Monday, the kids went with my husband to see a movie and I stayed home and worked on making pin maps. Thank you Jessica, from Keys of the Universe, for suggesting I don't wear myself out on this project AFTER I just made the mid-west look like it has a case of the measles.
Just figured out a new way to rotate pictures in Blogger. Well, rotate them in Picasa, not Blogger. Go here for more info. Half of this post wanted to load sideways.
Math: Addition Snake Game, Large Bead Frame double digit multiplication
Language: Moveable Alphabet, Advanced Grammar
Tuesday, I did a little tiny bit of school with each child...
S and I did the Addition Snake Game.
The Addition Snake game is a work the child will typically do after finishing golden bead work and stamp game work. The aim of this work is to help the child begin to memorize all single digit combinations that make 10.
There are three boxes of beads in this set. One box holds colored beads, one box holds the black and white bead stair, and the third box holds golden 10 bead bars.
In a first presentation (this isn't S's first lesson) the guide would set up a "snake" or trail of colored bead bars that flows from the left to the right. Initially I would place pairs of bead bars so that every two bars would equal ten: for example, 9 and then 1, 7 and then 3, 4 and then 6. After making a medium sized snake, we begin to count each bead from the left of the snake to the right.
We'd count 1, 2, 3...8, 9, 10 and then stop. If we came to the end of a bead bar, we'd put the bead bars we counted in a small cup to the right of our work area, and replace them with a single golden bead 10-bar. In later lessons when the pairs of beads don't always equal ten, the child may stop counting to 10 in the middle of a bead bar. In that case, when the child reaches 10, he/she would stop counting and place a golden bead 10-bar parallel to the snake beads that were already counted. The child would resume counting the rest of the beads in that last bead bar, like say, 1, 2, 3, 4. The child would then select a 4-bead black bead bar from the pyramid to his/her left and move this to the right of the golden bead 10-bar as a "place holder" before discarding the counted color bead bars in the cup to the right of the work space. The child would re-arrange the snake to make the length continuous, if needed, and then resume counting each bead, starting with the black beads.
S loves that the snake will turn golden.
To verify that all the golden beads match all the colored beads, we do a match-up. The child will pair up the colored bead bars into sets that equal ten, exchanging for smaller colored bead bars when necessary. The child may need a 2-bead bar to go with an 8-bead bar to make an even 10. If the child doesn't already have a 2-bead bar, he/she may exchange a 4-bead bar for two 2-bead bars to acquire the necessary bead bar to complete the even 10. If all goes well, the golden beads, and any left-over black bead bars (or partial 10s) will match the number of colored beads in the discard cup.
After the initial presentation the child will be able to make his/her own snakes and count and verify. There are other Addition Snake Game lessons that are presented later in the memorization of math facts sequence. MBT has a great post with a video about this here.
T and I started long multiplication with the Large Bead Frame. I've been dragging my feet on this work. Partially because he had been so caught up in the long division with racks and tubes, and partially because I needed to get the baby steps straight in my head. I didn't learn long multiplication this way, but now that we've done it a few times, long multiplication makes more sense then ever.
T has already done some checkerboard multiplication (which was a little out of order?), and used the Long Bead Frame (LBF) for addition and subtraction problems. We've also done some of the two digit multiplication with the golden beads from the Cultivating Dharma albums. So before we started T was already familiar with the hierarchies and the LBF and with commutative and distributive multiplication with double digits.
I followed the Keys of The Universe album lesson for this first presentation. We started out with a two digit multiplier and a four digit multiplicand: 7,346 x 43 =. T transcribed the problem on the left hand side of our LBF paper. (I purchased ours from Montessori Outlet.) Then we set to work analyzing what we were multiplying out. I asked T to envision the number cards, and asked him which number cards we would use to compose 43. He said, "40" and "3." I told him we first were going to multiply our multiplicand by "3" and then by "40."
On the right side of our paper we wrote down each "problem." 6x3, 40x3, 300x3, and 7,000x3. Then 6x40, 40x40, 300x40, and 7,000x40. Afterward, we discussed how difficult it would be to count out 40 6-bead bars, or 40 groups of 4-ten-bars. I suggested we do something a little different and "transfer" the ten. 6x40 can also be expressed 60x4. Wouldn't it be easier to count out 4 groups of 6-tens bars? So when we multiply 6 by 10, we add a zero, and this is what we did for each part of our multiplicand thus making our second round of problems 60x4, 400x4, 3,000x4, and 70,000x4. We crossed out our previous problems with the 40 multiplier, and then we were ready to multiply it all out on the LBF.
