Graphing

The arrival of Sophie's graphing calculator as I mentioned has led to an interest in functions and graphing. I love scurrying up mathematical rabbit-trails with my kids. Yeah, I'm a math geek. I guess it comes of discovering a surprising aptitude for higher math after years of being considered an artsy kid.

We started with the concept of a function machine, something I gleaned from way back in Miquon Math. A function machine is a number-cruncher. You drop a number in the top, and the function machine does stuff to it, and out the bottom drops the crunched number. You can have fun trying to figure out what the function machine is doing inside. You put in 1 and out comes 2. Make a guess about what the function is. Is it adding 1? Drop in a 2 and out comes 5. Hmm, adding 1 doesn't explain that one. Drop in 3 and out comes 10. Drop in 4 and out comes 17. Eventually you realize the equation is "square the number and add one." These are great mathematical puzzles for little math geeks.

Next I had Sophie work with a function machine that doubled the number and added 3. She created a table of results. The input number went in the left-hand column, and the output number on the right.

input	output
0	3
1	5
2	7
3	9
-1	1
½	4

All we did next was change the names. Instead of "input" we called that number x. Instead of "output" we called it y. And instead of drawing a function machine that said "multiply by 2, then add 3" we drew the function y = 2x + 3.

Next we went on to Cartesian co-ordinates. Sophie was familiar with grids and co-ordinates even if she hadn't worked specifically with Cartesian graphing. But we had some fun with the secret puzzles like those shown above. I wrote out the co-ordinates and her job was to plot them and drawn lines connecting them to find the secret shape.

Then it just remained to combine the "function machine" and its output tables of x and y values with the graphing we'd had so much fun with. After she'd plotted y = 2x + 3 and y = x² - 1, recognized and filled in the lines produced, we fed her calculator the same functions. She was thrilled to see the exact same lines taking shape in the display.

Today we were talking about why a knowledge of functions and graphing is useful. My example was doing a study to determine how many bath towels households have, as a function of the number of household members. You would collect data and then plot them, find the line of best fit and then describe a function that would explain the relationship between number of family members and number of towels. And allow you to make predictions based on that function. This was just silly enough for her to appreciate.

This is childhood

She has practiced piano. She has played with the dog, looked after the chicks, independently prepared herself breakfast and lunch, played with her siblings, climbed trees and on the roof of the house. She's looking forward to a party tonight with a whole bunch of grownups, siblings and young adult friends. And now she's swinging herself through the dappled forest green towards the blue of the sky.

Handel would be happy

Handel would be happy to hear his Sonata in D Major being played by a young violinist standing on a stump in the sunshine of a spring day in the mountains in Canada. (And the young violinist's mother was happy to be greeted by this scene and its accompanying sounds upon returning from her run.)

Sophie has busking aspirations this summer so she is eagerly reviewing an hour or two of repertoire and polishing it up. And I suppose practicing outdoors is good preparation for busking. One can practice dealing with butterflies, hair caught by the wind, curious dogs, crowing roosters and sun in eyes ... it's all part of the fun.

(Note mug of London Fog at her feet.)

It's raining gadgets!

We reached the end of the academic year with the SelfDesign program and hadn't managed to spend the kids' Learning Allowances. There's a rule that the government sets that says that homeschooling families enrolled in DL programs can't directly receive funds allocated for learning resources. It used to be just fine to spend the money, save and submit receipts and get reimbursed, but that's no longer allowed. Most DLs responded to this new rule by setting up purchase order systems with curriculum providers but that didn't fit well with the unschooling-friendly philosophy at the SelfDesign program. So they hit on a unique solution. They load a credit card with each student's learning allowance and give the parent signing privileges on that card. The money thereby goes directly from a SelfDesign Visa account into the vendors' accounts. If we need to pay someone who doesn't take Visa, we requisition a cheque made out to that person, and SelfDesign debits the amount of the cheque from the appropriate Visa account.

