Friday, February 7, 2014

Part 2 Wk 5 February 3, 2014

This week flowed pretty nicely. We didn't get a lot done but we accomplished more than nothing. I guess it was a just-right week.

I've decided to change our schedule around a little bit to accommodate D's new "no-nappy" schedule. I am moving up our start time, slowly, keeping our end-time the same which seems to be flexible anyway, and then switching to no afternoon classroom time. Our before schedule was, classroom time 5 days a week, 9am-12pm, and then 2pm - 3:30pm, while D napped, except on Tuesdays, when we had speech and no afternoon session. NOW, my goal is to shift our classroom time to 5 days a week, 8am - 12pm-ish and have no afternoon session. I figure a summer schooling schedule will be again slightly different, and once D can handle an afternoon session, we may work a different schedule then too. I am wondering how this will all work,and if this all will work. I guess the only way to find out is to try it.

Okay, now for the good stuff,
This is a little of what we've been doing:
Math: skip counting, golden bead division - static and dynamic, stamp game - static addition, racks and tubes - calculating distributions and remainders
Geography: puzzle maps
Practical Life: setting a table, supposed to be tonging-turned out to be whole hand grasp
Language: writing with the moveable alphabet

I figured out how to make Blogger NOT rotate photos...which is SO annoying. I am on a PC, so I drag the photo from the drive file to the desktop, double click on it, and orientate it the correct way in Windows Live Photo Gallery. Then I upload the photo to Blogger from the desktop and it loads with the correct orientation. Goodness.
T always goes for the puzzle maps when he needs a little R&R. Learning the political geography of Asia doesn't seem like R&R to me, but who am I to judge?
One thing I noticed was that the maps have "changed" and not for the better. I got these from Montessori Outlet which I'd say has a good price but their product is only so-so. First, the knobs keep falling out, which is okay because the kids are super on top of this and I can glue them back in. The kids are always telling me the knob fell out before those little white pieces of wood roll away somewhere to be gone forever. I feel like I am gluing SOMETHING nearly every day. This time I had to glue Moscow back into Russia.

Also, the puzzle pieces are beginning to warp a little bit. You may notice on the photo above that Russia doesn't lay flat any longer and its edge comes up above Mongolia and China. Also, some of the pieces have shrunk. (SHRUNK? REALLY? Now how can a country shrink?) In the picture below you can see a gap between India and Myanmar that wasn't there a year ago. I don't know about your child, but mine are very picky. That tiny little bit of wiggle room in the puzzle will drive little D nuts. He almost abandoned the Africa puzzle last week because Angola didn't fit in tight against Botswana and Namibia. Anyone have an idea about how to get Myanmar to grow a little? Maybe a hot humid summer in the bayou would do it. 

I can't tell you about the shrink-ability of other brands, but if your environment gets cool and dry in the winter, or any time of year for that matter, don't order your puzzle maps from Montessori Outlet.


S is finally into, and almost done with, Golden Bead Division. I took our lesson from the Montessori by Hand Primary Math Album. (So sorry for the wonky, dark pictures. I am trying to figure out another flash situation that isn't going to be so heavy it makes my arms feel like they are going to fall off as I wait for the shot.)
First we set up our Golden Bead materials. Typically this lesson would involve three children, one for each unit divisor. The Guide would compile the large number cards and select a quantity that divides evenly by three. Three sets of small number cards would be laid out on a mat a ways away from the work area. Each of the three children would bring a separate tray to the mat and the Guide would collect the bead quantity she has chosen and indicated with the number cards.

In our case, since S was the only student, we used green skittles from the stamp game to represent our "children" and divided our quantity up among them. 

I chose a dividend quantity, or a quantity to be divided up, and laid out the corresponding large number cards. S counted out the quantity in golden beads and began to distribute it evenly among the three skittles, starting with the largest hierarchy fist, the thousands. After distributing the thousand cubes, we verified that each skittle received the same amount. We also did a verification after each distribution for the hundred squares, ten bars, and units. 

