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Algebra StAIR Lesson: The Order of Operations Mrs. Lewis next Lesson Objectives This lesson will teach you everything you need to know about the Order of Operations. By the end of this lesson you will be able to… 1. 2. 3. 4. Understand and explain why we need an established Order of Operations State the correct Order of Operations Use the Order of Operations to simplify numerical expressions Use the Order of Operations to simplify algebraic expressions back next Instructions • Complete this lesson on your own and at your own pace. • Use the navigational buttons along the bottom to move throughout the lesson. • Take notes as you go. The objectives (on the previous page) will be assessed by a quiz at the end of this lesson and on our Chapter Test. • After linking to a website, simply close your browser window to return to this lesson. • Have a pencil, paper, and a calculator handy. • Have fun! back next Let’s warm up! 1. Simplify 2 4 a. 8 b. 2 c. 16 d. 1/2 Click here if you need a quick refresher on powers. Let’s warm up! 1. Simplify 2 4 Exponent Base Hint: The exponent tells you how many times to multiply the base! Go back and try again! back Let’s warm up! 1. Simplify Great! 2 4 2 4 4 4 16 next Let’s warm up! 2. Simplify 5 16 a. 11 b. -11 c. 21 d. -21 Click here if you need a quick refresher on absolute value. Let’s warm up! 2. Simplify 5 16 Absolute Value Bars Hint: The absolute value of a number is its distance from zero on a number line. (always positive) Go back and try again! back Let’s warm up! 2. Simplify Great! 5 16 5 16 11 11 next Let’s warm up! 3 3. Simplify (2) a. -6 b. -5 c. 8 d. -8 Click here if you need a quick refresher on powers. Let’s warm up! 3. Simplify 3 (2) Exponent Base Hint: The exponent tells you how many times to multiply the base! Go back and try again! back Let’s warm up! 3. Simplify Great! 3 (2) ( 2) 3 ( 2)( 2)( 2) ( 4)( 2) 8 next Now that’s all fine and dandy… …but what happens when we have to simplify an expression with more than one operation?! How do you know which operation to do first? next For example… 15 2 3 1 Take a moment to think about how you would solve this problem. When you have an answer in your head, click next. next Without an Order of Operations… Sally might do this… 15 2 3 1 13 3 1 39 1 40 Einstein might do this… 15 2 3 1 Mrs. Lewis might do this… 15 2 3 1 15 6 1 9 1 10 Billy might do this… 15 2 3 1 13 3 1 15 6 1 13 4 15 7 52 8 next Question of the day… Who is right? The truth is…if there were no established Order of Operations, everyone would be right. But that doesn’t get us anywhere! Maybe someone should decide on a standard order for doing mathematical operations so that we can all get the same answer every time! next The ORDER OF OPERATIONS Parentheses Exponents Multiplication/Division (Left to Right) Addition/Subtraction (Left to Right) PEMDAS next How am I supposed to remember that? Please Excuse My Dear Aunt Sally Watch a music video here! (Video will play after a short advertisement) next So who was right? Mrs. Lewis! Who did you think?! Let’s take a look at the problem again… 15 2 3 1 15 6 1 9 1 10 Parentheses? No. Exponents? No. Multiply/Divide? Yes! L to R Add/Subtract? Yes! L to R next Click play next Let’s look at some examples… 1. Simplify 4 24 3 2 2 16 24 3 2 16 8 2 16 16 Parentheses? No. Exponents? Yes! Multiply/Divide? Yes! L to R Add/Subtract? Yes! L to R 0 See another example Challenge me Let’s look at some examples… 2. Simplify 12 3 10 2 2 12 9 10 2 12 9 5 3 5 8 Parentheses? No. Exponents? Yes! Multiply/Divide? Yes! L to R Add/Subtract? Yes! L to R Review more Move on Challenge! Simplify Brackets are just like parentheses 425 ( 5 2) 2 a. 81 Parentheses? Yes! 2 sets. Work from the inside out. b. 96 Exponents? Yes! c. 0 Multiply/Divide? Yes! L to R d. 64 Add/Subtract? Yes! L to R Challenge! Simplify 425 3 425 9 4 16 64 2 Brackets are just like parentheses 425 ( 5 2) 2 Parentheses? Yes! 2 sets. Work from the inside out. Exponents? Yes! Multiply/Divide? Yes! L to R Add/Subtract? Yes! L to R next Let’s look at some examples… 3. Evaluate 21 x 2 5 for x 7 21 7 2 5 21 7 10 14 10 24 See another example Substitute 7 for x. Parentheses? No. Exponents? No. Multiply/Divide? Yes! L to R Add/Subtract? Yes! L to R Challenge me Let’s look at some examples… 4. Evaluate 5 (30 x ) for x 24 2 5 (30 24) 2 5 6 2 25 6 150 Review more Substitute 24 for x. Parentheses? Yes! Exponents? Yes! Multiply/Divide? Yes! L to R Move on Challenge! Evaluate ( x 2 ) (2 6) for x 6 2 a. 18 b. 78 c. 3 d. 152 Substitute 6 for x. Parentheses? Yes! 2 sets. Exponents? Yes! Multiply/Divide? Yes! L to R Challenge! Evaluate ( x 2 ) (2 6) for x 6 2 (6 2 ) (2 6) Substitute 6 for x. (6 4) 8 Exponents? Yes! 2 24 8 Parentheses? Yes! 2 sets. Multiply/Divide? Yes! L to R 3 next Let’s change things up… Choose the operation that makes the statement true. 12 6 9 Choose the operation that makes the statement true. 17 ( 12 7) 12 Choose the operation that makes the statement true. 108 ( 7 2) 12 Now it’s your turn… 1. Simplify 5( 1 2) (3 2) a. -6 b. -2 c. 4 d. 2.5 “That was absolutely dreadful.” Go back and try again! back Now it’s your turn… 2. Simplify (6 2 3) ( 9 7) 2 a. -6 b. 6 c. 3 d. -3 “You’re fired!” Go back and try again! back Now it’s your turn… 3. Evaluate 3( x 12 2) for x 8 a. 48 b. 72 c. -32 d. -48 “Bring me your torch. The tribe has spoken.” Go back and try again! back Time for a game… • You will now play a game of Order of Operations Millionaire! • After choosing a player and typing in your name, you will answer 10 questions. • Please print your certificate and turn in to Mrs. Lewis when you are finished. • Click here to play! next Review What is the correct Order of Operations? a. Always go straight from left to right. b. Do the easy parts first and then everything else. c. You get the same answer no matter what order. d. parentheses, exponents, multiply/divide, add/subtract You are nearing the end… Choose an option from the list below. I am completely lost! I need to go through the examples again. Can I see one more video explanation? I’m ready for the quiz! QUIZ Please record all work and your answers on a piece of paper and turn it in to Mrs. Lewis when you are finished. I’m ready QUIZ 1. Why do we need an established Order of Operations? 2. What is the correct Order of Operations? Be specific. 2 3. Simplify 5 8 4 16 2 4. Evaluate x y( y 2) for x 3, y 2 done Great job! You have completed this lesson! Turn in: Quiz Math Millionaire Certificate