Monthly Archives: January 2010

All in a Day’s Work – Arggg.

AV and JV need money.  They have their tank and their tank is naked (pronounced “neked”) and needs stuff.

They have debated and wanted to have hard corals.  These are the kind that grow very slowly and are, ready for it, very expensive.  A silver dollar sized war coral is priced at $150.  Sooooooooooo. The boys need jobs.

Their godmother stepped into their prayers and hired them to be pirates for 3 hours today.  The church where she serves as the Director of Christian Formation was having an adult meeting and needed child care.  She decided to go with the Veggi Tales movie: The Pirates Who Don’t Do Anything.  Lunch would be fish and chips (fish sticks and tater tots), oranges (to combat scurvy), and grog (ice cream and coke that would fizzz).  She needed waiters and movie monitors.  Tada insta pirates AV and JV.

The boys got fully into character and became pirates and combated spills, thrills, and chair switchers.  ARGGGGG.

AV don't make me smile. Pirates don't smile.

JV - just don't mess with his hair and your life will be spared

We ran to the fish store after getting home and finding clothes “to be caught dead in”.  I’ll post photos of what the tank looks like soon.

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Filed under AV, Going outs (Field Trips), Practical Life - Elementary, Salt Water Tank

The Kids are playing with glass again (and power tools, too)

Today is Glass day.  There is much rejoicing!

BR sprinkling frit into the underside of his sea urchin relief

BR arrived this morning ready to work out his color scheme for the blue reliefs he was planning on filling today.

He worked out the frit (crushed glass) colors through the blue of the glass and the visible light spectrum. Retrying his pattern until it looked like a sand dollar and a sea urchin.

See I wasn't kidding when I said it was like really thin spaghetti

JV’s project is overwhelming in its scope.  His concentration to putting tiny pieces carefully up against other tiny pieces is purely JV.

He has built a wall with some metal bars and is working from the left side to the right side water and kelp right now. Tweezers are the only way to go with work this tedious.

AV slicing glass for his fish scales.

AV’s work involved a band saw. We made it through without squirting blood. Yey!

His fusion plan worked well.  Mike the Glass Guy did his us usual amazing job helping us to figure out how to get the desired result in the kiln. He prepped AV for using the band saw and followed his progress from an unobtrusive distance.  He trusted a 12 year-old with a band saw.  Give this man a free box of doughnuts!  – Oops Lady Liberty brought some by today.

AV's rough fish scale pattern.

The glass cut into ribbons.

Scraps from the cross cuts.

AV telling JV not to mess with his stuff. JV enjoying this way too much

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Filed under Art, AV, BR, glass, JV

Photos from Hampton Plantation

The first two I took of them on the back portico – the first Adams style portico in Colonial America.  The rest are taken by Andrew in the front yard (facing the river) or along the nature trail.

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Filed under AV, Going outs (Field Trips)

What have we been doing part three

Ok enough math.

JV's hermitage

JV has been struggling with his obsessiveness when laying out his book of geometry.  Which has led to a defensiveness and isolation.  So.

He has created his “hermitage.”

JV has always loved small little spaces that he tricks outs.  He took a stool and has made a little table.  He moved the stereoscope to another nearby stool.  He added pillows to lean on, a poster of echinoderms, and taped a folded piece of paper to his stool to create a pouch to store his mini-pencils when not using them. He then finished this cubby space by adding reference books leaning against the outside of the stool to

JV quizzing on the presidents - all three names

further hedge him in.

He does pop out of it enough for the others to allow him to be a quizzer. They have been working through the countries of Africa and State facts/capitols/birds etc. (Got to love the Target $1. bins.

Yesterday we visited our last day trip location – Hampton Plantation.  AWESOME!

