Wednesday, May 13, 2015

Squaring and Cubing: Decanomial

Me Too is on track to finishing everything I had planned for him this year right on schedule.  He has been working so productively during our work sessions he had time to receive some math presentations before Kal-El has.  Kal-El will get to this soon, but in the meantime Me Too is the first to tackle the decanomial sequence in the "Introduction to Squares and Cubes" (Cultivating Dharma) or "Squares and Cubes of Numbers" (KotU) section of the albums.   MRD has this in its own chapter called "The Decanomial."

There are many "steps" or "levels" or layers to this work and each of the three albums I referenced do these things in a slightly different way and slightly different order.  I read them all, which was handy because everybody had different pictures, and did what made the most theoretical sense to me.  For another perspective, my friend Abbie has posted some of her son's work with the decanomial and in this post she links to a video series that shows a sequence of work for the decanomial.  The sequence they use is a little different than all of the albums I referenced as well.

One major difference between MRD and most of the others is that MRD has the child set up the decanomial from scratch several times, each time a different way.  In reality, in a classroom that is probably how it has to work.  Even if several other kids didn't also need the decanomial that day, it is unlikely that it would survive set up on the floor for five days like ours did (we did this on a Wednesday, Thursday and Monday).  If your child doesn't know their times tables and needs the extra practice, that might be the way to go.  My kids know theirs and would have gone bonkers setting this thing up five times.  We followed the sequence in the KotU album which has you set up the square once and then transform it several times.

First Me Too built the decanomial vertically one factor at a time.  1 taken 1 time, 1 taken 2 times, 1 taken 3 times, etc.,  Then, 2 taken 1 time, two taken two times, two taken three times.  This is the same as MRD step one.  Oddly, MRD has the child set up the decanomial the next time in the same way, except horizontally (1 taken 1 time, 1 taken 2 times...). The red strip winds up along the top instead of down the left side.  As this is a square that seems silly.  If I wanted to have my child build the decanomial horizontally I think I would have them build it so it looks the same in the end, but is constructed using a different sequence of facts.  I would have them build the first horizontal row 1 taken 1 time, 2 taken 1 time, 3 taken 1 time,  taken 1 time, etc.,

After the square was built.

Next Me Too found all of the existing squares (1x1, 2x2, 3x3, etc.,) and replaced them with an actual bead square from the bead cabinet.  We did all of this the first day.

Next we transformed the square using the commutative property.  1 taken 2 times is two and 2 taken one time is also two.  So, we replace the two "ones" with a single 2-bar and then continued such replacements throughout the decanomial.  That ended our second day.

On our third day he combined groups of bars to find additional squares.  For example, he combined 9x1 and 9x8, 9x2 and 9x7, 9x3 and 9x6, 9x4 and 9x5 to make additional nine squares.  I noticed in the EdVid video the guide combines any bars she wanted breaking up groupings in the process.  For example, grabbing two 9-bars from the 5x9 and combining them with the 7x9 group to make a square.  I think that is pedagogically bad.  Combine existing rectangles with another existing rectangle to make a square.

This, by the way, is one of the few times in the elementary sequence when I have not had enough bead bars.  I was short eleven 9-bars even after borrowing every one from the negative snake game.  I threw our bead square on the photo copier and we cut out the rectangles we needed.  I was also short bead bars when we did some of the multiples work, particularly when showing multiples of two-digit numbers.  We borrowed squares to make that work.  I don't think I'll buy another decanomial box, but I'm putting it out there.

After we made all of the squares Me Too stacked them on the diagonal.

"false" squares

Next Me Too exchanged all of the "false" squares for the real ones from the bead cabinet.

And of course he stacked them.  That ended our third day.  We could continue on to the paper decanomial(s).  However, those are on the KotU scope and sequence for year two and Me Too has numeration work that is more pressing.  He has finished multiples, but I would like him to ideally cover factors before beginning the geometric decanomial.  Now Kal-El is taking a turn with the decanomial beads.  He does need to do the paper decanomial(s) this year.  I'll see what Me Too is up to when Kal-El is finished.  If you are doing the MRD sequence you can now do everything we just did but BACKWARDS.  Start with the cube, exchange each cube for squares, lay out the squares as they were before, exchange each square for the corresponding bars, etc.,  Again, I'll see what Me Too is up to.

