Day 1 Debate: What Number is Best?

I know there’s a tendency to spend the first day of class talking about rules and expectations and grading policies and the syllabus and lots of other stuff that bores kids silly because, well, it’s boring. I mean, I know it’s all necessary for them to be familiar with, but do we really need to spend the first day doing that? It’s taken some time, but I’ve (mostly) changed to jumping right into something math related. Maybe it’s not a deep subject that we explore, but something to get students talking, and having fun, in class.

For my first day of Pre-Calculus, we didn’t hand out textbooks, we didn’t review the content standards, we didn’t sign out graphing calculators. Instead, the students fought. And laughed. And fought. And laughed. And laughed some more. Students entered the class and were told to think about their favorite number. (If they didn’t have a favorite, they were to make one up, and if they couldn’t, I’d give them one. Luckily, every student came up with one on their own.) I then told them to do some thinking, and come up with as many reasons why their chosen number was the best. Reasons could be from math of course, but also from pop culture, sports, numerology, other cultures, anthropology, mythology, religion, art, design, or whatever they chose. After five minutes of brainstorming, they discussed within their group of three or four which of their numbers was actually the best one. They then did further research for about fifteen minutes, using the Internet as a resource, to prepare arguments for why their own group’s number was awesome and the other groups’ numbers were boring. In the middle of their research time, I told students the story of the Hardy-Ramanujan number as well as the Interesting Number Paradox to give some incentive and inspiration.

When research time was up, we did a round-robin debate. I started with one group, and went around the room in a circle. Each group had up to 30 seconds to present an argument either for their number or against another number. I assigned each argument a subjective score of 1 to 3, and added it to that group (or subtracted from another group if they were arguing against another group’s number). I told them I’d keep going in a circle until I got bored with their arguments, but in both classes, the students were really impressive in their research and thought processes. During their research phases, I was also able to wander and listen to what they were thinking, how they discussed the math with their peers, and how they worked in groups.

I had some interesting arguments presented, and though I don’t remember even close to all of them, these were some highlights:

  • 4 is the only number that is spelled with its own number of letters.
  • 2 is the only even prime number.
  • 13 is the sum of the squares of the first two prime numbers.
  • 11 is both the number of points on the maple leaf of the Canadian flag and the number on the Loonie (Canadian one dollar coin).
  • There are 8 “quadrants” in 3d space (split by the xyxz, and yz planes). By the way – anyone know what they are called? Not quadrants, surely, since that’s how we refer to the 4 regions of the xy plane, but I don’t know right off.

In the end, students on winning teams got 10 points each, and runner up students received 5 points each. They aren’t extra credit, mind you – I’m doing away with extra credit, but that’s another blog post. These will go towards…something to be determined.

This was a great low floor, high ceiling activity where the richness of the mathematics was unbounded, but there wasn’t a single student who felt too intimidated to take part. One day doesn’t make an entire year, but this was a really fun way to spend our first day.

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4 thoughts on “Day 1 Debate: What Number is Best?

  1. In 3D space they’re called “octants.” They basically follow the same pattern as quadrants: I – IV are for z > 0 and then V – VIII are for z < 0. So, for example, the point (-1, 2, -3) is in octant VI.

    Liked by 1 person

    1. Of course! I really should have remembered that. It’s been awhile since I did much 3D graphing though. I’ll be sure to pass this on to my students, who will be thankful for the quick response. Thanks again!

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  2. As a Mid-Pen alumni (2008), 73. 73 is the best number. 73 is the 21st prime number. It’s mirror 37 is the 12th. And it’s mirror, 21 is the product of multiplying hold on to your hats 7, and 3. In binary 73 is a palindrome 1001001.

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