7) + (b + 6)2
(b2
[(5)2 + 7 ] + (5 + 6)2
(25 + 7) + (5 + 6)2
32 + (5 + 6)2
32 + 112
32 + 121
153
(Parentheses) or [brackets]
Exponents
Multiplication or Division (left to right)
Addition or Subtraction (left to right)
2. Evaluate:
3. Evaluate:
4. Evaluate:
If g = 8, then
(7g - 44)2 + (g)2
If x = 2 and y = 6, then
(-3x – 1)2 + -5y
If a = -1 and c = 7, then
(5a + 4)2 + 6c
(7 • 8 - 44)2 + (8)2
(56 - 44)2 + (8)2
(12)2 + (8)2
144 + (8)2
144 + 64
208
(-3 • 2 – 1)2 + -5 • 6
(-6 – 1)2 + -5 • 6
(5 • -1 + 4)2 + 6 • 7
(-5 + 4)2 + 6 • 7
(-7)2 + -5 • 6
49 + -5 • 6
49 + -30
19
(-1)2 + 6 • 7
1+6•7
1 + 42
43
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Periodic Review 1
Name _______________________
The order of operations shows the sequence that operations need to be performed.
Evaluate expressions by using the order of operations.
Step #1: Substitute the given value of each variable into the expression. (write)
Step #2: Evaluate the expression.
a. Determine which operation to perform first. Hint: Use PEMDAS.
b. Repeat the order of operations until no more operations can be performed.
Step #3: Compute the final value.
Step #4: Interpret your answer. “The expression has a value of ___________.”
(Parentheses) or [brackets]
Exponents
Multiplication or Division (left to right)
Addition or Subtraction (left to right)
1. Evaluate:
2. Evaluate:
3. Evaluate:
3v2
If k = -4, then
(-5k + -18)2 + -(6 + k)2
If j = 6 and x = 8, then
(-2j + 9)2 + -2x
If v = -2, then
+ (v + 7)2
3(-2)2 + (-2 + 7)2
3 • 4 + (-2 + 7)2
3 • 4 + (5)2
3 • 4 + 25
12 + 25
37
(-5 • -4 + -18)2 + -(6 + -4)2
(20 + -18)2 + -(6 + -4)2
(-2 • 6 + 9)2 + -2 • 8
(-12 + 9)2 + -2 • 8
22 + -(6 + -4)2
22 + -(2)2
4 + -(2)2
4 + -1 • 4
4 + -4
0
(-3)2 + -2 • 8
9 + -2 • 8
9 + -16
-7
4. Evaluate:
If q = 6 and w = -3,
then (2q + -18)2 + 10w
(2 • 6 + -18)2 + 10 • -3
(12 + -18)2 + 10 • -3
(-6)2 + 10 • -3
36 + 10 • -3
36 + -30
6
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Periodic Review 2
Name _______________________
The order of operations shows the sequence that operations need to be performed.
Evaluate expressions by using the order of operations.
Step #1: Substitute the given value of each variable into the expression. (write)
Step #2: Evaluate the expression.
a. Determine which operation to perform first. Hint: Use PEMDAS.
b. Repeat the order of operations until no more operations can be performed.
Step #3: Compute the final value.
Step #4: Interpret your answer. “The expression has a value of ___________.”
1. Evaluate:
If d = -4, then
– (d + 12)2
5d2
5(-4)2 – (-4 + 12)2
5 • 16 – (-4 + 12)2
5 • 16 – (8)2
5 • 16 – 64
80 – 64
16
(Parentheses) or [brackets]
Exponents
Multiplication or Division (left to right)
Addition or Subtraction (left to right)
2. Evaluate:
3. Evaluate:
4. Evaluate:
If n = 3, then
(-9n + 20)2 + -(-2 + n)3
If x = -3 and y = 10,
then (-6x + -12)2 + -4y
If p = 12 and z = -8, then
p2 + -9p + -5z
(-9 • 3 + 20)2 + -(-2 + 3)3
(-27 + 20)2 + -(-2 + 3)3
(-7)2 + -(-2 + 3)3
(-7)2 + -(1)3
49 + -(1)3
49 + -1 • 1
49 + -1
48
(-6 • -3 + -12)2 + -4 • 10
(18 + -12)2 + -4 • 10
122 + -9 • 12 + -5 • -8
144 + -9 • 12 + -5 • -8
(6)2 + -4 • 10
36 + -4 • 10
36 + -40
-4
144 + -108 + -5 • -8
144 + -108 + 40
36 + 40
76
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Periodic Review 3
Name _______________________
The order of operations shows the sequence that operations need to be performed.