After S had distributed the entire quantity, we counted what one unit skittle received and selected the corresponding small number cards. Then she selected small number cards to show the equal quantities the other two skittles received.

After this, I pulled a small number card for 3 units and placed it to the right of the large number card dividend quantity and stated, "3,728 divided by 3..." As I placed one of the small number card quantities to the right of our equation, I completed my sentence by saying, "equals 1,242 with a remainder of 2." (We had 2 left over we couldn't distribute evenly, so this became our remainder. Typically in a first presentation, the Guide will choose a dividend that divides evenly by three. This wasn't our first presentation.)

The first presentation of Golden Bead Division the dividend would divide evenly with no remainder. As the child progresses he/she will explore dynamic division in which there may be exchanges and remainders.

To give you an idea of where S is in the continuum, over the last 5 months we've covered golden bead static/dynamic addition, then static/dynamic multiplication, then static/dynamic subtraction, and now golden bead static/dynamic division. She has started some Stamp Game work with static and dynamic addition and has just begun skip counting using the bead chains. Next we are on to more Stamp Game, the Dot Game, and the Large Bead Frame. We'll continue using the bead chains as well. S is now officially 6 years old, and would have been a third year Primary student.



I FINALLY prepared this table-setting work for little D. He did it about five times in a row, and now hasn't touched it since. I'm beginning to realize that this is the way he likes to do things: get in there, do it multiple times, and then leave the work and move on. If you reintroduce the work many months down the road, he is game for another five go-arounds before he loses interest again.
I purchased the place mat from Walmart and traced each item with a Sharpie. The napkin I made from an old curtain way back when, the plate is from Ikea, the small glass is from GoodWill, and the flatware is heirloom sterling silver and the spoon is from the local Church sale.



S wanted to put a title on her clock, "what time is it?" We've been learning the green double letter sounds, so I've been encouraging everyone to use the Dwyer "key" spellings for writing works. For the long "i" sound, the key spelling is "ie." I think the cursive moveable alphabet inspired S.

Afterward, S did a lot more writing with the moveable alphabet, using the double letter spellings. (You can see the sandpaper letters up there in the corner for reference.) During this particular session she required a lot of support, but she wanted to keep trying.
Translation: The monkey ate the candy cane. The sheep came and saw the candy cane was gone.

So, I have a question for all you Montessorians out there, what do you do when the child runs out of letters? I helped her here cut out extra paper letters. Is it just that in a regular classroom the child would have access to multiple moveable alphabets and therefore wouldn't need more paper substitutes?
She was very proud of her hard work.
Here T is doing some light research into the Fundamental Needs of Humans and their need for defense. I was sorry that we needed to transition just as he was getting to this work, so I hope to encourage him to open the books again at a later date.

S here is doing a little dynamic stamp game addition. A thing to note: I debated whether to print this stamp game paper in black and white or in color. (This paper is from Montessori Print Shop.) So, to see what would happen I printed it in black and white. If she needed the color coded hierarchies, well then we'd do the color printed paper. But if she could do the notation in just black and white, it would be another step toward abstraction. 

Here, S was able to note the addends and the sum with no difficulty using the black and white paper. Then she quietly got her colored pencils and shaded in the squares green, red, and blue accordingly.
And T is back at the racks and tubes.

This time we moved toward abstraction. He has finished all the initial presentations that involve just beads and boards. He's done the zero place holders, the larger hierarchies, and the remainders. What is left is transitioning to just pencil and paper. 

We started off with Jessica's Keys of the Universe Math album exercises which include easier problems such as 7,872 divided by 32. There are no zeros, no remainders and easier-to-work-with numbers. After a sullen *sigh* from T we got through the first presentation. T then said, "there were no 9's. I like it when there are 9s so that there are a lot of beads to pick up." I said, "why don't you pick the next problem?" He picked THIS one with zeros, large numbers, and a remainder. T did the problem just fine.
We actually skipped a lesson altogether. Partly because I thought the sequence was a little confusing and partly because I thought that T would get the logic in the next lesson.

