Tuesday, November 25, 2014

Distance, Area, Volume Unit Study - Area of Triangles

Day 8: Area of Triangles
The kids developed a method for determining the area of triangles.

Previously, the kids learned to figure the area of right isosceles triangles by drawing squares and triangles, but today, the triangles were not right isosceles, so the method didn't work.

The formula for the area of a triangle is 1/2 the area of a rectangle with the same base and height as the triangle, but explaining that to my son caused confusion. Therefore, I gave him an isosceles triangle cut into two pieces. He rearranged the pieces so that they fit together in a rectangle as shown above. From the rectangle he was able to determine the area.

Next he was given only one of the triangles shown above and some time to think. He determined that the area was 1/2 the rectangle's area.

My seven year old was able to complete this and all of our other distance, area, volume activities as well.

Figures are abstract as compared with manipulatives which are concrete. Making the transition into abstract figures which represent objects can be very difficult for some children, including my son. Therefore, sketches on paper were created to review what the kids discovered and get them used to seeing sketches.

Sunday, November 23, 2014

Geology Unit Study - Gemstones

Week 3: We went mining for rocks and minerals and visited a historic mill where minerals were polished and turned into gemstones.

Gemstones are rocks or minerals which have been cut and polished. Many gemstones are used for jewelry and the rarer the mineral, the more valuable the gem.

Like miners, historic gem polishers had short life-spans. The toxic dust breathed while polishing usually lead to lung disease. Gem polishers worked on their stomachs using their feet to push the stone into the grinding wheel.

As technology improved, gem polishers began to work in an upright position, but continued to breath toxic dust.

Many minerals drastically change their appearance when polished like the fluorite shown in the above photo.

Digging for Gemstones in Idar-Oberstein
After learning about gemstones and polishing techniques at the Idar-Oberstein, Germany Historic Mill, we spent two hours digging for precious stones. The field was fortified with rocks and minerals from around the world, so a successful dig was guaranteed.

Searching for stones in newly turned over ground

Digging with a pick-ax

Just getting started

Sifting dirt for stones

Cleaning stones in the wash basin

Scrubbing off the mud

Two hours of digging is back breaking difficult work whether the field is fortified or not. We were glad this was a field trip and not a regular job. Often stones under the ground all looked alike. They were not obviously good finds until they were cleaned.

Digging in this fortified field was a bit expensive, but was totally worth it. We gained an appreciation of what easy mining is like and began a diversified rock collection. After returning home we spent several afternoons clean rocks and trying to identify them.

Saturday, November 22, 2014

Carving Soap Stone with Kids

Renaissance Unit Study

Week 8: We carved soap stone like Michelangelo carved marble.

The marble which comes from a quarry near Florence, Italy is some of the purest marble in the world and it was during Michelangelo's day too. It was removed by inserting wedges of wood into chiseled rock, and then swelling the wood with water. Once it was free from the hillside, it was rolled onto a mound of sand under which rested a series of logs which acted as wheels for moving the block.

Among the numerous famous works of Michelangelo is the Sleeping Angel which comes with an entertaining story. In order to receive a higher price for the statue, it was buried in the ground for a period to obtain an aged look, thus appearing antique. The plan worked and it was sold.

When carving marble Michelangelo often began with fired and sealed clay models. Chisels, drills, rasps and files were used to shape the marble. The video Carving Marble with Traditional Tools gives an excellent description of how the work was done.

Michelangelo by Diane Stanley describes his pieta, David and work on the Sistine chapel. Michelangelo's surprise was great the Laocoon was unearthed. The ancient Roman statue from Nero's house showed body structure detail and people moving. It was a great contrast to the non-moving statues of Michelangelo.

Carving Soap Stone

Soap stone is a soft rock which contains lots of talc and sometimes feels soapy or waxy to the touch. It has been used for carving throughout history since it is relatively easy to chisel and cut and can be found at craft stores.

Soap Stone
Hack Saw
Safety Goggles
Leather Gloves
Modeling Clay

The kids each began with a small chunk of modeling clay which was used to  form their plan.

My 12 year old daughter's flower

My 7 year old daughter's hedgehog

 Next, the kids began hammering away at their soap stone with chisels.

Hack saws were used to remove large chunks. Files were used to smooth out rough edges and drills were used to remove large interior sections.

This was an ambitious project which I never imagined doing. Now that we've been through the process, it doesn't seem much different than learning to sew a quilt. Both are skills which require time and effort, but are achievable. My girls really enjoyed this project and worked to complete their carvings after the afternoon class was over.

Flowers in stone by 12 year old girl

Ring Holder by 15 year old boy

 * I did not receive any compensation for this recommendation. I'm just a homeschooling mom who has found many products that I like. If you're interested in the products I recommend on this blog I want to make it easy for you to find them. 
** I am an Amazon associate and receive a small portion of the sales on orders made after clicking in from this site, which I promptly spend on homeschooling books and supplies for my children.

