Friday, March 18, 2011

Zoology & Taxonomy

Ah, science.  Of all subjects it was my weakest in high school: chemistry specifically.  I did alright in biology, mostly because my best friend and I were in the same class and studies together.  If you listened closely during tests and exams you might have heard us humming softly.  We found that the best way to remember the facts was to make up silly songs.  If only I had begun learning science the Montessori way!  Here is a sample lesson, one that can be repeated indefinitely without growing tedious.

Above you can see the (almost) completed lesson in zoology/taxonomy.    I use it as a launching board to talk about all different kinds of plants and animals, but mostly animals.  We begin with the most basic of categories: living and non-living.  Ella sets out two pieces of paper, one labeled "Living" and one labeled "Non-Living."

I've made up many cards (just using Microsoft Word, eight cards to an 8 1/2 x 11 page), the vast majority of them animals, for Ella to sort.  I've mixed them all up and divided them into small groups so she can grab a pile and sort through those that day.

Choosing items for non-living was very interesting.  Most things I chose were no-brainers, i.e. they are obviously non-living, but there were a few that were more challenging.  Fire is an excellent one as it has many characteristics of living things (can grow, can move, needs air, needs "food", leaves waste, etc.) and there are a few others that can catch one unawares.  Above you can see that included in this pile are lightening, stalactites, rocks, and a compact disc.  There was no doubt that the rocks and compact disc were non-living, but lightening has some similarities to living things as do stalactites.  It took quite a while for her to decide where to put the stalactites because in an earlier stack she had coral, which appears to be like a rock, but is actually living.  The sneaky ones are the most fun and they help reinforce the difference between the living and non-living.

I scoured the internet for the pictures I used for each card.  While I tried to focus on variety, keeping in mind that the majority of cards would have to be vertebrates, I did make an effort to put in plenty of animals that are native to our area, such as the ruffed grouse (bottom left), which is a popular game bird in New Brunswick.

After separating living from non-living we take our pile of living and divide them up between "Plants" and "Animals."  Yes, I know that there are more categories of living things than just those two, but as they are the most common and encompass almost every living thing with which a child is familiar we focus on them.  Fungus, protozoa, bacterium, etc. can come later.

 Most of this sorting Ella found very easy, but I tried to keep her on her toes.  The Venus flytrap, being carnivorous, gave her a moment's pause.  And she was convinced for a long time that coral must be a plant, which I grant you, is not an illogical conclusion!

This particular pile of cards only had three samples of plants.  Our discussion of the tree trunk was interesting as the tree itself was dead, and therefore neither living or non-living, but it was covered in moss (which was my target species) and the moss was clearly alive.  Ella decided that rather than having just two initial categories there should be three: living, non-living, and formerly-living/dead.  After all, wood was once a tree, and the radishes can't really be living if they've been pulled up out of the ground, chopped up, and pickled!  Smart girl.

After the plant/animal division, we take the animal cards and divide them between vertebrates and invertebrates.

Categorizing animals this way is a bit more challenging.  Because you can't actually see the backbone or spine in a vertebrate you have to think through how an animal moves, how it lives, and what its surface feels like.  Ella is just beginning to remember consistently to look for segmentation of the animals' bodies, hard exteriors such as shells (an exoskeleton), and over-all "smooshiness" (that the body is completely smooshy or soft, indicating that there are no bones).  

Again, putting in tricky cards gives the opportunity to discuss the "why is it this one and not that one?" question.  Above I included a sea horse.   Ella concluded initially that it was an invertebrate because it appears to have an exoskeleton, even though it is a fish, though like catfish sea horses do not have scales. 

Following the organization of the vertebrates and invertebrates we take the pile of vertebrates and then comes the real sorting fun!

With five categories to chose from there's a lot more room for error.  Each animal has to be evaluated in several different ways: what kind of "skin"  it has and/or if it has a skin covering (hair, fur, feathers), whether it gives birth to babies or lays eggs, if it lays eggs whether it lays them on land or in water, if the offspring look like miniatures of the parents or if they have another form entirely, if it has a mouth or a beak/bill, how it breathes, where it lives, if it is warm or cold blooded, and how it feeds its babies.  There are hosts of conversations to be had as we work through these cards, and I frequently find that Ella and I end up laughing, especially at odd animal behaviour or appearance.

Amphibians.  They have slimy skin, live in or near water, are cold-blooded, lay eggs in water, have babies that look nothing like themselves and whom they completely ignore, and usually can breathe right through their skin.  Their appearances have little variation: frogs and toads look similar as do salamanders and newts.  To give a bit more variety I've tried to include pictures of amphibians at various stages of development.