I will switch to the MRD album to complete the decanomial sequence at this point.  Much of the potential work with the paper decanomial(s) is in an extensions list in the KotU albums. There is nothing wrong with that, but the MRD happens to have a sequence for the extensions and full presentations with pictures so I might try that.  The MRD album has pictures of EVERY step for most of what we did above.  I mean pages of laying out the decanomial each time with one picture per row.  This was handy when transforming the square using the commutative property.  KotU could have used a few more pictures of that transformation.  MRD somehow manage to NOT have a picture of the critical transformation where you combine the bead rectangles to make squares.  That was the one time I really wanted a picture.  KotU had one.  Yea!  In COLOR.  The MRD pictures are also in black and white which is not ideal for this work.  It took several re-readings to determine that their first and second layouts were technically the same except for stripe direction.  Sigh.

I have to make our paper decanomials now (equations on graph paper, algebraic equations on graph paper, products on white and yellow paper).  I am going to store these, or some of these, in our old sensorial decanomial box (Square of Pythagoras box) instead of in envelopes.   One question I have is whether I should make these on graph paper. OR, because we no longer need our sensorial decanomial, I could use my label maker and use black ink on clear labels and put the equations on the actual pieces of our sensorial decanomial.  I could do the numeric on one side and the algebraic on the other.  The benefit of the graph paper is that you can see the number.  However, Montessori kids are so attuned to the color coding that they can "see" the number on those too.  Anyone have an opinion?

Wednesday, April 29, 2015

History Question Charts in Action

storing Montessori charts

Our history question charts are getting so much steady use that they needed a new home.  Behind the red couch wasn't cutting it anymore.  This is one of those vinyl gutter shelves you see all over Pinterest.  No tutorial needed.  Once it occurs to you to buy a vinyl gutter it's pretty self-explanatory.  Except maybe the part where it is very hard to cut vinyl gutter with a hand saw at the hardware store.  If you are lucky the hardware store guy will feel sorry for you and come help hold the gutter so it doesn't move around so much while you cut.  If you are VERY lucky he will cheerlead for you, assuring you that cutting a vinyl gutter with a handsaw is very tricky and that it is not just you.  I was very glad he said that because I was blaming my arms.  The guy at the hardware store won't offer to cut it with his power saw for you because, as it turns out, vinyl gutters splinter all over when you cut them with a power saw. T hat's what happened to mine when I got home and tried to cut them with the power saw.  I was so happy that I had thought to get out the safety goggles and leave them perched on top of my head during this experience.  If you want a tutorial, this would be my tutorial:  Remember to slide your safety goggles down over your eyes before you start cutting.  I posted the details on how I made our History Questions charts themselves here.  The only change I would make would be to mount the charts on wood instead of foam board.  I didn't realize how heavily they would be used.  I will remount mine sometime this summer if I get the energy.

I found a spot for this over the bead cabinet.  You can stuff a lot of charts in this gutter if you need to.  I have some more charts lurking about somewhere that might find their way in here.  The pretty hardware drawers to the right are housing our ETC word study kit.  To the left of the hardware drawers I nestled a couple of recipe boxes that house index cards to use on the charts.   

The recipe boxes were very girly and had pictures of roosters and wicker chairs on them so I had to give them a makeover.  The boys told me what to search for and we printed out some images to tape over the tops.  Me Too wants you all to know that his chariot image was a far superior choice to Kal-el's Roman soldiers.

Montessori history question charts

Here are the charts filled out as part of some of the boys' history work from last week.  They filled out the charts as they apply to the Mycenaeans on Crete.  Following are some more pictures so you can see the questions and answers if you wish.  As always, my pictures should enlarge if you click on them.

The boys fill these out in after listening to a portion of the The Story of the World Audiobook.  As you can see, we don't worry about filling everything in.  If a question is answered in the course of the story we answer it.  If not, we don't.  Sometimes the empty boxes spur further research.  Kal-El will occasionally get the urge to fill them all in and hit the encyclopedias.  The encyclopedias didn't have much on the Mycenaeans.  