Thursday, November 20, 2014

Interest Based Education - Reading

Until recently, my second grade daughter has shown very little interest in reading. Therefore, I consider reading our first major breakthrough using the interest based approach to education. Last year and previously, we read together and I required her to read to me. (After all, I feel reading is very important.) Unfortunately, despite the fact that she liked the books and even selected them herself, it was a constant struggle, since reading was required.

Enter Unschooling
One thing my seven year old is very interested in is Pippi Longstocking. In the past, I read her all four of the Pippi chapter books. Since then, she discovered Pippi cartoons on youtube. Although I personally don't have an issue with her watching the cartoons, I do have an issue with her spending all of her available time watching them. So I've been thinking about how to get her to change her focus.

Option 1 - Limit technology or Pippi time
Potential result: This will create a deeper desire for her to watch Pippi and more videos in the future. Plus, doing this is the opposite of encouraging interests.

Option 2 - Change her focus to a different educational video - In other words, encourage her to watch more videos (that are educational).
Liberty's Kids is a series of animated American History videos for kids. When episode one was turned on for me to enjoy, she quickly joined to watch the episode. I was hoping that she would turn on Liberty's Kids instead of Pippi on her own, but that didn't work. Perhaps she just needs a little more exposure to Liberty's Kids, or a series which she finds more interesting?

Option 3 - Offer to read the Pippi books again
This is where we had the breakthrough. While she was watching Pippi, I pulled the chapter books off the shelf and set them down next to her. I offered to read them then walked away so she could finish her episode. Once the Pippi video was through, she came downstairs with her nose in one of the Pippi books and announced that she would be reading them on her own.

Although the books are way above her level I have no doubt she will be finishing them on her own.

(Can you see the purple flashlight strapped to her head? She's reading Pippi in bed before going to sleep.)

She can read and is highly motivated to read the Pippi books. It just may take her a while to get through them all, but her reading skills should drastically improve.

Wednesday, November 19, 2014

Flowery Knit Hats

My mother knitted these flowery hats for the girls.

Although they appear complicated, they are actually basic hats adorned with knitted flowers. The flowers were created by knitting small rectangles and then rolling them into a coil. The leaves are slightly tapered rectangles.

Since this hat had so many strings coming inside when tying the flowers on, a small circle was knitted inside the hat to cover them. I love the way embellishing basic hats and other items can completely change the look.

What have you embellished? Do you have a favorite knit flower book or embellishing book? If you do please leave me a comment.

Tuesday, November 18, 2014

Area of Squares, Rectangles and Triangles

Distance, Area, Volume Unit Study
Day 7: Area - Squares, Rectangles, and Triangles
Measuring area answers the question how big is it. Formulas used to calculate area and perimeter were introduced to my son when he was exploring math on Khan Academy. Unfortunately, he didn't really understand what area and perimeter were, so he came away thoroughly confused.

Area is measured in squares. After learning about one square inch, he was easily able to determine the area of these shapes built from squares, simply by counting.

Next he determined the number of tiles we would need to redo our bathroom floor in one foot square tiles.

Then we explored triangles. On the right side of the picture below, there is a one inch string, a one square inch piece of paper, a one-half square inch of paper cut into a rectangle, and a one-half square inch of paper cut into a triangle. The middle column contains the same figures, but double the size.

After creating these figures, I asked the kids how big they were.

I asked them how big this two square inch triangle was and they were stumped. So I created a blue triangle the same size and cut it.

They quickly determined it was two square inches.

So they were given the large triangle and asked how big it was.

At first, they both wanted to measure the hypotenuse, but then both decided to draw lines on their triangles.

With different sets of lines they both arrived at the same answer.

This method of discovery mathematics is very important for my son. He learns best when he figures something out for himself. He is a natural problem solver who does not learn well with explanation and example.

Sunday, November 16, 2014

Geology Unit Study - Geodes

Week 2: We broke open geodes.

Geodes are hallow rocks formed underground. When ground water carries dissolved minerals into hallow cavities, geodes can form. The most common elements found in minerals are silicon and oxygen. When they combine with other elements to form minerals they are called silicates. These same minerals, most commonly known as quartz, are the most common found inside geodes.

We purchased the Discover with Dr. Cool Explorer Geode Science Kit, Set of 7 and broke open the geodes to see the crystals inside.

Pure quartz is made of silicon and oxygen and is hexagonal in shape. When other minerals combine with the silicon and oxygen of pure quartz, variants of quartz such as orange quartz, which are different colors are formed. Several of the geodes contained quartz crystals and the kids were thrilled each time a new one was opened.

* I did not receive any compensation for this recommendation. I'm just a homeschooling mom who has found many products that I like. If you're interested in the products I recommend on this blog I want to make it easy for you to find them. 
** I am an Amazon associate and receive a small portion of the sales on orders made after clicking in from this site, which I promptly spend on homeschooling books and supplies for my children.
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