Adventures in Algebra*

"A fish starts at a depth of d feet below the surface of a pond.  While searching for food it ascends 4 feet, then descends 12 feet.  Its final depth is 15 feet below the surface.  

What was the fish's initial depth?"

Before we deal with d, let's draw a picture.

Wait, we need a shark.
Never mind that it is a pond and not the ocean.
"Fish are friends, not food."

At this point, I stopped taking pictures, because equations are serious business.  I assure you, the problem did get solved.  The fish's initial depth was -7 feet.

She wrote the algebraic equation after she figured out the answer.  She is an immensely practical person and sees no reason for a variable equation if she can figure out the answer in her head.  But she is learning that if she wants to move on to the next question, she has to show the work in algebra language.  

d + 4 - 12 = -15

*It is really pre-Algebra, but that wouldn't make a pretty alliteration.

Narration

Government

History

Where We Are

(It is tiresome to read someone's apology for not posting and resolution to write more, so I won't say anything about my hope that I will be a more dedicated blogger this summer.)

I mostly want to write about where we are in our homeschooling.  My two youngest are still finishing this year's schoolwork, but Aravis has officially been handed her diploma and is now a high school graduate.

Mariel and Cornflower will do math all summer.  We are also doing a neurodevelopmental program.  I am learning more about how the brain works, which is very interesting: visual/auditory processing, hand/eye/ear/foot dominance. That sort of thing.  It goes on for four months and then we will see whether the results are worth the effort.  I mostly hope it will help with short term memory, organization and sequencing.  The girls are being good sports about it.  I promised Cornflower we would get her some workout clothes. :)

We take daily walks as part of the program.  We are going to get pedometers and once we have walked a total of 450 miles, we are going to visit friends that live 450 miles away.  That will be our reward for sticking it out.

Our work has changed too.   The Warrior Poet is working in a warrior shop now.  He sells guns and that sort of thing.  It's more his style than selling soap.  He is happy. This past year has been confused and frustrating, like a whirlwind, but the Lord has set us down in a good place.

I teach more private music lessons now, three afternoons/evenings per week.  I enjoy teaching music.  Funny how I always feel renewed after working with individual music students for a few hours.  I must be meant to do that sort of work.

We are still adjusting to the odd times of the Warrior Poet's retail and my after-school teaching schedule, looking for those golden hours when we are all available for family time.

Aravis still works at the Walgreens on the corner, although that may change once she gets her schedule for her first term at the university.  Mariel just started a job as car-hop at the nearby Sonic.  Cornflower aspires to work as well, and actually did have a twice-a-month gig this school year, teaching music-readiness activities to two of the brightest and sweetest little boys you ever did see.  They are off for the summer, but will begin again in the fall.  In the meantime, she plans to volunteer at the library.

Here are the books we read this year. An asterisk (*) means we are still working on it. A bold title is one I read also.  Italics means we read it together (at least some of us).  I am not including outside courses or curriculum-type things.  These are real books we read. We also did ALEKS math, Apologia sciences, Lost Tools of Writing, the Hillsdale online Constitution course, fine arts co-op, an outside Spanish class (Mariel), dual credit courses (Aravis), a personal finance course (Aravis), drama club, and orchestra/music lessons (Cornflower).  And we read the Bible together every school day.  Now.  These are the books we read:

Aravis (a cobbled-together Year of Ancients)-

The Iliad
The Epic of Gilgamesh
Vanity Fair
The Greek Way
The Roman Way
The Portable Greek Historian
The Portable Roman Reader
Heroes of the City of Man
The Christian Imagination
The Odyssey
Quo Vadis
The Blood of the Moon


Mariel (AO/HEO Year 9)-

A History of the American People
Hamlet
Founding Father: Rediscovering George Washington
*How to Read a Book
Land of Little Rain
Marie Antoinette and Her Son
Miracle at Philadelphia
Mozart (biography)
Ourselves
Salem Witchcraft Trials
She Stoops to Conquer
*Simond's History of American Literature
Reflections on the Revolution in France
Tale of a Tub
The Four Loves
*The God Who is There
*The Jesus I Never Knew
The Problem of Pain
The School for Scandal
The Sea Around Us
The Vicar of Wakefield
*Undaunted Courage
*Waverly
Poetry of Byron, Pope and Phillis Wheatley

