In our series this week on note taking, we have moved to day two. Todays lecture discussed differences in creatures in the deuterostoma category – particularly what happens after the notochord forms.
This is AV’s summation:
Bilateral symmetry is in all living things with a notochord – fish, lizards, people, etc. Echinoderms and a few other animals are radially symmetrical. Asymmetrical is when there is not symmetry like most sponges, some larvae and most alga.
To be a chordate an animal must have four characteristics: 1. Notochord – the notochord is often lost in the adult; 2. nerve chord – the nerve chord is not lost; 3. gill slits – in land animals it is lost as an embryo; and 4. postanal tail (debatable).
The embryo has three parts to its blastosphere: the gut (surrounded by the endoderm), the middle (mesoderm) and the outer wall (ectoderm). In the endoderm, a bulge begins to form, and eventually separates and this chord becomes the notochord. The notochord is now floating in the middle of the mesoderm. It influences the ectoderm to being to form a dip which grows to be a valley and finally inverts and forms a round doughnut. All this forms in the mesoderm too. The notochords job is done, and it dissolves. The doughnut becomes the nerve chord.
The link is here. Be sure to read the article. It has other fish they have filmed but did not show and a second video at the bottom.
I know I should not be as excited as I am at working through the equivalencies insets. But they are really hard to make out of poster board. Montessori materials are so precise. Darn that need for exactitude.
One of the disadvantages of teaching at home is the need to purchase only what I can’t make as far as materials go. So, that left us with no beautiful metal insets to study the beginnings of Euclidean geometry and lay the foundations for theorems. Eight presentations with 12 or so paper insets. That came after the triangle boxes had to be traced and made into papers for the visual only discussion of the topic. Plus the extensions for the boxes require tracing the tracings. Agggggggg. Breathing again.
Triangles are equivalent when their bases are equal and their altitudes are equal.
We are working on “note taking” skills. The boys want to research until the cows come home. This series of exercises is designed to provide them with a limited amount of information that they synthesis into paragraphs or in BR’s case isolated notes.
Also we are to begin with creatures with notochords this week. I realized the implications of the notochord and decided to move backward a bit to discuss differences among species beginning with creatures with a coelom and those without. This discussion has its roots in the embryonic development of creatures and goes to things like why there are no “identical twin” worms.
Coelom advantages and divisions among creatures with a coelom. By AV
A coelom is a cavity in the body that surrounds or almost surrounds the gut. If an animal has no coelom and during digestion if the animal has to make a sharp turn, 
the turn will cut off the digestive track. Think of it like a kink in a hose interfering so no food passes through. There are other reasons that a coelom is optimal. It protects organs, allows for more complex organs, allows for egg storage before release, allows for a true hydrostatic system, and the fluid in the coelom can help with respiration.
The formation of the coelom is simple. There are two ways to do it: protostomes’ coelom come from the ectoderm splitting away in the early stages of the embryo and deuterstomes’ coelom comes from an expansion of the gut in a pinch and pull action.
An early embryo begins as a ball of cells. This ball will develop a hole. When the hole forms in the protostomes, it become the opening for the mouth, but when it forms in deuterstomes, it becomes an anus.
JV went with his small is better theory of life. I photographed it.
BR did an amazing job of copying my notes and synthesizing the overheads we used into a good explanation. (The College of Charleston gave us their overheads as they were updating their curriculum. Thank you Dr. Wiseman)
What do you do with a child like JV. (It sings nicely if you use his first name.) He resisted every advance to memorize multiplication facts. He was the proud owner of a mini-Pythagorus board that he would whip out in a moment’s notice of math needs. I broke all rules and made him do worksheet after worksheet this past fall. The ability to estimate/approximate numbers left his desire to do square rooting on the shelf.
But now we have reviewed and learned multiplication tables and worked through skills needed again. Here we are standing at the brink of understanding squaring of polynomials.
JV working out a large trinomial square on the pegboard.
For this work, a peg board and pegs are needed. For all you not Montessori math folk, the colors are representative of place value – green: units, blue: tens, red: hundreds. One of the main reasons for this lesson is to help the child discover that the squares in polynomials “skip” a place in their squaring layout. For example: the square of 235’s layout would find the unit as a green unit in the simple family but the second square is red saying hundreds in the simple family while the third square is leaping over the green units of the thousands family to the blue of the tens in the thousands family.
This work requires multiple multiplication of multiplier to multiplicand in a broken out form: (200 + 30 + 5) x (200 + 30 + 5)= y.
So JV had to multiply – the horror.
200 x 200 = 40,000 (blue tens of thousands square)
200 x 30 = 6, 000
200 x 5 = 1,000
30 x 200 = 6,000
30 x 30 = 900 (red middle square in the layout signifying hundreds place)
30 x 5 = 150
5 x 200 = 1,000
5 x 30 = 150
5 x 5 = 25 (green for units)
The child sees how the other pieces fit into their hierarchal support positions.
JV's layout - oops didn't do one problem quite right - redo.
Now, suppose the child makes a mistake in his original calculation and comes up with 5 x 5 = 16 and tries to place 16 beads in the board, he won’t have a square and will see that the answer can’t work.
The usefulness of the visualization helps the child realize the pattern that numbers make in the higher orders of math and almost instinctively know when an error is about to be made and check themselves. I would predict that tomorrow JV will anticipate it.
Then the adding begins. All the original answers are added together to see what the square reads.
Did I mention this is tedious?
So, lets review. The child is working on:
- multiplication facts
- multiplying by 10’s
- place value
- geometry – study of area and study of square
- addition
- actual squaring of a three or four (or more) digit number
AV did tons of research for this project. Crinoids are relatively rare and sea lilies are extremely rare. There is very little research about them.
Sea lilies, one of the two types of crinoids, as they are more properly known, went nearly extinct. Those that still reman are closely related to starfish. So many of these aquatic invertebrates died that most of the is island of Malta is made up of their tiny calcified skeletons.
Sea lilies are essentially cups on stalks that filter out small animals like plantain or larvae in the water. The particles are trapped inside grooves in their tentacles (sometimes called arms or rays).
In these groves, there are tuber feet which pass the food to the mouth in the center disk that in sea lilies is known as the calyx or aboral cup.
Feather stars are also crinoids but they can swim having no stock. This helps in mobility. Although some sea lilies can lurch to where they want to go, feather stars have a distinct advantage in movement. Both sea lilies and feather stars feed the same way with groves in there rays.
One interesting anatomical part of a feather star are cirri. Cirri are similar to bird’s claws. In feather stars, it enables them to hold onto the rocks and move from place to place.
Crinoids are certainly animals that all sea vertebrates could not live without. They filtered all the oceans from a mostly calcium soup to the ocean we know to day. These small lesser known animals have changed the course of the sea’s history forever.
The guys are beginning their final week studding echinoderms. Today they eased into work by begging for the oven-bake clay. BR’s piece did require multiple firings and needed real shells to mold. It was an experiment that worked and well.
BR created a starfish prying open a scallop. He worked particularly hard on the legs to get the groove correct.
JV's piece is a cutaway of the internal parts color coded by system.
Here are photos of the acquisitions from yesterday’s pirate adventures.
JV purchased a dragon gobi. They clean your sand by taking mouth fulls and cleaning alga from the particles.
AV's Organ Pipe Coral. Look dead center. The darker shade of purple with the white "flowers". Imagine all the polyps out fishing. It is beautiful.
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.
