math practice

I had a request to outline a little more specifically what exactly we're doing for math practice.

For learning new math concepts, I stick to the Enki Education math stories, games and discovery process. This is moving the boys along at a nice, developmentally appropriate pace, and lets us work within the 3-fold learning process of open intake, artistic digestion, and conceptual output. This year we've been working on skip-counting (the introduction of the multiplication tables, which will morph into memorization work with that), and we'll spend a bunch of time with place value over the next few months. And then we'll move to working with borrowing and carrying, and measurement during the later part of the year.

But for practice we do a little work with the 4 processes (addition, subtraction, multiplication, and division) each day. I bring this to the boys from two different angles -- word problems and equations. And I also work to reinforce the connection between the two.

I initially struggled to come up with enough ideas for word problems, so I bought a couple of work books to help inspire me. I really like the one on the right, the Daily Word Problems book, because it is set up in sets of 5 related word problems (so they follow a bit of a story line on the same topic). Nice holistic feel, but not a large quantity of problems since it's only designed to offer one problem per school day, and I prefer to touch on all 4 processes each day (to help the kids see the interconnectedness and relationship between them). The other book, the Kumon Word Problem book, has many word problems per page, but they are generally unrelated to each other. Still, I use their word problems as inspirations to make up my own, as topic ideas when I'm feeling devoid of creativity. But if I was looking for a book to actually hand the kids to use (not the way I use them at all, I read the problems to the kids to work on developing their listening math skills as well), I would definitely choose the Daily book.

Like with so many other things, once I had the books and worked with them a little, I suddenly overcame my mental block, and I found that I haven't needed to use the books anywhere near as much as I thought I would. Nice to know they are there for ideas if I need a boost, though.

Each kid has their own blank tablet to write on, and I recite a word problem to them. Initially, I let them just write down the answer, but we've been at this for a couple of years, so at this point they are writing down the full equations. I purposely choose pertinent topics to their lives, as I think it accentuates the connection of math to the real world. Here's an actual example (from yesterday) of a World Problem session -- I have the "problem" that I recited to the right, the boys' answers are to the left:

"J was sick for 5 days. Zoo Boy was sick for 4 days. How many sick days did we have all together?"

"How many more days was J sick than Zoo Boy?"

"The doctor gave one of the boys some medicine. The bottles of medicine contain 10 doses each. If the boy needs to take 2 doses of medicine per day, how many days will one bottle of medicine last?"

I then asked how many bottles of medicine we needed for each boy. I didn't make them write their answers down, I just asked them to talk about how they figured it out, because they each have their own ways of going about this, and I think it's good for them to realize there's more than one way to solve a problem. Zoo Boy knew that 5 days was half of the total 10, so he knew he needed another bottle of 5, so that made 2 bottles. J divided 10 days by 5 days to get the answer of 2 bottles. (Which is very typical of their math styles -- Zoo Boy depends a lot on logic, while J almost always goes right away to an equation. Interestingly, that pretty much describes my style of doing math vs. The Map Man's as well. Hmmm....)

"Each boy has to take 2 doses of medicine per day for 10 days. How many total doses will each boy take?"

In addition to the 4 processes problems, I always add in a logic problem or two, because despite the answer being very obvious (to me and Zoo Boy), J has a bunch of difficulties with the comprehension of this type of problem, and Zoo Boy has problems seeing that there's an equation that describes the obvious answer.

A little background about this day's logic questions: With each dose of medicine, J ate a marshmallow, and Zoo Boy at a fun-sized three musketeer's bar. So here's how the logic questions read:

"How many marshmallows did J eat?" and "How many three musketeer's bars will Zoo Boy eat by the time he's done with his medicine?"

Our story theme of course changes each day, as does the order of the type of problems, but every day I make sure we have an addition problem, a subtraction problem, a multiplication problem, a division problem, and a logic problem, as well as a problem of some sort that I know J and Zoo Boy will work out differently so they can discuss their approaches to it.

In addition to the word problems, they also receive a list of equations to solve each day. For this I really do like using pages from math workbooks -- I favor the Kumon books -- I tear out one page per day for Zoo Boy, and two pages per day for J. The reason I tear them out is because there are pages I don't want the kids seeing (the pages that "teach" certain ways of doing the work -- all I want is the equation practice, I don't use these books for teaching). With my educator's discount at the various book stores, the workbooks wind up being about the same price as printing out my own worksheets (or those I search up on the Internet), and is a huge time saver because I have them all bound and waiting for me to just grab and use.

