1.5 Problem Solving Using Algebraic Models

p. 33

Name five problem solving strategies.

What is the 1st thing you should do when you have to work a word problem?

Verbal Model•(Remember your formulas!!!)•Boxes with words separated by math symbols such as +, =, *, etc.

Area of a rectangle = Length of

the base • Height

1. Use a formula

Algebraic Model•A mathematical statement with variables and math symbols.

A = bhwhere: A= area

b=length of base h=height

You must tell what each variable stands for!!

Example: Write a verbal model.

60

2731035,35 S

45.31035,35 S

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?

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

Total time

Average Speed

Total miles ÷=

hrmiS 111499.1113

Drawing a Diagram•RAILROADS In•1862, two companies•were given the rights to•build a railroad from Omaha,•Nebraska to Sacramento,•California. The Central•Pacific Company began•from Sacramento in 1863.•Twenty-four months later,•the Union Pacific Company•began from Omaha.

•The Central Pacific Company averaged 8.75 miles of track per month. The Union Pacific Company averaged 20 miles of track per month. The photo shows the two companies meeting in Promontory, Utah, as the 1590 miles of track were completed. When was the photo taken? How many miles of track did each company build?

Make a Chart

rate time distance

Central P 8.75 t 8.75t

Union P 20 t −24 20(t −24)

Total 1590

8.75t + 20(t − 24)= 1590

Look for a Pattern & Guess and Check

See examples 5 & 6 on page 36.

1.Name five problem solving strategies.Use a formula, draw a picture, make a chart, look for a pattern , or guess & check.

2. What is the 1st thing you should do when you have to work a word problem?

Read the whole problem.

Assignment

p. 37, 8-21, 28-29, Quiz 2, 1-8