So, what DID we do? In the first Racks and Tubes presentations the child will record only the divisor, the dividend, and the quotient. Now, the child will begin to do some of the number work that goes along with long division and at the end of the process, will be able to perform long division with just a pencil, a piece of paper, and their brain.

Our first step was to note what we were distributing.  For our first distribution, we had 7 million beads, 3 hundred thousand beads, 7 ten thousand beads and 9 unit thousand beads. T found that we could carry out one distribution and he wrote the number one in the thousands place since that is how many one unit skittle receives.

Then we counted up how many beads we distributed, or how many beads were on the boards. He came up with 3 million beads, 9 hundred thousand beads, 4 ten thousand beads, and 2 unit beads. We noted this number down on our paper below the dividend number, lining up the place values. Then T subtracted through, borrowing where needed, to find out the difference between what we had to distribute and what we actually did distribute. This difference was the partial remainder and the quantity of beads left in the cups. Finally, we checked the cups to verify that our "math" and our distribution matched. 

Then we exchanged our 3 million beads for 30 hundred thousand beads to be able to distribute 34 hundred-thousand-beads. After we brought down the next four cups to distribute: the 34 hundred-thousand beads, the 3 ten-thousand beads, the 7 unit-thousand beads and the zero hundred beads. Likewise on our paper, we needed to drop the zero hundreds place holder in the dividend and add it to the partial remainder. (This is essentially the lesson we skipped. In that lesson the child would record the partial remainder only, and then drop down the next digit to note what he/she has to distribute again.) Then we did a new distribution. We recorded the beads on the boards, subtracted through, and verified that this partial remainder matched what we had left in the cups. Then we cleared our board, exchanged, brought down four more cups and started our distribution again. 

All and all, T did very well with this work. He still needs a lot of work with his math facts and I think that is what holds him back. But the concept is pretty easy for him. I am amazed he just gets it since I am just now learning WHY long division works!
And there was some skip counting this week. S is still a little shaky with the tens and teens but T assisted her wonderfully.

D does these four cylinder blocks in all sorts of formations. I just don't know how he keeps track of it all! I don't prefer him to work with this material on the table since he can't get a good "bird's-eye-view" of the work because the table is so high. I don't remember every reminding him to put this work away. In D's world that means he really really likes the work.
And finally, a little bit of Valentine's day tonging. 
Hope everyone has a wonderful weekend!

20 comments:

  1. I love seeing other people's homeschooled kids in their jammies.

    I will really love rereading that explanation of the racks and tubes when we are in the thick of it.

    I am really confused whether D's "no nappy situation" means he's not sleeping in the afternoon, or he's out of diapers, LOL!

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    1. Jammies was what D picked out to wear that day. I think those weren't the ones he had worn to bed though. He just came in and said, "get dressed, these!"

      And the no-nappy, you are hilarious. :)

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  2. I am there with you on the transitioning of work times! I never expected Buddy Boy to give up his naps so soon ( some of my bigger ones still like naps sometimes!), but he did, and has been for a while, so we moved things around, too. That being said, I thought I would be sad to give up nap time in our house, but I am kind of enjoying not having to work around that constant in the day! It makes it easier if we are busy, or want to get back to a big project that we are working on, etc. :) I agree with MBT - I am going to look back on this explanation of racks and tubes. Although my children are older, and have done some abstraction, it made things so hard (especially for my oldest) that when we began to switch to Montessori, we abandoned ship with some of the Math and I chose to backtrack and make sure they understood what they had been doing. So, we are behind what would be a normal Montessori child's level, although still far past what a public school child would be doing for the most part. Also, not having the racks and tubes means I am working on a semi-home made version, which has taken a little thought! I love reading your weekly wrap ups! It's like a combination of my two of my favorite bloggers when you and MBT are both commenting on the same post!

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    1. Awww, thanks. See my comments below about the racks and tubes, DIY version...