Obviously, at the pace I'm going with those, J is working twice a fast (and twice as much) as Zoo Boy, which is just about right for their different developmental levels.

feasting, fun, and football

In a brilliant display of the irony that is my life, Zoo Boy was still sick yesterday morning, so despite my having spent the summer raising those danged birds, we did not get to partake of any of our own turkeys yesterday (the bird intended for us was cooked and consumed at my brother-in-law's in a whole 'nother state). News from friends (who enjoyed other birds from our flock) was that the turkeys were moist and tender and downright delicious.

That's OK, we made do nicely with some venison steaks (THANK YOU, CHUCK!!!) marinated in hoisin sauce and broiled to perfection, a little orange chicken, and some stir-fried rice and veggies. In fact, The Map Man and I are not such big fans of turkey anyway if truth be known (I prefer listening to mine gobble rather than gobbling them up!), while we both are HUGE fans of venison, so as far as we are concerned, we made out pretty good on the whole deal, and we QUITE enjoyed our feast!


"Tom" Brady -- J's rather appropriate attempt at Thanksgiving humor. (That boy, he's a crack up!)

Good food, good company, and a decisive win by our beloved Pats -- what more is there to be thankful for?? As far as we're concerned, it was one of the best Thanksgivings ever.

(And speaking of the Pats -- I really wish people would stop hating on our defense! Yes, they are young, and they have a lot to learn, but those boys are working darned hard and we're WINNING. What more do people want from them?? There, it had to be said....)



Incidentally, Zoo Boy is feeling MUCH better today, we managed to venture out for a bit for the first time in a week to pick up some much-needed supplies. That's quite enough illness to last us for the next couple of months, or at least I hope....

Happy Thanksgiving, everyone!

The view from our deck (actually ON our deck) this morning:

Anastasia, the Princess of Silli Billi

We've had another abbreviate week due both to the holiday, and to the fact that Zoo Boy now has the nasty illness that J had a couple weeks ago. Blech.

But we did read the story of Anastasia, the Princess of Silli Billi, the Czar's daughter who visited the village of Silli Billi and discovered that she needed to speak in syllables in order to be understood. Above is J's drawing, of Anastasia approaching the village, and below is Zoo Boy's drawing of Ansastasia, lost in the woods.

And below is how Zoo Boy accomplished his work this week -- from bed. My bed to be exact.

Hopefully we'll all be back to full health -- and full work! -- by the start of next week. There's really quite a bit I'd like to accomplish before the winter holidays.

Blog Post #1000!

Wow, time flies!!! I can't believe this is my 1000th Along The Crooked Path blog post. I've known this was coming up for the past several weeks and have been desperately trying to decide what I wanted to post for my 1000th entry. There's sort of a lot of pressure here, I mean, you only post your 1000th post once!

All I could come up with was to take a quick peek back to post #1 and see how far we've come. Then I realized that post #1 didn't have a photo with it. So here's the photo from post #2, from March of 2007:

It's only been 4 years (well, OK, closer to 5 at this point....) but WOW, have we changed! Well, not The Map Man so much -- he's still just as handsome and tolerant as ever. Maybe a little less hair (and a little less color to what's there). But still, you'd recognize him anywhere.

Me too, I guess. I actually think I'm heavier at this point (which is VERY disturbing...really need to do something about that). My hair got longer. Then shorter (right now it's very VERY short). I assume I'm wearing a different pair of glasses now, but can't tell for sure from that photo.

J stopped keeping his hands in his mouth years ago. In fact, J's undergone the largest transition since that time. We were still dealing with Autism on a daily basis back then. Now we go days at a time without even thinking of that term. I know for sure he wasn't potty trained yet back then. I think he had weaned (but probably only recently). Wouldn't he be thrilled to read this....

Zoo Boy has grown a whole bunch, but he's still basically the same funky little dude now as he was back then. And I say that in the most loving way possible -- he's a unique entity. He just recently expressed an interest in becoming an Author (which both surprised me and made total sense to me at the same time), and outlined his story idea for his first book to me just the other day. It's a great story line, he's already got fascinating characters developed and an interesting plot. I offered to be his scribe if he wanted to start writing it, and he's giving that some consideration. "But would anybody want to read a book written by a kid?" he wondered out loud. I think he'd be surprised at just how many would. My guess is that, even without having put down a single word yet, he'll be published before I of the many-pages-needing-editing will.

