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

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.


Short Story : The Encourager, Part 3

Amanda looked around the room again, and behind her to the empty hallway. She turned back and put her head in her hands.

Solomon spoke again. “Amanda, I know you can do this. I’ll tell you what: you can test it out on me.”

She looked up, brow furrowed. “What do you mean?”

“You Push me to do something I don’t want to, and we’ll see if I know what happened.”

Amanda shook her head. “That won’t work. How will you know what you wanted to do after I’ve changed your mind?”

Solomon reached into the folder and took out a sheet of paper. He retrieved a pen from inside his jacket, wrote a few words on the back of the page, and showed it to her.

“I, Solomon, do not wish to clap my hands,” she read. “So you want me to make you clap?”

Solomon nodded. “I’ll try my best not to clap, and after I do you can show me this page. If you can’t make me clap, you die. If I know you Pushed me without looking at the paper, you die.”

Amanda pursed her lips, then nodded. “Okay,” she said, and folded the paper in half. She settled back in the uncomfortable chair and crossed her arms.

Agent Solomon stared at her impassively.

She concentrated on him, gently suggesting to his mind that he should clap for her. It had to be as natural as possible so that he couldn’t detect her manipulation. She needed to fit the changes into his own mindset.

He smiled and started to applaud her, mockingly. “Oh, well done, Amanda. I had such high hopes for you, but it looks like your skill can’t save you. You might as well start thinking about what you’d like for your last meal.”

She grinned at him suddenly, and he stopped clapping as she unfolded the page and handed it back to him. He read it silently, then looked up. “Okay.”

The #24TweetStory Collected

For fun I thought I’d write a story over 24 tweets and share it one tweet per half hour for twelve hours. Since it might be kind of hard to read  later, especially in reverse-chronological order, I’ve collected it here in chronological order on one page.

It was a little weird to write it in 118-119 character chunks (the hashtag and progress indicator take a few characters). There is no paragraphing. I wrote it in about twenty minutes, so there wasn’t much editing for style (mostly just for length). Maybe I’ll write a longer version with the same idea later.

The #24TweetStory

I’ve been painting a large, detailed scene every day for the last three months. (1/24) #24TweetStory

I can usually finish two or three canvasses each day, so I’m probably up around two hundred fifty now. (2/24) #24TweetStory

It’s always the same picture, but I’ve never been sure I have it right. I can’t afford to make a mistake. (3/24) #24TweetStory

I have the power to change things, to alter reality as I see fit, but I have to paint what I want to become real. (4/24) #24TweetStory

It’s pretty simple; I paint the world I see, from my own vantage point, but I change something. (5/24) #24TweetStory

It can be something small or something large, but I can make that change a reality. (6/24) #24TweetStory

The bigger the change, the more exact the rest of the image must be, and the higher the cost to myself. (7/24) #24TweetStory

I’m trying to make a big change. It’s not a lot of paint, but it’s a big change in my reality. (8/24) #24TweetStory

The scene is my art room. It’s a small room, and I’ve gotten rid of anything that’s not essential. (9/24) #24TweetStory

The reason is simple: I can paint an empty room more easily than a full one. (10/24) #24TweetStory

So I’ve been working each day inside this little grey box. No windows, just a small light to work by. (11/24) #24TweetStory

My canvasses are mostly grey; I’ve perfected the mixture now. The chair in the corner is a series of blacks. (12/24) #24TweetStory

But that’s easy. I mastered the chair in just weeks. I can paint what’s in front of me. It’s the change that’s hard. (13/24) #24TweetStory

If I want to change my reality, I have to change what I see in my painting. I don’t want an empty chair in the corner. (14/24) #24TweetStory

My new paintings have my dead wife, now alive, sitting in that chair, watching me paint. (15/24) #24TweetStory

I can see her perfectly in my mind, but I can’t describe her perfectly with my brush. What if I get something wrong? (16/24) #24TweetStory

