Good Morning and Welcome to the 2011 Calcu-Solve Competition!

Good Morning and Welcome to the 2011 Calcu-Solve Competition! We hope you have a challenging and successful day! While we are waiting for all the teams to arrive, please: • Put your coats and lunches in the designated areas where your team sponsors can keep an eye on them. The only things you need to take to your team’s table are your sharpened pencils, calculators, and scrap paper (if you brought any.) • Make sure your team sponsor has completed the yellow registration/scoring card that is in the folder he/she received when you arrived. This card should be filled out completely and given to Mrs. Hoedeman at the Registration Desk. • Make a nametag for everyone in your group. Include your first and last names, school district, school name, and team number on the tag. Please wear the nametag during the entire competition. • Read over the information in the folder with your team sponsor. The rules and scoring procedures are explained. We will review these briefly just before the competition begins. • Each person on your team should take one stapled packet of individual answer sheets from the team folder and complete all the information on EVERY sheet. Print neatly and accurately! Your team number is displayed on the sign at your table and on your team folder. • Begin to practice for the competition by working on the Warm-Up Questions that are in your folder. We will go over the answers to these questions just before we begin the actual competition questions. • If you need help or further direction, please find a Boyce Ambassador or see Mrs. Hoedeman, Mr. O’Roark, Mrs. Hamel, or Mrs. Husak. Relax, Have Fun, and Good Luck!

Dr. Robert L. Furman Executive Faculty Program Director Educational Administration and Supervision

Mrs. Karen Brown Principal at Boyce Middle School

Mission - to create a stronger population of new engineering-, science- and mathematics-educated individuals that will ultimately increase and improve the pool of engineers and scientists seeking to tackle the tough and ever more complicated technical problems facing our nation and the world.

Warm-Up Answers • 1. 1/4 +1/4 +1/4 = 18 minutes; so 6+6+6 = 18 minutes; so it will take her 6 more minutes to walk the rest of the way home. • 2. Ursula-3m-Alma-3m-Cathy-2m-Lani-2m-Isabel-2m-Betty • 3. ÷2, ÷3, ÷4, ÷5, so 30 • 4. 11 bicycles (2x11=22); and4 tricycles (4x3=12); and 22+12=34 wheels • 5. to the game: cars 3 3 3 3 3 train 7 • from the game: cars 4 4 4 4 4 train 2 • so, there were 22 friends and 5 cars. • 6. 3: 3, 6, 9, 12, 15 ... 30...45...60 • 5: 5,10, 15,...30...45...60 • 15÷7≠R4; 30÷7≠R4; 45÷7≠R4; 60÷7 = R4 • Friend: 1 2 3 4 5 6 7 8 • Trades: 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0= 28 trades altogether. • 8. $700 = 70,000 cents; 25¢+50¢+100¢ = 175¢; • 70,000÷175 = 400 of each coin. • 9. 30 minutes= 12 minutes+12 minutes+6 minutes; 1+1+0.5 = 2.5 times as far; • so, Sue can walk 2.5 x 1.56 miles = 3.9 miles • 10. 7/12 = 14/24 and 5/8 = 15/24, so 15/24 - 14/24 = 1/24

Thank You from Mrs. Hoedeman and Mr. O’Roark • Ms. Fleckenstein • Mrs. Heins • Mrs. Husak • Mr. Wagner

SCHEDULE and EXPLANATION OF SCORING There will be eight Individual Questions - #s 2, 3, 4, 5 and 7, 8, 9, 10. You will be given 5 minutes to earn 5 points for a correct answer on each Individual Question, oryou may wait for a clue, work an extra 2 minutes and earn 3 points for a correct answer on each Individual Question. There will be two Group Questions - #s 1 and 6. Your team of students will be given 7 minutes to earn 10 points for a correct answer on each Group Question. We will complete Group Question # 1, Individual Questions # 2, 3, 4, and 5 and Group Question #6. Then we will take a short break and announce half-time scores. After the break, we will complete Individual Questions # 7, 8, 9, and 10. Following Individual Question # 10, we will break for lunch. If necessary, “tie-breakers” will follow lunch. Final scores will be announced and awards will be presented after ties are broken. Estimated concluding time is 1:30 p.m.

Guidelines for Tie-Breaking Situations Individual Tie-Breakers* • In the event of a tied individual score, a sudden death question will be given to those participants who are tied. If an answer is turned in and it is incorrect, the person may return to his/her seat and continue to work on the problem. The first person with a correct answer within a 5-minute time limit will be declared the winner. If at the end of 5 minutes, no one has submitted a correct answer ... • …another sudden death question will be given and step # 1 will be repeated. This procedure will be followed until a winner is determined. *These rules will be used to determine first, second, third, and tenth place individual winners. Group Tie-Breakers** Group tie-breakers will be handled in the same fashion as individual except that the entire group will participate. * *These rules will be used to determine first, second, and third place teams only.

