10.+Order+of+Operations

//If everyone completed the same problem in a different way, they would all get different answers. //      **Order of operations ** are the rules for solving problems with several steps. With order of operations, there is one set of rules for completing different problems, called **PEMDAS **. PEMDAS is an acronym for the order in which to solve a problem. A lot of people remember it by saying "Please Excuse My Dear Aunt Sally."

4(3 - 2) - 16  4 2  + 5 The first step to solving a problem like the one above is to start by what is in the parenthesis. 3-2 = 1 , so <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">4(1) - 16 <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">4 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; vertical-align: super;">2 <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;"> + 5 <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Next, look for any exponents to solve. <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">4 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; vertical-align: super;">2 <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">= 16 <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">, so <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">4(1) - 16 <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">16 + 5 <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Then solve any multiplication and division pieces working from left to right. <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">4(1) = 4 <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">4 - 16 <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">16 + 5 <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">and <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">16 <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">16 = 1 <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">, so <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">4 - 1 + 5 <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Finally solve any addition and subtraction pieces working from left to right. <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">4 - 1 + 5 <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">3 + 5  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">8

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Matho2 - Order of Operations Bingo Game] - This game is based on the game Bingo. You can play this by yourself or with up to four people. The computer gives you a problem to solve, and you need to use order of operations to find the answer. After you find the answer, click on it on the number on the table. Everyone should solve every problem for extra practice.

<span style="color: #0000ff; display: block; font-family: 'Times New Roman',Times,serif; font-size: 140%; text-align: left;">[|Operation Four - Order of Operations Game] - This activity is a two player game that links the board game, Connect Four, with order of operations. You can pick whatever level and time limit you would like, and play whoever you would like for the practice. I would start at the lower level and work your way up, so you can improve your skill level.

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**//<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 160%;">If you have any questions about order of operations, please feel free to use the discussion tab at the top of this page, and either myself, or one of your classmates, can answer them for you. //**

<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">__Numerical and Proportional Reasoning:__ Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies. <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 120%;">2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities. <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 120%;">21. Apply the order of operations and algebraic properties; i.e., commutative, associative, distributive, <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 120%;"> inverse operations, and the additive and multiplicative identities; to compute and solve  <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 120%;">multistep problems and explain solutions in writing. [|CT Mathematics Standards]
 * <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 18pt;">Connecticut 6th Grade Mathematics Curriculum Standards: **