I'm on my third computer since starting this blog (will be on my 4th as soon as finances allow me to replace this borrowed dinosaur -- it's QUITE limiting not to be able to view or edit video). To our farm we've added a horse, lost a horse, added turkeys, lost several wonderful dogs, gained several more including a Lab and a Big White Dog, both of which I wouldn't have ever thought we'd have. We've changed hay suppliers several times. We've changed grain dealers twice. We survived a major financial upheaval. J has plunged our family head-first into the world of dance, causing a major shift in both my work schedule and time for pursuing my own hobbies. We've gotten involved with an incredible group of fellow homeschooling families who have become good friends and valued fellow travelers on our journey.

I guess we've just sort of matured into our lives. And it's good. It's all good.

Ok, your turn. Valued reader, why do you read this blog (all 1000 posts of it!)? What are your favorite types of posts? Whatever the reason, I want to thank each and every one of you for taking the time to become a little part of our lives, and I hope you're still reading when I hit my 2000th post!

modern dance

I apologize about the weird coloration and poor resolution of these photos (but I thank Laurel immensely for taking and sending them!!) -- these are photos from our "Parent Observation Week" for J's Modern Dance class, which was held this past week. I think Modern is the perfect counter-balance for Ballet -- it's all about creativity and expression, whereas ballet is all about discipline and technique. Together, the two create a full dance experience for J, and I'm grateful that he has the opportunity not only to work with talented instructors in a class environment, but also participate with company performances in both as well. Enjoy the photos!

wrapping up Harriet Tubman

I read the final Harriet Tubman story to the boys last week, and they did drawings from the story. Above, J drew Harriet leading escaped slaves to freedom. Below, Zoo Boy drew Harriet pointing her gun at a slave that wanted to turn back. She knew that if he was caught, they would all be discovered, and she told him "Go forward, or die." He chose to go forward, and crossed the cold, deep river with Harriet and the other escaped slaves.

This ends our African American cultural block. It was SUCH a wonderful few months working in this culture -- we loved the music, the stories, the cooking projects, and the crafts. Next we'll be moving onto the British Isles culture , and will become familiar with the life of John Muir. Since the winter holidays will fall in the middle of this block, I'm going to take a bit of a different approach and hold off until January on doing the trickster and sage cycle, because I know that I wouldn't give it the consistency and attention it deserves if I were to start it now. So instead, we'll start by working with some Language Arts skill stories, and do another math block before the holidays, then bring in the tricksters and sage stories mid-way, finishing up with some more math and LA skills before we shift gears to a new culture in March.

Onward!

enrichment

Enrichment is a word that schools use to describe those things the kids are exposed to during their school day that are outside of their curriculum. Field trips, concerts, special programming all fall under the heading of "enrichment". If kids are lucky, enrichment encompasses about 3-5% of their schooling time. The benefit of enrichment programs is that it exposes the kids to other living cultures, allows them to practice functioning in the real world, and provides an opportunity to bring classroom learning to life.

For many of us that homeschool, activities that would be considered "enrichment" in the schools is what makes up the bulk of our "curriculum", so you almost never hear homeschoolers talk about enrichment. (Except maybe those that do "school at home" -- strictly following a school-based curriculum to keep pace with in-school learning -- which is one very valid way of homeschooling. Just not our family's way.) Our kids lives don't need to be "enriched" -- every day the kids are exposed to the real world, they don't need time set aside to practice their role in it.


This past week was a great example of this in our family's life -- it was one of those weeks where our "desk time" equaled about 2 hours and our "life time" made up the rest.

We started the week with our Monday Homeschool Classes "Share Day". The class that I taught, "The Life and Times of Harriet Tubman," offered a stage presentation about Harriet's life. The kids all donned their burlap sacks and bandannas, and each read a passage about Harriet's life. (In the photo, J is returning to his on-stage seat after his turn at the mike.) Between passages, we sang the slave spirituals we learned in class.


Our class quilt was on display (behind me and my assistant, Zoo Boy, who were seated below the stage to one side -- Zoo Boy said that his stage fright kept him from joining the rest of the class on stage, but he was perfectly happy to wear the class outfit and follow along nearby), and the kids and the audience both seemed to really enjoy the performance. I thought it made a great wrap-up to our Harriet Tubman unit at home, too, even though we hardly spent any time at home this week.

We also got to pick up the posters that the boys had made during their "Planet Protection Project" class. This was a class that the museum (who so generously donates their space to us for our Monday classes) offered to our community during our Monday class time at their nearby Nature Center. (That where those photos from a few weeks ago of the kids' "outdoor classroom" were taken.) This is Zoo Boy's poster, he clearly spent a lot of time working on it.

J's poster from the same class.