Cornflower (AO Year 6)-

*Be Ready to Answer (updated version)
God's Smuggler
Age of Fable
Albert Einstein and the Theory of Relativity
Animal Farm
Augustus Caesar's World
Carry a Big Stick
Genesis: Finding Our Roots
It Couldn't Just Happen
*Little Women
*Never Give In
School of the Woods
Secrets of the Universe
Story of the Greeks
*Story of the Romans
Story of the World Vol. 4
*The Bronze Bow
The Story of David Livingstone
Poetry of Alfred Noyes and Robert Frost

I've been feeling kind of down that we aren't finished with school yet.  That is a common small-talk question currently: "Are you finished yet?"  Well, no, we are not.  And it made me feel somewhat down, like we hadn't worked hard enough to get things done on time.  But we did a lot.  Maybe I shouldn't plan so much of everything next year.

Building a Tree

Today we went to the Kimbell for a lesson on architecture.  Little La's building intrigued me, so I am breaking the bloggy silence with a photo essay.

Building is much more friendly with two.  

"What is it going to be?"  

"A redwood tree."

Toothpick branches

Tissue, toothpicks and glue

It begins to resemble a tree.

Concentration

To be continued, perhaps...

Narration: Secrets of the Universe Ch. 1-2

LittleLa (age 11) wrote this narration last week:

Federal laws.  They're not the only kind.  There are natural laws, like the Law of Gravity.  Who voted on that law?  Nobody!  It's a law of nature.  Some people break federal laws, like speeding.  You can't break Gravity.  Every time you drop a ball it will fall down.  Not up, down.  Gravity is unbreakable.  

Scientific laws are just describing science.  Many scientists discover brilliant things because of one person, like Newton and Einstein.  Very rarely scientific laws do change because scientists find information that is more accurate and sensible.  Natural laws are mostly written in math equations.  This way it is easier for scientists to compute their experiments. 

Archimede's Principle: If you fill a tub to the edge with water, when you put an object in the water, the equal amount to the mass of the object will overflow out of the tub. 

I like this narration.  I can tell by the sentences that she was trying to summarize paragraphs.  This is a great exercise and can be difficult.  My favorite part is the point she makes about scientific laws.  We will have a bit of discussion to clarify that scientific laws never change, but man's understanding of them changes, and then man needs to bring his definition of the law into harmony with the actual law.  I also think she needs a better definition of natural law than she comprehended in this reading, so I will bring that to her attention next week.

She misspelled four words:  they're, experiments, accurate and equations. I corrected them here for ease of reading.  These words, along with any others she misspelled last week in written narrations, will be her spelling list for next week.  She will study the correct spelling until she can visualize it correctly with her eyes closed.  Then I will have her run around the outside of the house singing a song and after that I will give her a spelling test.  If she misspells them again, they go on the list again.

Math and Folk Songs, or Old Joe Clark's House

Yesterday morning Cornflower and I were studying integers: graphing coordinates to form a shape, then stretching, enlarging or reducing the shape by multiplying the original coordinates in different ways.

She had to make a new graph each time, which she found tedious.

She had just began to grumble when she discovered the shape she was forming was Joe Clark's house.

Old Joe Clark, he had a house

Eighteen stories high

And every story in that house

Was filled with apple pie.

(Lyrics adapted to fit Cornflower's graph and preferences.)

All she needed was to remember a favorite folk song and graphing became fun.  I call that true liberal arts education.  =)

(I guess I should point out that I did not make the connection for her.  I wasn't sitting at her elbow saying, "But look!  It's Joe Clark's house!"  I also did not contrive lessons containing folk songs having to do with integers and geometry.  She learned that song through her violin lessons and our folk singing at home.  It just happened to connect to her math today.)

Update 6/29:  Today, after a frustrating lesson on factoring, she exclaimed, "O, how full of briars is this working-day world!"  This is a quote from Shakespeare's As You Like It, and highly appropriate, I thought.

Finishing

"Better is the end of a thing than the beginning thereof."  --King Solomon

We have not yet finished all our AO/HEO readings for the year.  Here is a list of what we are reading or have read in the last three months.  Most of these books will be finished by mid-July or earlier.

The journey is vital and perhaps more important, but finishing is valuable too.

