Grade 4 Fractions

Here are a few of my son’s pages of his Fractions Main Lesson Book from 4th grade. I used the indications from Live Education, but there is really nothing all that earth-shattering in their Fractions book. You can probably make up any story, or adapt any story to introduce fractions. Although their multiplication and division story is quite funny!

I also used, as usual:

 
Making Math Meaningful: A Source Book for Teaching Math in Grades One Through Five

If you are unfamiliar with this book, I can tell you that it is not a ‘curriculum’, but it simply provides a guide for what to teach and some ideas on how and when to teach the concepts. I love the way that he explains dividing fractions. This is a concept I should go over every few months with my children.

So we began with one whole:

02 Fractions One

I gave my son a stack of circle cardstock that I bought at a craft store (Michael’s, I think), and we began to work on the basic divisions and equivalents. He drew the fractions on the circles, cut them out, then glued them on the page with glue dots. We reviewed the previous day’s fractions on the board before going on to the next.

03 Fractions 04 Fractions

05 Fractions 06 Fractions

Live Ed uses the story of a kingdom named Wylynn, where the land is parceled out for different activities such as farming, horse ranching, cattle ranching and such. Then each year the King’s advisor presents a tally of the kingdom to the King:07 Fractions Wylynn08 Fractions Wylynn

At the end of the year, he made a nice cover for the book:

1 Fractions Cover

After our introductory fractions block, we reviewed and expanded on what he had learned for the rest of the year. For this, we used the the Key to Fractions workbooks. This set works well for us. The authors really present fractions in a manageable way. My daughter flew through this set in fourth and fifth grade. There are so many repetitive problems in this series, that I had her skip many of them. I would put a box around the problems that I wanted her to do each day. For my son, the repetition seems worthwhile, so I have him do most of the work in the book. For that reason, he only finished the first book last year, and he has just started (in fifth grade) the second book.

 
Key to Fractions

In addition to all of that, it is fairly easy to find fractions all around us, so I try to frequently ask my children things like, If I cut the pizza into thirds, and then I cut each piece in half, how much of the pizza will each piece be? If Dad eats three pieces, how much of the pizza will he have eaten? I don’t know why, but fractions always seem to lead to food!

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Grade 3–Hebrew Letters

As I was organizing our old schoolwork, I came across the Hebrew letters that I painted during my daughter’s third grade year. We had a good time with this block, as she loves language and lettering. The Hebrew letters are not only beautiful, they also have spiritual meaning. I bought this book for our studies:


The Book of Letters: A Mystical Hebrew Alphabet

We loved this book! It is even bound on the right hand side, making the study seem very authentic indeed. This book looks interesting too:


The Wisdom in the Hebrew Alphabet

We painted the letters on ruby red cardstock with gold paint. The gold paint smelled terrible, so we painted them outside. We tried to write a word in Hebrew for each letter, plus a little reminder about the meaning of the letter. These pages are so beautiful in person, but I could not really capture their beauty with my camera!

 01 Hebrew Letters 02 Hebrew Letters 03 Hebrew Letters 04 Hebrew Letters 05 Hebrew Letters 06 Hebrew Letters 07 Hebrew Letters 08 Hebrew Letters 09 Hebrew Letters 10 Hebrew Letters 11 Hebrew Letters

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Grade 4 – Man and Animal (Zoology)–Block 2

My fourth grader’s last block of the year was Man and Animal (Zoology). We studied different types of animals and their characteristics. We looked at the types of teeth and other specialized qualities of the animals, which make them unique and amazing. We then talked about how each of these qualities have been given to humans and we bring them together in a balanced way.

I think this is an inspiring way to present this block, as so often zoology can easily dissolve into a study in how humans have negatively impacted the animals of the world. It seems to me that it could get a little depressing for the fourth grader to hear that over and over, so I like the idea of planting a seed in my children that they have been given special gifts. Those gifts are to be used to bring goodness into the world for humans and animals alike.

My other zoology posts.

The cover page was inspired by a cover page at jamedarisgrade4.weebly.com:

01 Cover

02 Penguins

03 rodents

04 carnivores

05 horses

06 animals

07 animals

Here are a few of my artworks:

08 wolf mom painting09 wolf mom pencils

10 horse mom

Why is it that some people seem born able to draw horses? I am not one of those people… I can’t believe how hard it is after all these years!

Posted in Grade 4, Man and Animal / Zoology, Watercolor Painting | 1 Comment

Grade 6 – Roman History

Now that the school year is officially wrapped up, I will try to post the children’s finished books as I find the time.