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  3. Since you are both here, I was looking in to this work, and wondered what your opinions are of these test tubes from Amazon. I have printable division boards for the long division, that I have printed and laminated, and regular pony beads in the correct colors. I thought about trying a less expensive DIY racks and tubes, and wanted to get a second (and third) opinion on it! http://www.amazon.com/60-Tube-16x150mm-Clear-Plastic/dp/B004PD9ULS/ref=sr_1_3?ie=UTF8&qid=1391874926&sr=8-3&keywords=test+tubes

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    1. I can tell you that my good friend (local) made her own racks and tubes with test tubes from the science supply store, holders out of foam from the fabric store and boards out of pegboard from the hardware store. She was really happy with it. That looks like a a pretty economical way to get a bunch of test tubes to me. The test tube that came with our racks are also plastic, only 3 inches long, and 7/16th in diameter. I think you need to know the exact size of your beads before you order tubes. You want to make sure you can get the right number of beads in the tube. If you have 3" tubes like mine but with a larger diameter and use bigger beads they might be too short if that makes sense. Ideally you won't be able to put in too many either, BUT you can always shove a cotton ball in the bottom if they are too tall.

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    2. Oh - good point! I will definitely have to check out the size they are vs. what I would need. Thanks for suggesting it! :)

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    3. Hi all!! coming up for a bit of air here. February is a big birthday month...and next week is valentine's day ahhhh.

      Okay, racks and tubes...
      A few things, from my perspective...first the boards: punched cardboard could work, drilled 1/4" masonite could work (could glue this to a backing or not), or your laminated printed version could work. The only caveat with the last option I see is the beads slipping around. One little jostle after putting down 81 beads could make quite a stir, this is why those little depressions "keep" the beads in place.

      Peg board seems like a good option, maybe pretty economical too, though I haven't checked it out...the holes might be farther apart than the manufactured board, and therefore make the entire 81 hole board larger. And I don't know if this would impact your ability to "scoop" up the beads into the tube. One of the things T loves so much is to run his fingers and the tube along the board and just "scoop" all the beads in one motion. It also makes it a lot easier to get everything back in the tubes.

      So, on to the next thing...beads. The beads I use are spherical. The are exactly like the beads in our large bead frame. This aids in the scooping, and the staying in place in those little depressions, and of course rolling away from you every chance they get. I'd take a look at Fire Mountain Gems for beads in what ever size and color you need.
      http://www.firemountaingems.com/itemdetails/H202444PB

      http://www.firemountaingems.com/itemdetails/H206942PB

      http://www.firemountaingems.com/itemdetails/H202443PB
      These are Wonder beads, and they are acrylic, in blue, rose, and medium green, they are in 8mm round (and available in 6mm), they are sold in a 16" strand, which is about 50 beads, and is $3.12 per strand. There are more options on this site, and from I see their pony beads are round too. Mine are not, they are flat on the sides like tires.They have a ton of other beads, and you can get them to send you a catalogue if you'd like...I think shipping from them is $5 flat, and I found this company way back while planning a birthday party for my daughter.

      As for the rack, I think this picture is a pretty good version, though way expensive, of the foam rack MBT was talking about...
      foamtest tube rack for 10mm tubes
      http://www.amazon.com/Thomas-945271-Foam-Test-Tubes/dp/B006H903J6

      MBT: how did your friend color code her racks? The only other way I'd do this is to drill again holes in wood pieces and then paint the wood. But again, I like power tools.


      need to do this comment in two segments...blogger doesn't want more than 4,096 characters...

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    4. Okay, we're back...
      And as for the test tubes, my set is 1cm wide and 8.5cm tall. The beads that came with the set are I believe 7mm. Like MBT said, choose the beads, and then choose the tubes. The diameter needs to be right of course so that the beads fit in, and aren't likely to get stuck, but also it must be narrow enough that the beads stack well. Also, the length of the tube matters for the same reason MBT said. We teach the child to count by 2s as they fill the tube, but it is also nice to see that when the tube contains 10 beads the tube looks "full." Oh, also think about how large your child's hands are. These materials may seem tiny to us, but they may be just the right size to the child.

