Section 1-1 Using Variables SPI 21C: Translate a verbal expression into an algebraic expression or vs. SPI 22B: Translate a verbal sentence into an algebraic equation or vs. Objectives: Model relationships with variables Model relationships with equations, and formulas Vocabulary Variables A symbol that represents one or more numbers (unknown amount) Represented by any letter of the alphabet. EX: a, z, y, h, etc. Expression A mathematical phrase that includes numbers, variables, and operation symbols. EX: n + 7 Equation A mathematical sentence that uses an equal sign. EX: 3x + 4 = 10 Open Sentence An equation that contains one or more variables. Ex: 3x + 4 = 10

+-x or () or ÷ or / sum total more than increased by difference fewer than less than decreased by product times multiplied twice divided by quotient fraction Common Translation Operations Determines operation(s) to be performed Hours Worked Pay (Dollars) h Write an algebraic expression relating the pay to number of hours worked. 1. What is the pay for 1 hour? 2. What is the pay for 2 hours? 6.50 x 2 3. What is the pay for 3 hours? 4. What is the pay for h hours? 6.50 x x h 5. Write an expression to relate pay to the number of hours worked x h or 6.50h The word “Quantity” indicates the use of parenthesis

Write an algebraic expression for each phrase. a. Seven more than n n + 7 b. The difference of n and 7 n – 7 Begin with 1 st value of n c. The product of 7 and n 7n d. The quotient of n and 7 n Divide 1 st term by 2d term 7 e. Two times a number plus 3 2n + 3 f. 7 less than 3 times a number 3n - 7 Write an algebraic EQUATION that models the problem below. Music Plus sells all CDs for $10. Write an equation for the total cost of a given number of CDs. How many variables do you need to define? C = total cost n = # of CDs bought Relate by writing the equation: C = 10n

The data in the table represents the number of gallons used for the number of miles traveled. Write an equation for the data in the table. m = 20g Gallons Miles Write an Equation from a Table of Data Relate Miles to number of gallons. Miles equals 20 times number of gallons Define variables. m = miles traveled g = gallons Write an expression representing the problem.

For each problem, (a) define a variable and (b) write an expression that models the problem. Kagan Structure: Sage-N-Scribe x = number of months; x x = number of months; (x – 1)

n = number of people after the first person n n = number of games played n