One of our favorite blocks of the year was Roman History. Such rich stories, filled with inspiring, brave, cruel, and even amusing characters! And there are so many opportunities to discuss moral issues, as the struggles of the Romans are so very relatable to our modern ideas of loyalty, patriotism and justice.

To present the stories of Ancient Rome, I listened to Eugene Schwartz’s conference. This was the most inspiring resource for me. I also found a few things in Live Ed that were helpful (particularly the stories of the first seven kings of Rome). Live Ed recommends the source books by Livy, which I read as well. I really only found Livy helpful for the first seven kings, and maybe a bit during the republic, but it is difficult and slow at times. He does go on and on about this person and that… he is essentially recording just about every historical event of Ancient Rome, and that is just too much to cover, in my opinion. But it was helpful for my study, and I did read some passages to my daughter.


Livy: The Early History of Rome, Books I-V

Ancient Rome by Charles Kovacs was an excellent resource:


Ancient Rome (Waldorf Education Resources)

We also checked out several books from the local library that illustrated the life in Ancient Rome:


Ancient Rome


Ancient Rome


City: A Story of Roman Planning and Construction


Augustus Caesar’s World

I came across this book after the block, and it looks very good. I think I may try it out next time:


Famous Men Of Rome: History for the Thoughtful Child

The cover and table of contents were made at the end of the year:

Rome 01 Cover PageRome 02 Contents

We began with a review of Aeneas, who escaped the burning of Troy and finally settling in what would someday be Rome.

Rome 03 Aneas and Troy

Next we studied the first seven kings of Rome, beginning with Romulus:

Rome 04 Romulus and Remus Writing Rome 05 Romulus and Remus

Rome 07 Horatius and Curiati Rome 08 second and third kings

Lucius Tarquinius’ hat was stolen by an eagle, which according to his wife, was a sign that he was meant to be king of Rome:

Rome 09 Lucius Tarquinius Rome 10 Fourth and Fifth Kings of Rome

Rome 11 Map Rome 12 Sixth King Servus Tullus

Rome 13 Tarquinis the Proud seventh king Rome 14 Republic

One of the most inspiring stories of the Republic of Rome is that of Horatius bravely guarding the bridge to Rome. There is a very long and beautiful poem called ‘Horatius’ by Lord Thomas Babington Macaulay that is in the The Waldorf Book of Poetry: Discover the Power of Imagination, but it can also be found many places online. She put part of the poem in her book, and she absolutely fell in love with the whole piece, so she is trying to learn it. It is 8 or 9 pages long, and she has so far learned about half of it! She wants to continue working on it over the summer, but we’ll have to see how that works out!

Rome 15 Horatius Bridge Rome 16 Horatius Bridge

Rome 17 Hannibal Rome 18 Hannibal

We talked about Roman decadence and the differences between the plebeians and patricians. It is said that the very wealthy would eat lying down, being served by slaves, and left their food waste on the floor to be cleaned up by slaves!

Rome 19 Roman Home Rome 20 Roman Home Eating

Rome 21 Roman Numerals

Rome 22 Antony Cleopatra Augustus Rome 23 Antony Cleopatra

The portrait of Julius Caesar was made with watercolor pencils.

Rome 24 Julius Caesar Rome 25 Julius Caesar

I am so grateful to have had the opportunity to hear Eugene Schwartz’s lectures in his sixth grade conference about the life of Jesus. We spent a week or so on the subject, and my daughter was thrilled to have the story completed for her in the context of history. Absolutely wonderful. She chose to draw the Flight into Egypt in soft pastels because “they are easier than pencils”. She really wanted to go out an play!

Rome 26 Flight into Egypt Jesus Rome 27 Flight into Egypt Jesus

She may not have gone out to play on the day she drew Constantine. This beautiful drawing took a couple of hours, but we were all very pleased with it!

Rome 30 Constantine Rome 31 ConstantineRome 32 Constantine

We saw these paintings of the famous Roman aqueducts somewhere in our Waldorf School Calendar, and had to give them a try. My daughter’s painting is on the left, mine is on the right.

Rome Aqueduct 6th Grader Rome Aqueduct Mom

Posted in Grade 6, Roman History, Watercolor Painting | 4 Comments

Grade 6–Charcoal Drawing

Every other Friday, we have a watercolor painting lesson. Well, we used to paint every week, but we started a nature program every other Friday, so now we paint on our off-Friday.

However, this year I decided that my sixth grade daughter would work with charcoal during the usual painting time. My fourth grade son is still painting on Fridays, so my daughter likes to paint along with him (it is so hard for her to resist), and the lessons can go on very late as a result!

