1.1 Variables and Expressions

Goals

• I can evaluate a variable expression.

• I can write variable expressions from word phrases.

• I can write a variable expression that models a real life situation.

A.SSE.1.a Interpret parts of an expression such as terms, factors, and coefficients

Section 1.1 – Variables and Expressions

Vocabulary:

• Variable- a letter or symbol that can be used for a value that can change.

Numerical expression – a mathematical phrase that contains only constants and/or operations and NO variables

• Constant – a number or value that does not change.

Algebraic expression – a mathematical phrase that may contain one or more variables, constants, and/or operations

We have to be able to “translate” words into expressions

What words indicate a particular operation?

Add Subtract SumPlus

More thanIncrease(d) by

PerimeterDeposit

GainGreater than

Up (flights of stairs)Total

MinusTake awayDifference

Reduce(d) byDecrease(d) by

WithdrawalLess than

Fewer (than)Loss of

We have to be able to “translate” words into expressions

What words indicate a particular operation?Multiply Divide

TimesProduct

OfTwice (×2), double (×2), triple (×3), etc.

Half (×½), Third (×⅓), Quarter (×¼)Area (by)

Percent (of)Square (times itself 2 times)Cube (times itself 3 times)

… to the power of ___(times itself ___ times)

Split into __ partsCost eachQuotient

One-half (÷2), Third (÷3), Quarter (÷4)

IntoPer

Percent (out of 100)

1.1 – Variables and Expressions

Let’s try an example of “translating” a phrase into an algebraic expression:

Nine more than a number y

“more than” means add

Answer: y + 9

y 9

?

1.1 – Variables and Expressions

Let’s try another example of “translating” a phrase into an algebraic expression:

4 less than a number n

“less than” means Subtract

Answer: n – 4.

Why not 4 – n?????

4 ?

n

1.1 – Variables and Expressions

Let’s try another example of “translating” a phrase into an algebraic expression:

A number a divided by 12

a? ? ? ? ? ? ? ? ? ? ? ?

1.1 – Variables and Expressions

This one is harder……

5 times the quantity 4 plus a number c

1.1 – Variables and Expressions

1. John types 62 words per minute. Write an expression for the number of words he types in m minutes.

2. Joey earns $5 for each car he washes. Write an expression for the number of cars Joey must wash to earn d dollars.

1.1 – Variables and Expressions

We can use an expression to represent a real life situation.

d = rt (Distance traveled equals rate (speed) multiplied by time traveled.)

I=Prt - Simple interest earned by an amount of money P, at an annual rate r, multiplied by the amount of time (t) in years.

Example

You plan to ride your bicycle to school and back at an average rate of 6 miles per hour for a distance of 10.5 miles. How long will it take you?

Example

Approximately fourteen 20 ounce plastic bottles must be recycled to produce 1 square foot of carpet.

Write an expression for the number of bottles needed to make c square feet of carpet.

Assignment

pg. 7 #9-33 odd, 41, 43