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What’s Worse than Losing?

What’s Worse than Losing?. In a Race. Are you finished if you lose? When are you finished? Is there a difference between a race being finished and a person being finished?. Finished. By Richard Holden. Overview. The race The challenge The diameter path The hypotenuse path The winner

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What’s Worse than Losing?

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  1. What’s Worse than Losing?

  2. In a Race • Are you finished if you lose? • When are you finished? • Is there a difference between a race being finished and a person being finished?

  3. Finished By Richard Holden

  4. Overview • The race • The challenge • The diameter path • The hypotenuse path • The winner • The final words

  5. Dreams of Championship • Sarah (age 13) • Bicycle enthusiast • Fiercely competitive • “Win at all costs” • Sarah’s goal • Win the grand race • Beat her friend Katie • Brag to everyone • Show off her trophy

  6. The 100 Mile Race • Sarah’s average racing speed is 12.5 mph • Sarah’s strong point is her extremely fast start • Last year’s champion finished in 7 ½ hours • At 12.5 mph, Sarah would finish it in ____ hours 8 Solution: 100 miles ÷ 12.5 mph = 8 hours

  7. The Challenge • Somehow, Sarah would need to reduce her time by at least _____minutes to win • She saw only two possible options: • Pedal faster (an impossible task!!!) • Reduce the distance she actually travels 30 Solution: 8 hrs – 7 ½ hrs = 30 minutes

  8. Save Time by Saving Miles • Reducing her time by at least 30 min means reducing her distance by at least ____ miles • Hint: If Sarah travels 12.5 miles in one hour, how many miles would she travel in half an hour? 6.25 Solution: 12.5 ÷ 2 = 6.25 miles

  9. Cut Total Distance? HOW? • Sarah’s secret is: • She knows the area of the race • She knows of two shortcuts • Her initial break-away can get her secretly to the shortcuts • She only needs to know if the two shortcuts will save her at least 6.25 miles

  10. 24 miles 15.7 miles The Race Track (100 miles) 23 miles 13 miles 20 miles 4.3 miles

  11. 24 miles 15.7 miles The First Shortcut 23 miles Hint: C= πD 13 miles 20 miles 4.3 miles

  12. 24 miles 15.7 miles 10 mi The First Shortcut 23 miles C= πD 2*15.7 = 3.14D 31.4 = 3.14D 3.14 3.14 10 = D 13 miles 20 miles 4.3 miles Miles saved by the first shortcut? 15.7 – 10 = 5.7 miles

  13. 24 miles 15.7 miles 10 mi The Second Shortcut 23 miles 12 mi 5 mi Hint: Use the Pythagorean Theorem ? 13 miles 20 miles 4.3 miles

  14. 24 miles 15.7 miles 10 mi The Second Shortcut 23 miles 11 mi 12 mi A2 + B2 = C2 52 + 122 = C2 25 + 144 = C2 169 = C2 13 = C 5 mi 13 mi 13 miles 8 mi 20 miles 4.3 miles Miles saved by second shortcut? 12 + 5 – 13 = 17 – 13 = 4 mi

  15. The Objective is Met! • Objective was to save at least 6.25 miles • First shortcut saves 5.7 miles • Second shortcut saves 4 miles • 5.7 + 4 = 9.7 miles saved • The objective is met with miles to spare!!

  16. Change of Events Unfortunately--- Or perhaps fortunately--- Things did not go as planned for Sarah

  17. 24 miles 15.7 miles 10 mi 23 miles Sarah is Finished!! Banned from all future races 11 mi 12 mi 5 mi 13 mi 13 miles 8 mi 20 miles 4.3 miles

  18. The Winner!!! Katie! • Sarah’s best friend • Finished in 7 hrs 45 min. • Followed all the rules • Was cheered by everyone! • Received a well-earned trophy

  19. Sarah’s Final Words “Trust me— It’s better to finish the race, than to be finished racing.”

  20. Credits • Character names taken from book, The Cheat, by Amy Goldman Koss • Sarah • Katie • Pictures and graphics from MicroSoft’s Clips Online

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