Mammals.* We are warm-blooded, have fur or hair, live all over,  breathe air with lungs, give birth to babies that look similar to the parents (usually!), and feed our offspring with milk from our own bodies.  Isn't it great to be a mammal?  There are quite a few unusual mammals, like whales, manatees, platypuses, etc.  It can be fun to emphasize the similarities between humans and other mammals, as well as the differences.  Thank God for opposable thumbs!  Plus, as a nursing Mum, it's interesting to discuss how other species nurse.  In the case of whales, Ella would not believe me that they were mammals until I found a video of a beluga whale giving birth and nursing her baby!

Fish.  They live in water, are cold-blooded, and breathe through gills.  Some species give birth to live young, but most lay eggs.  The level of parental involvement is usually low to nonexistent.  Although there are three different classes of fish, for the young child and early elementary student so many details can be confusing, so I lumped all the fish together.  When (or if) I ever have time to set up an aquarium again we will certainly get into closer examination of fish classes.

Birds.  Feathers, beaks, wings, and two legs are the most easily recognizable traits.  They are warm-blooded, breathe air with their lungs, lay eggs, and are frequently attentive parents.  One of their families (the penguins) are even able to survive in the harshest climate on earth and one of their species (emperor penguins) stay in that climate during its harshest season in order to go to extraordinary lengths for the purposes of mating, bearing, and raising offspring.  In my opinion, birds are way cool!

Reptiles.  Some like life where it's hot and dry and others would prefer to stay wet all day long.  But they all have scales, breathe with their lungs, are cold-blooded, lay eggs on land, and their babies look like miniature adults.  They are also very good for frightening grandmothers and mothers when brought in from outside with a cheerful, "Look what I found, Mum!"  (Please note: this refers to something my brother did to my mother and grandmother, not something my children did to me.  I would not be so chicken-hearted... I hope!)

After all the sorting has been done, we clip each section together with other cards of the same category, to play with and discuss later.

Eli added his own artistic touch to the non-living card!

And, as is so often the case with homeschooling Montessori Mums, how to store materials effeciently is of great concern, so here's what I did.  I found this tray and this box at the local Dollarama store.

The tray perfectly fits half of an 8 1/2 x 11 piece of paper (or cardstock), which is what I used for the category titles, and the small crate is perfect as a card holder!

*Please note:  While all the photographs taken above were mine, the pictures in the photographs are not.  They were all found online through Google search.  The human family in the mammals is unknown to me, but it was the best photo I could find of nude humans that was neither graphic (in the negative sense) nor of poor quality.  Since all the other animals were au naturel, I figured it was only fair that the humans were as well.  For the record, I think it is a beautiful and tasteful photo... though I don't think I'd be comfortable with my family posing in such a manner, or at least displaying it!

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Saturday, March 05, 2011

Addition Table with the Bead Bars

Here is a super-simple presentation of an addition table from one to five.  It is mainly to work on memorization of basic addition, but it also shows the pattern of sums.

I printed a 6x6 grid (3x3 grids on four pieces of cardstock, cut and pasted together), though you could easily draw it out on bristol board.

We left the upper left square blank, representing zero.  Then we put in our addends: one through five across the top row and one through five down the first column. I got her started by going across the second row verbally: "One plus one is two."  (Then placing the green two bar in the square where the red ones meet.)  "One plus two is three."  (Place the pink three bar.)  "One plus three is four." (Place the yellow four bar.)  And so on.

Ella took over with the bead bars and when I came back I discovered that she had decided that because by six the bead bars were too long to go straight across the squares that she could bend them so they would fit in nicely!  She doesn't do that anymore.  I showed her (as you can see with the sixes and sevens) that they would fit if put diagonally.

This lesson can easily be expanded to 10 + 10 by expanding the grid.  And let me emphasis the importance of saying aloud each equation.  Ella cannot understand why I insist on this, but it does help with memorization and (very important for busy mums) you can hear what your child is doing while doing housework/writing papers/changing diapers/folding laundry or whatever else needs doing!

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Friday, March 04, 2011

Working with Words and the 3-Period-Lesson

Besides doing Montessori I'm also using a few workbooks with Ella which are grade-specific.  Usually she enjoys doing them and it means that I can compare what she is able to do with what the public curriculum expects.
What she is learning in Montessori I supplement with the workbooks and what she is learning in the workbooks I supplement with Montessori.  Here is an example of the latter.

The workbooks have been going over nouns and verbs.  I have not yet got the material for grammar through Montessori (though I plan to), but I did make up a couple hundred word cards that she could use to make sentences.

