1.5 Problem Solving 1.5 Problem Solving Using Algebraic Using Algebraic

ModelsModelsAlgebra 2

Learning TargetsLearning TargetsI can use a general problem-solving plan I can use a general problem-solving plan

to solve real life problems.to solve real life problems.

I can differentiate between verbal and I can differentiate between verbal and algebraic models.algebraic models.

Verbal ModelVerbal Model

• Boxes with words Boxes with words separated by math symbols separated by math symbols such as +, =, *, etc.such as +, =, *, etc.

Area of a Area of a rectanglerectangle

Length of Length of the basethe base

HeightHeight

Algebraic ModelAlgebraic Model• A mathematical statement A mathematical statement

with variables and math with variables and math symbols.symbols.

A=bhA=bh

where:where: A= areaA= area

b=length of baseb=length of base

h=heighth=heightYou must tell what each You must tell what each

variable stands for!!variable stands for!!

ExampleExample: Write a verbal : Write a verbal model.model.On August 15, 1995, the On August 15, 1995, the

Concorde flew 35,035 miles Concorde flew 35,035 miles from NYC to NYC in 31 h 27 from NYC to NYC in 31 h 27 min. What was the min. What was the average speed in mi/h?average speed in mi/h?Average Speed

Total miles

Total time

Now solve the problem using the verbal model as a

guide.

60

2731035,35 S 45.31035,35 S

hmiS 111499.1113

Example• The Bullet Train runs between the

Japanese cities of Osaka and Fukuoka, a distance of 550 kilometers. When it makes no stops, it takes 2 hours and 15 minutes to make the trip.. What is the average speed of the Bullet Train?

Distance Rate Time= X

Example• The Bullet Train runs between the

Japanese cities of Osaka and Fukuoka, a distance of 550 kilometers. When it makes no stops, it takes 2 hours and 15 minutes to make the trip.. What is the average speed of the Bullet Train?

550 Rate 2.25= X

Algebraic Model

r

r

r

trd

24425.2

550

25.2550

Formula

Substitute known values

Divide each side by 2.25

Use a calculator.

The Bullet Train’s average speed is about 244 kilometers per hour.

Example• A watersaving faucet has a flow rate of at

most 9.6 cubic inches per second. To test whether your faucet meets this standard, you time how long it takes the faucet to fill a 470 cubic inch pot, obtaining a time of 35 seconds. Find your faucet’s flow rate. Does it meet the standard for water conservation?

Volume ofpot

Flow Rate Time= X

Algebraic Model

r

r

r

trv

4.1335

470

35470

Formula

Substitute known values

Divide each side by 35

Use a calculator.

The flow rate is about13.4 in.3/sec which does not meet the standard.

Using other problem solving strategies

• When you are writing a verbal model to represent a real-life problem, remember that you can use other problem solving strategies like drawing a diagram or looking for a pattern or guess and check to help create the verbal model. Pgs. 35 and 36 have other examples if you need them.

Pair-share classworkPair-share classwork• Work on 1.5 Work on 1.5

Practice APractice A

Resources:• http://www.taosschools.org/ths/Depar

tments/MathDept/spitz/Courses/Algebra2/presentations.htm