1. 1. If x = 4, then what is the value of x2?
Learning Objective
We will evaluate1 expressions by using
the order of operations.
Common Core Standard 7.AF1.2
Name: _________________________
Tuesday, February 18, Per: ____
What are we going to learn?
What does evaluate mean?
Evaluate means __________.
CFU
Activate 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?
2. If x = 3, then what is the value of x2? 42
= 4 • 4 32
= 3 • 3
= 16
= 9
Students, you already know how to substitute a number for a variable. Now, we are going to use substitution to evaluate expressions using the order of operations.
Make Connection
1 simplify
Vocabulary

2. If both operations are present, work left to right.
Concept Development
The order of operations shows the sequence in which 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.
If x = 4, then 5 + (x - 2)2 • 7
Order
Operation
Example A
 Other Examples
1st
(Parentheses) or [brackets]
5 + (4 - 2)2 • 7
2nd
Exponents
• 7
3rd
Multiplication or
Division
5 + 4 • 7
28 ÷ 4 • 3
If both operations are present, work left to right.
4th
Addition or
Subtraction
5 + 28
28 – 4 – – 3
Final Value 33
For the problem:
6 • (5 – 7)2 + 2 which operation would you perform first? How do you know?
A 6 • 5
B 5 – 7
C 7²
– which operation would you perform first? How do you know? A
B 7 – 6 C
In your own words, what does the order of operations show us? The order of operations shows us _______.
CFU
2 letter that represents an unknown amount
Vocabulary
Flashcards: Order of Operations

3. Evaluate the expression.
Skill Development/Guided Practice
(Parentheses) or [brackets]
Exponents
Multiplication or
Division (left to right)
Addition or
Subtraction (left to right)
The order of operations shows the sequence in which operations need to be performed.
Substitute the given value of each variable into the expression. (write)
Evaluate the expression.
Determine3 which operation to perform first. Hint: Use PEMDAS.
Repeat the order of operations until no more operations can be performed.
Compute4 the final value.
Interpret5 your answer. “The expression has a value of _______.”
Evaluate expressions by using the order of operations. 1 2 3 4 a b
How did I/you determine which operation to perform first?
How did I/you know to repeat the order of operations?
CFU 2a 2b
1. Evaluate:
2. Evaluate:
3. Evaluate:
4. Evaluate:
If x = 9, then
(6x – 21) + (11 + x)2
If x = 6, then
(3x – 10) + (3 + x)2
If x = -3 and y = 4, then (2x – 1)2 + 3y
If x = -2 and y = 5, then (3x – 4)2 + 6y
(6 • 9 – 21) + (11 + 9)2
(3 • 6 – 10) + (3 + 6)2
(2 • -3 – 1)2 + 3 • 4
(3 • -2 – 4)2 + 6 • 5
(54 – 21) + (11 + 9)2
(18 – 10) + (3 + 6)2
(-6 – 1)2 + 3 • 4
(-6 – 4)2 + 6 • 5
33 + (11 + 9)2
8 + (3 + 6)2
(-7)2 + 3 • 4
(-10)2 + 6 • 5
8 + 92
• 4
• 5
8 + 81
433 89 61
130
3 figure out
4 solve mathematically
5 explain (synonym)
Vocabulary

4. Evaluate the expression.
(Parentheses) or [brackets]
Exponents
Multiplication or
Division (left to right)
Addition or
Subtraction (left to right)
The order of operations shows the sequence in which operations need to be performed.
Skill Closure
Substitute the given value of each variable into the expression. (write)
Evaluate the expression.
Determine which operation to perform first. Hint: Use PEMDAS.
Repeat the order of operations until no more operations can be performed.
Compute the final value.
Interpret your answer. “The expression has a value of _______.”
Evaluate expressions by using the order of operations. 1 2 3 4 a b
1. Evaluate:
If x = 3, then (7x + 6) + 4x
2. Evaluate:
If c = 8 and w = -2, then (-c + 6)2 + 7w
(7 • 3 + 6) + 4 • 3
(-1 • 8 + 6)2 + 7 • -2
(21 + 6) + 4 • 3
(-8 + 6)2 + 7 • -2
• 3
(-2)2 + 7 • -2
4 + 7 • -2 39
-10
Constructed Response Closure
If x = 2
5 + (3x + 2)2
Maria’s answer: 5 + (3 • 2 + 2)2
5 + (3 • 4)2
144
Maria did not evaluate the expression below correctly.
Her final value was 144. What did she do wrong? Explain.
Summary Closure
What did you learn today about evaluating expressions by using order of operations? (Pair-Share)