I used cardstock in three colours.  The nouns are on red paper, the verbs are on yellow, and what we are currently calling "helping words" are on blue.  I have told her that there are a lot of different kinds of "helping words" and they have names, just like verbs and nouns do, but for right now we're just focusing on the verbs and the nouns.

To present the material I began laying out all the nouns that were the names of places.  I asked her to explain what was the same about these words.  Didn't take her long.  Then I began to lay out nouns that referred to people or were people's names and asked her to say what she thought they had in common.  Finally I laid out all of the words that identified objects and again got her to point out what was similar about them all.

"All of these words are called nouns," I explained.  "Nouns name either a person, a place, or an object."

We repeated the lesson with verbs and talked about how verbs were an action or what someone or something is.

Then we began to make sentences.  Very soon she knew how to use the cards and made longer and longer sentences, sometimes making them rather complex.

Although I had made all the verbs to be present, third person, singular she found that too confining and began to use the word that came after a verb to cover up the superfluous "s."

During our second lesson using the word cards Ella learned the difference between subject and object.  For this I used the 3-period-lesson.  If you're not familiar with the 3-period-lesson here it is in simple form:

First Period: Tell the child what he or she is touching/experiencing.  E.g. This is the subject.  In a sentence the subject is what does the action.  This is the object.  In a sentence the object is what receives the action done by the subject.  The key to the first period is keeping it simple and to-the-point.  With a younger child, such as my sons, I would endeavour to use as few words as possible and keep the emphasis on the word I am trying to get them to learn.  So, when I am presenting the colour red from the first set of colour tablets, I lay the tablet on the table in front of the boy I'm working with and say, "This is redRed."

Second Period: Get the child to indicate the correct object when you ask.  E.g.  Where is the subject?  Show me the object.  With my boys I'd ask, "Where is red?"  or "Which is red?" (if I had already presented more than one colour.  If the child has difficulty then you go back and repeat the first period lesson again.

Third Period:  For this you want the child to do the explaining and to use the correct vocabulary without prompting.  E.g.  I would point to the subject and ask "What is this?" or "What part of the sentence is this?"  Then Ella would answer "It's the subject.  The subject is what's doing the action."  With the very young you are simply trying to teach them to identify, they can learn to explain later.  So I would ask, "What is this?" or "What colour is this?"  Henry is my talker and he will usually answer verbally, "Wed!"  Or, sometimes, "'Ellow!" and then I have to correct him.  Eli may or may not answer and after giving him a chance I will give him the answer, "It's red!"

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Wednesday, March 02, 2011

Square of Pythagoras - Some Extentions

Yet again we used the square of Pythagoras, although this time we worked together at arranging it, Ella dividing up the pieces between us, although she always kept the squares.  "After all, I'm the student!" she explained.

Ella and I have made the square of Pythagoras.  Then I directed her to build the tower with the pink cubes.

Without any prompting on my part she took the smallest square and put it on the smallest cube of her tower and said, "Look Mummy!  They go together!"

We then "related" the pink cubes with the square of Pythagoras.  I asked how she knew where each would go and she explained that each side of a cube was a square and that therefore the pink cubes would go on the actual squares in the square of Pythagoras.

Ella then proceeded to relate the two materials in the same way as she had done with the red square and the smallest pink cube.

Then she did it horizontally.

After we had put away the pink tower and reorganized our square of Pythagoras I got out the bead square for her to relate them together.  She told me that it was pretty easy since they all matched in colour.

Here she is almost done.  I then extended the lesson a little by giving her an early glimpse into multiplication; though we are not yet "naming" it as such as I would like her to absorb the ideas sensorially first.  I would touch each bead square, while it was superimposed on the square of Pythagoras and say, "One one is one.  Two twos are four.  Three threes are nine," and so on.  After each statement I would pause for her to touch the square and repeat what I just said.  I expect this activity will continue in a variety of ways until we are actually doing "real" multiplication.

Our "fancy" storage container for the square of Pythagoras - a plain wood tray from the dollar store.

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Tuesday, March 01, 2011

Square of Pythagoras - First Presentation

Thanks to all who inquired.  No, I'm not dead!  It's been almost a year and a half since my last post, and while my life has been moving quickly onward I've been facing it mostly with glazed eyes and an air of confusion.  Such is life with twin boys.

My sons are now 2 and are healthy, mischievous little fellows.  I've begun to do some early Montessori work with them, which you will hear about in an upcoming post.

Ella is now "officially" grade 1, in that she is 6 and that is the typical grade 1 age.  And there ends all that is "typical" about her.

