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

VocabularyVariables• 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 SentenceAn equation that contains one or more variables. Ex: 3x + 4 = 10

+ - x or () or • ÷ or /

sumtotalmore thanincreased by

differencefewer thanless thandecreased by

producttimesmultiplied twice

divided byquotientfraction

Common Translation Operations

Determines operation(s) to be performed

Hours Worked

Pay (Dollars)

1 6.50

2

3

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 23. What is the pay for 3 hours?

4. What is the pay for h hours?6.50 x 3

6.50 x h5. Write an expression to relate pay to the number of hours worked.

6.50 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 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 term7

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 costn = # 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

4 6 8 10

80 120 160 200

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 traveledg = gallons

Write an expression representing the problem.

For each problem, (a) define a variable and (b) write an expression that models the problem.

Kagan 2.1.8

Structure: Sage-N-Scribe

x = number of months; 150 + 475x

x = number of months; 199 + 688(x – 1)

n = number of people after the first person20 + 15n

n = number of games played10 + .25n