borrowing -- bringing forth the calculation

This is the 2nd part of my post about borrowing, a continuation of my previous post entitled "borrowing -- the story".

To bring forth the calculation process of borrowing, I added actual counting boxes and jewels on top of my story drawings (above). Then (below), beginning on the right side of the page, I asked the kids how we could take 7 jewels from a wooden box that only had 6 in them. Right away they saw how they could "borrow" a china box's worth of jewels (10 of them) from the 10s column. So we took those jewels out and added them to the 6 that were already in there. (I did the same on the paper, changing the 4 to a 3 in the 10s column, and adding a 1 in front of the 6.) We then took 7 jewels from the wooden box and moved the remaining 9 to the wooden box at the bottom of the page (the solution line).

The kids totally (and easily) saw how this worked, so we did the same thing for the china boxes (borrowing a silver box's worth of china boxes) and the silver boxes (borrowing a golden box's worth of silver boxes), moving boxes as needed and changing numbers in the equation to correspond to what we were doing. Below is the final solution to our problem:

While we were all working the problem together on my drawing, the boys kept up as well with their own equations (which I'd provided for them at the start of the activity). Below is Zoo Boy's work. (By the way, I didn't even say anything to them about doing it on their own pages, they just naturally knew to follow along, it was obvious to them where we were headed by this point.)

The following day, we did some problems together using the base 10 blocks rather than the counting boxes and jewels. It was a very easy, obvious transition to the boys. This week, we dropped the manipulatives altogether (tho my drawing was still available as a reference if needed), and the boys have been doing long subtraction with carrying on their own without support from me or the manipulatives.

I'm VERY pleased with how this little math unit went, and am so glad I decided to broach the topic now by using the same characters and manipulatives they had used throughout their place value work. When we reawaken this work in the fall, it will be with a whole different story line, focusing on tribes rather than counting boxes.

borrowing -- the story

For the past two weeks we've been working on borrowing (long subtraction). I wrote my own story to go with the series of stories we'd used to introduce place value work (long addition and subtraction) and carrying in long addition. It's a two-part story, designed to leave the kids enough room to discover the answer on their own. In the story, the King of Jewel is trying to figure out a way to help his friend, the King of Other, get home to his Kingdom of Other, but his ship is damaged and cannot sail. Both of my boys decided to draw Tricky Mischief discussing the problem with the King of Jewel (J's drawing above, Zoo Boy's below).
Eventually they decide to collect all the jewels in the Kingdom and count them, then take the jewels that are needed to pay the Ship Builder to build a new ship. Tricky Mischief counts out 9,146 jewels into her counting boxes (see my other posts about the Kingdom of Jewel stories for an explanation about the counting boxes). The King then tells her to take 287 jewels from those to pay the shipbuilder. But when Tricky goes to collect 2 silver boxes, 8 china boxes, and 7 jewels from the wooden box, she discovers there aren't enough of each type of box available. What is she to do?? That's where I left the first part of the story, for the kids to ponder the solution to the problem. I did a story drawing along with them, but I simply drew the 9 golden boxes, the 1 silver box, the 4 china boxes and a wooden box with 6 jewels in it, and left it where the kids could see it and think about it.

In the 2nd part of the story, Tricky tells the King that they don't have enough jewels to pay the Ship Builder, and explains the dilemma with the boxes. The King assures her that there are plenty of jewels, and that she should try borrowing to get the amount she needs. So Tricky heads back into the village to collect more jewels from the townspeople, but soon discovers they don't have any more to give. Frustrated and confused, she returns to the castle and begins shouting up at the throne room. (J drew that in the above picture.) She shouts that there aren't any more jewels to be had, because they are all in boxes. That's when she realizes that, indeed, all the jewels are in the boxes. She rushes back to the counting room, grabs the jewels she needs, then joins the Kings at the edge of the sea and pays the Ship Builder his 287 jewels. (I do not explain how she went about counting them out, I left that for the possibility of discovery learning.) She confides to the King of Jewel that she borrowed to get the jewels, and he congratulates her and sends her out to redistribute the remaining jewels. So Tricky goes back into the Kingdom, redistributes the remaining 8,859 jewels, and waves goodbye to the King of Other as he sails away on his new ship (in Zoo Boy's drawing, below).