It started out as "once in a while." Once in a while eventually became every week.  And now, every day my boys spend a period of time drawing while listening to Story of the World (SOTW).  The reason I purchased SOTW in the first place was because it has an audiobook format and Maria Montessori recommended that the children listen to their history lessons while drawing.  I didn't want to be tied to reading aloud.  I already do a lot of that.  

Many people miss what Maria Montessori has to say about teaching history because  in The Advanced Montessori Method her writings on teaching history are split among the sections on teaching reading, a section on teaching history, and the section on drawing.  The link will take you the full text. If you use the search function to search the document for the word "history" you will find the sections you need. If you are at all familiar with the Jim Trelease book 
and/or The Well-Trained Mind  you will not be very surprised by what she has to say.

What surprised me about SOTW was how well it works with the history question charts.  The stories that are told answer most of these questions as if they were written to do so.  What also snuck up on me was how much the history question charts mimic what we do with Writing with Ease.  Therefore, it has occurred to me that the work with the history question charts are a major part of how we teach writing in the Montessori environment.

In this photo the cards cover up the questions.

In case you are confused, you can buy Writing with Ease as either a book or as a series of workbooks.  Everything that is in the workbooks is already in the book.  There are two differences.  The book has  several chapters prior to the actual daily work that are akin to the "theory" pages in a good Montessori album.  The workbook has all of the copywork prepared on handwriting paper and the book does not.  If you are using a specific style of handwriting paper in your homeschool, you won't use those pages anyway and may be happiest with just the book.  

I think that most parents, whether they homeschool or not, do not have a good handle on what individual skills are that form the web that is "writing" nor the normal developmental stages for each of those skills.  The theory pages should almost be required reading for any parent or teacher.  I highly recommend that everyone check it out from the library and read those chapters.

Here I have moved the cards off of the questions so you can see.

If you read those "theory" chapters you will quickly understand why several successful learning philosophies such as Montessori, Classical, and Charlotte Mason and likely others have certain key elements in common such as copywork, dictation, and narration.  You will also understand how your expectations of how the child will complete these things at different levels.  

How we fill in answers on the index varies.  Being able to listen to a reading and answer questions afterward is a skill.  Being able to answer in a complete sentence is a higher level of that skill.  Being able to write down the answer that you thought of is an even higher level.  In Writing with Ease the writing process is broken into different elements.  The child spends some time copying sentences that someone else wrote.  They spend some time listening to literature and answering questions about it and the answers on not written down.  Some times the child answers a question and the adult records their answer for them.  The different activities have different purposes.

Every child will be different, but in our homeschool having the boys write down all the answers every time would be highly unsuccessful.  History has replaced science as Kal-El's favorite subject.  He is obsessed.  However, the first day he and Me Too took turns recording the answers for the history questions charts after listening to SOTW Kal-El said, "Well, that really ruins history." That was funny because we have been answering questions after we listen from the very beginning.  The only thing that was different that time was that the kids wrote down their answers.   I have no interest in dampening his interest in any subject.  So, we will continue to work on writing separately until he is comfortable enough with it that it no longer "ruins" anything.   In the meantime, we listen, I ask the questions, they answer the questions, I record the answers.  Every once in a while, as we did last week, I have them write down the answers in order to take the temperature of how things are going.  It made what normally takes five minutes take thirty and the boys were not thrilled.

It is likely obvious to anyone who reads this blog regularly that I have added some "curriculum" to our Montessori experience over the years.  I always do this carefully and for a specific reason.  I thought I would wrap up today with some more concise information on the resources I mentioned today.  A lot of the posts I have sitting in draft have to do with this "additions" and perhaps it would be helpful for some of you to know what I've added, why, if I plan to continue, and if it is "necessary."

What:  The Story of the World
Why I added it:  I read in The Advanced Montessori Method  that the child should be listening to a specific type of history resource.  The SOTW fit this description.
Will I continue:  Yes.  Not only is it part of the method, but it is bringing in the history question charts and is becoming an important part of teaching writing in our environment.  Also, the resource book that I purchased to go with it has long lists of fiction and non-fiction books to go along with every topic.  I check out every single one from the library and the boys are reading 15-20 history books a week as a result.
Is it necessary:  SOME kind of history resource is necessary.  In my opinion, it might as well be this one.

