2. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Please Excuse My Dear Aunt Sally An Order of Operations Tutorial By Matt Bolton

3. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Please Excuse My Dear Aunt Sally Objective and Common Core Curriculum Standard: Objective:The objective of this multimedia tutorial is to introduce students to the order of operations, provide opportunities for students to practice simplifying equations using the order of operations, and to assess student learning of the order of operations. Standard:CCSS.Math.Content.5.OA.A.1- Students will use parentheses, brackets, or braces in numerical expressions, and evaluate expression with these symbols. Directions: You will need scratch paper and a pencil to work the practice problems in this tutorial. Use the navigation buttons at the top of the screen to go directly to a particular section. Use the buttons at the bottom to move back to the previous screen, to the next screen, or use the home icon to take you back to the first screen. Click on the Practice button for the practice problems. When you are finished, please take the quiz, which can be reached by clicking on the Quiz button. While you are all familiar with these operations, especially the addition and subtraction, this tutorial will provide a refresher on some of the basics associated with these operations.

4. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Please Excuse My Dear Aunt Sally Please excuse my dear Aunt Sally. Is this something you tell your friends who come over while your crazy Aunt is visiting? Well, maybe. It is also an acronym used in algebra. An acronym is where you take the first letter of a group of words and form a saying to help you remember something. This particular acronym helps us remember the order of operations. Not whether or not having your tonsils removed in the hospital comes before having your knee operated on. Operations in math refer to things such as adding, subtracting, multiplying, dividing, or squaring. You can even have (parentheses) in your math problem. In fact, if it is not a number, it is probably an operation. Using this acronym can help you remember what order to go in when you have more than one operation to solve in an algebra problem. Below is a rap song that will help you remember the order of operations! Before starting the video, make sure your headphones are plugged in and that you are using them so you do not disturb your neighbor! Clicking on the link will open a new window in your browser. Please click this link to take you to the YouTube video.this link

5. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Please Excuse My Dear Aunt Sally Does it really matter which operation we solve first in an algebra problem? The answer is yes. It matters. A lot. What if your teacher gives you the following algebra problem and asks you to solve it: 2 6 × 4 - 12 ÷ 3 – 8 + (6-2) - 2 On your scratch paper, solve this problem from left to right, like you were reading a sentence, and see what answer you get. Di you get -2? Did you get a different answer? What if I told you the correct answer is actually 4? When you are working an algebra problem with more than one operation, order does matter. Remember: Calculate an algebra problem in the wrong order and you will get THE WRONG ANSWER! Remember the acronym “Please excuse my dear Aunt Sally” and you will remember which order to work an algebra problem that has more than one operation.

6. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Please Excuse My Dear Aunt Sally Before we continue, let’s go over our rules for the order of operations in an algebraic expression: ORDER OF OPERATIONS 1. Parentheses - ( ) or [ ] 2. Exponents or Powers 3. Multiply (from left to right 4. Divide (from left to right) 5. Add (from left to right) 6. Subtract (from left to right) If you remember to Please excuse my dear Aunt Sally, you will remember the order of operations

7. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Parentheses With the order of operations, always do parentheses first. Parentheses are a type of bracket used in mathematical expressions. Parentheses and brackets are used to denote precedence, which means when you see parentheses or brackets in a math problem, you should work this operation first. Besides parentheses, some other types of brackets you might see in a math problem are: [ ] Square Brackets { } Braces (sometimes called “curly brackets” Angle Brackets (these can sometimes be confused with greater than or less than symbols, so be careful!) Most of the time you will see parentheses in a math problem, but if you see any of these other types of brackets, treat them just like parentheses and perform that operation first ! If you have more than one operation inside the parentheses, follow the order of operations inside the parentheses. 2 For example, if you have 5 x (3 x 2 + 1), work inside the parentheses first, but follow the order of operations inside the parentheses. So, we would have =5 x (9 x 2+1) = 5 x (18+1) = 5 x 19 = 95

8. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Exponents Do exponents second, after parentheses. Exponents, also called powers, are a short way to show how many times a number, called the base, is multiplied times itself. A number with an exponent is said to be “raised to the power” of that exponent. 2 Exponents can be read different ways. For example, 8 can be called eight to the second power, eight to the power of two, or eight squared. The exponents two and three are different than the rest. Two can be called squared, and three can be called cubed. Whatever we call it, we need to figure out the product of 8 x 8, which is 64, 3 For example, 2 can be six to the third power, six to the power of three, or six cubed. Mathematically speaking, it means we figure out the product of 2 x 2 x 2, which is

9. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Multiplication and Division Multiplication and division are on the same level. When you have a math problem with both multiplication and division, work these operations from left to right. Let’s review some key concepts about these operations. Multiplication: (Remember that multiplication is a shortcut for repeated addition). Also remember that in algebra you may not see a multiplication sign. A number written beside a variable, such as 3a, means multiply 3 times a. A number written before parentheses also means multiply. You might see 3(9-1). The multiplication sign is understood and not written so you don’t think it is a variable. When you multiply, you're increasing a number over and over again. Basically, multiplication is adding something more than once. For instance, if you eat 2 pieces of candy, then you eat another 2, then 2 more, you can say that you multiplied the amount of candy you ate. Here, we have two pieces of candy three times, and this would be written as 2 x 3. Remember, with multiplication, the order the numbers are written does not matter. 2 x 3 is the same thing as 3 x 2. Both equal 6. Division: Division is splitting something equally. For instance, let's say you have 4 raffle tickets, and you'd like to share them with 5 friends. You divide the tickets among your friends. Each friend gets an equal number of tickets. This would be written as 4 ÷ 2. Each friend would get two tickets. Remember: Order matters with division. 4 ÷ 2 is not the same thing as 2 ÷ 4.

10. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Addition and Subtraction Our final two operations are addition and subtraction. Just like with multiplication and division, addition and subtraction are on the same level. When both operations appear in a problem, work them from left to right. Addition: Addition is a way to put things together. When you add two amounts, you are putting them together, as one larger amount. Addition happens every day in real life (so does subtraction!). What if you already have two dogs, and your parents give you three? This would be written 2 + 3, or 3+2. Order does not matter with addition. + Subtraction is taking things away. When you have an amount and you subtract from it, the amount becomes smaller. Subtraction happens a lot in real life. If we have a plate with five cookies and your brother comes and takes two, we would be left with 2 cookies. This would be written 5 – 3. Order matters with subtraction. 5-3 is not the same as 3-5.

11. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Practice The next few pages will have some practice problems. Remember these things, however, when you are working problems on your own that contain more than one operation: First, copy the problem down exactly as you see it. Second, go through each level of operations according to the order of operations (Please excuse my dear Aunt Sally!). If you have two operations that are on the same level (multiplication and division are on the same level, as are addition and subtraction), solve the operations within each level from left to right. Third, write the answer directly below the operation. And fourth, do not re-use any numbers. Let’s try a couple of examples. PLEASE USE YOUR HEADPHONES SO YOU DO NOT DISTURB YOUR NEIGHBOR.. Use your scratch paper to solve each problem, and click on the correct answer. YOU MAY USE YOUR CALUCLATOR. You will hear applause when you click on the correct answer, and the box will flash yellow. Nothing will happen if you click on an incorrect answer. Ready? Let’s try some practice problems. Click the forward arrow to take you to the next page of practice problems. You will see the words “End of Practice” after the last practice problem. When you reach the end of the practice problems, click on “Quiz” at the top and take the quiz. Make sure you read the Quiz directions very carefully. Good luck! 3 3 + 2 - (9 +1) = 13

12. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Practice 2 1). 66 - 2 + 4 = 58 2 2). 3 × ( 1 + 9 )= 12 2 3). 4 × ( 7 - 1 ) = 729 66 192 30 2 4). 4 × (1 - 2 ) = 2 5). 2 × ( 7 + 5 ) = 4-4 288108

13. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Practice 3 6). 45 - 2 + 4 = 37 5 7). 5 × ( 1 + 4 ) = 45 2 8). 9 × ( 9 - 1 ) = 576 41 720 25 2 9). 8 × (6 - 2 ) = 2 10). 5 × ( 7 - 5 ) = 128272 20220

14. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Practice 3 11). 17 - 3 + 4 = 6 2 12). 9 × ( 5 + 9 ) = 126 3 13). 0 × ( 3 - 4 ) = 5 -6 0 306 4 14). 9 × (2 - 2 ) = 2 15). 8 × ( 7 + 5 = 0 126 752432

15. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Practice 4 16). 15 - 2 + 4 = 5 3 17). 4 × ( 3 + 2 ) = 38 3 18). 0 × ( 2 - 2 ) = 6 3 0 44 3 19). 8 × (3 x 0) = 2 20). 6 × ( 5 - 5) = 216 0 160180 Once you are finished with number 20 you are done with practice. Click on quiz and take the quiz. Make sure you follow the directions. Good luck!

16. Multiplication and Division Addition and Subtraction PracticeExponentsParenthesesHomeQuizIntroduction Objective and Standards Quiz Now it’s time to take your quiz. You will need your pencil, a sheet of blank scratch paper, and your calculator. Please remember what you have learned about the order of operations. Read each problem carefully and solve each problem on your paper. Choose the correct answer from the choices below each question. There is only one correct answer per problem. Good luck! Please click here to open the quiz. The quiz will open in a new window in your browser. Make sure you enter your first and last name as well as your classroom email address that is assigned to you.click here to open the quiz. You are finished with this tutorial! Please make sure you log out of your computer when you are finished. Make sure you take all of your belongs with you when you leave the computer.