Two Juneau students will compete in a national math competition as part of an Alaska team coached by a local teacher.

Dzantik'i Heeni Middle School students Logan Spencer and Robbie Sylvester will join Devon Preston of Eagle River and Logan Daum of Fairbanks on the Alaska team, coached by Dzantik'i Heeni teacher Mary Borthwick.

Spencer said math is a fun subject although he prefers lunch.

Sylvester said he enjoys math "because you actually learn a lot in math, compared to other classes."

"I like to be able to do things that other people can't," Spencer said. "I just like to do things that are hard because it's fun."

"I can't really look at some math problem and say, OK, I don't get it," Sylvester said. "I can't just walk away. I need to know stuff."

Two hundred and twenty-eight students are expected to participate in the Mathcounts National Competition for middle-school students on June 14 in Chicago, organizers said.

Borthwick said she has prepared her students for Mathcounts every year since it began 19 years ago. What does it offer students that they wouldn't get in the classroom?

"No. 1, a challenge," she said, organizing her thoughts numerically. "Part of that challenge is it stretches their mind. They learn what they can do and can't do.

"No. 2, it provides me a venue to talk about math topics the textbook doesn't cover," such as number theory, probability and statistics.

How hard are the math problems in the competition? Well, expressing it in numbers, on a scale of one to 10, Borthwick describes the problems, at least the hardest ones, as 12s.

A sample problem on the organization's Web site http://mathcounts.org is: Suppose the nose of a first-generation organism measures 15 centimeters long. If each successive generation's nose is 2 percent shorter than the preceding generation's nose, which generation will be the first to have a nose shorter than 13 centimeters in length?

"I guess some of the problems are stuff we heard from class," said Spencer, a seventh-grader. "But a lot of it was something I didn't know and (Borthwick) had to teach it."

"A lot of what I show are techniques," Borthwick said. "They know some algebra. They know some geometry. What they have to do is put them together."

To get to the nationals, the students did well at the in-school competition in January, the Southeast contest in Juneau in February, and the state competition in Anchorage in March.

Spencer placed third in the Dzantik'i Heeni, Southeast and state meets. Sylvester won the school competition, was second in Southeast and fourth at state.

Although students participate in four-person teams, they also are scored individually based on their work in two of the three rounds. In the first round they answer 30 questions in 40 minutes. In the second round they have six minutes to answer each of four sets of two problems. In the third round they work as a team to solve 10 problems in 20 minutes.

Sylvester said he prefers the team round.

"There's always somebody in a team round who has inspiration," Spencer agreed.

At state, Spencer won the Countdown Round, held for the top 10 individuals. It doesn't count in the state meet standings, but at nationals it determines the individual winner.

At the state meet, Spencer and Sylvester also underwent a separate competition for the top four finishers called the Masters, in which students working alone must solve a series of questions related to one big problem, and then explain their answers to a panel of university professors.

"Boy, did they grill you," said Spencer, who placed second.

Borthwick put it differently: "I always thought they asked leading questions to guide you into the answers you don't have yet."

As for the above-stated problem about organism's noses, the next generation will have a nose that is 98 percent as long, which can be calculated by multiplying 15 times 0.98, which is 14.7 centimeters. By continuously multiplying by 0.98 until students get a value under 13, they can find the answer.

But Mathcounts encourages students to look for equations that will get them an answer quicker. The Web site shows students how to come up with the logarithm.

Still an unanswered question is how to calculate the volume of food that can go into a middle-school student's mouth.

"I love competitions because there's always food," Spencer said.

Eric Fry can be reached at efry@juneauempire.com.

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