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1.5 Problem Solving Using Algebraic Models

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india-schmidt
13 diapositives · 305 Views · Nov 28, 2014

1.5 Problem Solving Using Algebraic Models. Algebra 2. Learning Targets. I can use a general problem-solving plan to solve real life problems. I can differentiate between verbal and algebraic models. Verbal Model. Boxes with words separated by math symbols such as +, =, *, etc.

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1.5 Problem Solving Using Algebraic Models
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  1. 1.5 Problem Solving Using Algebraic Models Algebra 2

  2. Learning Targets I can use a general problem-solving plan to solve real life problems. I can differentiate between verbal and algebraic models.

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

  4. 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!!

  5. 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.

  6. 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

  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? 550 Rate 2.25 = X

  8. 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.

  9. 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

  10. 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.

  11. 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.

  12. Pair-share classwork • Work on 1.5 Practice A

  13. Resources: • http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/Algebra2/presentations.htm