5. Evaluate the expression.
Independent Practice 1
(Parentheses) or [brackets]
Exponents
Multiplication or
Division (left to right)
Addition or
Subtraction (left to right)
The order of operations shows the sequence in which operations need to be performed.
Substitute the given value of each variable into the expression. (write)
Evaluate the expression.
Determine which operation to perform first. Hint: Use PEMDAS.
Repeat the order of operations until no more operations can be performed.
Compute the final value.
Interpret your answer. “The expression has a value of _______.”
Evaluate expressions by using the order of operations. 1 2 3 4 a b
1. Evaluate:
2. Evaluate:
3. Evaluate:
4. Evaluate:
If b = 5, then
(b2 + 7) + (b + 6)2
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
[(5)2 + 7 ] + (5 + 6)2
(7 • )2 + (8)2
(-3 • 2 – 1) • 6
(5 • )2 + 6 • 7
(25 + 7) + (5 + 6)2
( )2 + (8)2
(-6 – 1) • 6
(-5 + 4)2 + 6 • 7
32 + (5 + 6)2
(12)2 + (8)2
(-7) • 6
(-1)2 + 6 • 7
144 + (8)2
• 6
1 + 6 • 7
1 + 42
153
208 19 43

6. Evaluate the expression.
Independent Practice 2
(Parentheses) or [brackets]
Exponents
Multiplication or
Division (left to right)
Addition or
Subtraction (left to right)
The order of operations shows the sequence in which operations need to be performed.
Substitute the given value of each variable into the expression. (write)
Evaluate the expression.
Determine which operation to perform first. Hint: Use PEMDAS.
Repeat the order of operations until no more operations can be performed.
Compute the final value.
Interpret your answer. “The expression has a value of _______.”
Evaluate expressions by using the order of operations. 1 2 3 4 a b
1. Evaluate:
2. Evaluate:
3. Evaluate:
4. Evaluate:
If v = -2, then
3v2 + (v + 7)2
If k = -4, then
(-5k + -18)2 + -(6 + k)2
If j = 6 and x = 8, then
(-2j + 9)2 + -2x
If q = 6 and w = -3,
then (2q + -18)2 + 10w
3(-2)2 + (-2 + 7)2
(-5 • )2 + -(6 + -4)2
(-2 • 6 + 9) • 8
(2 • ) • -3
3 • 4 + (-2 + 7)2
( )2 + -(6 + -4)2
( ) • 8
( ) • -3
3 • 4 + (5)2
22 + -(6 + -4)2
(-3) • 8
(-6) • -3
3 •
22 + -(2)2
• 8
• -3
4 + -(2)2 37
• 4 -7 6
4 + -4

7. Evaluate the expression.
Independent Practice 3
(Parentheses) or [brackets]
Exponents
Multiplication or
Division (left to right)
Addition or
Subtraction (left to right)
The order of operations shows the sequence in which operations need to be performed.
Substitute the given value of each variable into the expression. (write)
Evaluate the expression.
Determine which operation to perform first. Hint: Use PEMDAS.
Repeat the order of operations until no more operations can be performed.
Compute the final value.
Interpret your answer. “The expression has a value of _______.”
Evaluate expressions by using the order of operations. 1 2 3 4 a b
1. Evaluate:
2. Evaluate:
3. Evaluate:
4. Evaluate:
If d = -4, then
5d2 – (d + 12)2
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
5(-4)2 – ( )2
(-9 • )2 + -(-2 + 3)3
(-6 • ) • 10
• • -8
5(-4)2 – (8)2
( )2 + -(-2 + 3)3
( ) • 10
• • -8
5 • 16 – (8)2
(-7)2 + -(-2 + 3)3
(6) • 10
• -8
5 • 16 – 64
(-7)2 + -(1)3
• 10
80 – 64
49 + -(1)3 16
• 1 -4 76 48