Cornflower (AO Year 5)

Story of the World Vol. 4 by Susan Wise Bauer
Book of Marvels by Richard Halliburton (finished yesterday)
Age of Fable (this will go for another year)
Poetry of Paul Dunbar and John Greenleaf Whittier
Usborne Complete Book of the Human Body (not my first choice, but I couldn't find our copy of Christian Liberty Nature Reader 5, and this is what we had at hand)
This Country of Ours (almost finished after three years!)
Inventing the Future (biography of Thomas Edison-- finished)
Passion for the Impossible (biography of Lilias Trotter)
The Sciences by Edward Holden (almost finished)
Kim by Rudyard Kipling
Battlefield of the Mind for Kids by Joyce Meyers

Mariel (HEO Year 8)


English Literature for Boys and Girls
The Case for Christ (finished)
The New World (2nd volume of Churchill's History of the English Speaking Peoples)
Essays of Sir Francis Bacon
Christopher Columbus, Mariner (finished)
A Coffin for King Charles
Secrets of the Universe (Fleisher)
The History of Art by Jansen (almost finished-- we are going to read Van Loon's art history book next year as a group)
Kon Tiki (finished)
Poetry of Milton
How to Read a Book (Adler/Van Doren)
Ourselves by Charlotte Mason

Aravis (HEO Year 11)


The Hiding Place (finished)
Is God a Moral Monster? (finished)
A Short History of Western Civilization 
Testament of Youth (finished)
The Men Behind Hitler (finished)
Economics in One Lesson (finished)
On Writing Well
Six Easy Pieces
The Microbe Hunters (finished)
Amusing Ourselves to Death (finished)
The Chosen (finished)
Fahrenheit 451 (finished)
The Hungarian Revolt (finished)
Nuremberg:  the Justice Trial (finished)
Brideshead Revisited (finished)
Darwin's Black Box
History of Art (Jansen)
When God goes to Starbucks
A History of the American People by Paul Johnson
Ourselves by Charlotte Mason

All of Us Together


Leviticus (finished)
Numbers
1 & 2 Corinthians, Galatians, Ephesians, Philippians, Colossions, 1 & 2 Thessalonians, 1 & 2 Timothy, Titus, Philemon, Hebrews, James 1 & 2 Peter, 1/2/3 John, Jude (finished-- we read these fast because we wanted to read the letters as *whole epistles*-- the way they had been read originally)
Revelation
Romans (with our church)
The Holy War by John Bunyan
Emma by Jane Austen
Madam How and Lady Why (Mariel and Cornflower and I-- almost finished after two years!)

Appreciating Shakespeare

Today we had the Shakespeare class over to watch a movie version of the play we just finished reading.  We watched "As You Like It" (1936) with Lawrence Olivier and Elisabeth Bergner.

I think the kids enjoyed the movie.  They seemed to like the actor's portrayal of Touchstone, thought Duke Senior was a little overdressed for the forest, and wondered whether "our" Corin should have a beard.  They were disappointed at some of the cuts.  They went for more snacks during the "Seven Ages of Man" monologue.  They looked at me knowingly when Audrey sang the right tune to "It was a Lover and His Lass".  They thought Rosalind was cute, although she whacked people too much with her stick.

Our class' favorite scene is when Orlando says he "can live no longer by thinking" and Silvius explains what it means to love (Act V Scene II).  The scene is cut short in the 1936 version.  This raised an outcry.  They wanted ALL the now-familiar lines.

In our class reading of "As You Like It", that scene had been a sort of tipping-point.  It was then that I knew for sure all of us were on the same page.  At the end of the reading, the kids had burst out laughing, then talked excitedly.  They wanted THIS scene for Family Night.  The other teacher and I had already cobbled together a script of short scenes for the end-of-year program, but I want you to know we took it apart and redid it.

Many times, especially at the beginning, students told me, "I don't get it."  Some of them had never read a real Shakespeare play.  I gave background, but tried not to explain too much.  I told them Shakespeare wrote for regular (16th Century) people.  I told them to grasp what they could and leave the rest, to listen to the rhythm if they couldn't catch the sense, to focus on the subject and verb in the sentence because the rest was decoration.  We paraphrased a scene into postmodern English.  We paraphrased in our narrations.  We made an ANI chart on the issue of whether Rosalind should have deceived Orlando.  One by one, week by week, students engaged, and by the day we read Act V Scene II... the last act, although not the last scene... all of us together appreciated Shakespeare.  "As You Like It" is now our play.