It works beautifully. But as I say, we just hadn't managed to spend the money yet. We'd paid for piano lessons, aikido, viola lessons and a few books but there was still a fair chunk on each kid's account. Homeschooling isn't very expensive for us. Violin lessons are free, so is orchestra, quartet, group class, Summit Strings.

So this week we had a bit of a spending spree. Craft supplies, proper running shoes, fiction and non-fiction books, writing journals, sketchbooks. And each of the three SelfDesign kids got a gadget.

Sophie got a TI-84 Plus Silver Edition graphing calculator. Truth be told it'll be most useful for Erin over the next little while, but both Noah and Sophie will benefit from it, and it has prompted Sophie to develop a serious interest in the connection between the early algebra she's doing and the graphing of functions. It's great fun playing with trigonometric functions and trying to create wild-looking curvy graphs.

Noah got a Flip UltraHD camcorder. Our camcorder broke before Christmas. We've been able to borrow my mom's from time to time, but Noah is our digital media guy and he's been sorely pining for something like this. We also know that recording his far-too-infrequent lessons in Calgary on video will allow him to get a fair bit more mileage out of them. And being able to record and review rehearsals is going to be lovely. We recorded this one last night and while the audio quality suffered a fair bit from the compression of uploading, on our home computer the audio is great and the video sharpness is absolutely amazing -- true HD.

Fiona got the ultimate metronome. We have two or three little metronomes kicking around, but this was our excuse to get something multi-talented, loud and versatile. It does things we haven't even explored yet, including counting vocally aloud "one-ee-and-a-two-ee-and-a-three-ee ...," recording and measuring tapped tempos, subdividing and grouping beats in a variety of ways and varying the emphasis of beats and sub-beats any way you want. Fiona just loves rhythmic reading and the methodical discipline of metronome work while practicing, so she is thrilled.

Gap mouth

It was dangling in the front of her mouth for a week or more. Finally, in the midst of a tickle fight in the middle seats of the van with two teenaged friends out it came.

She wanted to know what she looked like, so I took this over-the-shoulder shot while driving, which she then peeked at on the camera. It turned out okay!

Runniversary 2

It's two months since I began running. I ran 34 kilometres this week, up from the 10 or 11 I ran my first week. In the past month I've been running a lot more on the trails, now that the snow has pretty much gone, and that's been really enjoyable. I no longer spend my time running concentrating on the good I'm doing for myself and on the running itself. Instead I'm enjoying the scenery, the changes in the natural world, the sights and smells, and the meditative experience of just trucking along.

I had hoped this month to crack the 10-minutes-per-mile barrier and I managed that quite easily. My fastest 5k pace last month was 10:24 per mile (6:27 per km), and that on a relatively flat route. This month on my usual hilly 5k my fastest pace was 9:35 per mile (5:57 per km). So my speed has come up a lot.

Mostly, though, I've been enjoying the longer slower runs. I usually take the dog, and sometimes Sophie accompanies us on her bike. My weekly "long slow distance" has more than doubled from 7 km to 14.5 km. I'm beginning to toy with the possibility of running a Half Marathon (21 km) next year. My goal for the year is 500 miles. The past two months have put me a quarter of the way there.

A green yard

Look at the green! Every year it astonishes me. Chuck remarked that it seems particularly green this year but I suspect it has something to do with our retinas being burned by the bright orange walls inside the house. After supper it's still bright outside, and today it was still actually warm. So the kids and dog headed outside for some crazy running around and playing with sticks.

The dog loves her sticks. Even the ridiculously long ones, which she runs about with like a maniac, tripping people. She's really strong these days. Look at that muscle-bound chest! I guess that's from doing the Couch 2 5k program with me. She is good for about 8k before she starts dragging. The only thing is ... the Couch25k program didn't really work for her, because she still jumps on the couch.

Precious few dandelions, you'll notice. That's because the flowers are all in a pot, waiting to become dandelion syrup. We also harvested asparagus and loads of rhubarb today.