Tomas Wildgruber writes about the sixth grader in Painting and Drawing in Waldorf Schools: Classes 1 – 8 (fabulous book, by the way):

To put aside watercolour paintings for a while, with their more naïve pictorial experience, and to work instead with nuances of light and shade between black and white, is a way of coming to meet pupils’ violently fluctuating soul life at this age.

The exercises in the book begin with “plane exercises”, then move to “illuminated objects”. We have yet to begin the illuminated objects, so it will have to wait until early seventh grade. Below are our plane exercises:

01 sphere 6th grader 02 sphere 2 6th grader

03 bowl 6th grader 04 two forms 6th grader

05 scales pointed 6th grader 06 scales curved 6th grader

A “free” composition:

11 charcoal free composition

For the cover of her book, she used a black crayon and pencil, so that it wouldn’t smudge:

00 Cover charcoal drawings

And here are my pictures (the ones I could find, anyway):

07 sphere 2 mom

09 scales pointed mom 10 scales curved mom

Charcoals are quite inexpensive, which is a welcome relief. We bought a few different kinds and we are still experimenting to find what we like best. Most of the drawings above were done with compressed charcoal, then we discovered willow and vine charcoal. It is easier to get soft grays with the willow and vine than the compressed charcoal.

I suggest the following supplies:

Good Drawing Paper
Onion Skin or Tracing Paper (to put between finished works)
Willow or Vine Charcoal 
Compressed Charcoal Sticks
Charcoal Pencils
Kneaded Rubber Eraser 
Blending Sticks
Fixative

That is a long list, but you really just need the paper and the charcoal to get started. You can do all of the lessons with just those two supplies. The other supplies are nice to have, maybe as the projects get more involved, but not necessary.

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Grade 6 – Economics

This is our first venture into the world of business math. Using Eugene Schwartz’s lectures as a guide, I introduced a few economic ideas during the block, then we practiced the mathematic concepts more during the rest of the year.

We started with a history of bartering and money:

1 history of bartering

2 history of money

Then I presented a lesson about the first international banks, created by medieval knights during the crusades:

3 history of banking

And we further explored the modern concepts of banking, loans, and interest:

4 banking and interest

5 interest

In preparation for this block, I read Mathematics Lessons for the Sixth Grade by Ernst Schuberth, but I did not find much of it helpful. Maybe a chapter or so. I found a few more helpful bits in Math Lessons for Elementary Grades by Dorothy Harrer. I often use Making Math Meaningful as a reference and guide, and this block was no exception. However, I used Eugene Schwartz’s information more than anything else.


Making Math Meaningful:
A Middle School Math Curriculum for Teachers and Parents

Posted in Economics, Grade 6, Math | 4 Comments

Grade 6 – Physics

One day, I was lamenting to my dear friend that I was putting off our physics block because I was daunted by the amount of materials needed, the planning time, and the subject just seemed overwhelming. Since she has a fifth grade son, she offered to come over every day during the block and we would do the lessons together. It worked out very well! We began the week following spring break, so I spent most of spring break doing lesson plans for physics. This block really does take a lot of time to prepare. There are the materials to gather, demonstrations to practice, plus the lesson book work. It was a blessing to have two teachers this month!

I listened to Eugene Schwartz’s lectures, plus he has videos of many of the demonstrations by Roberto Trostli. Those were the basis of our lessons. Roberto Trostli has a book called Physics is Fun, but I haven’t read it yet:


Physics Is Fun

01 cover page

On the first day, we talked about “What is Physics?” The word physics comes from the Greek word, physis, which means ‘nature’. So physics is the study of nature, in order to understand how the universe behaves. I told the children about the larynx, and how we are able to produce many sounds. I placed myself where they could not see me, and I made many ‘mystery’ sounds… lighting a match, pounding blocks together, using scissors, closing a book, etc., and they each took a turn guessing the sound. That was fun! Then we drew the picture above, to be the cover of the main lesson book.

02 acoustics

At the end of the first day, my friend presented the first demonstration of the block… ‘Musical Sounds’. Since all of our children are musicians and very familiar with many instruments, she went to a music shop and borrowed a banjo and a cello, plus she purchased an inexpensive slide whistle, so that we would have some instruments that were interesting to them. The acoustics picture above is so beautiful! It took my daughter hours to draw. My friend is a wonderful artist, and my daughter was so inspired that she wanted to create something very beautiful, and she did!

