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, 2014 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

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 5 + 22 • 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 – 10 + 5 – 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 11 + 7 – 6 + 2 which operation would you perform first? How do you know? A 11 + 7 B 7 – 6 C 6 + 2 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

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 33 + 202 8 + 92 49 + 3 • 4 100 + 6 • 5 33 + 400 8 + 81 49 + 12 100 + 30 433 89 61 130 3 figure out 4 solve mathematically 5 explain (synonym) Vocabulary

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 27 + 4 • 3 (-2)2 + 7 • -2 27 + 12 4 + 7 • -2 4 + -14 39 -10 Constructed Response Closure If x = 2 5 + (3x + 2)2 Maria’s answer: 5 + (3 • 2 + 2)2 5 + (3 • 4)2 5 + 122 5 + 144 144 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)

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 • 8 - 44)2 + (8)2 (-3 • 2 – 1)2 + -5 • 6 (5 • -1 + 4)2 + 6 • 7 (25 + 7) + (5 + 6)2 (56 - 44)2 + (8)2 (-6 – 1)2 + -5 • 6 (-5 + 4)2 + 6 • 7 32 + (5 + 6)2 (12)2 + (8)2 (-7)2 + -5 • 6 (-1)2 + 6 • 7 32 + 112 144 + (8)2 49 + -5 • 6 1 + 6 • 7 32 + 121 144 + 64 49 + -30 1 + 42 153 208 19 43

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 • -4 + -18)2 + -(6 + -4)2 (-2 • 6 + 9)2 + -2 • 8 (2 • 6 + -18)2 + 10 • -3 3 • 4 + (-2 + 7)2 (20 + -18)2 + -(6 + -4)2 (-12 + 9)2 + -2 • 8 (12 + -18)2 + 10 • -3 3 • 4 + (5)2 22 + -(6 + -4)2 (-3)2 + -2 • 8 (-6)2 + 10 • -3 3 • 4 + 25 22 + -(2)2 9 + -2 • 8 36 + 10 • -3 12 + 25 4 + -(2)2 9 + -16 36 + -30 37 4 + -1 • 4 -7 6 4 + -4

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 – (-4 + 12)2 (-9 • 3 + 20)2 + -(-2 + 3)3 (-6 • -3 + -12)2 + -4 • 10 122 + -9 • 12 + -5 • -8 5(-4)2 – (8)2 (-27 + 20)2 + -(-2 + 3)3 (18 + -12)2 + -4 • 10 144 + -9 • 12 + -5 • -8 5 • 16 – (8)2 (-7)2 + -(-2 + 3)3 (6)2 + -4 • 10 144 + -108 + -5 • -8 5 • 16 – 64 (-7)2 + -(1)3 36 + -4 • 10 144 + -108 + 40 80 – 64 49 + -(1)3 36 + -40 36 + 40 16 49 + -1 • 1 -4 76 49 + -1 48

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 • -3 + -7)2 + -(5 + -3)3 (-2 • -5 + -13)2 + 5 • -6 (-2)2 + (-2)3 + -5 • (-3)2 -2 • (5)2 + (6)2 (12 + -7)2 + -(5 + -3)3 (10 + -13)2 + 5 • -6 4 + (-2)3 + -5 • (-3)2 -2 • 25 + (6)2 (5)2 + -(5 + -3)3 (-3)2 + 5 • -6 4 + -8 + -5 • (-3)2 -2 • 25 + 36 (5)2 + -(2)3 9 + 5 • -6 4 + -8 + -5 • 9 -50 + 36 25 + -(2)3 9 + -30 4 + -8 + -45 -14 25 + -1 • 8 -21 -4 + -45 25 + -8 -49 17

Flash Cards (Order of Operations) 1 Which operation would you perform first? 4 + 17 – 20 + – A. 4 + 17 P E M D A S B. 17 – 20 A S

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. 4 + 2 A S

-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? -4 + 9 – 2 • 6 + – • A. -4 + 9 P E M D A S B. 9 – 2 M C. 2 • 6 A S

-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? -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) 5 Which operation would you perform first? 7 – 5 + 12 – + A. 7 – 5 P E M D A S B. 5 + 12 A S

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? 15 + 6 • 7 – 32 + • – A. 15 + 6 P E M D A S B. 6 • 7 M C. 7 – 32 A S

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 – • ² A. 18 – 2 P E M D A S E B. 2 • 10 M C. 10² S

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 • ( ) ² + A. 4 • 5 P P E M D A S E B. 5 + -3 M C. -3² A D. -3² + 7

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

Flash Cards (Order of Operations) 10 Which operation would you perform first? 19 + 8 – 3 + – A. 19 + 8 P E M D A S B. 8 – 3 A S

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 ÷ 10 + -7 • 5 ÷ + • A. 40 ÷ 10 P E M D A S B. 10 + -7 M D C. -7 • 5 A

[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. 6 + 8 A S D. 8 • -5 Back to Concept Dev