Erin is off singing in a bunch of choir concerts this weekend. Poor girl misses out on rhubarb desserts and all this crazy outdoor play. She is currently on a push to finish up her course work for school. Normally school ends in the third week of June, but she's hoping to finish next week, except for the provincial exams in mid-June. She'll be very glad to be done, although she is talking of going back in the fall.

Poonybug

Poonybug is the name of the pear sapling we planted the spring after Noah was born. Noah thinks of it as his tree and named it a few years ago. It's now big enough for Fiona to climb. Just like children, trees grow.

May Days

May Days is a long-weekend community celebration here. Basically an invitation to the community to come out and play. There are dances, actual sporting events like a bike race and ridiculous events like canoe-jousting, three-legged races and potato sack races, there's an outdoor market, game tents like fish ponds, carnival food like ice cream, elephant ears and cotton candy, outdoor entertainment, a parade, raffles and the honouring of community citizens for their volunteerism. And dozens of other events.

As usual my kids were contributing musically. Noah's quartet played a couple of numbers. They had a long wait during a folk duo, so they milled around with their instruments and chatted with Fiona on the swings.

Erin had been commandeered into playing the keyboard for the Maypole dance. Sophie looks rather underwhelmed by the skipping kids with ribbons, doesn't she? The Maypole was unusually successful this year, with no tangled kids needing to be rescued and no one crying. Must have been the great music accompaniment!

Summit Strings played too. Some of you complain about never seeing pictures of me, so I included one of me introducing the group. Yes, I actually exist, even if I'm usually holding the camera!

The best part of this May Day was the unstructured stuff, though. Fiona had her first cotton candy -- what an adventure! I didn't get any photos of Sophie at all (except tucked in behind the second music stand on the mainstage) because she was off doing stuff in the park with her friend, hanging out at the petting zoo, lining up for various sugar-laden treats and just enjoying herself.

Erin and Noah had a lovely time hanging out with friends ... and, surprisingly, just with each other, even after their friends left or got busy with other things. They wandered around being strange, chatting with various adult friends, goofing around with each other, checking everything out.

There's something so wonderful about living in a town where kids can just run loose like this, safely and comfortably, enjoying themselves and each others' company and all the interest and excitement that a community event offers.

Origami coaster

Years ago at the Nikkei Centre we were given a kaleidoscopic origami creation made by an elderly local Japanese-Canadian lady. "Traditionally" the ladies around here made them from salmon tin labels, I suppose since prior to internment in this area many of the internees worked in the fishery and in canning plants. The one we were given has lingered on our mantel ever since. Yesterday Sophie carefully unfolded it to figure out how it was made. Then, not having salmon tin labels, she used 34 sheaves of drug-company doctor-notepad paper to create her own.

Ticker snapshot

"Some kind of happiness is measured out in miles ...."

Today's tally has me breaking 100.

My goal is to run 500 miles by the end of the year. I started almost 3 months into the year, and am currently on pace (15+ miles per week) to reach that goal. However, there are things like summer heat, winter cold, snowstorms, music schools and various other lifestyle impediments to contend with. I've loaded the continually-updating version of the ticker at the very very bottom of my blog page. If you see me flagging, do me a favour and give me the gears about it, won't you?

Deck hope

The sad truth is that aside from the addition we put on 12 years ago and a kitchen renovation 3 years ago, our home and furnishings have been "unimproved" for fifteen years. The carpet, deck, walls, the stuff that was old when we moved in, is now rotten. Our appliances are not so happy. The washing machine does a terrible job unless it's only half full. The dishwasher is almost in the "why bother" phase, as half the dishes need to be hand-washed when they come out.

The wingback chair in the living room is ... well, thread-bare squared might be a good description. There's very little of the seat upholstery intact. The couch is in better shape but even still would be considered pretty decrepit by most standards. Now that I have cunningly painted the walls colours that completely clash with the upholstery it is possible that re-upholstery is in the cards. We shall see.