8. Evaluate the expression.
Independent Practice 4
(Parentheses) or [brackets]
Exponents
Multiplication or
Division (left to right)
Addition or
Subtraction (left to right)
The order of operations shows the sequence in which operations need to be performed.
Substitute the given value of each variable into the expression. (write)
Evaluate the expression.
Determine which operation to perform first. Hint: Use PEMDAS.
Repeat the order of operations until no more operations can be performed.
Compute the final value.
Interpret your answer. “The expression has a value of _______.”
Evaluate expressions by using the order of operations. 1 2 3 4 a b
1. Evaluate:
2. Evaluate:
3. Evaluate:
4. Evaluate:
If x = 5, then
-2x2 + (x + 1)2
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
(-4 • )2 + -(5 + -3)3
(-2 • )2 + 5 • -6
(-2)2 + (-2) • (-3)2
-2 • (5)2 + (6)2
( )2 + -(5 + -3)3
( )2 + 5 • -6
4 + (-2) • (-3)2
-2 • 25 + (6)2
(5)2 + -(5 + -3)3
(-3)2 + 5 • -6
• (-3)2
-2 •
(5)2 + -(2)3
9 + 5 • -6
• 9
25 + -(2)3
-14
• 8
-21
-49 17

9. Flash Cards (Order of Operations) 1
Which operation would you perform first?
– 20 + – A P E M D A S
B. 17 – 20 A S

10. Flash Cards (Order of Operations) 2
Which operation would you perform first?
6 – 4 + 2 – +
A. 6 – 4 P E M D A S B A S

11. -4 + 9 – 2 • 6 + – • A. -4 + 9 P E M D A S B. 9 – 2 M C. 2 • 6 A S
Flash Cards (Order of Operations) 3
Which operation would you perform first?
– 2 • 6 + – • A P E M D A S
B. 9 – 2 M
C. 2 • 6 A S

12. -2 + 12 • 6² + • ² A. -2 + 12 P E M D A S E B. 12 • 6 M C. 6² A
Flash Cards (Order of Operations) 4
Which operation would you perform first?
• 6² + • A P E M D A S E
B. 12 • 6 M
C. 6² A

13. Flash Cards (Order of Operations) 5
Which operation would you perform first?
7 – – +
A. 7 – 5 P E M D A S B A S

14. 15 + 6 • 7 – 32 + • – A. 15 + 6 P E M D A S B. 6 • 7 M C. 7 – 32 A S
Flash Cards (Order of Operations) 6
Which operation would you perform first?
• 7 – 32 + • – A P E M D A S
B. 6 • 7 M
C. 7 – 32 A S

15. 18 – 2 • 10² – • ² A. 18 – 2 P E M D A S E B. 2 • 10 M C. 10² S
Flash Cards (Order of Operations) 7
Which operation would you perform first?
18 – 2 • 10² – •
A. 18 – 2 P E M D A S E
B. 2 • 10 M
C. 10² S

16. 4 • (5 + -3)² + 7 • ( ) ² + A. 4 • 5 P P E M D A S E B. 5 + -3 M
Flash Cards (Order of Operations) 8
Which operation would you perform first?
4 • (5 + -3)² + 7 •
( ) +
A. 4 • 5 P P E M D A S E B M
C. -3² A
D. -3² + 7

17. 24 ÷ -8 • 9 – 10 ÷ • – A. 24 ÷ -8 P E M D A S B. -8 • 9 M D C. 9 – 10
Flash Cards (Order of Operations) 9
Which operation would you perform first?
24 ÷ -8 • 9 – 10 ÷ • –
A. 24 ÷ -8 P E M D A S
B. -8 • 9 M D
C. 9 – 10 S

18. Flash Cards (Order of Operations) 10
Which operation would you perform first?
– 3 + – A P E M D A S
B. 8 – 3 A S

19. 40 ÷ 10 + -7 • 5 ÷ + • A. 40 ÷ 10 P E M D A S B. 10 + -7 M D C. -7 • 5
Flash Cards (Order of Operations) 11
Which operation would you perform first?
40 ÷ • 5 ÷ + •
A. 40 ÷ 10 P E M D A S B M D
C. -7 • 5 A

20. [3 – (2 • 6)] + 8 • -5 – ( ) + • A. 3 – 2 P E M D A S P B. 2 • 6 M
Flash Cards (Order of Operations) 12
Which operation would you perform first?
[3 – (2 • 6)] + 8 • -5 –
( ) + •
A. 3 – 2 P E M D A S P
B. 2 • 6 M C A S
D. 8 • -5
Back to
Concept Dev