Me Too has been continuing his squaring work. This is an on-paper extension of the work he did with the short chains and squares last week.
I don't know if he just likes this work a lot or just likes the fact that he is a presentation or two ahead of his brother, but he has been requesting presentations in this thread. Tuesday we started the notation of cubes.
He also likes me to "surprise" him with work that he can do without including his brother. My response to a recent request was to throw some music notation work at him.
He also completed the next level, some three-part cards. Me Too likes to take his own pictures of his work. He posed Spotty with his cards and took this picture. Spotty has been doing a lot of work with Me Too lately.
Kal-El decided he didn't want to be left behind and tackled some more of the squaring sequence at the end of this week.
The boys learned 90% of their facts through the Montessori memorization sequence. However, they were slow or stuck when 7's, 8's, and 9's were in combination. The boys and I have been reviewing the multiplication facts for a different tricky number each month. In September we chose eights. In October we chose sevens. That actually solved our problem because if they needed to multiply by nine they would just use the commutative property and do the equation the other way. However, for November we decided to work on nines anyway. We are using this song to help with the memorization.
For one of his "kid's choice" works this week, Kal-El got it in his head to write out every possible equation that he could think of that results in nine.
I plan to have Kal-El do more work yet with the checkerboard and flat bead frame. However, he watched how I used long multiplication on paper to check his work when he lost his place on the checkerboard a few times. That was all he needed to make the leap to paper. I never thought my child's first long multiplication completely on paper would have a multiplicand into the millions and a multiplier into the thousands, but it did. Yeah Montessori!
Here is the very first long-multiplication equation he ever did completely on paper (last week). He "invented" the equation himself and only came up to me to ask one small question about how to "shift all the numbers for the zeroes" when he came to his first partial product (Because on the checkerboard you multiply THEN add your zero. He realized he had a problem after he wrote down his first partial product and didn't know how to shift the numbers when the paper wouldn't slide like on the flat bead frame.)
I think he did all the carrying in his head for the equation above. Below you can see that I showed him the more traditional way to notate what he needs to carry.
However, he refuses to write the carried numbers SMALL. You can see below what a mess that makes. However, he is otherwise doing things correctly.
Me Too has been working on R-controlled vowels. We use the movable alphabet a lot for that work.
We have been working, still, in the KotU geography album, Waseca Biomes curriculm, and BFSU. I have been coordinating my favorite lessons from all three into work the past week on the effects of the tilt of the Earth's axis. That means hours of daylight, the arctic and antarctic circles, By "favorite" that means we've been basically doing everything straight out of the KotU album. The best lessons on these topics in the BFSU are so almost word for word from the Montessori albums that I have to believe that they were Montessori-inspired. I spent a lot of time spinning globes with flashlights pointing at them the past few weeks.
We are getting a lot of use out of our geography impressionistic charts from ETC.
Here Me Too is working on one of the last few lessons in All About Spelling, vol 1.
He was writing words as I dictated them to him. The word "shrunk" inspired him to write "Papa shrunk." Hi Papa! We are thinking of you! As you can see, if I notice that he writes a letter backwards or with the improper strokes I demonstrate how to do it correctly and have him write that letter five times. This day we had trouble with k's and b's. He has done all of the Montessori writing work from birth (except that we didn't start with cursive). He has done HWT level K twice. He has done HWT grade one twice. He is not ready for HWT grade two. He is too old for me to pull off changing the cover on the grade one book and tricking him into doing it a third time. So, I bought him Zaner Bloser levels K and Grade One (and artfully covered any references to grade level with dog stickers). He can see and understand what he's doing wrong. After he is written a page I can ask "do you see any letters you wrote backwards" and he can circle them all. It's not just reversals though. He confuses lowercase and capitals (while writing, he can identify them just fine). He uses completely invented strokes sometimes. Oh well. Let's just be thankful he's not in second grade.
Kal-El is interested in astronomy again. One of his many "kids choice" moments this week involved drawing the solar system on our new extra whiteboard. I wish I had snapped a photo later, after he had added the asteroid belt in red. Long story short, Kal-El likes to draw on the white board we use for All About Spelling. Using the whiteboard for AAS inadvertently erases anything drawn on it. I was cleaning our Montessori storage space recently and found an extra white board. Problem solved, and the new white board is seeing daily use.
