International Regions Mathematics League (IRML)
Organizing Practices:
Practice is essential, partly to develop mathematical skills, partly to create a team that works efficiently and effectively. ARML's authors respect the talent of the students taking ARML/IRML so the problems not only cover a variety of topics but include a variety of ways of thinking. Many students discover that they've taken too narrow an approach to problem solving in the past. Studying past ARML problems and taking the contest can truly help students and teachers develop their talent.
The Team Round: students need to learn to make sure that all the problems are being worked on, they need to post answers, they need to post either confirmation of the answer, or a different answer, and if students disagree, they need to work together to come up with a common answer. Before the questions have been passed out, the best teams write the numbers 1 through 10 on the board, leaving space for answers and second opinions. If teams don't do this, they often find that only 1 person did a problem and that person got it wrong. So practice sessions should include sample team rounds of from 5 to 10 questions to give students practice in organizing their work as a group.
The Power Question: it is useful at several practices to do part of a previous Power Question. These should be graded at the site and the results gone over with the students. Many students are not used to doing proofs and often they are dogmatic and don't properly justify their reasoning. They can also see methods that they may know, such as mathematical induction used on problems where they might not have thought to use it. The solutions given to the PQ are more fully developed in many cases than we would expect the students to accomplish.
The Individual Round: at each practice 3 to 4 pairs of individual questions should be given. Typically, in each pair there is an easier problem and a more difficult problem. Often either problem #1 or #9 is the easiest and #10 will be the most difficult. If we hope that 85% of the students will get the first problem correct, we expect that less than 5% will get the last problem correct. Practices will help the students get a feel for the amount of time that they have. Just getting one of the two correct is a good result so students need practice in deciding which problem they have the best shot at. A common mistake is to write the correct answer in the wrong form. Students need to practice to automatically write the answer in the correct form. See the conventions form for a discussion of the right form to use.
The Relay Races: since these are considerably different from other contests, they require a lot of practice. I've attached a sample of 6 relay races with an analysis of each one to show the kind of thinking involved. While these are easier than the regular relays, they still present the kinds of problem solving opportunities that students face when tackling relays.