MUMS quartet has a head for numbers

RANDOLPH — A quartet of Middlebury Union Middle School students kept their thinking caps on Saturday, March 16, and earned fourth place as a team in the 30th Vermont State MathCounts competition.
One of them — eighth-grader Ronan Howlett — won the individual championship and will represent Vermont at the national contest.
His teammates were seventh-graders Greta Hardy-Mittell of East Middlebury, Laura Whitely of Weybridge and Julian Schmitt of Middlebury. Their coach is Diane Guertin.
The winning team represented the F. H. Tuttle Middle School. Camels Hump Middle School was second and Essex Middle School was third. In total, 16 schools and 80 students took part in the state final at Vermont Technical College; all had qualified in earlier rounds of competition.
Howlett is no stranger to the winner’s circle. Three days before winning the MathCounts title he won the state spelling bee — for the second year in a row. Howlett, of Cornwall, was invited to travel to Washington, D.C., for the MathCounts National Competition on May 10-13.
MathCounts is a national organization designed to help students in grades six through eight build math skills, enhance logical thinking, and sharpen analytical abilities. Students participate in school-based clubs and can qualify for local, state, and national competitions.
The MathCounts goal is to secure America’s global competitiveness, inspire excellence, confidence and curiosity for U.S. middle school students through fun and challenging math programs. It provides teachers, students and parents with free materials to aid them in math enrichment and to help them prepare students for a high-tech future that will require mathematics-related skills to achieve success.
Among the local sponsors for the MathCounts competition are Otter Creek Engineering Inc., Phelps Engineering Inc., and Vanasse Hangen Brustlin Inc.
Sample questions from 2005 MathCounts competition
SPRINT ROUND (no calculator; 30 problems in 40 minutes; students work alone)
Problem 1: A rectangular tile measures 3 inches by 4 inches. What is the fewest number of these tiles that are needed to completely cover a rectangular region that is 2 feet by 5 feet?
Problem 2: How many combinations of pennies, nickels and/or dimes are there with a total value of 25 cents?
TARGET ROUND (calculator permitted; 6 minutes for each of 4 pairs of problems; students work alone)
Problem 3: What is the greatest whole number that must be a factor of the sum of any four consecutive positive odd numbers?
TEAM ROUND (calculator permitted; 10 problems in 20 minutes; students work with three other team members)
Problem 4: A four-digit perfect square integer is created by placing two positive two-digit perfect square integers next to each other. What is the four-digit square integer?
COUNTDOWN ROUND (no calculator; head-to-head challenge between two students; ?rst-to-answer; no more than 45 seconds permitted)
Problem 5: When Bob exercises, he does jumping jacks for 5 minutes and then walks the track at 4 minutes per lap. If he exercised for 73 minutes on Monday, how many laps did he walk?
Problem 6: What number is 17 less than its negative? Express your answer as a decimal to the nearest tenth.
See the answers below, keep scrolling down.
Answers: 1. 120 tiles; 2. 12 combinations; 3. 8; 4.1,681; 5. 17 laps; 6. –8.5

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