According to Roberto Trostli, Rudolf Steiner cautions against becoming ‘magicians’ instead of teachers. So we are to present these ideas very simply, for the most part. Sometimes the children would complain… “I already know all of this!” But during the review the next day, they would often struggle to put into words what they had experienced the day before. So although many of the demonstrations seem simple, there is a real value in the way physics is presented. But, we still had a few ‘wow’ moments!

During the next lesson we explored pitch, and the children had the opportunity to make a scale with water in glasses.

03 acoustics

The pages above represent our study of how sound waves travel. The demonstration, picture, and text was inspired by Live Ed. We also experienced sound traveling through an old-fashioned string-and-cup telephone. It worked beautifully!

string and cup telephonestring

We used plastic cups and nylon string. The children punched holes in the bottom of the cups and used beads to keep the string from pulling through. Hold the cups so that the string is nice and tight. You need to experiment to find out how far away to have your mouth when you speak into the cup. We found that it worked best if we spoke with our mouths an inch or two outside of the cups, if that makes sense!

04 chladni plate

chladni plate 2 chladni plate 1

To end the week of acoustics, we experienced the visualization of sound. A fella named Ernst Chladi discovered this method. My friend’s husband took two steel plates (purchased from a home improvement store), and drilled holes into the top, exactly in the center of each plate. Then he secured them each with a thick dowel (maybe 1”) with a screw. The dowels were secured to a stand with a screw (I think). For one of the plates he used an old Christmas tree stand, and the other was a piece of wood. I am sorry that I don’t have a picture of these things from the side! We sprinkled the tops of the plates with salt,  and used a cheap cello bow (bought on eBay and heavily rosined) to ‘play’ the plate, dragging the bow along one of the sides. If we placed our thumb in a different place under the plate to steady it, we would get a different tone, and as a result, a different pattern would arise in the salt. We also got different patterns on the two plates because they were different thicknesses. Roberto Trostli demonstrates how to do it in Eugene Schwartz’s videos.

heat

05 heat

For the study of heat, we began by experiencing several sources of heat, and then the effects of heat of solids, liquids, and gases. Next we demonstrated how heat travels.

I guess this is where I should mention that although many of the items needed could be found around the house (or borrowed) I did  buy some supplies, like flasks, prisms, and the like from Home Science Tools. I spent about $100, and it was well worth it! I am sure that I will use most of the supplies again later for physics and chemistry blocks.

07 color

On the third week, we studied color and light. We began with the primary colors, and experienced their compliments (ghost colors) by staring at the colors and then looking at a white paper. The children mixed and painted the colors they saw. We also used our newly developed geometry skills to create a color wheel.

08 light

IMG_3786

We had a demonstration to show why the sky changes colors. On another day, the children looked through prisms at black and white shapes, and drew what they saw into their main lesson books.

09 reflection

We also worked with reflection by using two mirrors taped together to see objects multiplied, and we sent sun signals to each other in the park!

06 magnets

Magnets were a big hit! The children were in awe of the demonstrations that we presented. We gave the them a slew of household objects and they had to put each item in the ‘magnetic’ or ‘non-magnetic’ pile. Then we tested the piles, and talked about what makes something magnetic (iron, nickel, and cobalt). I also had a large selection of black rocks, one of them being magnetite. We waved a strong magnet over all of the rocks, and only the magnetite was magnetic. So, we talked about the history of magnetite (loadstone), and how it’s usefulness for navigation was discovered. The children were given an assignment to write a story involving magnets.

compasses
Our homemade compasses.

magnetic field
Two magnets placed under a sheet of paper, with iron filing sprinkled on top to show magnetic fields.

We had several more magnet demonstrations, which were great fun. I also showed them how to run a strong magnet over a wall until it stuck. It was fun to let the children figure out why the magnet stuck to the wall. What is it attracted to? Nails? Once you have found nails, you have found your studs! You can even leave the magnet up on the wall to remind you where the stud is.

And finally, almost every day of the block we spent a little time painting. These paintings take many layers of light colors to create. Eugene Schwartz has a free video to demonstrate the technique.

color wheel painting mom 1color wheel painting mom 2color wheel painting 6th grader

The first two color wheel paintings are mine, and the last one is my daughter’s. The fifth grade boy that did these lessons with us had a difficult time figuring out where to put the colors, and dealing with this technique at the same time. So we painted the scene below, in which he became more comfortable with the technique, and we created a color wheel with compasses to reinforce where the colors go and why.

The color wheel paintings were inspired by exercises in Colour Dynamics:


Colour Dynamics

IMG_3806
Here is my sixth grader’s atmosphere picture. I can’t find mine… I am sure it is in one of these stacks of paper!

Posted in Grade 6, Physics, Watercolor Painting | 1 Comment