What:  Writing with Ease
Why I added it:  narration, copywork, dictation, and high quality literature are supposed to be part of Montessori education and I couldn't seem to make it happen organically in our homeschool.  The resource provided a way for me to make it happen.
Will I continue:  Yes, for now.  Every week we read excerpts from great literature and I have approved of every selection so far.  It has served as our personal "Reading Rainbow" because the boys want to hear the rest of every book.  I will be tempted to keep using it for that reason alone.  But, also,  Kal-El doesn't mind writing in conjunction with literature but seems to mind it elsewhere.  This is a safe way to keep him working on it.
Is it necessary:  No.  The "writing curriculum" is organically hidden all throughout the Montessori method.  If your child is journaling, making booklets, if you are having them narrate their reading throughout the week, if you are practicing dictation, if they are reading quality literature you have it covered.  I notice that because these things don't have "materials" that you can buy and their own presentation pages that they are precisely the type of thing that can easily fall by the wayside.  I think it everyone should know the theory from the first chapters of the book.  If you can apply the WWE steps to the history question charts you will be far along your way.  However, be honest with yourself and assess whether you are really doing these things.  If your not, WWE might help you.  I notice that as I get more experienced I need these extras less and less and am more inclined to stick with the elements already in the method.

Wednesday, April 22, 2015

Etymology: Free Command Card Link

This week I have been on a search for the perfect etymological dictionary.  An etymological dictionary a recommended resource for any Montessori classroom, particularly at the  9-12 age. Etymology is yet another example of how Montessori students learn with many subjects interconnected.  They may encounter an interesting word during a botany or math work and then when they look at the etymology they are also exploring world history as well as maturing their spelling, vocabulary, and pronunciation.

Fortunately if you have right teacher you don't always have to attend a Montessori school or homeschool to learn in a fantastic way.  While on my dictionary search I stumbled across a blog post by Alycia Zimmerman, a a third grade gifted and talented classroom teacher in New York City:

Exploring Etymologies:  The Story of our Words by Alycia Zimmerman

What she did with her class looks a lot like the way my boys learn.  I encourage you to click over and read her blog post.  I was really inspired.  In fact, I started giving our language shelves a mini-makeover.

I don't think I've found a perfect etymological dictionary yet, but I've ordered the two books Alycia Zimmerman recommended:

In a Word: 750 Words and Their Fascinating Stories and Origins
Scholastic Dictionary of Idioms

We already have a good Merriam-Webster Children's Dictionary and Scholastic Children's Thesaurus  on our shelves.  I am adding the Scholastic Rhyming Dictionary.  (A dictionary, thesaurus, rhyming dictionary and etymological dictionary are all standard recommended supplies for an upper elementary Montessori classroom and are listed on the language supplies list in the KotU albums.)

I will be looking into the books that got Alycia Zimmerman's students so fired up about etymology:

Miss Alaineus: A Vocabulary Disaster

Her students were also doing a lot of reading about Greek mythology which we already have covered.  We've just hit the Greeks in our SOTW work and the boys have been gobbling up all of the recommended literature.  I can't speak highly enough about all of the "additional literature" recommendations in the The Story of the World Activity Books.  The boys are devouring 10-15 history books a week thanks to those.

I think when I get this all put together it will be time to take out our Marie's Words and figure out how we are going to use those (Rotating display? In the box?  On a ring?  If you search for these on the internet you'll find a lot of blog posts with ideas.  I haven't decided yet.).  There is also a now an app for these!

And finally, we have some command cards.  Command cards are sometimes a solution that Montessori homeschooling families use to help with inspiring ideas for follow up work.  In a traditional Montessori classroom the child might have 20-30 classmates.  They observe their classmates doing many different projects and it gives them ideas, keeps them aware of their options, and inspires them to do work of their own.  Since it is just the three of us kicking around in here, command cards often are a partial substitute.  Ms. Zimmerman sent her students home with a list of 20 open-ended project ideas to choose from.  If you cut up a list of ideas or project starters, voila, you have command cards.  However, they weren't in the format that we typically use in our homeschool.  Many of you will just want the list and you can access that directly on Ms. Zimmerman's blog post.  I wound up reformatting the list into a "ETC-style" card format.  I cut and pasted the projects in, but they are in a larger font, have added images, and are labelled on the top right so that misplaced cards can find their way home.   I am sharing the link to my file below.  It is in Google Drive.

