INTRO TO EQUATIONS Some pictures are from the

INTRO TO EQUATIONS *Some pictures are from the Virginia DOE vocab cards

AGENDA • Define fundamental vocabulary • General problem solving steps • Translation table • Examples

FUNDAMENTAL VOCABULARY • Constant • Variable • Coefficient • Term • Like terms • Expression • Equation • Solution • Simplify

CONSTANT • A constant is a number by itself. 87 – 2 f = 5 Examples Which of the terms above are constants? 4 -7 π In Context

VARIABLE • A variable is a symbol, usually a letter, for an unknown quantity whose value may change. Examples in Context

COEFFICIENT • A coefficient is the number Examples in Context being multiplied by a variable usually written in front of the variable.

• A term is a constant, a variable, or product of constants and variables. TERM Examples in Context

• Like terms are terms with the same variable raised to the same exponent. LIKE TERMS Examples 4 x 5 x -10 x 14 -41 133 6 xy 2 -8 xy 2 Examples in Context 7 x + 4 – 11 x +3 +5 x How many terms are there? Which ones are like terms?

EXPRESSION • An expression is a group of Examples terms separated by plus (+) and minus (-) signs.

EQUATION • An equation is a mathematical statement that uses an equal sign to show that two expressions are equal. Examples in Context 2 + 3 = -8 + 13 41 = 3 x + 99 3(p+11) – 52 = 123456789 Definition from http: //www. icoachmath. com/math_dictionary/equation. html

• Solutions are the values of the variables that make an equation true. SOLUTION Examples 7 m + 12 = 47 7(5) + 12 = 47 35 + 12 = 47 47 = 47 5 is a solution because it makes the equation true

SIMPLIFY • Simplify means to rewrite so there are no like terms or parenthesis. Example Not Simplified 4(x – 12) 4 x – 48 3 x + 7 + 6 x 9 x + 7

AGENDA • Define fundamental vocabulary • Problem solving steps • Translation table • Examples

GENERAL PROBLEM SOLVING STEPS 1. Determine what it is you need to know to answer the question. 2. Identify any useful information or formulas that will help you find what you to need to know. 3. Create labels for given information and unknown. 4. Create an algebraic model for situation and solve.

HELPFUL TRANSLATIONS Courtesy of Robbinsville Highschool Algebra Summer Packet Don’t forget to mention product should be under multiply

AGENDA • Define fundamental vocabulary • Problem solving steps • Translation table • Examples

EXAMPLE 1 The sum of three and five times a number is -42. What is the number? 3 5 x -42

EXAMPLE 2 13 more than the difference of nine and twice a number is zero. What is the number? 9 2 x 13 0

EXAMPLE 3 The sum of Kyleisha’s and Nasir’s weight is 240. If Nasir weighs 30 more pounds than Kyleisha, how much do Nasir and Kyleisha each weigh? k = Kyleisha’s weight n = Nasir’s weight n = k + 30 k n k k + 30 240

EXAMPLE 4 • REAL LIFE PROBLEM: I missed breakfast, so I was extra hungry by the time lunch came. I went to the corner store across the street, and poppy charged me $2 for each empanada instead $1. 50. Then he taxed me $3. 47!! If the total came out to be $29. 47, how many empanadas did I buy? ? e = number of empanadas I bought total = cost of empanadas + tax 29. 47 2 e 3. 47