A love letter about the ICTM Math Contest

Yes, my previous post about Penn Holderness has inspired me to write this post about the old ICTM math contests. Let’s also be honest… this also serves as a reminder to do a “brain dump” and write down things I remember, as well as to give myself a reminder to find my old ICTM contest sheets (I don’t have them all, but I did save some of them).

The ICTM website gives a little of the history of the regional and state math contests in Illinois, and I’ll add a little from a participant’s perspective. My high school was a AA school (there were two divisions back then, four now). So while my future undergraduate home would host the A competitions, we would always go to Northern Illinois University for regionals, and then Illinois State University for finals.

The day consisted of three different kinds of competition^[1]Something that math and forensics have in common: a lack of lunch breaks.:

Round 1 was the written test for each of the four levels of math: Algebra 1, Geometry, Algebra 2, and Pre-Calculus. Each test had 20 questions, and each right answer was worth 2 points toward the team score. Although many of the students competing were often a year (or more) ahead of their level, the questions were by no means easy. ^[2] Cue “in my day” alert: Students now get to use calculators in the first round. I never got to. No wonder scores have gotten higher. I say this as a former state individual qualifier — the scores were often quite low. ^[3]Side note: The 4A regional results (warning: possibly inaccessible PDF) show that several schools had perfect scores for their teams in Algebra 1. Grade inflation. But then again, I’ve also seen … Continue reading

This is where my memory gets a bit fuzzy, since I did most of the events at one time or another. There were other rounds (I can’t remember if there were one or two extra rounds – now there are 3 rounds of competition). But I do remember the events:

• Calculator: Yes, that’s right, there was an event where students were allowed to use calculators. 5 people from mixed classes (1st year through senior) were given 20 questions to solve in 20 minutes.
  
  Example problem: Tom’s math teacher had each of the 20 students in class write four questions for the final exam. The teacher made sure that each of the students’ questions were different and then promised that all 20 questions on the exam would be taken from the student questions. Determine the probability that at least one of Tom’s questions would be used. Express your answer as a common fraction reduced to lowest terms.^[4] The answer is 218789 divided by 316316. This would have been a worthy problem for my sophomore-level Probability and Statistics course in my undergraduate math major!


• 2 person team: One of my favorites. 10 questions, two students either freshmen/sophomores, or juniors/seniors. Three minutes per question: 6 points for getting the question in the first minute, 4 points for the second minute, and 3 points for the third minute, with a 2 point bonus for being the first team to get the problem correct. ^[5] Calculators are now allowed starting on question 6. Again cue the “In my day…”
  
  Sample question: A number is selected at random from the set A, which consists of integers between -8 to 8 inclusive. Determine the probability that the number selected is BOTH a solution for x to x² – 3x – 28 ≤ 0, and a possible length of the third side of a triangle with sides of 5 and 7. Express your answer as a common fraction reduced to lowest terms.^[6]5/17 is the answer. (x-7)(x+4) is the factoring of the left side of the first equation.


• 8 person team: Also fun. No more than 4 seniors (or sophomores for freshman/sophomore). 20 questions, 20 minutes. No calculators (at least some things remain the same!). 5 points per correct answer.
• Oral competition: I think this one changed. I don’t remember having a partner help me. The new rules are 10 minutes to prep, 7 minutes to present. Then 3 minutes prep for 3 minutes of extemporaneous questions. Up to 2 students may participate per oral topic area (there were normally two different oral areas).
• Relay: Yes, this was the best! There were four people who would sit in chairs one behind the next. The first person would get a problem. The answer to that problem was needed in the second person’s problem – so they could start working, but would need the answer in order to finish their problem. The third person relied on the second person’s answer, and the fourth relied on the third person’s answer. There were three rounds, with a maximum of 30 points. I think I only got to do this once, since it seems that you had to qualify as a team (which we did at least once) in order to do that event.

In addition to moving to 4 divisions and being a MUCH bigger competition than it used to be, the ICTM contest even has a state song.