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Objectives: Model relationships with variables

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.

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Objectives: Model relationships with variables

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  1. Section 1-1 Using VariablesSPI 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

  2. Common Translation Operations Determines operation(s) to be performed The word “Quantity” indicates the use of parenthesis 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? 3. What is the pay for 3 hours? 6.50 x 2 4. What is the pay for h hours? 6.50 x 3 5. Write an expression to relate pay to the number of hours worked. 6.50 x h 6.50 x h or 6.50h

  3. 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 1st value of n c. The product of 7 and n 7n d. The quotient of n and 7 n Divide 1st 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. C = total cost n = # of CDs bought How many variables do you need to define? Relate by writing the equation: C = 10n

  4. Gallons 4 6 8 10 Miles 80 120 160 200 Write an Equation from a Table of Data 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. 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. m = 20g

  5. Apply Expressions in the Real-world For each problem, (a) define a variable and (b) write an expression that models the problem. Structure: Sage-N-Scribe x = number of months; 150 + 475x x = number of months; 199 + 688(x – 1) Kagan 2.1.8

  6. n = number of people after the first person 20 + 15n n = number of games played 10 + .25n

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