Link to Etymology command cards I formatted.  Again, these are Ms. Zimmerman's exact project ideas.  All I did was reformat them into the style that we would use on our shelves in our home.  All credit belongs to her.  They are for personal use.

The way Google Drive used to work, you could click on the link and immediately print from the page that comes up.  It seems that you now have to do some additional clicking and/or perhaps put the file in your own Google Drive.  I think it has something to do with the first page that comes up being some sort of "preview."  It will work, just experiment.

Monday, April 20, 2015

Whole Tone Scales

Somebody wasn't happy that the Tone Bars weren't out and took it upon himself to set them up.

Next we took out the red glass beads and I asked him to start with the first tone bar (G) and then build a scale using all whole steps.  He played it.  Then, I asked him to start on the G# and do the same thing.  He played it.  I asked him to start on the A and do the same thing.  He observed that even though we had a different starting point we used the same bars that we did when we built the scale on the A.  Then he predicted that this would happen if we used any starting note from the first scale.  He quickly realized that although we have 12 potential starting points, there are only two possible sets for the whole tone scale.  

It would probably be more consistent with the rest of the Montessori music materials if I were to make green and white scale pattern strips for all of the scales we plan to learn (major, minor(s), chromatic...which would be all white by the way, whole tone, pentatonic, and octatonic).  However my boys didn't need them for chromatic and whole tone.  Also, I was inventing this lesson on the fly.  It is a lot easier to grab glass beads that pull a two-color oversized laminated scale strip out of my hat.

Afterward he built some major scales using the scale strip.  It looks like we have E major up there.

To stimulate some more practice building major scales I added an extra point of interest.  After building the scale with the strip the boys can mount the scale on the Scale Ladder.

Friday, April 17, 2015

Presentation, demand

You know your kid really loves learning about history when you walk into the school room to start your day and they greet you with signage that has presentation demands.  Kal-El was anxious to start studying ancient Rome.

Thursday, April 16, 2015

Daffodils, and Scalpels, and Magiscopes, Oh My!

The boys became very intimate with daffodils today.  Does anybody else feel bad when they say that daffodils have inferior ovaries?

Me Too labeling his daffodil parts

Yesterday I dissected and labeled the first daffodil.  Today the boys did their own with their own dissection kits.  It took some convincing to stop Me Too from going outside with his scalpel to cut his daffodil.  I told him that scissors would do the trick.  Our dissection tool sets are the 17-piece "Advanced Dissection Tools" from Home Science Tools.  I am not happy with the case.  It doesn't fit the tools well.  A lot of things are just shoved on top before you close the lid.  It does hold the scalpel and scissors nicely and safely and for that reason I would stick with this set again.  The "basic"  and "deluxe" sets have what look to be nicer cases BUT the scalpels are not housed safely and safety is the most important thing when you have a first grader using a scalpel.  Bear in mind that the "basic" set is not stainless steel and is the only set offered that will rust.  Their other sets are stainless.

Kal-El was so pleased with his dissection tools that he labeled his tools right along with his daffodil.  He did it without my help so I missed the opportunity to improve his vocabulary (and spelling).  Next time I'll have to let him know that his "poackers" (pokers) are called "teasing needles," his "nails" are really "pins," and his "tweezers" are "forceps."  My favorite part of his work is the "leftofers" section (leftovers).  Apparently he had some pieces left after he was done dissecting.

When they were finished we grabbed the Magiscope.  Without electricity or preparing slides were were able to get up close and personal with the parts of our daffodils.  In the photo above Kal-El was looking at the calyx.  I took a closer picture (below) so you could see how easy it was to throw this into any clear container (container only necessary in order to keep the lumirod clean) and put it on the deck.

Bulky item, no problem.  If an item is too large we can just remove the optical tube and use it without the stand.

I took a photo through the eyepiece with my iPad so you can see the calyx.  We have all the different lenses but haven't explored with anything beyond our 5x eyepiece and 4x objective (giving us 20x magnification).  If we used our 10x eyepiece and 40x objective we would have 400x magnification, enough to see bacteria, blood cells and protazoan.  Click here for more information on Magiscope lenses.

Me Too's favorite part was looking at the ovules in the ovary.  He loved this work and looked at every part of the daffodil under the Magiscope.  I learned something new today as well.  I learned that if I didn't want the vignette effect I could pinch zoom in.