And then there's the deck. Well, it was sagging and rotting and I pulled it down two years ago to save injury and to salvage some of the wood for a chicken corral, hoping that removing it would expedite the appearance of a replacement. By last year I was reduced to conjuring an imaginary deck.

But now, look! Fallen cedar trees have been transformed by a local guy with a portable sawmill into lumber for joists and decking. Who knows? We may get a deck again some day!

Girl and dog

We had sunshine a few times today. And snow up on the ridges. And rain here several times. And hail.

At one well-timed moment, Fiona and the dog got out for a walk. Here they are heading up the driveway towards the highway. Limpet loves her walks and runs. Even if the pace is slow she comes back happy and tired.

It's lovely to have cotton-shirt weather and sunshine, even if it only lasts half an hour at a time.

Pip's midnight adventure

Last night I was putting Fiona to bed when she commented on the rhythmic shrill cheeping coming from the basement. At first she thought it was some sort of electronic alarm. "Oh, it's just a chick," she said, after listening again. I almost thought nothing of it. We can often hear the chicks from upstairs. But the fact that Fiona had noticed this particular cheeping as unusual made me wonder.

Sophie and I went down to see why someone was making such a racket at midnight. Nothing seemed amiss in the chick box. Except then I did a double-take and realized that there were only six chicks. There was Peep, diligently giving a noisy distress call, with only five siblings beside him.

There was a brief "oh no!" moment. Our basement is very small but there are about a million places for a frightened chick to hide. But Pip was quickly located tucked in behind the back corner of the box. Just sitting there, quietly wondering what had happened to his family, and where the lovely warm red light had gone. He was none the worse for wear.

The chick box now has a chick-escape barrier on top.

The new little family

For now they're either named 10, 12, 13, 17, 19, 20 and 22 or else Pip, Peep, Poop, Chip, Cheep, Choop and Lamarr. That's Lamarr/22 in the bottom right. He's the smallest, having just hatched out last night, while Pip/10 is the hulking thing in the middle. They'll get their permanent names as they feather out and exert their personalities.

They're almost needing bigger digs. Fiona and I will be picking up a proper chick waterer today and we'll have to recycle a large cardboard box to house them for the next month or so until they're ready to be outside.

If anyone has any tips for introducing new chicks to an existing flock without too much hen-pecking trauma we're all ears.

It is orange and red

One colour at a time, one coat at a time, one wall at a time.

It is orange

My home improvement quest continues. The carpet in the piano room is all gone. Thank goodness! It went off to the dump today, and for once I don't feel guilty about landfilling something. That carpet was evil, and good riddance!

More hardwood floor samples are on order thanks to Steve, my friendly building supply guy. I have the phone number of a good flooring installer. Some momentum is building.

Yesterday we began transforming the living room. We painted one wall orange. Really orange. Really, really orange. I love it.

The wainscoting is going to be a deep dark red. (You can see a test of a couple of shades off to the left.) It's not really wainscoting. It's just some panelling constructed to hide the electrical circuitry and cinder-block kneewall that forms the foundation for the log walls. But from an interior design standpoint we're considering it wainscoting and giving it a coat of deep contrasting paint. This room has one unfinished log wall, a vaulted wood ceiling and this panelling. Too many different wood grains and stains to also add hardwood flooring beneath. So the panelling is getting paint. Sophie is applying the white primer-sealer and the red will go on tomorrow. We'll do at least one more orange wall and all the panelling will be red.

This is fun. The changes are big and bold and, in this phase, are taking shape quickly.

Not a penguin

I had to wait a few days to make sure it wasn't a fluke, but it seems clear now. I am not a penguin anymore.

In the running community on-line a penguin is someone whose running pace is closer to a waddle than to a sprint. Generally a pace slower than 10 minutes per mile puts you in the penguin category.

My first week of running was those Couch-to-5k walk-run intervals (2 minutes running, 1 minute walking, that sort of thing) and my pace was around 13 minutes per mile. Waddle waddle. By the time I had eliminated the walk intervals I had sped up a good bit, to about 11.5 minutes per mile.

