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Order of Operations Sometimes there may be more than one way to go about solving a mathematical expression. The answer will depend on how you look at the problem. But, mathematics cannot work if the same problem produces a different answer. To eliminate confusion, an “order of operations” was developed. The order simply states what operations take precedence over other operations. A common technique that is used to help students remember this order is called “PEMDAS”, which is the phrase, “Please Excuse My Dear Aunt Sally”. It stands for parentheses, exponents, multiplication, division, addition and subtraction. Most students are able to memorize this acronym; however it is more difficult for them to remember how to apply this in simplifying various expressions. Students who lack the skills to simplify problems using the correct order of operations: Work problems from left to right, ignoring the correct order of operations Do not recognize various grouping symbols other than parentheses. Examples of grouping symbols are parentheses, brackets, braces, absolute value bars, fraction bars and radical symbols. Work with parentheses first regardless of the purpose of the parentheses. For example, when a student sees the problem 25 5(3) , they will multiply first because they see some parentheses; therefore they think the multiplication comes first in the order. The Pellissippi State team envisions a maze game as a way to show fluency with order of operations. At each turning point the student will either choose the next operation to be performed or the correct answer to the next operation until they successfully get through the maze. An Order of Operations game may progress as follows. Expressions involving addition and subtraction only o Example: 5 16 8 23 o Example: 12 (8) (3) 49 Expressions include addition, subtraction, multiplication and division o Example: 8 7*9 o Example: 4*3 8*6 o Example: (14) 7 *5 o Example: 3*5 (15) 4 6 Expressions include all of the previous operations plus exponents and radicals o Example: 12 42 o Example: 33 2*5 o Example: 2 49 42 o Example: 16 (5) 36*33 92 Expressions include all previous operations plus grouping symbols. Problems should become increasingly more difficult as the student progresses. o Example: 12(2 7) 24 12 o Example: 6 5 3 2 o Example: 82 52 24 6 32 o Example: 6 o Example: 16 4 2 22 2 9 4(2)(3) 10 NOTE: All currently designed games require students to work quickly through the problems to demonstrate their math fluency. The examples for order of operations represent problems that students should be able to simplify quickly. If speed is not an important factor for demonstrating fluency in this area, more difficult problems will need to be included in the game. Test Questions MATH 0801 11. Simplify. Show each step on your paper. 862 12. Simplify. Show each step on your paper. 4 32 7 12 13. Simplify. Show each step on your paper. 4 4( 7) 3 4 2 2