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One Step Equations Solving problems ONE STEP at a time Slide 2 One Step Equations What am I Learning Today? How will I show that I learned it? Use order of operations to solve mathematical equations Write and evaluate algebraic expressions, including those with exponents Solve simple one step equations using the four basic operations and rational numbers Slide 3 Vocabulary Equation: A mathematical sentence that contains an equal sign Variable: A letter or symbol used to represent a number Algebraic Expression: A mathematical phrase involving one or more variables and operation symbols Evaluate: Perform operations to obtain a single value for a numerical or algebraic expression Order of Operations: The rules that must be followed when simplifying expressions Exponent: Tells how many times the base is used as a factor Slide 4 Who is right? How did the boy solve this problem? How did the girl solve this problem? When performing arithmetic operations there can be only one correct answer. We need a set of rules in order to avoid this kind of confusion. Mathematicians have devised a standard order of operations for calculations involving more than one arithmetic operation. Slide 5 Questions Notes Questions Answers What are the Order of Operations? How can I remember the Order of Operations? What if there are several multiplication and division or addition and subtraction operations? - Parentheses: Simplify the inside of all parentheses first - Exponents: Simplify the exponent of every number - Multiplication and Division: Simplify one at a time - Addition and Subtraction: Simplify one at a time Please Excuse My Dear Aunt Sally (PEMDAS) ** Always keep things in order - Solve operations as they appear from left to right - Multiplication DOES NOT have to be solved before division - Addition DOES NOT have to be solved before subtraction **Rewrite the equation after solving each part from left to right Slide 6 Lets Talk about Exponents A number is in exponential form when it is written with a base and an exponent. Base 73737373 Exponent = 7 7 7= 343 Find the value. 2 6 = 2 2 2 2 2 2 4 x 2 x 2 x 2 x 2 8 x 2 x 2 x 2 16 x 2 x 2 32 x 2 = 64 Slide 7 Lets Talk about Parentheses Parentheses ( ) or brackets [ ] or { } are like a cocoonwhat is inside must be complete before it can leave the cocoon. Order of operations MUST be used inside parentheses or brackets if there is more than one operation being used. Always complete the operations in the parentheses or brackets the furthest inside For Example: {[24 For Example: {[24 (2 x 3)] + 9} 7 = ? Slide 8 Order of Operations: PEMDAS Evaluate the expressions. [7 + (24 6)] 3 4 2 + (3 7) [7 + 4] 3 11 x 12 132 Perform operations within parentheses. Multiply.Add. 4 2 + (21) 16 + 21 37 Find the value of the number with the exponent. Multiply.Add. Slide 9 Now Try This! Evaluate the expression. [24 (9 6)] (3 3 10) Perform operations within brackets and parentheses. Multiply. 8 (27 10) 8 x 17 Perform operation in parentheses. 136 Find the value of the number with the exponent. [24 (9 6)] (3 3 10)[8] (3 3 10) [24 3] (3 3 10) Slide 10 Order of Operation Practice 1. 35 7 5 = 2. 80 x 2 40 1 = 3. 2 + 2 x (5 + 4) (2 + 4) = 4. 8 + (2 x 5) x 18 9 = 5. 12 x [2 x(4 3)] 6 9 = 0 3 5 28 87 Slide 11 Dice Substitution Find a partner. Find a partner. Designate each color dice #1 and #2 Designate each color dice #1 and #2 Roll dice #1. Substitute the value for the variable and evaluate. Roll dice #1. Substitute the value for the variable and evaluate. Roll dice #2. Substitute the value for the variable and evaluate. Roll dice #2. Substitute the value for the variable and evaluate. Find the sum of the determined values. This is your score. Find the sum of the determined values. This is your score. The person with the highest score wins! The person with the highest score wins! Slide 12 Paired Discussion Turn to someone around you and discuss the following: Why do you have to use the order of operations to evaluate each expression? What would happen if there were no order of operations rules? When performing arithmetic operations there can be only one correct answer. We need a set of rules in order to avoid confusion and help us evaluate the expression in the same way each time. People might perform operations in different orders and arrive at different solutions. The purpose of the order of operations is to guarantee that every numerical expression has a unique value.