Wednesday, April 29, 2015

Feeling SLOW

This time I am feeling slow. I don't know why, I just am. This too shall pass and I'll return to my normal up at the crack of dawn, energetic self again.
Here we have some renewed interest in the metal insets!! Hooray!! D was so very uninterested in this material. But he needed help handwriting. So, how to bridge that gap....?
Lately, he's been asking for a lot of paper mazes and a lot of coloring pages. I think that this pencil practice has been very helpful.
Slowing down was also extremely helpful. When he goes around the inset like Sonic Dash, he makes mistakes and then he gets frustrated. When he proceeds slowly and takes his time, he traces beautifully, gracefully and easily. I think that this increased success really helped make this material interesting to him again.
He has no interest in creating more than one shape per piece of paper, and no interest in drawing inside the forms he traces. We are holding off on holding the inset and tracing around it until the cast comes off. For now, he is sticking to tracing the inside of the frame.
I also took the hack saw to his colored pencils. As you best see in this shot, his PrismaColor Premier pencils are all about half the size you'd find in the store. I "recycled" a used set that was all different lengths and cut them each down to about 4" with the saw and then stuck them in the pencil sharpener. I suppose I could have cut a regular set in half, and used each half set separately. But by using hand-me-down pencils I only wasted less than an inch off each pencil. You can burn through that much pencil just by over sharpening. D seems to like working with his shortened pencils and he naturally uses the proper rounded hand pencil grip each time.
I wrote more about this material here, and here.
D really got going this week. He is getting better at matching and grading the sound cylinders. I wrote more about this work here.
More knobless cylinders. I wrote more about this work here.
After he constructed the binomial cube outside the box, he told me that the work was too easy. I wrote about this work here.
I think this is a shot of everyone looking outside at the two mocking birds in the tree. 
S is still working on the multiplication finger charts. I am getting ready to introduce the Elementary math very soon.
And T is back to racks and tubes. This work makes me remember that he still needs a lot of work with his math facts. Ugh. This first problem, he even organized the boards backward, the blue-tens board should be on the left and the green-unit board on the right, but he got the divisor skittles in the right paces. T did a fair amount of this work last year, so this year we are reviewing and really working toward abstraction. If you have the albums, you know that the problem he is working above is about half way through the sequence. He is writing the quotient at the top of the problem. He is writing down the quantity that he means to distribute to the divisor skittles on the boards. He counts up the quantity that he does distribute, subtracts that from what he had to give out and finds his partial remainder. This partial remainder he finds on paper magically is the same as the bead amount that remains in the left-over cup. Then he clears the boards of beads and on paper brings down the next category of beads. Then he starts to distribute the new quantity among the divisor skittles and repeats the process.

Here we are working with a two digit divisor to keep it relatively simple. As long as he needs the practice, he will work though three and four digit divisors, and divisors with zeros. Finally, we will be estimating the quotient by category first and then distributing this many times. This last step is essentially how I was taught to do long division when I was in school. And I am hoping that we can get to this point before T tires of the beads. The albums say, and I've read elsewhere, children begin to not want to manipulate all the beads and small objects starting around 8 years old. T is almost 9. They were flying all over yesterday. FLYING and ROLLING.

S is journaling here.
I just finished making 30+ little geometry definition booklets. I printed them back to back, cut them out, laminated each page, and spiral bound them. 

We are way behind in geometry in my mind, which is somewhat interesting considering that the kiddos cheer each time I mention geometry. Here we are working on identifying triangles by their angles and by their sides. We also did a bit of working notebook follow-up drawing and labeling different kinds of triangles. 
The KotU albums tell you what definitions to include in your booklets, but the wording of each definition and each illustration is up to the author. I wasn't sure exactly what to put in the booklets, but I felt that for my comfort and for my children I'd err on the more technical side. I also decided to include a few mathematical notation concepts as well. Here, the single hash marks on each of the triangle's sides indicates that they are all equal in length.
The next day, we continued exploring the angles and sides of triangles. T determined that this triangle is an acute, scalene triangle; meaning that none of the angles measure more than 90 degrees and all the sides are different lengths. 
To help drive home the angle and side nomenclature we played the detective triangle game. I don't remember where I read this in the albums...but you can find a description of the lesson here. 

I also didn't get a lot of photos of our work since it all went kind of quickly and the lesson was upside down from my point of view.

Basically, we have a wooden box that contains a set of 63 plastic triangles that represent all the different types. Each type is in three different colors: red, blue and yellow, and three different sizes, small, medium and large. There are right, acute, and obtuse triangles, as well as isosceles, equilateral, and scalene triangles.

I first wrote on a single slip of paper "the triangle" and asked the children to give me what is written on the paper. Both T and S sighed, and rolled their eyes saying that they were going to fall for this, and asked me immediately "which triangle" and for more information about which triangle I wanted. 

So I took another slip of paper, wrote down the word "large," and placed it in front of "the triangle." T said "large the triangle" didn't make sense. S tried to rearrange it and I handed her a scissors. She cut "the triangle" into two single-word parts and inserted the slip of paper that said "large" in between. Then they sorted out all of the large triangles and put all of the medium and small ones back in the wooden box. And then they asked for more information about the triangle I wanted.

