1. 1.5 PROBLEM SOLVING USING ALGEBRAIC MODELS Algebra 2

2. Learning Targets Students should be able to…  Use a general problem solving plan to solve real life problems.  Use other problem solving strategies to help solve real-life problems. Essential Questions  How can we develop a plan to solve real life problems using algebraic models?  How can we use algebraic models to solve real life situations?

3. Warm-up

4. Homework Check Section 1.4 Page 29 – 32 #4, 6, 8, 24 – 29, 46 – 56 even

5. Vocabulary Rates: the key word is per time– Some examples:  mph, gallon per minute, doughnuts made per hour Verbal Model: word equation using known formulas Algebraic Model: using the verbal model to make a mathematical statement.

6. Problem Solving Plan 1. Write a verbal model 2. Assign labels 3. Write an algebraic model 4. Solve the algebraic model 5. Answer the question

7. Example 1. On August 15, 1995 the Concorde flew 35,035 miles from New York City to New York city in 31 hours and 27 minutes. What was the average speed? 1. distance = rate * time 2. d = 35,035 miles, r = ?, t = 31 hours, 27 minutes 3. 35,035 = r ( ) 35,035 = r(31.45) 4. r = 1,114 5. 1,114 miles per hour

8. Example 2. Concorde flies at a rate of 1114 mph, how long will it take to fly 3,469 miles from New York City to London?

9. Example 3. A shower head advertises a maximum flow rate of 2.5 gallons per minute. Find the flow rate if it fills a 22 gallon bathtub in 9.5 minutes. Is this within the advertised limit?

10. Vocabulary Unit analysis – making sure the units follow the mathematical correctly

11. General Conversions Examples: 1. 20 ft convert to inches 2. 158 seconds to minutes 3. 920 hours to minutes 4. 700 ft/min to miles/hour

12. Other Problem Solving Strategies:  Draw a diagram  Look for a pattern  Guess, check, and revise Do you have any other ideas?

13. Additional Examples EX 4: Two trains leave Chicago at the same time and travel in opposite directions. One train averages 40 mph, and the other train averages 50 mph. How long will it take them to be 450 miles apart?

14. Additional Examples EX 5. You drove 280 miles, using 15 gallons of gasoline that cost $1.15 per gallon. If you get 24mi/gal on the highway and 16 in the city, how much did you spend for fuel for highway driving and how much for city driving? Total miles = 280 Fuel efficiency (highway) = 24 Amount of gas (highway) = x Fuel efficiency (city) = 16 Amount of gas (city) = 15 – x Total miles = fuel efficiency (hwy) x amt. gas + fuel efficiency (city) x amt. gas

15. Additional Examples EX 6: A fire truck is called to a scene. Three minutes later, a second truck is called. The first truck averages only 30 mph, but the second averages 60 mph. The trucks travel a total of 12 miles and arrive at the same time. How long from the first call did the trucks take to arrive? How far did each travel? We must first remember to change miles per hour to miles per minute.

16. Additional Examples EX 7: The table gives the heights from the floor to the first few steps of a flight of stairs. Determine the height of the 14 th step. To do this we must look for a pattern. Height to top of a story = h Height of landing = 4 Height per story = 8 Story number = n Height to top of story = height of landing + height per story x story number We will substitute 15 in for n. StepLanding123 Height (in.)4122028

17. Closure

18. Homework Page 37 – 38 #8 – 11, 18 – 24, 28, 29