      This is what I found on Amazon...
      90 Test tubes, Karter Scientific 207D313X100mm clear placti test tube set, will not need caps nor rack
      http://www.amazon.com/90-Tube-13x100mm-Plastic-Scientific/dp/B00CSWFMOC/ref=sr_1_2?s=industrial&ie=UTF8&qid=1391950738&sr=1-2&keywords=test+tube+13X100mm+plastic

      25 pk plastic test tubes w/caps SEOH
      http://www.amazon.com/SEOH-100mm-Plastic-Test-Tubes/dp/B002JA5NMY/ref=sr_1_1?s=industrial&ie=UTF8&qid=1391950738&sr=1-1&keywords=test+tube+13X100mm+plastic

      About the pegs, I have gotten a lot of things from Casey's Wood, which is located in Maine and they have a "tot-peg" that looks pretty similar...I don't know about their shipping cost to you, and you may very well be able to get these from your craft store, but these seemed to be about right:
      Tot Peg
      http://www.caseyswood.com/shoppingcart/zen-cart/index.php?main_page=product_info&cPath=294_46&products_id=378

      They are 15 cents each.

      And lastly the cups...a paper towel tube, or toilet paper tube, cut to size and given a bottom could be the right size. These also need to be color coded. I was in the party store a lot this month already, so I think I remember finding small cups/dishes for hors d'oeuvre that also could be colored coded. Maybe the dollar store would have something like this too. You'd need 7.

      Anyway, I hope that some of this was helpful...Do let me know how it all works out, what you use, and how you like using it! I am working on a racks and tubes video, and kind of negotiating with my son about how much he wants to help out. (He has it in his head that "school" isn't "cool" because that is what Calvin says from Calvin and Hobbes. Gotta censor around here a little more. :) )

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  4. This talk of making the racks and tubes. I am VERY economical and I tried so hard to get myself to make this material. In the end, I decided it was worth (for me) the $75 to buy the whole things from IFIT. Too many pieces to coordinate, cut, sand, drill - and I had SO many other things to do at the time.
    I used to have a $5 per month Montessori materials budget - I kid you not. If it could made with food products (or packaging from food products) - it was (we had food stamps at the time).

    Everyone who makes their own: you are very brave and you have ALL my respect!

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  5. I LOVE your posts!
    (Gushing done - for now ;) )

    My son, at age 9, still likes to get out his toddler placemats for the sheer fun of it - then go digging in the cupboard for the dishes I used to make them - just the same as you did, except I had to go over my lines with a paint marker after the fact to keep them from fading too fast. I had some wood-handled cutlery picked up at Goodwill that had a small mouth-part on the spoon and fork (perfect for toddlers but not too small for most adults when needed) and used the small plates from our dishes set. Only the glass tumblers we had back then have been replaced with mugs (I am the only one who breaks glasses in our home - he has only broken one, which was just a couple of months back and had nothing to do with eating or being at the table!).

    Movable alphabets: when the child is writing that much, is when you want to move to the tiled movable alphabets - you can fit more letters into one compartment. Some places call them "small movable alphabet". I have a photo of ours here:
    http://montessoritrails.blogspot.com/2012/03/movable-alphabet-in-our-home.html
    (ours are now entirely separated by color - for use in other presentations/work ----- I printed ours out (shared the file on KotU), using red and blue in the first box for our first work; transitioning to separating into a blue box, a red box and a black box for word study, phonograms, etc. ---- later, with the co-op, I had to go back and re-organize so I now have both styles: red/blue (like the wooden movable alphabet) and the 3 colors separated for older child work)

    For the stamp game paper, you could also use colored pencils to note the categories in their proper colors (saving some money on colored ink! AND helping the abstraction portion.

    I just love how Montessori breaks it all down into tiny baby steps - and then, yes, we can skip the steps the child truly gets and move right along - no bogging down in details they don't need, but plenty of opportunity to focus on one new skill at a time.