Sample Problem Given the following pattern: 1, 1, 2, 3, 5, 8… what is the first perfect square greater than one to occur in the sequence?

Sample Problem - Clue Given the following pattern: 1, 1, 2, 3, 5, 8 what is the first perfect square greater than one to occur in the sequence? Clue:There is a famous pattern known as the Fibonacci Sequence where each number after the first two numbers is the sum of the preceding two numbers.

Official Competition

Group Question Set timer for 7:00

Boyce Ambassadors Please pass out the 1st group question face down and the 1st group answer sheet.

Question 1 - Group Daniel has a piggy bank full of coins. One day he counted them and said that he had an equal number of pennies, nickels, dimes, and quarters. His father handed him three coins. Daniel now had $7.22. What were the three coins that his father gave him?

Question 1 Answer He had an equal number of pennies, nickels, dimes, and quarters. His father handed him three coins. Daniel now had $7.22. What were the three coins that his father gave him? Solution: .01 + .05 + .1 + .25 = .41 therefore the original amount of money had to be a multiple of 41 cents. The greatest multiple that is < $7.22 is $6.97. $7.22 – $6.97 = .25 which is…. 1 nickel, 2 dimes

Individual Question Set timer for 5:00 Set timer for 2:00 for the clue

Boyce Ambassadors Please pass out Problem 2 (Individual Question #1) face down.

Question 2 In Hogwarts School of Witchcraft and Wizardry, Year One, 32 students like The Care of Magical Creatures, 34 like Potions, 38 like Charms, 19 like The Care of Magical Creatures and Potions, 8 like Potions and Charms, 10 like The Care of Magical Creatures and Charms, 2 like all three classes, and 15 (probably Muggles) don’t like any of the classes at all. How many students are in Year One at Hogwarts School of Witchcraft and Wizardry?

Question 2 Clue In Hogwarts School of Witchcraft and Wizardry, Year One, 32 students like The Care of Magical Creatures, 34 like Potions, 38 like Charms, 19 like The Care of Magical Creatures and Potions, 8 like Potions and Charms, 10 like The Care of Magical Creatures and Charms, 2 like all three classes, and 15 (probably Muggles) don’t like any of the classes at all. How many students are in Year One at Hogwarts School of Witchcraft and Wizardry? Clue: Do you know how John Venn is?

Question 2 Answer In Hogwarts School of Witchcraft and Wizardry, Year One, 32 students like The Care of Magical Creatures, 34 like Potions, 38 like Charms, 19 like The Care of Magical Creatures and Potions, 8 like Potions and Charms, 10 like The Care of Magical Creatures and Charms, 2 like all three classes, and 15 (probably Muggles) don’t like any of the classes at all. How many students are in Year One at Hogwarts School of Witchcraft and Wizardry? Solution: Sum of all – doubles – triple + 15 extra 32 + 34 + 38 – 19 – 8 - 10 – 4 + 15 78 students

Question 3 In the last two times around the Monopoly board, Wendell thought he was a goner. First, he had to pay half of his money in rent to Kate. He then had to pay $25 because of a “Chance” card. After that he landed on another property where he had to pay 3/5 of his remaining money in rent. Fortunately, on his next turn he passed “Go” and collected $200. However, he landed on a property that whacked him for half of his money. Next he got another “Chance” card and landed in jail. After he paid $50 to get out, the poor guy only had $70 cash left—no property, no nothing. How much did he have at the beginning of this narrative?

Question 3 Clue In the last two times around the Monopoly board, Wendell thought he was a goner. First, he had to pay half of his money in rent to Kate. He then had to pay $25 because of a “Chance” card. After that he landed on another property where he had to pay 3/5 of his remaining money in rent. Fortunately, on his next turn he passed “Go” and collected $200. However, he landed on a property that whacked him for half of his money. Next he got another “Chance” card and landed in jail. After he paid $50 to get out, the poor guy only had $70 cash left—no property, no nothing. How much did he have at the beginning of this narrative? Clue: Try working backwards!

Question 3 Answer How much did he have at the beginning of this narrative? Solution: Work backwards: 70 + 50 = 120 120(2)= 240 240-200 = 40 40=2/5 of what he had, so he had 100 100+25= 125 125 (2) = ….. $250

Question 4 Five families decided to hold family reunions at the Expo Hotel. Each family occupied a suite on a different floor. The Antelope family was on the floor directly below the Zebra family. The Panda family was on the floor below all the others. One floor intervened between the Bear and the Panda families. The Bear children had to ride the elevator up seventeen floors to visit the Skunk family. The Zebra children were not on the sixteenth floor, but their friends, the Antelopes were. These same friends (the Antelopes) were ten floors above the Panda family. On which floor was the Skunk family staying?