Evaluate expressions by using the order of operations.
Step #1: Substitute the given value of each variable into the expression. (write)
Step #2: Evaluate the expression.
a. Determine which operation to perform first. Hint: Use PEMDAS.
b. Repeat the order of operations until no more operations can be performed.
Step #3: Compute the final value.
Step #4: Interpret your answer. “The expression has a value of ___________.”
1. Evaluate:
If x = 5, then
-2x2 + (x + 1)2
(Parentheses) or [brackets]
Exponents
Multiplication or Division (left to right)
Addition or Subtraction (left to right)
2. Evaluate:
3. Evaluate:
4. Evaluate:
If a = -3, then
(-4a + -7)2 + -(5 + a)3
If x = -5 and y = -6,
then (-2x + -13)2 + 5y
If b = -2 and c = -3,
then b2 + b3 + -5c2
-2(5)2 + (5 + 1)2
-2 • (5)2 + (6)2
(-4 • -3 + -7)2 + -(5 + -3)3
(12 + -7)2 + -(5 + -3)3
-2 • 25 + (6)2
-2 • 25 + 36
-50 + 36
-14
(5)2 + -(5 + -3)3
(5)2 + -(2)3
25 + -(2)3
25 + -1 • 8
25 + -8
17
(-2 • -5 + -13)2 + 5 • -6
(10 + -13)2 + 5 • -6
(-3)2 + 5 • -6
9 + 5 • -6
9 + -30
-21
(-2)2 + (-2)3 + -5 • (-3)2
4 + (-2)3 + -5 • (-3)2
4 + -8 + -5 • (-3)2
4 + -8 + -5 • 9
4 + -8 + -45
-4 + -45
-49
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
4 + 17 – 20
A. 4 + 17
B. 17 – 20
P
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MD
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A
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
6–4+2
A. 6 – 4
B. 4 + 2
P
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MD
S
A
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
-4 + 9 – 2 • 6
A. -4 + 9
B. 9 – 2
C. 2 • 6
P
E
MD
M
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
-2 + 12 • 6²²
A. -2 + 12
B. 12 • 6
C. 6²
P
E
M
MD
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
7 – 5 + 12
A. 7 – 5
B. 5 + 12
P
E
MD
S
A
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
15 + 6 • 7 – 32
A. 15 + 6
B. 6 • 7
C. 7 – 32
P
E
MD
M
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
18 – 2 • 10²²
A. 18 – 2
B. 2 • 10
C. 10²
P
E
M
MD
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
4 • (5
( + -3)²
)² + 7
A. 4 • 5
B. 5 + -3
C. -3²
D. -3² + 7
P
E
MD
M
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
24 ÷ -8 • 9 – 10
A. 24 ÷ -8
B. -8 • 9
C. 9 – 10
P
E
MD
MD
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
19 + 8 – 3
A. 19 + 8
B. 8 – 3
P
E
MD
S
A
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
40 ÷ 10 + -7 • 5
A. 40 ÷ 10
B. 10 + -7
C. -7 • 5
P
E
MD
MD
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
Which operation would you perform first?
( • 6)]
) + 8 • -5
[3 – (2
A. 3 – 2
B. 2 • 6
C. 6 + 8
D. 8 • -5
P
E
M
MD
AS
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.
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7th Grade Algebra & Functions 1.2 (1Q)
Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2.
Lesson to be used by EDI-trained teachers only.