National Association of Math Circles Wiki
Wrangle

Tatiana Shubin is taking the lead on a Math Wrangle for the 2012 Circle on the Road festival.

AUDIENCE: High School students (maybe even middle school students)

PLANNING ABSTRACT:
A math wrangle is a competition that is similar to a debate between two debate teams.

The teams are first given an hour to solve eight math problems and prepare presentations of their solutions.

After this initial preparation the teams meet before an audience and a
panel of judges. The teams take turns challenging each other to solve
one of the eight problems. After one team presents a solution, the other
team tries to either improve the solution or point out flaws or errors.

The panel of judges award points to the teams for the both solution and
rebuttal based on correctness, completeness, clarity and style.

Since the teams will be selected before the festival, it will be a challenge to figure out how to involve the audience. Perhaps the audience should include teachers
and there should be some discussion about organizing wrangles???

How should the public abstract be adjusted?

PUBLIC ABSTRACT (Draft):
A math wrangle is a competition that is similar to a debate between two debate teams.

The teams are first given an hour to solve eight math problems and prepare presentations of their solutions.

After this initial preparation the teams meet before an audience and a
panel of judges. The teams take turns challenging each other to solve
one of the eight problems. After one team presents a solution, the other
team tries to either improve the solution or point out flaws or errors.

The panel of judges award points to the teams for the both solution and
rebuttal based on correctness, completeness, clarity and style.

APPRENTICES: Diana White, Jason Ermer, Leszek Gawarecki, Rossitza Marinova, Bob Sachs, Susan Wildstrom, Ed Kepplemann

DISCUSSION:
This one is a math Wrangle. This is like a debate between two teams, but the questions are mathematical. I think there will be warm-up wrangles before the festival. This is what we discussed a bit ago:

We would have four teams
team 1, team 2, team 3, team 4 and would randomly pair them up before the workshop
having team 1 compete against team 2
and team 3 compete against team 4 perhaps one week before the workshop.

(I think Susan has already been working on this first part. Where do we stand?)

During the morning session of the festival we would have the two teams that lost in the first round
play for 3rd place.

During the afternoon session we would have the two teams who won in the first round play for first and second place.

Each session plus awards would have to fit into a 1 hour time slot.

One interesting question here is how do we include audience interaction?

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It is essential that both Bob and Andy run practice sessions which are as close in format (described in the rules) as possible. The only variation for practicing might be that the problems could be given to kids in advance for solving at home since the main goal of practicing should be to train them to present problems and do the rebuttal; also, to work as a team and get some sense at strategizing - which problems to chose for challenging, who does what presentation, when it's better to bounce a challenge, etc.
This might be especially important for younger kids since they're absolutely unfamiliar with the task of presenting their solutions orally. From my experience, even with the best and brightest - and wonderful problem solvers - the firs trial is a disaster. But by the third time, the change is miraculous - which more than makes up for the time spent.

--

To include an audience --

If a problem gets bounced, the team that had proposed it has a choice of either accepting it or bouncing it further - to the audience, at which point the value of the problem goes up to 14 points. If a volunteer from the audience accepts the challenge, both competing teams watch their presentation and then decide together how to rebut the presentation and send one representative to deliver the rebuttal. The jury splits 14 points 4 ways - between the Audience, the Jury, and both teams (the teams get equal number of points).
If the audience declines the challenge, i.e., there is no volunteer, then the wrangle continues according to the existing rules (and the problem goes down to 10 pts.).

AttachmentSize
math_wrangle_rules_revised_9feb12.pdf47.17 KB
MW 2012 Practice 2 - St_opt.pdf1.18 MB
MW 2012 Practice 2 Slns_opt-small_Part1.pdf1.66 MB
MW 2012 Practice 2 Slns_opt-small_Part2.pdf731 KB
MW 2012 Practice 3 Slns.pdf98.86 KB
MW 2012 Practice 3-St.pdf120.75 KB
MW 2012 Practice Round 1 - St.pdf536.58 KB
MW Golden Section 2012 - Solns.pdf524.73 KB
MW Golden Section 2012.pdf23.89 KB