For my story drawing for this 2nd part of the story, I just wrote "9,146" on the previous days' drawing below the corresponding boxes, then wrote "- 287" below it (lined up in the proper place value columns), then drew a line across the page below that and drew in 8 golden boxes, 8 silver boxes, 5 china boxes, and a wooden box with 9 jewels in it. Again, I left the drawing where the kids could see it and think about it.

I will post next about how we took our story work and moved into the actual calculation work.

If anybody would like a copy of my story, The King of Other's New Ship, just leave a comment on this post with your email address and I will happily send it to you. I only ask that you keep it for your own use rather than sharing it further.

two quick updates

Update #1: If anyone is looking for my year-end summaries to update my kids' progress with school work, you're going to have to wait another couple of weeks. We're spending this week and next working with borrowing in long division. I don't usually go this long with our school year, but the situation called for a couple more weeks now, which will sort of balance out an anticipated lull in the action come January/February due to the new baby.

Which leads right into:


Update #2: Here's my latest ultrasound photo, from 2 weeks ago, of our little country bumpkin. This is a profile shot, you can see nose (already prominent like Mommy and Daddy!) and lips pretty clearly. That white blob over Bumpkin's head is her/his hand -- a drama queen already!

The horrible morning sickness seems to have left the building (KNOCK ON A REALLY LARGE CHUNK OF WOOD!), and so has the ridiculous exhaustion, which is an enormous relief. Things are going really, really well, and despite my "advanced maternal age" they are treating me like any other pregnant woman because, well, there's just no reason not to, I'm healthy and everything's going great.

Next (and I assume last) ultrasound is in another month, they'll do a close-up look at Bumpkin's organ functioning to make sure all is well, and we should find out the sex then as well. This pregnancy is just so different than my others, I can't help but think it's a girl. Guess we'll see soon enough!

what I did last week

I was stuck in a distant town for 3 1/2 hours every day last week while the boys were in their camps, but if you're going going to be stuck somewhere, it may as well be someplace with a view like this from the parking lot!




I set up a little "office" for myself under these lovely trees, with the above view, and got quite a bit of my planning done for our fall semester. I also discovered that there is really one more math process (borrowing in long subtraction) that I would like them to have a base in before we start with new topics in the fall. I could wait and do it along with the other new work, but I really would like to introduce it with the same story line we used for long addition, long subtraction, and carrying. So while I sat under the trees, I wrote a new Kingdom of Jewel story to read and work with this coming week.

We'll see how much resistance I meet with, the kids thought they were done other than binding our good books. But seeing as we've not bound those books yet, I feel like the door is still open for another couple weeks of schooling.


We joined some friends at this really cool pool on Friday afternoon -- it's a town pool in the town where Jacob dances, and since one of my friends lives there, we have access to it for quite a nominal fee. This won't be our last visit here this summer! We also went to the CT Science Center one afternoon after camps.

Below is a rainbow over our barn after one afternoon's rain.

modern dance intensive

J spent the week at a modern dance intensive for youth, run by the same company he danced with this past winter. The Map Man attended the performance at the end of the week, which I unfortunately had to miss because I was attending Zoo Boy's Art Show at his photography camp. (Such is the way of things when you have two children with different interests!) Fortunately, he took some pictures for me to see so that I didn't feel like I had to completely miss out on it. It certainly looked VERY interesting!

Some of the things they did this week were modern dance, Chinese dance, Chinese calligraphy, ballet, and work with props. And lots and lots of improvisation. (This company is REALLY big on the improvisation.)

My son, the human pretzel....

J of course had a fabulous time. He's really looking forward to the 2-week ballet intensive that he'll be attending in August.

photography camp

Zoo Boy spent the past week at Photography Camp. They made oatmeal box pinhole cameras (pictured at left along with a 3-dimensional photo frame he made), then developed their own negatives and prints (above) from the photos they took with it in the darkroom.