So, I wrote down "yellow" on a slip of paper, and placed this in front of "the large triangle" to read "yellow the large triangle." They giggled and rearranged the phrase. I asked them why they were switching around the slips of paper and they said the way I had placed them didn't make sense so they needed to fix it. They culled all of the yellow large triangles and then asked for more information. We went through the same process with "obtuse" and "scalene" and they finally found the triangle I wanted. (I actually hadn't planned to ask for a large yellow obtuse scalene triangle, but that was how it turned out.)
Then we got out our grammar symbols and labeled the parts of speech. T thought it was so funny that there were so many adjectives. I think we played this game a couple more times before packing up the materials. (I am pretty satisfied with our set of triangles. They are from Montessori Outlet.)
D really, really, REALLY, wants to do the spindles lesson. I told him that he needed to work with his number rods and cards before we could do the spindles lesson. 

I am having a challenging time assessing when to move on with him. He wants to charge on through without demonstrating anything near mastery with the prerequisite equipment. I don't want to squash enthusiasm and I do want to follow the child. I just don't want to make future lessons more difficult for him because he thinks we are moving backward when we revisit a prior work and therefore refuses to engage in the work that he actually needs to gain the basic skills he will need later on.
This lesson is called number rods and cards, and it comes after the sandpaper numerals. This work helps the child associate the quantities 1-10 with their written numeric symbols. Up until now, the child has worked with the quantity and the symbol separately. 

There are a bunch of exercises in this work sequence, but we just did the first presentation. The rods were laid out on the mat, or two mats, in a random order. Typically, they are orientated with their first red band to the left. D kind of was picking stuff up and moving it around, so some of his rods ended up perpendicular. Then I handed him a random card with a number on it and he was to assign this symbol to the corresponding rod. I'd say, "this is how we write 8, can you place this 8 next to the rod of 8?" And he would. He didn't make any mistakes assigning numeral names to each rod. He also verified each rod's length by counting its bands of color before he placed the numeral name card beside the rod.

After he had finished the first time, I asked for the cards back and we repeated the lesson. He did mention to me that this was a "hard work."
T made this rod formation. The next exercise in the sequence is to show the card with the number and fetch the corresponding rod that is set on the mat in a different part of the room.

We have family coming in from out of town, so we'll be away from the classroom and the computer for a bit. Hope you will be having a nice time in between.


  1. I left a comment on your last post but it's missing now. If you deleted it for me because I said something I shouldn't have, thank you.

    I'll be interested to see what you mean by "estimating the quotient by category." You would think that would be all the information I would need, but I can't picture what you are doing. Your paragraph makes it sound like T is writing down the quantity he will distribute to the divisor BEFORE he has distributed them? When Kal-El did this he distributed the beads first and then recorded what he distributed by category. Am I interpreting you correctly? Now he takes turns. One day he does the equation completely abstractly with no materials. The next day he does it with the racks and tubes as I described. Then the next day he's back to abstract. When he does this abstractly he "estimates" the number he will be placing in the quotient and does the multiplication on his paper to know what number to write down as shared out. Is T doing that in his head? Is that what you meant? Maybe I'm underestimating him, but I think Kal-el could only do that if there were no carrying.

    Me Too is just about finished with one-digit divisors (primary version of racks and tubes) recording only the quotient. He still messes up the procedure for setting everything up at the start so we are mainly doing those equations until he masters the procedure, then we'll move on to two-digit divisors.

    1. SLOW at blogging, and SLOW at replying. I didn't ever see a last comment sorry!! It got eaten up by the blog monster that likes to frustrate us so and eat our comments before they can ever be published to the world.

      Estimating quotient by category: T isn't yet doing what you describe above. He writes down the number of beads he has ready to distribute. (like these are the partial remainders) Then he distributes the beads, sees how many he's put down on the boards, and subtracts what he actually put down from what he had available to put down and finds his next partial remainder. He isn't yet estimating how many distributions he can make.

      I believe estimating the quotient is one of the last steps in this process is...oh, we have this many beads (6 tens and 2 units), I need to distribute this many at a time (say 3 tens and 1 unit), I estimate that I can make two distributions. I write down that one unit skittle will receive two unit beads in the quotient space on my problem page. Then I make two distributions to see if my estimate was indeed correct.

      I guess some would do some estimating multiplication work in the head, like, okay, 6 ten beads, need to put down three at a time, let's see, 3X2 is six, maybe I can put down two ten beads for each tens skittle. Now, let's see if I can put down two unit bead distributions for each unit skittle. The child may also know that okay, I have 6 ten beads, one distribution would leave me 3 ten beads, let's see if I can make another distribution. Or, maybe the child would actually need to write all that estimating multiplication down on paper. But I am assuming it is likely that doing that estimating on paper isn't necessary if the child has their math facts down, and they have been doing the category multiplication with carrying in their head successfully for a while. I am guessing though, we haven't gotten there yet.

      It sounds like Kal-El is just abstracting and that you are making him do the bead part. :) I think that he'd be able to do the "estimating" in his head? He seems to have his math facts down pretty pat. Have you started category multiplication yet? :)

  2. The detective adjective triangle game? That is in the primary album - loads of fun with ALL ages ;)

    Math work - he can do 1-3 or so things at a time (in varying stages) in the numbers 1-9 section - to shake things up a bit. When you do something that feels like going backward, you can remind him, "Oh, but there is MORE!"

    So where are the pictures of the birds they were watching? ;)

    1. Yes, Detective adjective triangle game. Sorry I think I mangled the name. We just didn't get to adjectives in primary.

      Thank you for the reassurance. D is just so ready to charge ahead.

      The birds. :) Didn't get a shot of the them. They were very cute. But they probably would have been blurry in a photo since my low-light lens isn't a zoom and I would have been shooting through bug screens. :)