TRANSLATING VERBAL PHRASES

Verbal Phrase Expression

The sum of six and a number 6 + xsum +six 6number x

Eight more than a number y + 8more than +

A number plus five n + 5plus +

A number increased by seven x + 7+increased

A number decreased by nine n – 9–decreased

Ten times a number

Seven divided by a number

10 • n

7x

times

divided

•

The sum of six and a number 6 + x

Eight numberEight more than a number

fivenumberA number plus five

sevennumberA number increased by seven

ninenumberA number decreased by nine

Ten numberTen times a number

8yy + 8

1010 • nn

5nn + 5

7xx + 7

9nn – 9

or ( )10n10n( )n(10 )n10(10n)

Seven 7x

number

USING A VERBAL MODEL

In Mathematics there is a difference between a phrase and a sentence. Phrases translate into expressions; sentences translate into equations or inequalities.

ExpressionsPhrases

Equations or InequalitiesSentences

USING A VERBAL MODEL

Phrase Expression

The sum of six and a number

The sum of six and a number is

6 + x

6 + x =is =

Sentence Equation

The sum of six and a number is twelve. 6 + x = 12 is twelve. = 12

Sentence Inequality

The sum of six and a number is less than twelve.

6 + x < 12 is less than twelve.

< 12

The sum of six and a number 6 + x

The sum of six and a number is 6 + x =

The sum of six and a number is twelve. 6 + x = 12

In this sentence, “is” says thatone quantity is equal to one another.

In this sentence, the words “is less than” indicate an inequality.

The sum of six and a number is less than twelve.

6 + x < 12

number is twelve. 6 + x = 12

is less than twelve.

6 + x < 12

USING A VERBAL MODEL

Use three steps to write a mathematical model.

WRITE AVERBAL MODEL.

ASSIGN LABELS.

WRITE AN ALGEBRAIC MODEL.

Writing algebraic expressions, equations, or inequalities that represent real-life situations is called modeling.

The expression, equation, or inequality is a mathematical model.

Writing an Algebraic Model

You and three friends are having a dim sum lunch at a Chinese restaurant that charges $2 per plate. You order lots of plates. The waiter gives you a bill for $25.20, which includes tax of $1.20. Use mental math to solve the equation for how many plates your group ordered.

Understand the problem situation before you begin. For example, notice that tax is added after the total cost of the dim sum plates is figured.

SOLUTION

LABELS

VERBAL MODEL

Writing an Algebraic Model

Cost perplate • Number of

plates = Bill Tax–

Cost per plate = 2

Number of plates = p

Amount of bill = 25.20

Tax =

1.20

(dollars)

(dollars)

(dollars)

(plates)

25.20 1.20–2 =p

2p = 24.00p = 12

Your group ordered 12 plates of food costing $24.00.

ALGEBRAIC MODEL

A PROBLEM SOLVING PLAN USING MODELS

Writing an Algebraic Model

Ask yourself what you need to know to solve the problem. Then write a verbal model that will give you what you need to know.

Assign labels to each part of your verbal problem.

Use the labels to write an algebraic model based on your verbal model.

Solve the algebraic model and answer the original question.

VERBAL MODEL

Ask yourself what you need to know to solve the problem. Then write a verbal model that will give you what you need to know.

Assign labels to each part of your verbal problem.

Use the labels to write an algebraic model based on your verbal model.

Solve the algebraic model and answer the original question.

Check that your answer is reasonable.

ALGEBRAIC MODEL

LABELS

SOLVE

CHECK

Using a Verbal Model

JET PILOT A jet pilot is flying from Los Angeles, CA to Chicago, IL at a speed of 500 miles per hour. When the plane is 600 miles from Chicago, an air traffic controller tells the pilot that it will be 2 hours before the plane can get clearance to land. The pilot knows the speed of the jet must be greater then 322 miles per hour or the jet could stall.

a. At what speed would the jet have to fly to arrive in Chicago in 2 hours?

Is it reasonable for the pilot to fly directly to Chicago at the reduced speed from part (a) or must the pilot take some other action?

b.

LABELS

VERBAL MODEL

Using a Verbal Model

Speed ofjet • Time =

Distance totravel

Speed of jet = x

Time = 2

Distance to travel = 600

(miles per hour)

(miles)

(hours)

600=

x = 300

ALGEBRAIC MODEL

a. At what speed would the jet have to fly to arrive in Chicago in 2 hours?

2 x

SOLUTION

To arrive in 2 hours, the pilot would have to slow the jet down to 300 miles per hour.

You can use the formula (rate)(time) = (distance) to write a verbal model.

Using a Verbal Model

It is not reasonable for the pilot to fly at 300 miles per hour, because the jet could stall. The pilot should take some other action, such as circling in a holding pattern, to use some of the time.

Is it reasonable for the pilot to fly directly to Chicago at 300 miles per hour or must the pilot take some other action?

b.