JV pretending to be the Swamp Fox running to the rice fields from the approaching British Soldiers

This is Archibal Rutledge’s home. Initially built in the very early 1700’s by the Horry family who married into the Pickney family. Mrs. Horry served dinner to Bloody Tarlton while Francis Marion hid in the rice fields.  Over the years it became home to the southern author Archibald Rutledge who is famous for his outdoor adventure tales. Hampton Plantation has been trusted to the State of SC and is a wild, beautiful place. We walked the three mile foot path around one of the rice fields.  JV saw a doe.  He was transfixed. AV will post some photos here and is working on putting his photos on a photo blog. (When he gets done reading his book, maybe…)

The brick columns speak of a time (1700) when brick making was a major industry in this area.

On the way home we drove 15 miles along a sand road that bordered on impassable without a big truck. We were rewarded by a beautiful church – St. James Santee. We walked through the graves seeing the continuity of families from 1732 through 2009. The boys noticed the sign CSA, not the veggies, but the Confederate States of America. It was a first for them.

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Filed under AV, BR, Geography and World Studies, Going outs (Field Trips), JV, Montessori

What have we been up to part two (Updated)

So we left off with binomials, trinomials, quintonimials, and the decanomial.

Montessori bead box - one is red (one bead), two is green (two beads)

From a small age, the Montessori child touches the beads and sees one is one thing and that three groups of three is a total of nine things.  He can physically see that 1 x 2 has the same product as 2 x 1.

AV laying out the decanomial with paper

He can also see that when 10 groups of 10 beads are laid side by side they make a square and can count that it totals 100.  They also see if you have 10 x 10 and 10 high that equals 1000.  This cubing is not abstract it is really a cube. Really. Go get your legos and build it.  I had a rocket scientist (literally) stand in awe as his 5 year old laid out the six chain and then laid down each square and then as his son brought the cube look at me and say that he never thought that a cube was a real thing.  You are in good company if you never thought so.

When the 9 year old is ready, one of the last things he does in lower elementary is begin to lay out the decanomial.  One red bead, next to it two red beads, next to that three red beads, etc. all the way across to ten. Then the next row 1 green (2) bar, next to it 2 green bars, and so on continuing across to 10 and down to 10. The tedium and need for perfectly aligned rows stressing the nine year old. Then come the first years. The little guys gather round ever so carefully not to upset the rows and rows of perfectly aligned beads. The six year old watches with rapt attention or asks to hand the builder his needed beads. The second years watch from a distance in their aloof state.

Then the exchange begins.  2 red beads equal the same as 1 green (2) bar with its two beads. “The red ones roll a bit. It might be more stable if we substituted the 2 bead bar. Let’s change it to a green bar.”  We change them all out.  Then the child discovers that we have the squares cutting right down the middle and flanking it if we regroup the beads they make squares that when gathered all together make a cube.  The secrete of the decanomial is that it is really all the cubes of 1 to 10 put together.

AV with having laid out the algebra tickets for each factor

I say all this to say that AV has done all this work. Now, he has laid out the decanomial once again.

AV's long paper - measuring 10 feet - with the polynomial equation written out. It reminds me of his 1000 chain papers from 3 to 6.

This time with paper representations which we carefully looked at before placing letters over the multiplier and multiplicand.  We then write it all down on one long piece of paper.

So 1 x 2 became a x b.  We began the proof of equivalence between all the mathematics of the internal beads and the (a+b+c+d+e+f+g+h+i+j)squared.

The Algebraic paper representation with each the communicative law in affect.

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Filed under AV, Bead Boxes, Binomial & Trinomial Cube - Cube rooting, Geometry, Mathematics, Montessori, Pythagorean theorem

What have we been up to

In the bleak mid-winter, we have been studding echinoderms and math more than anything.  In addition to the Montessori geometry lessons, we have been working on bi, tri, and larger nomials.

Brooks wanted to shade his squares.

The boys have reviewed the process of creating binomials and trinomials.  We began with a review of the products of a monomial (one number) and a binomial (two numbers added together).  For example:  3 x (5 + 4).  I am really figuring out 9 x 3.  But sometimes in math it is easier to break apart a number.  So away we go.