Evidently she's doing some things on a grade 4 level, and she was teaching our 17 year old babysitter about geography.  Her reading is about average, or perhaps a bit above average for her age, and her handwriting in abominable!  Though much of what she writes looks like the hen-scratchings of a preschooler, what she writes is very well done.  I guess we just didn't do enough of the sandpaper letters or the metal insets.

I have a vast backlog of photos and lessons to share and I hope to do so over time.  For today, here was our afternoon lesson: the first presentation of the square of Pythagoras (also called the deconomial square).

The square of Pythagoras is basically the multiplication times table in visual form.  The smallest square is 1x1 cm and is red in colour, which coordinates with the colour of the bead bars.

The next three shapes are green, like the "2" beads and are 2x1 cm, 2x1 cm, and 2x2 cm square.

The next five shapes are pink, representing "3" and are (2) 3x1 cm, (2) 3x2 cm, and a 3x3 cm square.

In the above photograph, Ella is laying out the 4s.

I find that she really enjoys making the square of Pythagoras as she thinks that the pattern is beautiful.  I think so too.

The completed square (as done by Ella).  As you can see it goes from 1x1 cm to 10x10 cm.  It is meant to coordinate with the pink cubes, the brown/broad stair/rectangular prisms, and ultimately can be used as a guide to laying out the bead bars in the deconomial.  Hopefully I will be showing these extensions in the near future.

As for the Square of Pythagoras material itself.  It is really hard to find to purchase. Ideally it is supposed to be made out of wood, but I found it much easier to make it out of foam sheets using a large paper-cutter.  (An office-sized paper cutter can be invaluable when making materials.)  I've also seen beautiful square of Pythagoras lay-outs made of felt or other fabrics, plastic duo-tang covers (though I don't know how easy or difficult it would be to find the colours you want), and painted cardboard or bristol board (though they can tend to warp).

Initially I planned on making it using inches as a base, rather than centimetres.  Bad idea!  It was HUGE and very unweieldy.  I'm very glad I downsized, though what I'm going to do with all that extra foam is beyond me!

The first presentation of the square of Pythagoras is not meant to teach the multiplication table, but like the binomial and trinomial cubes it is a sensorial introduction to a more complicated mathematical concept.  Right now we call all the green rectangles and square the "twos,"  all the pink the "threes" and all the yellow the "fours."  It will be some time before we begin to name individual rectangles 2x1 or 4x3.

To present it I simply named the material, "This is the square of Pythagoras." and I began making the square, beginning with the red, then the green, then pink, and so on.  It didn't take long before Ella got the idea and just took over.

She was rather frustrated by the fact that her square of Pythagoras wasn't as "perfect" as mine, but with a bit of reassurance that it took practice she became satisfied with her results.  I'm looking forward to her reaction to the extentions.

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Monday, November 23, 2009

Montessori Mathematics: The Complete Bead Material - Part 5

Making the Bead Squares

The bead squares are not much more difficult to make than the bead bars, but there's no quick-and-sneaky way to make them. There's no easy way to make the bead squares either, so you might as well get used to it! Keep in mind that when it seems that it will never end, you get to the bead chains and speed will again be a factor.

Many of the steps for the bead squares are the same as for the bead bars, so I'm not going to elaborate on those steps, although I've included the photographs for your benefit. There are some differences, though, and that is what this post will focus on.

Step 1: Gather your materials

Step 2: Cut your plastic canvas. You will need to cut two sections that are (1 square) x (N x 2 - 1). For my example, using 5, I cut 1 x 9 squares. (1 square) x (5 x 2 - 1 = 9). There is one exception to this. When doing your 2 square, you only need one piece of canvas cut.

Step 3: Cut your wire.

Step 4: Make a wire curl.

Step 5: Straighten the wire.

Step 6: Thread your first bead. It's really easy to forget at first that you're making a bead square, not a bead bar, and I've mindlessly begun to make bead bars while the plastic canvas laid right in front of me!

Step 7: Add your first piece of plastic canvas. You will need to thread the wire through the first square.

Step 8: Thread the rest of your beads, minus one. So, if you're doing five, you've already got one bead on and you need to bring the number of beads to four.

Step 9: Add your second piece of plastic canvas. Again, you put the wire through the first square.

Step 10: Thread your final bead.

Step 11: Twist the loose end.

Step 12: Clip off the excess.

Step 13: Make a tight wire curl at the angled end of your row of beads.

One row done!

Step 14: Begin your next row. Basically you follow steps 1-6 and when the time comes to put the wire through the first piece of plastic canvas you skip one square and put it through the following one. In the five bead square each row of beads threads through the canvas at squares 1, 3, 5, 7, and 9.

TA-DA! You've made a bead square.

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