They also made scratch negatives and used those to make solar prints.

I was really impressed with how photo-oriented the camp actually was -- I had really expected it to be more of a general camp with a few photo activities, but they really took the kids through the entire photographic process in a very hands-on way. Zoo Boy just loved it!

A collage he did in camp. They also did half-and-half prints (they cut a photo in half, glued it to a paper, and drew in the other half by hand), and created a photo album to put their pictures from the week in.

Below are a few of the photos he took this week on various topics, including still life, nature photography, and landscape.

finishing up

Above is my very amusing (or so he thinks) elder boy, who in today's journal entry complained about the fact that we've not bound our good books yet. Here is the text a little bigger so you can read it:

We need supplies from Staples in order to do our binding, but we've just been too busy to actually get out and get them. Honestly, it's not been all errand-running! In fact, it's been very little errand running (after all, if we had been running errands, we certainly could have fit Staples into the schedule) -- it's just that our Summer has gotten underway full-swing before we had a chance to really finished up our school year. Summer Dance started a couple weeks ago, and Zoo Boy started Karate class last week (below in the front row on his first night):

Plus we've been attending park days and going to fireworks displays and free movies, and playing with puppies (and swimming in Christine's pool) and going to piano lessons (and swimming in their pool), and the lake opened for the season.

But I've not been a complete sloth -- I've already begun my fall planning. This is the first year I'm involving the kids in the process -- I made slips of paper with all the activities they want to do next year on them. Then I handed them out (Zoo Boy had 3 slips, J had a dozen) and told them to put them in order from what was most important to them down to what was least important, and to rip in half any activity they've decided they don't want to do. While they were sorting, I taped a schedule grid up onto the wall and stuck up the things that are important to me that they do (Monday Homeschool Classes, main lesson (curriculum) work on the other mornings, and some co-op type classes and activities on Tuesday, Wednesday and Friday afternoons, including Form Drawing, Handwork, Foreign Language, and Science). Then we discussed the other things they wanted to include (swimming and museum classes for both, Karate for Zoo Boy, and a variety of dance options, piano/guitar lessons, chorus, and social coaching for J) and either found places to tape them into the schedule, or taped them up off to the side to try to fit them in as possible with time and money constraints.

J surprised me by ripping up Jazz classes and Tap classes. But we had already discussed the fact that he and his ballet instructors thought that private instruction would be a good idea at this point (in addition to ballet classes), and I'd explained to him that private instruction was going to mean he had to give up some other stuff in order for us to afford it. In fact, he had ranked ballet privates as his top priority for the fall, followed by ballet classes and the pre-professional program he was involved with last year. Followed by Modern dance and Piano lessons. Everything below that I put off to the side for later consideration (as money and schedule allows), and he tore up the other dance tickets, knowing there was no way we could afford all of that. He's pretty focused on Ballet, and I'm relieved to have him make the decision to keep our schedule and budget in tact, rather than me having to make him give up things that he loves to do. But sacrifice is a big part of choosing a career in dance, and he's already preparing himself for that. That's a lot of maturity for a 10 1/2 year old!

Stalking Wolf, chapter 5

Honestly, we finished this up last week, we've just not been home long enough for me to blog about it yet!
We finished up our work with Stalking Wolf by reading the final chapter of our sage story. Above is J's drawing, below is Zoo Boy's, both chose to draw Stalking Wolf meeting the boy Tom, sifting in the stream for fossils.

Above is J's chapter summary, below is Zoo Boy's.

This story really resonated with the boys, as I knew it would. It was a great unit to wrap up our school year with. Now both boys are insisting that they are shaman, and spend a lot of time stalking squirrels and tracking rabbits at the park. Zoo Boy can often be found squatting in the barnyard, studying the behavior of the pony or the chickens, and J is working on a snow-bringing spell to use next winter. (I did beg him to wait until winter to try it -- you know, just in case....)