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What are we going to learn? What does evaluate mean? Evaluate means __________.

Learning Objective. Name: _________________________ Tuesday, February 18, 2014 Per: ____. We will evaluate 1 expressions by using the order of operations . Common Core Standard 7.AF1.2. What are we going to learn? What does evaluate mean? Evaluate means __________. CFU.

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What are we going to learn? What does evaluate mean? Evaluate means __________.

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  1. Learning Objective Name: _________________________ Tuesday, February 18, 2014 Per: ____ We will evaluate1 expressions by using the order of operations. Common Core Standard 7.AF1.2 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. 42 = 3 • 3 = 4 • 4 32 = 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. 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. CFU 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 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 In your own words, what does the order of operations show us? The order of operations shows us _______. Flashcards: Order of Operations 2 letter that represents an unknown amount Vocabulary

  3. 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. Evaluate expressions by using the order of operations. 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 _______.” 1 How did I/you determine which operation to perform first? How did I/you know to repeat the order of operations? CFU 2 2a a b 2b 3 4 If x = 9, then (6x – 21) + (11 + x)2 If x = -3 and y = 4, then (2x – 1)2 + 3y If x = 6, then (3x – 10) + (3 + x)2 If x = -2 and y = 5, then (3x – 4)2 + 6y (6•9 – 21) + (11 +9)2 (2• -3 – 1)2 + 3 • 4 (3• 6 – 10) + (3 +6)2 (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 49+ 3 • 4 8 + 92 100+ 6 • 5 33 + 400 49 + 12 8 + 81 100 + 30 433 61 89 130 3 figure out 4 solve mathematically 5 explain (synonym) Vocabulary

  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. Skill Closure Evaluate expressions by using the order of operations. 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. Interpretyour answer. “The expression has a value of _______.” 1 2 a b 3 4 (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 4+ 7 • -2 27+ 12 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)

  5. 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. Evaluate expressions by using the order of operations. 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. Interpretyour answer. “The expression has a value of _______.” 1 2 a b 3 4 If b= 5, then (b2 + 7) + (b + 6)2 If x= 2 and y= 6, then (-3x – 1)2 + -5y If g= 8, then (7g - 44)2 + (g)2 If a= -1 and c= 7, then (5a + 4)2 + 6c [(5)2+ 7 ] + (5 + 6)2 (-3• 2 – 1)2+ -5 • 6 (7• 8 - 44)2 + (8)2 (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 49+ -5 • 6 144+ (8)2 1+ 6 • 7 49+ -30 144+ 64 1+ 42 32+ 121 153 19 208 43

  6. 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. Evaluate expressions by using the order of operations. 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. Interpretyour answer. “The expression has a value of _______.” 1 2 a b 3 4 If v= -2, then 3v2 + (v + 7)2 If j= 6 and x= 8, then (-2j + 9)2 + -2x If k= -4, then (-5k + -18)2 + -(6 + k)2 If q= 6 and w= -3, then (2q + -18)2 + 10w 3(-2)2+ (-2 + 7)2 (-2• 6 + 9)2+ -2 • 8 (-5• -4 + -18)2 + -(6 + -4)2 (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 9+ -2 • 8 22+ -(2)2 36+ 10 • -3 12 + 25 9+ -16 4 + -(2)2 36+ -30 37 -7 4 + -1 • 4 6 4 + -4 0

  7. 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. Evaluate expressions by using the order of operations. 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. Interpretyour answer. “The expression has a value of _______.” 1 2 a b 3 4 If d = -4, then 5d2 – (d + 12)2 If x = -3 and y = 10, then (-6x + -12)2 + -4y If n = 3, then (-9n + 20)2 + -(-2 + n)3 If p = 12 and z = -8, then p2 + -9p + -5z 5(-4)2– (-4+ 12)2 (-6• -3 + -12)2 + -4 • 10 (-9• 3 + 20)2 + -(-2 + 3)3 122+ -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 36+ -4 • 10 (-7)2 + -(1)3 144 + -108 + 40 80– 64 36 + -40 49+ -(1)3 36+ 40 16 -4 49 + -1 • 1 76 49 + -1 48

  8. 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. Evaluate expressions by using the order of operations. 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. Interpretyour answer. “The expression has a value of _______.” 1 2 a b 3 4 If x = 5, then -2x2 + (x + 1)2 If x = -5 and y = -6, then (-2x + -13)2 + 5y If a = -3, then (-4a + -7)2 + -(5 + a)3 If b = -2 and c = -3, then b2 + b3 + -5c2 -2(5)2+ (5 + 1)2 (-2• -5 + -13)2+ 5 • -6 (-4• -3 + -7)2 + -(5 + -3)3 (-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 9+ 5 • -6 (5)2+ -(2)3 4 + -8 + -5 • 9 -50 + 36 9+ -30 25 + -(2)3 4 + -8 + -45 -14 -21 25 + -1 • 8 -4 + -45 -49 25 + -8 17

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

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

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

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

  13. Flash Cards (Order of Operations) 5 P E M D S A Which operation would you perform first? – + 7 – 5 + 12 A. 7 – 5 B. 5 + 12 S A

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

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

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

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

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

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

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

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