This was just a part of our work today.  In order to keep myself blogging I thought I would try just posting some of our work instead of feeling like I need to show a whole day, week, or write a big post on a particular topic.  I hope to do those other things as well, but just not quite as often as I was.  

Wednesday, April 15, 2015

Finally...warm enough for some botany

We have had a bad case of spring fever this week.  The boys are doing a lot of their schoolwork outside, on the porch, on the patio, on the lawn, up trees...  The dog is ecstatic.  I've been waiting, waiting, waiting...and when we returned from spring break our hundreds of daffodils had bloomed!  We can dig back into some "from our own yard" hands on botany.   

We've done more than once, but the last time I posted about it was three years and two days ago.  The weather is a little different this year.  The variety of daffodil we dissected last time hasn't bloomed yet and I somehow also had tulips.  I don't know if the two extra days will make the difference or if the squirrels finally finished off all of the tulips.  

Today we reviewed the story of the flower, the parts of the flower, the parts of the pistil, and the parts of the stamin as well as types of venation, types of stems, and growth habits of stems.  I read definitions out in the field and the boys determined that we had a flower growing on a single, rigid stem on a plant with parallel leaf venation.  They determined that the flower was complete with an inferior ovary (below the corolla).  This type of daffodils are interesting because they have a "cup" in addition to individual petals. We noted the cup today, but did not get into types of petals.

Tomorrow we are going to do this again.  I demonstrated today.  I demonstrated how to cut the flower, dissect the parts and label them. Tomorrow the boys will be in the driver's seat and will each choose and dissect their own flower.

I planted these en masse so we were able to observe all of the daffodil flowers facing east early this morning and facing south late this evening following the sun.

The boys and I had a meeting today and decided that this spring, summer, and fall we are going to dissect and examine all of the interesting plants we find in our yard and accessible parts of our neighborhood.  The dissection trays are going to see a lot of action.  The boys were so very very excited to find all the eggs in the ovary and wanted to go plant them right away.  I explained that the pollen hadn't been transferred by an insect and traveled down the pistil to be fertilized yet because it was so early.  I told them that we could do this again later this summer and we might find something different inside the ovary.  They are excited to examine seeds and roots when we plant and harvest our garden again.  

I also told them that they were going to have to be detectives.  Some flowers are complete and some are incomplete.  We are going to find both and they are going to have to tell me what the incomplete flowers are missing.  Me Too literally quivered at the thought of this responsibility.  They also have a mission to find what types of things we do NOT in our garden so that we can, if at all possible, plant some for next year.

Tuesday, March 31, 2015

School Day

I am having trouble with our camera.  I think it's the external flash.  I haven't been photographing our work lately which makes me less likely to blog.  So, this week I picked ONE day, Monday, and took pictures of most of our work.  This way you can see what things are looking like around here, or at least how they looked on Monday.  I took all of these photos with my iPad so the quality is not great.

Copywork from  Writing with Ease.  

Circling multiples of different numbers on a printed hundred board.  This is part of the traditional Montessori elementary sequence for multiples.  You can read a great post about the multiples with good pictures over at Lycee International Montessori.

We pulled out the Leprechan's Luck multiplication facts game for St. Patrick's day and the boys have been playing it daily ever since.

The Leprechan's Luck game reminded them of the division race game (division facts) so we've been playing this daily too.  You can read more about these games in this post.  I suspect they choose them every day because the winner gets three M&M's, second place two, and third one.  If Mom get's second place (Me Too ALWAYS gets first place) she gives one of her M&M's to the second place winner.   They were already good with their multiplication and division facts, but now they are getting FAST.

Me Too seems to finally understand long multiplication on the large bead frame well enough that I don't have to sit right next to him.  Here he is perusing our form drawing idea book to find a fresh way to decorate between his equations.

Kal-el is working a long division equation from our racks and tubes set without the racks and tubes.  Just old-fashioned long division.

He is slowly working his way through the grammar boxes.  I haven't been pushing these so it will take a while.  No worries.

He made a Waseca stencil map of Europe.  All of his The Story of the World work has brought new meaning to the rivers on these maps and he likes to trace them and label them.

