1.5 Problem Solving Using Algebraic Models Algebra 2 Mrs. Spitz Fall 2008

Objectives Use a general problem-solving plan to solve real life problems. Differentiate between verbal and algebraic models

Assignment Pgs #4-15, 18Pgs #4-15, 18 Review for quiz pg. 40 to see an example of quiz # Review for quiz pg. 40 to see an example of quiz #

Verbal Model Boxes with words separated by math symbols such as +, =, *, etc.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 mathematical statement with variables and math symbols. A=bh 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? Average Speed 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? DistanceRateTime =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? 550Rate2.25 =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 RateTime =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.