Well... some uses of the white board are more productive than others.
Kal-El discovered this little surprise from the science supply store tucked in the drawers this week and we all enjoyed some freeze-dried ice cream.
One of Me Too's many "kid's choice" works this week was to pick a card out of the bin of geometry command/task cards. You can see it on the far left in the photo above (there is a triangle on top of it). This card asked him to trace all of the triangles in the geometric cabinet and then use the angle measure from the box of geometric sticks to identify all of the angles of each triangle.
He was very careful not to miss any angles and checked them off as he went along.
Me Too has been working with the large bead frame. This week he started doing actual equations with the apparatus. We are starting with multiplication equations with multiplicands up to seven digits and multipliers of one digit.
When we reach multiplication on the large bead frame I always (well, twice, once with each kid) feel like there is a step missing in the Montessori math sequence somewhere. Me Too knows his facts so in the equation above he knew when he multiplied 9000 by six that his answer was "54 thousand." But, then he starts to move the thousands beads FIFTY-FOUR times! What works is if I write "54" down in the margin, ask him how many zeroes to add (3), then he SEES that he needs to move five ten-thousand beads and four thousand beads. It just seems to me that there should be a work that teaches the child who knows his facts to transfer the extra digits of a product to the appropriate categories without having to write it down in the margin. You can see how full my margin became and this was only an equation with a one-digit multiplier. When Kal-El was doing equations with larger multipliers we needed scrap paper just for that. The checkerboard does a better job of teaching this actually (I realize as I write this). Maybe we need to bump on over to the checkerboard for a little while. I am open to suggestions.
I mean, who doesn't love meerkats?
Kal-El's cursive work has inspired Me Too to use some of the more complicated patterns for decorating between his math equations. He gets ideas from a little book I put together and bound. It has a few pages of "equation decorating" patterns and a ton of metal inset design suggestions. The boys also love to invent their own. However, sometimes without a classroom full of kids to inspire ideas, you have to put some in a book so they don't do the same things over and over.
Kal-El pulled out the handmade book from our long ago continent swap (the gift that keeps on giving!). He really enjoyed reading every word and had a lot of questions. It was an excellent example of Montessori comic curriculum at work. He "thought" he was studying geography, but was seriously practicing reading. He was super excited to read about the "Capricorn Caves" again realizing after our lessons the past few weeks that it was likely called that due to the location of the Tropic of Capricorn. The geography lessons the past few weeks gave him a new appreciation of how and why the seasons were backwards for the child in the book living in Australia. He enjoyed it when the book mentioned it being December 1st, near the start of their summer, and that the temperature by 11:00 a.m. was 36 degrees Celsius. I wrote out the two equations for converting from Celsius to Fahrenheit on and index card (to be stored in our measurement drawer later) and helped him convert that temperature to Fahrenheit. He was able to do the multiplication and addition on paper but was a bit irked that he had to do the division on the test tubes. We'll all be glad when he's fully abstracting!
Me Too is still working on the division bead board. He is almost done. Er, either he or his dogs are. Me Too clearly had the camera again.
See? Only 21 more quotients to work through.
He will be SO glad when he finishes the division bead board because then I will let him start racks and tubes. He is SO OVER the stamp game. I have to agree. Exchanging all those stamps is tedious.
As you can see, we don't even have enough stamps.
Kal-El is working with two-digit divisors on the racks and tubes. He is not happy that Me Too is going to start that material before he is finished, but he is just going to have to be tough. I think he will comfortably be into three-digit divisors when Me Too starts so that should help him feel like there is a "buffer" of several levels between them.
Putting all of those beads on the board might be just about as tedious as the stamp game, but exchanging sure is easier.
I noticed this week that we are not remembering to work on things in the multiples/divisibility thread (part of the numeration thread, I guess). I will have to find a way to put that onto our work plans. It is a great time for the boys to be working on that because they will be able to make us of and practice all of those facts that they know and love.
We are having a great time together and are so happy to homeschool.