Will she be a shell of herself? Will she remember me? Will this work at all? (17/24) #24TweetStory

I’ve tried little things. I’ve made a flower blossom. I’ve even turned lead to gold, just to see. (18/24) #24TweetStory

It’s hard to do, and it hurts. After the flower blossom I was unconscious for days. (19/24) #24TweetStory

I don’t know what it’ll do to me, but it doesn’t really matter. I have to try, even if it kills me. (20/24) #24TweetStory

But I’m afraid. As hard as it is to suffer with only memories of her, it would be worse to ruin those memories now. (21/24) #24TweetStory

Her expression isn’t right. It’s too happy. She wouldn’t be happy that I’m doing this. (22/24) #24TweetStory

She’ll be mad that I brought her back, probably. I have to do it anyway. (23/24) #24TweetStory

I take out a fresh canvas. (24/24) #24TweetStory

Short Story: The Encourager, Part 2

Solomon stood and started to pace in front of the girl, waving the file folder in one hand as he spoke.

“I need a Pusher who is so good that I can’t tell she’s a Pusher. I need someone who can lie so well that no one would even suspect that she has the skill, even when she’s using it against them.” He stopped pacing and looked intently at her. “I need you to Push for me, just once, and then you can go free. If you don’t… well, your other choices aren’t favourable.”

Amanda didn’t answer him, but her mind was whirling. This was a new tactic, for sure. Was he trying to get her to demonstrate her skill so that he had the excuse he needed to execute her? She flicked her eyes up to the cameras in the corners of the room near the ceiling. If she Pushed too hard in this place, she was dead.

“They’re switched off, Amanda. No one is watching. Even Brant is gone.”

Amanda turned and looked behind her and saw that Solomon was right. The metal door was open, but Brant wasn’t in sight. Ghost, she thought. She turned back.

“I’m not a Pusher,” she said at last. “Let me go.”

Solomon shook his head and settled back into the chair. “Yes you are. We both know it. Let me speak plainly.” He looked intently at her, his dark eyes boring into her blue ones. “If you don’t help me, we’re going to kill you today. If you do help me, you’ll be able to leave here freely tomorrow. That’s all.”

Amanda considered. He certainly was speaking plainly, and she knew there couldn’t be an audio feed on those cameras or he would never have said that. The CPD monitored everything in these rooms. She doubted he would have spoken even if the video feed was live for fear of having someone read his lips. She was starting to feel hope trickling up again.

“Why do you want me to Push?” she asked finally. Nothing to lose, she thought.

He smiled again. “I think it’s more important to know whom I want you to Push.”

“Fine, who?”

He handed her a photograph from inside his uniform jacket’s pocket. It showed a woman in her late thirties, serious-looking and professionally dressed. She was posing for the camera, and the backdrop was one of those artificial drapes like you see in school photos.

“Melissa Clement. She’s an entrepreneur and a politician. Her platform involves reforming and dismantling the CPD, and she’s about to make a speech that will put a lot of pressure on the government to fold up my Division. I want you to change her speech, and I don’t want her to know that you’ve done it.”

Amanda had a sinking feeling in her stomach. What Solomon was asking wasn’t supposed to be possible.

“You don’t know what you’re talking about,” she told him. “Everyone knows you can’t Push someone without them knowing it.”

He cocked his head to one side. “I know you can,” he said, and the certainty in his voice chilled Amanda. “I know that if you’re given enough time, anything is possible for you.”

Short Story: The Encourager, Part 1

Her face was blank mask, and she knew it. She practiced each day in front of the small, grimy mirror, removing every trace of emotion and thought from her features.

Amanda used to cry when they questioned her, hot fury and poisonous despair destroying her control, but she had been a child. Now she faced them in perfect silence, and still they knew nothing.

It wasn’t easy to purge the effects of feelings. It wasn’t that she didn’t feel at all, but rather she had trained her body to no longer respond unless she willed it to. Her training was far more painful than the questioning ever was, but she turned herself to stone in order to survive.