Question 4 Clue • DFive families decided to hold family reunions at the Expo Hotel. Each family occupied a suite on a different floor. The Antelope family was on the floor directly below the Zebra family. The Panda family was on the floor below all the others. One floor intervened between the Bear and the Panda families. The Bear children had to ride the elevator up seventeen floors to visit the Skunk family. The Zebra children were not on the sixteenth floor, but their friends, the Antelopes were. These same friends (the Antelopes) were ten floors above the Panda family. On which floor was the Skunk family staying? CLUE: Try to draw a picture

Question 4 Answer 5. Skunk On which floor was the Skunk family staying? 2. Zebra 17 floors 16th 1. Antelope 10 floors 4. Bear 1 floor 3. Panda 25 So they are on floor #…

Question 5 9 apes weigh as much as 4 bears. 8 bears weigh as much as 15 cougars. 10 cougars weigh as much as 27 deer. How many deer weigh the same as 4 apes?

Question 5 Clue 9 apes weigh as much as 4 bears. 8 bears weigh as much as 15 cougars. 10 cougars weigh as much as 27 deer. How many deer weigh the same as 4 apes? Clue: They are little cute deer.

Question 5 Answer 9 apes weigh as much as 4 bears. 8 bears weigh as much as 15 cougars. 10 cougars weigh as much as 27 deer. How many deer weigh the same as 4 apes? Solution: 9 apes = 4 bears so 8 bears = 18 apes. 18 apes = 15 cougars so 10 cougars = 2/3 of 18 = 12 apes. 12 apes = 27 deer so 4 apes =… 9 Deer

Group Question Set timer for 7:00

Boyce Ambassadors Please pass out Problem 6 (Group Question #2) face down.

Question 6 - Group Candy and Sandy compete in more than one event. No one else competes. In each event, the winner gets the number of points, W, and the loser gets the smaller number of points, L. There are no ties. Candy wins the competition by a score of 22 to 13. If Sandy wins exactly one event, what is the value of W?

Question 6 Answer If Sandy wins exactly one event, what is the value of W? Solution:There are the same number of total wins and losses so letting x be the number of games we can say xL + xW = 35 or x(W + L) = 35 This tells us that sum of the points for winning and losing and the number of games played are either 5 or 7. From there you can guess and check to find... 5 points

Snack Time We will dismiss by tables. Please wait until you are dismissed and then take 1 cookie and 1 drink.

Question 7 Ann can paint the walls of a classroom in 30 minutes, but it takes Akshar 40 minutes to do the same job. How long would it take them to paint a room if they work together? Round your answer to the nearest whole minute.

Question 7 Clue Ann can paint the walls of a classroom in 30 minutes, but it takes Akshar 40 minutes to do the same job. How long would it take them to paint a room if they work together? Round your answer to the nearest whole minute. Clue: What fraction of the room can Ann paint in one minute?

Question 7 Answer Ann can paint the walls of a classroom in 30 minutes, but it takes Akshar 40 minutes to do the same job. How long would it take them to paint a room if they work together? Round your answer to the nearest whole minute. Solution: Ann can finish 1/30th and Akshar can finish 1/40th of the room in 1 minute. They finish 7/120ths of the room per min. Divide that into 1 whole room and get… 17 minutes

Question 8 A leather jacket was originally priced at $200. When Justin Bieber was spotted wearing one just like it, the price of the jacket increased by 30%. Later, when the jacket went out of style, the price decreased by 40% from the price when it was popular. This current price of a jacket is what percent of the original price?

Question 8 Clue A leather jacket was originally priced at $200. When Justin Bieber was spotted wearing one just like it, the price of the jacket increased by 30%. Later, when the jacket went out of style, the price decreased by 40% from the price when it was popular. This current price of a jacket is what percent of the original price? Clue: People stopped liking it when they learned it was made from 3 baby cows – Baby, baby, baby…

Question 8 Answer A leather jacket was originally priced at $200. When Justin Bieber was spotted wearing one just like it, the price of the jacket increased by 30%. Later, when the jacket went out of style, the price decreased by 40% from the price when it was popular. This current price of a jacket is what percent of the original price Solution: 200 x 1.3 = 260 260 x .6 = 156 156 / 200 = …. 78%

Good Morning and Welcome to the 2011 Calcu-Solve Competition!

Good Morning and Welcome to the 2011 Calcu-Solve Competition!

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