We then moved to squares of binomial.  Using a hundereds square, we discussed how many beads total in a one hundred square (100 – it is not a trick question) then we discussed how many rows across and down (10 by 10).  We knew the answer and knew the problem 10 x 10 = 100. But we thought we could find another way to find the product.  Lets divide the 10 into 7 + 3.

We took a rubber band and placed it around the bead square three in from the side and another and placed it seven down from the top.  Then we wrote out our new problem (7 + 3)squared.  Then we looked at the shapes formed.  Two perfect squares and two rectangles.

the problems reads (7 + 3)sq = 7sq + 3sq + (7×3) + (3×7)  or 49+9+21+21                 and wow it equals 100.

We then applied what we knew to trinomials using a box of flat pieces of plastic sized to each possible factor – ie: 1 square wide by 9 squares long. We transfered that to the papers.

More on xnomials later.

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Filed under Bead Boxes, Biology, BR, JV, Mathematics, Montessori, Peg Board - squaring/rooting, Science

Echinoderms – BR

BR’s writing is really improving.  He went back several times to add new information or clean up his rough thoughts.

Echinoderms

Echinoderms are a group of marine animals.  Their name comes from the Greek meaning “spiney” “skin”.    Echinoderms are split into three main orders that do not look alike.  They reproduce by sperm and egg.  Their mouths and tube feet are on the oral (bottom) of the body and the anus is on the aboral (top) of the body.  They have tube feet.  To use the tube feet, they suck in water and push it out madrephorea. They have eyes on each of their appendages.

Sea cucumbers look a good bit like sea slugs but are not.  They are in the phylum Echinodermata and class Holothurian.  Sea cumbers are not like any other echinoderm.  They have no arms or hard spines.   All sides of the sea cucumber do not look alike. They have a ring of feeding tentacles which are highly modified tuber feet. They use them to push in food. When the sea cucumber is scared they squirt out their intestines for a defense mechanism. Sea cumbers can not swim and are benthic. They are edible and are a common food in Spain.

Sea urchins are in the phylum Echinodermata and class Echinoida.  The life cycle of a sea urchin starts with an egg then progresses to the aechinoplutes (larval stage) and then they go through a metamorphosis and finally an adult sea urchin.  They eat using a structure called Aristotle’s lantern. It is located in a sea urchin’s mouth.  In Aristotle’s lantern is a set of five teeth that come together.  The teeth are very strong so they can scrape off alga from rocks.

Sand dollars are flat cousins of sea urchins. When the sand dollar is alive, it is covered in short spines. When the sand dollar is dead and sun bleached, it is smooth and grey or white. Their short spines help them burrow into the sand. They only live on sandy bottoms so they a place for protection from waves and predators and a way to obtain food. The sand dollar burrows, while digging tiny food particles fall between their spines and then cilia and tube feet drag it to the mouth.

Sea stars are not “fish”, so the name star fish is a misnomer. The proper name is sea star. They are in phylum Echinodermata and class Asteroidia.   Sea stars come in all shapes and sizes.  The largest starfish can be over four feet in diameter and the heaviest weighs over 13 pounds. Starfish can have between five and ten legs. They use their tube feet to burrow into the sand to find food.  Small clams are what they prefer.

Brittle stars are in phylum Echinodermata and class Ophiuroida. The life cycle of a brittle star begins with an egg and progresses to an ophoipluteus (larve).  Then they go through metamorphosis and an adult brittle star appears.  They live on jetties and rocks.  They shun daylight. To hide they go under seaweed, rocks and other dark places. They also find food in those places.  They have a really effective defense mechanism.  They can make their arm fall off for their predator to eat while the brittle star gets away.  It then grows back its arm.

Even though the Echinoderms seem very diverse, there are numerous similarities. All echinoderms are marine meaning there are no fresh water species and only a few can live in brackish water.  All Echinoderms are radially symmetrical.  This means you can cut them apart and they will grow a new whole creature from each cut up creature. They will eat anything and are opportunistic eaters.  They help the ocean to be clean.

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Filed under Biology, BR, Science