T made three groups of 6 units, or six taken three times (6x3). He figured out that this was 18 units, or 1 ten and 8 units. So we recorded this as our first partial product right under our problem on the left side of our paper. T put an 8 in the units column, and a tiny 1 in the tens column. Then we multiplied through again (40x3) making three groups of 40 (or 4 tens) which was 12 tens, or 1 hundred, and 2 tens. (Here we were leaving the beads from our first multiplication problem and just adding the beads from our second problem.) So T noted 2 in the tens column and added this to his previous 1 to make 3-tens and he noted a very small 1 in the hundreds column. And then we multiplied through the remaining problems. (The problems with the multiplier of 4, will compose the second partial product and this should be written underneath the first partial product.)
After we found both partial products, T added them together to find our final product and the answer to the problem.
After doing the Addition Snake Game with S and the LBF with T, D and I did some practical life making cupcakes and then cleaned up afterward.
And then clowned around a little bit.
This was D's version of cleaning up.
On Wednesday, we finally got back into the classroom and did some pretty worthwhile stuff.
T got back to it doing Large Bead Frame multiplication. This time, he ended up doing a bit of it in his head. He still prefers to have the tens "list" so he can "see" what to do with the multipler and the multiplicand. We are also working on where to "carry" and how to notate things like "21-hundreds." It would be 2-thousands and 1-hundred. Sometimes he gets this on his own and sometimes he needs a reminder.
I told him that he was "cracking the code" by solving the problem and this made him laugh. He said that after he cracked 10 codes he should get a treasure, i.e. get a Lego set. I told him that Mama would have to be able to afford the treasure, for him to get a treasure, but that cracking the codes could get him closer to his birthday.
S is reminding Mama again that she needs the tiled alphabet. I have one already formatted to fit in the box we have on hand, it is just the cutting and laminating that I dread.
Again, we are going with the Dwyer key spellings here for "ou" and "ee."
After the Large Bead Frame, T got into the grammar again.
At first, we were discussing "cheese stick" and how interesting it is that although usually "cheese" and "stick" are used as nouns, in this case "cheese"serves a different function. He thought that was pretty cool that the words could change like that. We also discussed where we place adjectives with respect to nouns. He thought that "car-red" didn't sound right and that "red-car" did sound right. I said usually our adjectives come before the noun they describe, and that in this case, because "cheese" came before "stick" we can deduce that "cheese" is describing what kind of "stick" we have.
Then T came up with this sentence and began assigning grammar symbols to each word. (Translation: I want to see a big hairy tarantula.) He was zipping along (from the end of the sentence to the beginning) until he came to "want to see." When he didn't know which kind of verbs they were he got very excited and said, "maybe they are some of those new ones!!" So we started looking up verbs in our grammar book and we found a "test" for transitive and intransitive verbs. (I liked this test, since other comparisons we looked at included words like "direct object" which we haven't covered yet.)
The test is: if the verb can answer "whom" or "what" then the verb is transitive, or a regular verb. If the verb cannot answer those questions, then the verb is intransitive.
In this case there is no "whom or "what" for the verb want. He "wants to see," but there is no what, nor any whom. So T's verb was intransitive and he got to use a new Montessori grammar symbol. He was so very excited.
Disclaimer: I am no grammarian. PLEASE, PLEASE, PLEASE, if you are a better grammarian than I and know that my explanations are a bunch of bunk, PLEASE leave a comment. You will NOT be hurting my feelings. BUT if you are going to make a correction, would you please also provide an explanation? Thank you!
All this talk about transitive and intransitive, and auxiliary and linking (from last week) got T on a roll, and he wanted to write down ALL the advanced grammar symbols.
I haven't read all the grammar lessons in my Keys of the Universe and Cultivating Dharma albums but as far as I can tell, neither source gives much information about how and when to present these advanced grammar symbols.
I think I've read that they are generally introduced as a means of exploration and are presented as they come about in the classroom. I am glad that T is leading the way along this trail. I don't know that I could have initiated this since I don't know a lot about grammar. If you do know anything about these topics, would you leave a comment about how you've introduced these "advanced" grammar symbols to your homeschooled child or elementary classroom? Thanks!
T: "Mommy, I can't wait to learn all the rest of these grammar symbols!"
Me: *thinking* "Goodness, I am going to need to read up a little bit more!"