Tuesday was a busy day -- it started with dentist appointments for the boys (which, although a necessity of life, didn't stop the kids from expanding on their knowledge of teeth and dental health!). Then we attended a Homeschooler's Open House at a new Athletic Facility -- the kids spent an hour playing organized sports games on the enormous indoor athletic field, then most of the group went on to spend an hour in the pool. (We didn't -- we get plenty of swim time and had other things to do.) This facility is going to be offering the homeschoolers a swimming program on Wednesdays and a general athletics program on Fridays. We're moving our homeschool sports program there, because playing sports on indoor fields is FAR more appealing than being stuck in a hot, smelly gym during the winter!

From there we headed to OT. I've decided to drop the Therapeutic Listening program (that I never really found time to blog about) -- I've given it a good 6 month trial, but am not seeing any real, lasting benefits from it, and there were a couple of things of concern that seemed to clear up once I stopped doing it. I think it's a program with value for some kids, mine just weren't benefiting enough from it. I've been promised Speech during December for Zoo Boy, so we'll stick out the OT until the end of the year and see what comes of that -- if we can make Speech a regular or at least semi-regular thing, we'll keep on going. But with $2000 a year in co-pays, not to mention the gas (and time!) to trek half way across the state and back, I need to see some fairly immediate benefit, otherwise I'm going to find a more beneficial way to spend that time and money.

At least we took advantage of being all the way over there on Tuesday by joining some friends at the Jump Zone in Canton. The kids jumped and bounced and slid and had a rollicking good time for several hours, before heading home exhausted.

Wednesday the farrier came out to trim the horses' feet, so the morning was spent on farm type stuff. We did read our final Harriet Tubman installment that morning (a follow-up to the previous story) and worked with that on Friday -- I'll post separately with those drawings. I had a Doctor's appointment for myself in the early afternoon, and the boys each read the next installment of their book series -- J is still working on "Secrets of Droon", while Zoo Boy is about mid-way through the "A-Z mysteries". Later in the afternoon, the kids had an art class on Printmaking at the local children's museum. Here's a collection of J's prints from that class.

And here's Zoo Boy's prints.

Thursday is always a busy out-of-the-house sort of day. We started with J's first guitar lesson, which he just loved. Then the boys got to play with their friend I, until we all left for swimming. After the always-fun pool time, we headed down to our Spanish class, then they spent an hour or so playing at the children's museum before heading over to J's busy busy night of dance, including a ballet class, a modern class, and rehearsal for a modern company's show that he's been invited to participate in.

Friday morning we actually DID spend a little time at home doing "school work", but Friday afternoon it was off to our Science Explorations at our friends' house. We did some corrosion experiments, and made lemonade. Then more dance. And, um, more dance.

Here's a quick photo from J's tap class. He's now dancing 8 times a week, and loving every minute of it. Honestly, I'm not sure how he would be able to do this if he was in school. When do schooled kids who are this involved in dance do their homework?? We're not getting home until 9:30 some nights -- how do schooled kids manage to get up in the morning? We just don't bother setting alarms the following mornings and let him sleep as long as he needs to. It's no big deal if he's not ready to start working at 8am, we can just as effectively (more effectively, since he's well rested!) start at 10 instead.

I tell you, I give credit to those parents who are willing to deal with school schedules and juggle homework and activities. I just don't have the stamina for that sort of thing! The very, very best part of homeschooling to me is that we don't have to sacrifice anything for the kids to be involved in whatever they want to be. We don't have to make time for "enrichment" -- their lives are already enriched!

times table intro wrap-up

It was a very abbreviated week this week, due to J's illness (he's doing much better now, although he's on antibiotics for the first time in his life). So we only had time to work with one story -- a perfect time for my custom-made story, "A Strange Thanksgiving". I told the story yesterday, and the boys LOVED it. Then today we recalled the story, then did a free drawing.

Above is J's drawing, near the end of the story, where Busy Boy is holding perfectly still for the first time in his life, while the rest of the Strange Family scurries around the Dolphin tank trying to figure out why the Dolphin is sick. (Since this story was custom-written for my kids, I was able to incorporate memories from a recent visit to the Aquarium, and was able to set it as Thanksgiving approached -- I just love the flexibility of homeschooling!!)


Zoo Boy's drawing is above, of the suitcase that each of the Strange Family packed -- Father packed his items one by one; Grandmother packed two bags, one with her clothes, the other with scarves that she's knitting for her grandchildren for the winter holidays; Little Brother packed his backpack by shoving in three garments at a time; Big Sister crammed far too many things in her suitcase; Mother collected her belongings from all over the room and neatly packed them; and Busy Boy was so busy watching everyone else get ready to leave, he forgot to pack anything at all! (That got big laughs from my kids!)

