1. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. Rich Tasks = Meaningful Math Presentation by: Diane Leighty and Nancy Taylor Part 1: Gasoline Rates Part 2: Explore Several HOT problems in groups 1

2. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ How far would you drive for cheaper gas? VAILL Conference 2015 Diane Leighty and Nancy Taylor2

3. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. Acknowledgements : VAILL Conference 2015 Diane Leighty and Nancy Taylor3 The problem presented today is a modification of a problem presented by Christine Belledin at the TCM conference 2015 and is based on a problem created by Landy Godbold, who teaches at the Westminster Schools in Atlanta, Georgia. Doyle, Dot, and Dan Teague, “The Gas Station Problem”, Everybody’s Problems, Consortium, Number 88, COMAP, Inc. Lexington, Massachusetts, Spring/Summer, 2005.

4. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor4 THE PROBLEM: On the way to school or work you observe the price of gas at different stations day-to-day. On the internet you can find the station that has the cheapest gas each day. Is it worth the driving the extra miles off your normal route to go to the station with the cheapest gas? What information is important to know to solve this problem? Where do you start?

5. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor5 SIMPLIFY THE PROBLEM: Create a specific case for students to so they understand the problem, define the variables and parameters, and formulate a solution to this model. Suppose that there is a station on your route to school that sells gas for $2.50 per gallon. A station 5 miles off your route sells for $2.35 per gallon. Should you travel the extra distance to buy the cheaper gas?

6. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VISUALIZE THE PROBLEM: VAILL Conference 2015 Diane Leighty and Nancy Taylor6 What information do you need to know to solve this problem? Do you need to get even more specific?

7. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor7 Station A Miles out of your way: Total cost of gasoline: Cost per gallon of useable gas: SCENERIO 1: Your car gets 32 mpg and you are filling your 12 gallon tank. 0 miles $2.50 x 12 = $30.00 $2.50 /gallon

8. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor8 Station B Miles out of your way: Total cost of gasoline: Gas used to/from the gas station: Useable gas: Cost per gallon of useable gas: 10 miles $2.35 x 12 = $28.20 10 miles ÷ 32 mpg = 0.3125 gallons 12 - 0.3125 = 11.6875 gallons $28.20 ÷ 11.6875 gallons = $2.41/gallon

9. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor9 SCENERIO 2: Your car gets 32 mpg and you only need a half of a tank of gasoline. Summarize your results.

10. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor10 Can we make the decision using a different metric?

11. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor11 ASSIGNMENT: Create a formula that could be used based on miles off route, cost per gallon, gallons to be purchased, and fuel efficiency that could be used to determine the cost per gallon of useable gas. Enhance: Use an excel spreadsheet, calculator, or program software to have a workable model that a person could use to help them decide if it is worth it to drive the extra distance or not.

12. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor12 Braking Distances While Driving DRY Pavement Speed Thinking Distance (feet) Possible Braking Distance (feet) Overall Stopping Distance Can Be: (feet) (mph) 20 40 25 3358 30 4676 35 6297 403979118 4544102146 Wet Pavement Speed Thinking Distance (feet) Possible Braking Distance (feet) Overall Stopping Distance Can Be: (feet) (mph) 20 2646 25 4368 30 5989 35 82117 4039108147 4544135179

13. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor13 Braking Distances While Driving DRY Pavement Speed Thinking Distance (feet) Possible Braking Distance (feet) Overall Stopping Distance Can Be: (feet) (mph) 20 40 25 3358 30 4676 35 6297 403979118 4544102146 Cell Phone Used Speed Thinking Distance (feet) Possible Braking Distance (feet) Overall Stopping Distance Can Be: (feet) (mph) 20432063 25523385 306246108 357562137 408579164 4595102197

14. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor14 Braking Distances While Driving Cell Phone Used Speed Thinking Distance (feet) Possible Braking Distance (feet) Overall Stopping Distance Can Be: (feet) (mph) 20432063 25523385 306246108 357562137 408579164 4595102197 Wet & Cell Speed Thinking Distance (feet) Possible Braking Distance (feet) Overall Stopping Distance Can Be: (feet) (mph) 20432669 25524395 306259121 357582157 4085108193 4595135230

15. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor15 o Perspectives o Planning and Organizing: A Tennis Table Tournament o Apple Orchard Task o Skeleton Tower o Sidewalk Stones

16. Edit the text with your own short phrases. The animation is already done for you; just copy and paste the slide into your existing presentation. VAILL Conference 2015 Diane Leighty and Nancy Taylor16