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    1. Just a test to see if I can reply to you...this is weird. Blogger makes me go bonkers sometimes.

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    2. okay, when I am leaving a silly test comment it publishes just FINE!! but when I need to post something specific, NOOO. goodness.

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  6. Thank you all for all the great information! This is definitely something I am going to be thinking on a LOT and making the decision! Abbie - you are right. There is a great deal of sliding. I might have to break down and buy the boards. We have used the multiplication board in the same way, with just the printed, laminated sheet itself, which saves space when you don't have much, because it can fit in one color-coded folder along with all the charts, but does take some sliding around and did get frustrating sometimes!

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  7. Ugh. The comment form is being weird. I don't think this comment is going to next like it should. Sorry.

    Abbie: Yes, her racks were like the one in the link you posted, but of course cut to be just the size needed, and of course, homemade. She turned them upside down and gave them a quick, thin coat of spray paint. She didn't bother to spray enough to get a "solid" color, just enough so you knew the category.

    Jessica: Good point. I must say that my friend made hers about 8-10 years ago. I'm sure there wasn't a $75 dollar option available at that time. There is so much more available now. By the time you buy materials you are going to be pretty close to $75.

    Movable Alphabet: Lots of styles of small movable alphabets available free here: http://jmjpublishing.com/hope4melanguage.html

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    1. MBT I feel like we just talked about the printed alphabet... :) your boys are too quick and didn't want to get bogged down in the "moveable" part of it all. :) Thanks for the link. I already made a print - printed alphabet, so I think I am going to just go back and make a "double" batch of cursive printed alphabet and stick it in the same wooden box.

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    2. S did it again today, she ran out of "l" so there I was, stuck making more out of paper for her. That was after she said she didn't want to write anything today.

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  8. Okay, Now Blogger will not let me REPLY? Is it because I fixed the picture rotation problem and now it is trying to get back at me?

    ANYWAY, Jessica:
    That is too funny! I wonder if D will be doing the same. I am thinking of your son, because I hear "legos" upstairs right now!

    I forgot to add, but you might have picked it up from the photos, that the dish is a typical "salad-plate" not a dinner plate, and the cup is a smaller low-ball, and the flat-ware is child-sized. The place mat had to be long enough and roomy enough to contain all the items with lines around them, so that is the only thing that is "adult-sized." Is this the way the child would do it in a traditional classroom--with child-sized dish-ware?

    Ah, thanks for the printer-ink tip. Someone should compile a way to save colored printer ink while making Montessori materials. S beat me to it though, and colored in the black-and-white print out!

    Are you feeling better now that your subbing has ended?

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    1. I meant to say before - even Nienhuis maps gets screwy and warped. It's the wood - and humidity/dryness. And it's frustrating. :) The knobs come off all companies materials at one time or another, too. Probably more often with some than others.


      I'm having trouble with replying too (so I'm typing this up in my e-mail and I'll try later to post ;) )

      Toddler-dishes - yep, schools use the smaller versions of adult dishes (tumblers, salad plates, etc.) - way more affordable and appropriate than making "child-size" dishes. I remember one teacher saying that "child-size" (appropriate for the children) does not always have to be "child-ish" (cheap junk). She had a point :)

      For the movable alphabet - one thing I have seen in schools is that the children will borrow from their previous words, not leaving very long passages or lists on their mats. But the child does this once or twice, the teacher notices, and they are introduced to the letters on the tiles for future use. Or the children will borrow from another movable alphabet box - but this causes problems all its own - bad idea ;) (I spent a month dealing the "bad" portion of that "idea" ;) )

      I AM feeling better, but still coughing some stuff out. Thank you for asking :)

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  9. Abbie! Sorry if I'm repeating myself. I don't know where my first post went. Anyhow, I just wanted to tell you that I enjoyed meeting you at Jennifer's home. I got fired up after talking with you and I love your blog. Thank you for inspiring others with your dedication to Montessori education. Blessings. Carolina

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