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Solving Real-Life Problems with Algebraic Models and Verbal Models

This lesson focuses on using algebraic models and verbal models to solve real-life problems. Students will learn to differentiate between the two types of models and apply a general problem-solving strategy. By examining concrete examples, such as calculating average speed and flow rates, learners will gain practical skills in formulating and interpreting mathematical expressions that represent real-world situations. The lesson encourages creative problem-solving approaches, such as drawing diagrams and searching for patterns to assist in the modeling process.

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Solving Real-Life Problems with Algebraic Models and Verbal Models

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  1. 1.5 Problem Solving Using Algebraic Models Algebra 2 Mrs. Spitz Fall 2008

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

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

  4. Verbal Model • Boxes with words separated by math symbols such as +, =, *, etc. Area of a rectangle Length of the base Height

  5. 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!!

  6. 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.

  7. 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

  8. 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

  9. 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.

  10. 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

  11. 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.

  12. 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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