Variables and Expressions

Variables and Expressions

Unit 1

Expression

Expression: A math statement w/ at least one variable and/or numbers and operation symbols (Does NOT contain an "=" SIGN)

Variable: A symbol/letter that takes the place of an unknown number

Coefficient: A number multiplied by a variable.

Constant: a number on its own, does NOT change or have a variable

Multiple Choice

In the expression 

 $5w^2-6x+13$ , what is 13?

• variable

• constant

• coefficient

• operator

Multiple Select

Select the coefficients of the expression: $3x^2-14x+8$  

• -14

• 8

• 3

• 14

Open Ended

Write an expression with two different variables, and a constant.

Types of Expressions 

-algebraic / numerical / variable expression is an expression built up from numbers and symbols

-Verbal expression is a mathematical statement that is expressed in words

Multiple Choice

sum means

• add

• subtract

• multiply

• divide

Multiple Choice

The difference of

• add

• subtract

• multiply

• divide

Multiple Choice

the product of means

• add

• subtract

• multiply

• divide

Multiple Choice

the quotient of means

• add

• subtract

• multiply

• divide

Steps to translate a verbal expression to an algebraic expression

• Read each statement

• Identify the math terms and keywords in the statement (ie, variables, coefficient, constants, operations, etc.)

• Translate all the terms to an algebraic expression, being sure that you write them in correct order to what the statement is asking

• Reread your algebraic statement and make sure it is what the original statement is asking

Words to look for

Many words and phrases suggest mathematical operations . The following common words and phrases indicate addition, subtraction, multiplication, and division.

Open Ended

write the algebraic expression for:

Kim has 7 more than 5 times the amount Sylvia has.

Open Ended

write the algebraic expression for:

The length of a rectangle is 3 feet less than 4 times its width.

Open Ended

Write an expression to represent how much a realtor will earn at a 6% commission on a house that costs x dollars.

Making a Word Problem using an expression

Step 1: Identify the variables.

Step 2: Identify the coefficients for any of the variables.

Step 3: Identify the constant(s), if any, in the expression.

Step 4: Identify the operation(s) that are used in the expression. 

Step 5: Identify any possible formulas that may have been used to create the expression.

For example: 3x+30

• Identify variables: x

• Identify coefficients: 3

• Identify constants: 30

• Identify operation: terms are being added, if talking about money, 3x is being increased by 30.

• Identify possible formulas: none

3x + 30

Paul is the delivery driver for a local pizza shop. He earns $3 for each customer that he delivers to in the area. He also earns a flat rate of 30 dollars per shift.

The 'X' in this problem represents what?

Multiple Choice

Write a word problem that represents the algebraic expression:

5x+40

• A plumber makes $40 an hour plus a $5 flat rate per job.

• A cowboy pays $40 to enter a rodeo but makes $5 per entry.

• A waitress makes 5% tips and $40 dollars an hour.

• An electrician charges $40 for showing up to a job plus $5 per hour spent on the job.

Solving Expressions when given variables

• Substitute any numbers for the given variable/s

• Use order of operations and solve

Multiple Choice

Evaluate when x=6

15-x

• 10

• 8

• 9

• 7

Multiple Choice

Evaluate when a = 4, b=2 and c=16

a + b

• 4

• 6

• 5

• 7

Multiple Choice

Evaluate when a = 4, b = 2 and c = 16

bc

• 32

• 26

• 28

• 216

Poll

Stoplight Review: How do you feel abou today's topic?

• Green Light - Full Speed Ahead

• Yellow Light - I'll get there slowly with practice

• Red Light - I don't know where you are at?