Math Problem: How many area codes do we need in Canada?

via wintersixfour at morguefile.com

I was thinking about this recently while going through session proposals for On The Rise. Presenters gave contact information, including phone numbers, when submitting their proposals. I noticed quite a few area codes in there.

In my area we’re part of the geographically massive 705 area code, but we acquired another, overlapping area code (249) last year. I haven’t heard of it being used yet, but we’re now on 10-digit dialing. I had a friend who lived in a small community near Waterloo, Ontario, who said that they were on 5-digit dialing for a very long time, into the 1990s, I believe. In my own community all of the phone numbers are of the form 705-248-****.

So, geography definitely has informed the distribution of area codes and exchanges (I believe that’s what the next three digits are called) because of the wired phone lines of the past. I imagine that the need for that kind of segregation of codes is technically past, although it’s still nice to know that someone calling from a 519 area code is based in Southwestern Ontario (although they could be next door on a cell phone).

Here’s the math problem

“How many area codes do we need in Canada?”

This question could be posed at a variety of grade levels. I think grade 4 or 5 students could handle the more basic parts of the problem, while it’s still very interesting for grade 12 Data Management students. A related (but surprisingly different) question is “How many phone numbers do we need in Canada?”

I will give my answers in another post, but maybe you can think about it. If you have a class of students, try asking them. Record the thinking, and post/link to it in the comments. I bet you’ll be surprised at the complexity of the questions and the richness of the answers.