Next year I want to read Hamlet.

Narration: Economics in One Lesson

By Aravis

There is a curious proposal known as “buying back the product” which unions and “amateur economists” (Hazlitt’s words, not mine) like to wave around.

The idea is that the workers in each industry should be paid enough to buy the products they are making. But then the people who make Fords will not be paid as much as the people who make Cadillacs, and the unions won’t have that. (This is a special case of the “purchasing power” fallacy, which we have looked at before. In order to give the employees 30% more purchasing power, the employers raise wages by 30%. But now there is a discrepancy in their bookkeeping, so they raise prices by 30% and the employees have just the same purchasing power as before.)

The biggest issue with this is that the employers do not fund the product. All the people who buy the product fund it, and all the people who contribute towards its creation: the people who make the supplies, the gas stations that fuel its transport, the automotive technicians who make the trucks to carry it, and the architects who design the stores to sell it. So any price-fixing must be done by all who have contributed – not by the employer alone. This is clearly an impossible task, which is why it is best to leave the economy alone.

“If we try to run the economy for the benefit of a single group or class, we shall injure or destroy all groups, including the members of the very class for whose benefit we have been trying to run it. We must run the economy for everybody.”  --Henry Hazlitt

Narration: Bacon's Essay, "Of Studies"

By Mariel

Books are a gift; when you study books are using that gift; so if you love to study books and ponder them in your heart, you love to use this wonderful gift. Study is a delightful thing to do. When you are bored on long car trips and everyone is being very loud, you can take out your history and literature tomes and say, “SHH! I’m studying!” and the car will instantly become quiet.  It causes you to have something to say when you are in a group discussion of Churchill’s The English-Speaking People. But just remember, you are a true scholar when you can be like this man:

Once there was a man who loved to study. He had a wife with a huge social life who loved her husband, but quite frankly, didn’t think that her husband would ever amount to anything. He was so quiet!

One night when they came back from a fancy formal dinner party, the wife started berating her husband. 

“When we were talking about drills, you didn’t say a word! You know tons about drills! Why didn’t you speak up!?”

The husband answered quietly, “I already know what I know, but by keeping quiet, I can learn what others know too.”

You don’t learn to show off, you don’t learn to make money, you learn to glorify God.

What did the English Civil War and the French Revolution have in common?

A narration by Mariel from The New World:

The English Rebellion of the 1600's and the French Rebellion of the 1700's are very similar. Battles, failed flights from the country, imprisoned royalty, decapitated monarches, a new tyrant who is in charge of the 'Republic', even the son of the dead monarch becoming king after the Republic failed. The same things happened. The kings were imprisoned and killed for treason and stupidity. Only Louis XVI did not have the courtesy of a trial. England, and the new Republic are headed for ruin. Cromwell will be Lord Protector. But what is a Lord Protector? I have heard that term so many times that it has lost the meaning. The internet defines it as the head of the Commonwealth of England, Ireland and Scotland. Watch out, UK! You've killed a tyrant—and invited another one in. The sad thing is is that Cromwell is so convinced that he is doing the right thing. You know what? Charles thought he was doing the right thing also, and look where he is. Barely cold in his grave. Look out, Cromwell. Soon Charles II will hide in an oak.

Kipling, Physics and Economics

 The final paragraph of a narration by Aravis from Six Easy Pieces: 

Although there is always the same amount of energy in the universe, it is not always available. For example, the sea has a certain amount of energy, because it is always a certain temperature; however, it may take more energy than it is worth to collect all the sea’s energy in one place so that we can use it (meaning that we may expend more energy than we collect). While the sun has a tremendous amount of energy, only one-two-billionth of it falls on the earth (the rest falls on stars, Mercury, Pluto and the rest). If we could harness all the sun’s power, we would have an incredible supply of energy – however, we could easily destroy something necessary out in space by depriving it of energy. And here, O Best Beloved, is where physics intersects with the science of economics.

Term 2 Exams: The 11yo's take on Austen's Emma...