I gave the presentations introducing the measurement of angles.  The boys really liked this and were tripping over each other to put different fraction pieces (pies AND squares) onto the protractor.  

Then Kal-El wanted some obtuse angles to measure and brought out triangles from the geometric cabinet.

Me Too likes to fill out the fraction tickets.  If I made these again I think I would leave off the line that is supposed to go under the answer.  Me Too insists on using it as his fraction bar.  He also refuses to write "zero" instead of "zero sevenths" because he says the latter is "more interesting."

Sunday, March 15, 2015

School Days

Me Too working with the sticks after a presentation on consecutive and adjacent line segments. 

We are having a wonderful school year.  I am so happy that we have the freedom to homeschool and live in a state where we can do so without having to waste our time on standardized tests or submitting "work" to a "certified teacher" for a stamp of approval.  We are busy learning!

I have been soaking up the days and living in the moment.  My hands have been busy helping move beads on the racks and tubes boards for not one but two students, participating in the "Bank Game," reading history books and playing "Simón dice" with two boys who need to learn the names of their body parts in Spanish.  I have been drawing right alongside them while we work through our new drawing tutorials.  My hands have been too busy to hold a camera lately.  Today's post will have fewer photos than usual and only of some of our newer works.

Me Too finding the value of the bead tower (KotU Squaring and Cubing, Game Two)

Kal-El building the rectangles for the third squaring and cubing game.

Here he has separated the square of each number at the top and replaced it with a bead square.  The child notes that as the squares increase in size the remaining rectangles decrease in size.  Then you do some computing that involves adding the values of the squares and rectangles and then for some mysterious reason subtract to find the differences between adjacent rectangles.  Then you subtract the differences of adjacent differences.  All of the differences eventually come to "two."  Kal-El pointed out that if you keep going they all come to zero.  You are supposed to stop when you reach the twos.  I don't understand the point of this, but I was educated using traditional math not Montessori math and perhaps don't have the skills to understand why.  Determined that my kids shall not have that problem we did the exercise as in the album.  They didn't seem to be bothered by it.  At any rate, they didn't say "so?" at the end like I did in my head.  Maybe I'll figure out why it's important as we go through the rest of the sequence.  I have been reading through my album and feeling perplexed.  Thankfully Abbie's son is a few lessons ahead of us.  Her pictures and the links to videos she provided have cleared everything up for me.

I tweaked both boys' work plans.  I made myself a work plan, on pink paper, complete with pink paperclips.  Kal-El has started using a work journal.  We are doing a lot of spelling, vocabulary, writing, long division, long multiplication, fractions, Bible study, history, art, geography, and Spanish.   Me Too is barreling through reading presentations as fast as I can present them.  We have done many, many read-alouds.  We recently finished Pollyanna.  Kal-El in particular seems to have found that book to be life-changing.  It was Me Too that I was hoping it would rub off on.   A favorite Me Too quote often repeated by his uncle is, "I don't like fun."  A recent task card asked him to recount a time when he was glad and he said, "I've never been glad."  If anyone could benefit from playing the "glad game" it's THAT KID.  We are listening to A Christmas Carol in the car.  "Bah Humbug" suits Me Too's sensibilities just fine.   We are also in the middle of Little House.  Me Too says he doesn't like it.  Kal-El says they are living his dream life (off the grid). I tried reading that to them a few years ago but had to stop because Kal-El became too upset whenever it told of the children misbehaving.  The boys love the "supplemental literature" suggested for each Story of the World chapter so we have been reading a lot of old fables and fairy tales from India, China, and the Middle East.  This week it will be ancient Africa. We made the recipes provided in SotW for that chapter and they were VERY good.

We have been learning about Mozart and singing "Eine Kliene Nachtmusik." It is "performance" season around here.  The boys have been busy playing recitals and music festivals.  Every time I try to record them for the blog we have some kind of musical disaster.  I guess their talents are meant to remain private for now.  In the meantime, I'll keep trying.  In addition to the violin Kal-El has been experimenting with the trumpet and played taps at the end of the cub scout Blue and Gold dinner in February.  The boys have been busy with their dad building their cars for the Pinewood derby.    Kal-El scored his first basket in a basketball game in the last game of the season.

I'll end with a little clip from the "boy who doesn't like fun" and "has never been glad."  Wink.