For the last three weeks I've been trying to increase both my speed and my distance, hoping to graduate from penguinhood. I've added 3 km (2 miles) to my distance, and my speed has been coming along gradually. Within the last week my faster flatter runs have hovered right around that 10-minute pace. Was I still a penguin? I wasn't sure. A few seconds this way or that, a few missing metres could make the difference either way.

But today I definitively discarded my penguin status, pulling off a 9:55 pace on my 3-mile (5 km) hill route. I'm sure of the time and distance on this one, and with an elevation gain on the outgoing leg of almost 100 metres, this route isn't a casual stroll. So there you have it. I run. I no longer waddle. And, best news of all, the dog is occasionally breaking into a lope, and panting alongside me, tongue lolling and finally looking like she's getting a workout too.

Corazón Concert

Erin's youth choir (based in Nelson) came to our town to do a couple of performances last weekend. They sang a lot of songs -- a full concert program all to themselves. Some were musically stunning, some beautifully theatrical, some had great solos. This one is just plain inspiring. It incorporates the "Lost Generation" poem from AARP's YouTube contest "U@50" and there's just something about all these teenagers earnestly holding up cards and then singing so beautifully that makes me want to cry. Enjoy.

Edited to add: Okay, I watch my kids play their violins and pianos and violas and it's all cool. But I sit here and watch videos of their choral performances over and over and over again ... and I cry every time. What's with that? Clicking "play" yet again ...

Fiona's first Vivaldi

It's always a bit of a landmark the first time a violin student performs a concerto movement. Fiona's first chance to do so was this weekend, when she played the first movement of Vivaldi's violin concerto in a minor with the other "senior" kids from around the area. She did really well, and enjoyed being part of the "big kids' group." And gosh, Sophie looks so much more confident as a player than she did even a couple of months ago. 'Timid' is fast vanishing from her violin vocabulary.

La Follia

Last year Sophie performed the Corelli version of this. Summit Strings has now learned Vivaldi's composition based on the same theme. Some day we hope to do an entire concert devoted to this theme and some of the many compositions that have used it. We have three other versions and ideas for some video footage.

Csardas revisited

My three older kids and three of their friends at today's regional Suzuki Celebration Concert. They had only 10 minutes with their accompanist before the performance. The accompanist, unfamiliar with the piece, set the opening tempo much too fast, and the kids gradually reeled her in. I thought they did very well and handled that little glitch very professionally. This is a very fun piece to play and they enjoy it a lot. They first learned it at the SVI last summer, and we decided to keep it in their repertoire and keep polishing it because it's such fun and such a crowd-pleaser.

Today's Uglee

The Chick Formerly Known as Egg 13 hatched just as we headed off to the regional Suzuki Celebration Concert this morning. We were able to watch him emerge from his shell and snap a photo of him in a state of maximum ugliness. Egg 17, visible below him in the photo, is the next in line to hatch, so it'll be Thursday or so before we get another little Uglee. By then this guy will be the cutest little ball of fluff in the universe. Hard to believe.

Another hatching

Yesterday just before the choir concert we noticed that Egg 12 was moving about and peeping. By bedtime it had a small crack and pip hole. We were pretty sure that we'd have another chick by morning. And indeed ...


... there it was. Still wet and ugly, not always capable of balancing its head up off the floor of the incubator, but perking up gradually after its exhausting fight out of its shell. This one has a bit of reddish colouring. I wonder if it will look a bit like Skunk, our favourite chicken ever, who met an untimely death at the claws of a black bear a year and a half ago. Skunk was an Ameraucana with red and iridescent green-black plumage.


Then again, it's really hard to tell with Ameraucana chicks. Here is The Former Egg 10, all fluffed up and downy. This is pretty much what Skunk looked like when we got him from the hatchery as a day-old -- he didn't give us even a hint of his mature colouring as a hatchling, and it was only later that we began to see his colours. So time will tell. Pullets, cockerels, red, wheaten, silvery, who knows?