Again today she brought up the memories of the CPD bludgeoning her father to death with their batons, then of her mother stalking purposefully from the porch. She saw again how the armoured men wilted before the woman, tearing off their helmets and vomiting as they fell, great welts appearing suddenly across their faces. And inevitably she saw them draw their pistols and fire round after round into her body, continuing long after she was dead.

The memories hadn’t changed, and her mind’s reaction was still horror and shock and rage, but her face remained cool, her heart rate steady. Amanda was the master of herself.

She started in surprise as the door to her room banged open behind her. She felt the rush of adrenaline, both familiar and frustrating as it threatened her facade, and she fought down the reaction her body was insisting upon. In seconds she was ready, and she turned around.

Brant stood in the doorway, silhouetted by the blue-white fluorescents buzzing in the corridor behind him. He stepped into the light of her room; he was wearing his crisp, brown uniform and polished black boots. She couldn’t imagine how she hadn’t heard him coming.

“It’s time, Amanda” he said quietly. He was always quiet. Like a ghost.

She looked at his grey eyes and saw the same thing she always saw: pity.

She nodded and followed him from the room.

They passed by dozens of doors identical to her own, each home to a pathetic soul whose parents had been murdered by the Citizen Protection Division. Most were twisted wraiths, barely recognizable as human. Some were loud in their defiance, but she knew their fear was louder still. Some rooms were empty, the former occupants having been “set free”.

Only she had survived intact, overcome the torture, the drugs, the equipment, the provocations, and the endless, endless questions. She was a rock.

Eventually the too-bright hallway ended at a too-familiar steel door with a six-inch safety glass window to the other side. She didn’t need to look; it was the room she had visited every day for longer than she could understand, and she knew every inch of it in terrifying detail.

Brant reached for the handle and pulled the door open on its shrieking hinges, then waved Amanda into the room. The scent of bleach and latex assaulted her and her stomach rebelled. She held her breath for just a moment before willing herself to breathe normally.

There was a man seated in a stainless steel chair in the centre of the room. He was wearing the same kind of uniform as Brant did, although it was clearly of better quality. He was reading the contents of a file folder which had a photo of her fastened to the corner with a paperclip. He looked up and smiled.

“Come in, Amanda; I’ve been waiting for you. I’m Solomon, Agent Solomon, with the CPD. Please sit.”

He motioned to the only other piece of furniture in the room, a chair placed opposite him and a few feet away. His face was open and honest-looking, but she knew better. She stood impassively just inside the door. Agent Solomon’s smile became slightly forced.

“Please,” he repeated, “join me for a moment.”

She relented and sat in the chair, neither relaxed nor tense. She wore her mask and she sensed she needed it now more than ever.

He continued to peruse the file for a moment, then looked into her eyes. “You’re a Pusher.”

She did not respond.

He smiled again, humourlessly this time. “You’re a Pusher, and we both know it. You’ve been able to Push for years, and you’re the best I’ve ever seen at keeping it to yourself, but you’re still a Pusher.”

She looked at him without expression.

He leaned back and crossed one leg over the other knee. “You see, I’ve been watching you for a long time. Since shortly after you arrived here, actually. Because both your parents were Pushers, so we figured there was a good chance you were too.” He paused. “We weren’t aware that your mother had the skill when we went to apprehend your father, you know. It wasn’t until she attacked our men that we found out.”

Solomon started to flip through the folder, pausing to turn it sideways from time to time. Amanda assumed he was looking at photos; she couldn’t see to be sure. He made small noises to himself as he turned pages.

“Do you know how long you’ve been here?” He waited for her to respond, but continued after a moment. “One thousand, four hundred sixty days.” No reaction. “That’s four years, Amanda. Or it will be tomorrow.”

She felt her eyes widen. Four years. No wonder she was being questioned by an Agent. No one lasted four years in a CPD orphanage. The law said that after four years they had to let you go. She felt hope bubble up hot inside her, and she crushed it mercilessly.