I asked LittleLa to tell what has happened so far in the novel, Emma, which all of us ladies are reading together.  Here is her written reply:

Frank Churchill left after they planned a ball and does not expect to be back soon.  Mr. Elton is married and brought back his bride from Bath, Mrs. Augusta Elton.  She thinks she is the best thing that has ever happened to anyone.  Emma thinks Jane Fairfax and George Knightley have something going.  Emma thinks her recreational date is Frank Churchill!

Term 2 Exams: The Holy War

This is Little La's narration of The Holy War by John Bunyan.  This is the episode after the surrender of Mansoul in which the townspeople petition Emmanuel three times:

Well, first they tried coaxing him and sweet talking, “O, powerful one! We look back and see our sinful ways!” Secondly, they tried guilt-tripping themselves. “We know our worthless place, O great Son!” Thirdly, they sent 3 this time with ropes about their necks for when they were to die. They honestly poured out their hearts. Emmanuel was crying! He dressed them richly and went to Mansoul. Emmanuel went to his palace and everyone rejoiced!

And this is Mariel's:

The People of Mansoul have surrendered. After living in suspense for a little while, they sent some messengers to Prince Emmanuel and beg for their lives. The first messengers went to the Prince and bowed very, very low.  “Please, O Mighty Prince,” they said, “Please have mercy on us and the rest of the miserable wretches in the unfortunate Town of Mansoul!”

But although the Prince treated them with kindness, he told them to go back. The messengers were filled with fear and trembling. They went back and said, “The Prince will not have mercy! O lackaday! Lack a couple of days!”

Everybody moaned for a while, but soon, they decided to send new messengers.  They came back with the same experience. But when they told everyone, someone said that this horrible news needed to go to the Mayor, My Lord Will-be-will and the Recorder.

They told these three men of the trials that the messengers had gone through. Then one wise old man shook his head and said, “We must send these important men-the Mayor, Will-be-will and the Recorder- to the Prince, in sackcloth and ashes, and they must beg for the lives of the people in the wretched town of Mansoul.”

 So they went to the Prince, clothed in sackcloth and ashes, with ropes about their necks.  They threw themselves at His feet and said, “O Lord and Prince Emmanuel, we were led astray! We know that You are in the right, and we know also that if it is Your Will, we will die for the sins we have committed.

“But we entreat You, we beseech and implore You, to have compassion and mercy on us. We are but insignificant worms, not worthy to lick the dust off of your feet. Please have mercy on us, the sinners.”

The Prince turned and smiled, and at that smile, the prisoners knew that they were to live. The Prince washed their feet, removed the sackcloth, ashes and the rope, clothing them in magnificent velvets, silks, brocade and feathers. The Prince gave them a flag and told them to go back to Mansoul.

SLOW-MOTION MOMENT: Picture this scene in a movie. Three men, in brilliant arrays, come running over a hill, a glorious flag streaming in the wind. They are shouting, “We are SAVED!! We are SAVED!!

This is what we need to do every day. Wake up and say, “I am SAVED.”

Term 2 Exams: Biography

Here is Aravis' response to the question, "How did Anne Frank serve others?"

Anne Frank didn't realize she was serving others. She never meant to share her diary – it was her only girlfriend at a time when friends were scarce – but the little book gave a face to the millions of ordinary people who were killed in the Holocaust. Anne had a normal, happy childhood until she had to go into hiding, not long after she started her diary. The rambling journal tells about the tension between her and her mother, her inability to relate to her sister, the awkwardness of falling in love and the constant bickering between the families with honesty, directness, and more than a little dissatisfaction with her own role. “They don’t ever seem to understand me,” she often complained to the diary she called “Kitty”. “One day I’m Anne who is so clever and nearly grown-up, and is allowed to hear all sorts of interesting things. The next day Anne mustn’t stick her nose into the grown-ups’ business and ought to tend to her studies.” Any girl could sympathize with Anne’s angst, which draws the reader in to the story of Jews in hiding. Her Everyman quality made people care about the individual victims of the Holocaust.

(I wish she had added paragraph breaks!  But I like the content.)

