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1.5 Problem Solving Using Algebraic ModelsPowerPoint Presentation

1.5 Problem Solving Using Algebraic Models

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## PowerPoint Slideshow about ' 1.5 Problem Solving Using Algebraic Models' - boris-thornton

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Objectives

Use a general problem-solving plan to solve real life problems.

Differentiate between verbal and algebraic models

Assignment

- Pgs. 37-38 #4-15, 18
- Review for quiz pg. 40 to see an example of quiz #2 1.3-1.5

Verbal Model

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

Area of a rectangle

Length of the base

Height

Algebraic Model

- A mathematical statement with variables and math symbols.
A=bh

where: A= area

b=length of base

h=height

You must tell what each variable stands for!!

Example: Write a verbal model.

On August 15, 1995, the Concorde flew 35,035 miles from NYC to NYC in 31 h 27 min. What was the average speed in mi/h?

AverageSpeed

Total miles

Total time

Now solve the problem using the verbal model as a guide.

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

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 of

pot

Flow Rate

Time

=

X

Algebraic Model

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.

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