I made another mistake: missing out on inquiry and authenticity

I’m teaching MDM4U (Data Management) this semester and we’re starting to talk about probability. We’ve spent the last few weeks learning a bunch of counting techniques (permutations, anyone?) and soon we’ll be applying those techniques in this new context.

But I’m concerned about how teacher-directed everything has become, and how comfortable my students seem to be with that mode. When does their curiosity take control of our journey? How will their interests drive our learning?

On the first day of the probability section I was speaking with the entire class about the sorts of probabilities they would be familiar with: chance of rain, poker, winning a football game, etc. One student asked, “What are the chances of winning the lottery?”

And I made a big mistake.

I told him, “We’re going to look at that when we have a few more tools to work with.”

I should have said, “Let’s try to figure that out. Now.”

His curiosity would certainly have driven him and other students to pursue an answer to that question. No, they don’t necessarily have the skills to answer that yet (some would), but I also don’t need to teach a bunch of lessons before they can start.

I should have encouraged him to frame that question mathematically, identify the information that would be needed to solve it, and begin to do so.

Instead I put him off and went on with my boring talk about rolling dice and flipping coins. I missed a great opportunity for authentic learning in favour of simple, canned questions.

So, my deepest apologies to that young man and to the rest of the class. Tomorrow, I fix it. Tomorrow, you will decide what you want to learn, and then you’ll learn it, and I’ll be there to coach you along the way.

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My answer for “How many area codes does Canada really need?”

I posed a question a few days ago: “How many area codes do we need in Canada?” Here are some of my thoughts. I don’t think this is a complete answer (you’ll see why at the end), but I do think it’s a good back-of-the-napkin attempt. I also think it’s worth considering this problem from the point of view of younger students, who won’t have a lot of math in their pockets yet.

Canada has about 33.5 million people. How many phones should each person have? Well, some of those people are children, some are parts of families, some work, some have cell phones… it’s not simple, is it?

Well, let’s assume most children under 10 years of age don’t need a phone to themselves (I sincerely hope that’s true). I estimate (but haven’t bothered confirming) that there are about 5 million such children in Canada. That leaves 30 million potential phone owners.

Let’s suppose that every one of those individuals has a personal phone (like a cell phone), and that every one of them also has an organization phone (e.g. for a business, church, club, etc.). This isn’t realistic, since most churches don’t have a phone for each member, but also most church-going folks also work, so I’m hoping for some balance here.

That’s a ballpark of around 60 million phone numbers so far.

Also, I’ll guess there are something like 15-20 million families who probably have another shared phone line (like a “landline”), so we’re rounding upwards to 80 million.

Okay, let’s step back and consider the numbers themselves.

Looking at the last 7 digits, they’re broken into the exchange (3 digits) and the end part (4 digits – see my technical jargon there?).

Exchanges can’t start with 0 or 1, so that leaves 800 possible exchanges. The end parts can be anything, so there are 10000 possibilities there. Multiplying those two values gives us 8000000 (8 million) phone numbers per area code.

(Yes, there are a few other exchanges you can’t have, like 555 and so on. They’re small potatoes in this calculation. I’m sure my rounding up other stuff overwhelms them).

All right, so now we have 8 million numbers per area code and a need for 80 million numbers. That means we can have 80 million / 8 million = 10 area codes, right? Hey, that’s just about one per province/territory!

Except the population isn’t evenly distributed across the country. There are 12.8 million people in Ontario and 3.6 million in Alberta. How to resolve this?

Well, let’s round our 80 million up some more to make the numbers nicer. Let’s say we want to future-proof this a bit in case there’s a sudden population increase. Let’s bump it up to 3 phone numbers per person, which is just north of 100 million numbers total. Then we can distribute numbers based on the populations in each region, taking care to not let area codes cross provincial/territorial boundaries for convenience (thank you to Wikipedia for the numbers):

Province/Territory Population Phone Numbers Needed
Ontario 12851821 38555463
Quebec 7903001 23709003
British Columbia 4400057 13200171
Alberta 3645257 10935771
Manitoba 1208268 3624804
Saskatchewan 1033381 3100143
Nova Scotia 921727 2765181
New Brunswick 751171 2253513
Newfoundland and Labrador 514536 1543608
Prince Edward Island 140204 420612
Northwest Territories 41462 124386
Yukon 33897 101691
Nunavut 31906 95718

Okay, so that leaves Ontario with 5 area codes, Quebec with 3, BC with 2, etc., until we arrive at a minimum of 21 area codes for the country. If I’ve counted correctly there are currently 37 in use, which is quite a bit more than my napkinning would suggest is necessary.

Of course, there are other factors I haven’t considered here. How many devices have phone numbers attached that are not for humans talk with? For example, what about automated calling systems? How many people acquire new phone numbers in a given time period? It would be nice to prevent numbers from being reused for a long time (say, a year), which would increase amount of available phone number space needed.

There are probably some other things I haven’t considered – anything come to mind?

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

A photo of the top of a telephone booth showing the word TELEPHONE

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.