The story went on to talk about the family they were going to visit, then they arrived, had their reunion, and ate their dinner. Then the phone rang, and it was the Aquarium where cousin Twyla worked as a dolphin trainer -- her favorite dolphin was sick! The family rushed to the aquarium to help, each in his own way, until Busy Boy discovered the truth -- that the dolphin had a ball stuck in his throat! My drawing below shows the victory celebration, with Twyla and her dolphin putting on the best Thanksgiving Day dolphin show ever held anywhere!

(If anyone would like a copy of the actual story, leave me a comment with your email address and I'll be happy to send it to you.)

While we were recalling the story this morning, I revealed some drawings I had prepared of the rest of the Strange Family: Auntie, Uncle, and the four cousins, Nina, Tina, Ellen and Twyla. (Their traits are described in the story itself, I only put the name of the number they represent on the drawing, not in the story.) I had already listed the counting-by numbers on the opposite side of the page. Here's what they looked like:

After we were done with our drawing, I hung all the extra drawings with the others in the hallway. Here they will sit while I let the entire topic "rest" for a few months. (We'll be moving on to another math topic after some more cultural and Language Arts work.)

preparing for winter

November has really settled in around here. The leaves are off the trees and have been blown by the wind to the back corners of the pastures. (That's April, our Akbash Dog, on patrol in the sheep pasture this morning.) We had our first measurable snowfall yesterday morning (a couple inches of a disgusting snow/sleet/freezing rain mix). It's time to make winter preparations here on the farm.

We spent a chunk of time on Sunday setting up a new sheep shelter abutting the back side of the barn. This should help protect it from the worst of the damaging winter winds. We used bent steel cattle panels as a framework, and a tarp from our old hay tent as the covering, so we had no expense. The shape and steel mesh of the frame will hopefully make removing snow from the shelter unnecessary.

Our old sheep shelter, a pipe tent that has served us well for several years. It was always a challenge to keep the snow knocked off the rather high roof, and we were constantly repairing the tarp grommets as they tore away in storms. This weekend we'll deconstruct it, scavenge usable pieces for future projects, and remove the rest. I'll be happy to be rid of it, it's become a bit of an eyesore over the past couple of years. The new shelter is better hidden and less intrusive. (Note the snow at the bottom of this photo, leftovers from yesterday's storm.)

Speaking of the sheep, it's time to do some winter flock adjustments. Time to sell what lambs we want to sell, butcher those that we want to eat, and covert those that are no longer producing well into food for our dogs. As much as I would love to keep them all, it's just not practical -- it costs a lot of money to feed sheep through the winter, by cutting our flock in half, we'll cut the feed bill in half as well, and will pay for much of the food from the sale of the lambs. We'll be keeping our 4 best ewes and our ram, and by next year at this time, our flock will be back to about this size and we'll go through this all again.

Since we're on the cheery topic of butchering, here's what our turkey flock looks like all grown out. Butchering starts this Wednesday and will go on a few birds at a time until we're down to just 3 birds, two chocolate hens and a chocolate tom, which we'll keep to hopefully produce next year's flock.

Our duck flock is also in need of some winter thinning. Half of these ducks are drakes (males), and you only need a few drakes to breed the 9 or so hens we have. So the vast majority of the boys have a date with orange sauce. They're on the docket for after the last of the turkeys go.

The chicken flock will get trimmed a bit, too, although historically I've had good luck selling the extras rather than having to eat them, and this year looks to be no different. We'll be keeping most of our young white leghorns, who have just begun laying adorable little white pullet eggs at just over 4 months of age. (The eggs will get larger as they mature.) Our older birds and the birds of other breeds will be sold off over the next week or two.

Not on the sale list is our very handsome Blue Andalusian rooster, "Falcon" (aka "world's best rooster"). So long as Falcon keeps behaving himself (meaning being non-aggressive towards humans and not crowing at stupid hours of the night), he can enjoy his home and his harem, and maybe we'll hatch out some of his progeny next year.

A batch of black-eyed susans resisting frost, freeze, and snow at the back corner of the barn. The last item on our "to do list" before moving the sheep to their new shelter is to transplant this cluster to the kids' garden. The thought of the sheep mowing them down after they've so heartily withstood the advancing winter is just too unbearable to us.

And one more sign of the season -- sick days. J's got a fever/headachy sort of thing going on. So we've had a couple days of absolutely nothing (even less than our usual "nothing" type days). He's either been sleeping or reading, while Zoo Boy's either been reading or....well, more reading. Seriously, NOTHING happening here....