Term 2 Exams: Picture Study

This is Aravis' description of her favorite picture by this term's artist, Norman Rockwell:

The poignant Little Girl Looking Into Mirror was certainly one of my favorite Rockwell paintings from this term. A little girl sits outside on the grass, before a gold-framed mirror tilted against a chair. Her abandoned doll lies against the mirror, with one foot on either side of the frame. The girl, her hair pulled up into pigtails, scrutinizes her own face carefully; she appears to compare it to that of a woman in the book spread on her lap. She does not look either pleased or displeased with the comparison, merely thoughtful.

In class, I heard many theories about the symbolism of the picture. The book in the girl’s lap might be a magazine with a beautiful movie star in it, or a photo album with a portrait of her mother; perhaps the girl wonders whether she will grow up to look like a famous lady, or like her own mother. The doll represents the girl herself – alone and thoughtful, with one foot in adulthood and one in childhood. The mirror also represents this: the elegant frame and spotless glass rest against a red wicker-bottomed chair outside in the backyard. There is a quiet tension to the picture, as the girl contemplates her move from child to young lady.

Exam Week: Fishergirls on the Shore of Tynemouth

Mariel wrote the following answer to the question, "Describe your favorite picture from this term's picture study."  She refers to this picture by Winslow Homer. She wrote her answer in the style of a newspaper article, and took imaginative liberties with unknown details. (I'm not sure what I think about that.)  If you will, imagine yourself as a citizen of Tynemouth:

In this wonderfully proportioned painting, local artist Winslow Homer has captured, in a sepia tone, the authenticity.  Homer, a 48-year-old American, has painted over ten paintings of the locals here in Tynemouth.  This one portrays our mayor's two lovely daughters.  As you know, Elisabyth (on left) is pregnant with her first child, but still loves to help her sister Magdolyn, with the knitting.  "it was a great pleasure and honour to be able to paint these two ladies," says Homer.  "They are the epitome of happiness.  I have given them prominent positions in other paintings."  We love Homer's paintings and hope that he will find the best picturesque places in our little Tynemouth.

Exam Week: Analysis and Synthesis

Here is another exam narration from Little La.  The book is Madam How and Lady Why by Charles Kingsley.  La gets a bit cute with her answer on this one, and had a hard time spelling "analysis", but I'm glad she understands the difference between analysis and synthesis and has begun to see the importance of each.  I corrected spelling for reading ease (emphasis hers):

Analysis and Synthesis were brothers and the grandchildren of Madam How.  Analysis took apart and analyzed.  Synthesis put them back together again.

One day, Synthesis captured Analysis because he wanted all the power.  He starved Analysis in the dungeon and forced him to tell him how things worked.

Madam How was not pleased.  Not ONE bit.

But after months Analysis escaped.  He analyzed, but no one could do Synthesis' job.  So, analysis and Synthesis made up and were nice.

Madam How LOVED this.  Many bits.

Exam Week: The Berry Pickers

(I removed the image because, although it appears to be public domain, I am not absolutely sure.)

Little La's narration of the above painting by Winslow Homer.  The question is, "Describe your favorite picture from this term's picture study:

There are four girls and three boys and they all have hats and a little silver bucket to collect blueberries.  It looks about 1 o'clock in the afternoon.  They are by the seashore and about to have a picnic.  I do not know what this picture is called.  One of the girls is leaning on a big rock.  There are big mountains and a village across the seashore.  There are a lot of flowers, too.

Exam Week: John Bunyan's Holy War

Last week the children took AO/CM exams for Term 1.  I am posting some of their answers this week.

This answer was written by Little La (formerly known as Cornflower).  The book is The Holy War by John Bunyan.  (It is recommended in Year 8, but the girls and I are reading it aloud together.  Little La is in Year 5.)  The exam question is, "Tell how Diabolus took over the kingdom of Mansoul."

Diabolus and his minions set up camp at Eargate, right outside of Mansoul.  Each day a new bad guy would go and tell a speech to the town of Mansoul.  Now, Mansoul was ruled by King Shaddai.  Diabolus was taking over, or, really, succeeding.  When Diabolus stepped up to talk to Mansoul, his speech was very convincing.

"My friends in Mansoul!" he started, "You are such kind, wonderful people!  So true to your King!  But, have you considered why he's not making you kings?  Greed!  Greed!  If you let us in, and help us defeat your King, make me King, I'll let you rule with me!"

Mansoul started cheering.  They were corrupted and let Diabolus in.