Solomon continued. “So that’ll be it. Tomorrow you’ll be a free woman. It’s never happened here before, you know. No one has ever left this facility alive. Ever.”

His casually polite voice had turned gritty and dark on the last word, and Amanda became certain she would not break the streak. She had long ago resigned herself to dying in this prison, and her dull despair reasserted itself.

Solomon started to tap his fingernail against the chair, the metallic ring echoing ominously.

“Do you understand me, Amanda?”

Uncharacteristically, Amanda swallowed and then spoke, her voice rusty with disuse.

“I understand. You’re going to kill me,” she replied.

His serpent’s smile reappeared. “No, I don’t want to kill you. I want to hire you.”

I’m not doing any more work tonight

I’m the e-Learning Contact for our board, which means I’m responsible to teachers and students who are using digital tools for learning. I provide access to the virtual Learning Environment, I ensure people have their account credentials, I copy content into and between courses, I connect our classes with students from outside our board,…. It’s a pretty long list.

We don’t have a ridiculous number of students (about 10000 from K-12, or about 4500 from 9-12), so my work is different from that of eLCs in very large boards. I spent today, the first day of semester two, getting e-Learning students and Blended Learning teachers into their virtual classrooms. As these things go, it was a fairly smooth day. Between last night and this afternoon I enrolled about 900 students into new courses, emailed all of the e-Learning students and their parents/guardians/guidance counselors, and copied content for a bunch of Blended Learning classes. Objectively, it was a very successful day.

And I feel guilty.

Not because I let things slide; I didn’t. Not because I let people down; for the most part I came through on my promises.

No, I feel guilty because there are still unread and un-dealt-with emails in my inbox. There are still items on my to-do list, things that I could finish that would enable other people to move forwards. But I’m writing this blog post instead, taking 20 minutes or so for myself, and I feel guilty for doing it.

A quick peek in that other tab, the one I’m avoiding at the moment, shows 112 unread messages. About half of those are from today, and another quarter are from the weekend. That’s not a reasonable number to try to get through in a single evening. I know that. I still feel a kind of pressure to get at least some of it done.

I had this problem last year. I spent most of the school year working double time, burning up evenings and weekends with “essential” and “critical” items. I promised that I wouldn’t fall into that same pattern, that same trap, this year.

And so far it’s been pretty good, and I’ve kept the “after hours” work to a manageable level. Keeping it that way has come from making a conscious, daily decision to not let work take over my life.

I believe in the value of what I do, that the work is good work, and that it’s worth doing. But it’s not worth doing whatever the cost to me and my family, so tonight I’m leaving the rest of those messages unread. I’m sure they’ll still be there tomorrow, and I’m sure that everyone will understand if it waits a little while longer.

Be patient: it’s a semester change

Tomorrow begins the second semester for most Ontario school boards (some Northwestern Ontario boards began a week ago), and I’m trying not to stress about it too much. I’m pretty well-prepared, with e-Learning courses mostly created last June or this fall, Blended Learning courses about 80% ready in November.

But there are a few courses left to complete, a host of e-Learning student accounts to create/maintain, and several hundred emails to send (mostly mail merges, thankfully). I made promises to have things ready for people this week that I wasn’t able to deliver when I said I would, and I really hate that (I imagine the people counting on me hate it even more). And just like F2F classes, there are always last-minute shuffles (for us, two teacher changes) which increase everyone’s stress level.

So I’m trying to be calm about the whole thing, to recognize that some things won’t work, that some email addresses say “.com” when they should say “.ca”, that messages will be missed or misunderstood.

And I’m hoping everyone else will do the same. Be very patient with the people who try to keep the system running: guidance counsellors, school leaders, IT technicians, administrative assistants, eLCs, and so on. It’s hard work, it’s complicated, and everyone’s doing their best.

Be gentle with us. We’re trying.