Spider Web Math-Art

We used geometry to create a math-art spider web design.

Math often exist within art to levels not detected by the viewer. Learning about the connections not only makes art more interesting, but serves as a very enjoyable way of learning about mathematics.

We have often selected geometric mandalas and used a compass and straight edge to recreate them. The challenge is a math puzzle and an exciting problem solving exercise.

This mandala which looks a bit like a spider web, from the book Das gro�e Mandala-Malbuch f�r Vorschulkinder was redrawn using only a compass and ruler. Here are the steps.

1. Draw a circle with a 2" radius.

2. Use a ruler to draw a line through the center of the circle.

3. Draw a perpendicular line passing through the center of the circle. Increase compass radius (3 inches or so), place the point of the compass on the line where the circle and straight line intersect and draw tick marks just outside the circle on both sides. Move the compass point to the opposite side and repeat.

Place a ruler to line up with the tick marks and draw the perpendicular line passing through the center.

4. Bisect the perpendicular lines. Place the point of the compass where the circle and line cross. Make a tick mark outside the circle about half way between the perpendicular lines. Repeat on the opposite side of the line. Repeat placing the compass at the other three points where the circle and lines cross.

Place a ruler so that the tick marks are lined up and draw two angle bisectors passing through the center of the circle. (The circle should be divided into eight pieces.)

5.  Bisect the eight angles within the circle following the procedure detailed in step 4. Note the bisecting lines are not needed within the circle and are only drawn lightly outside the circle.

6. Draw the outer web arches. Set the compass to the initial radius of 2". Place the pencil part of the compass on the line where the circumference and line passing through the center meet. Place the point on the adjacent line outside the circle. Sketch an arc as shown above. Repeat until the outer web of eight arcs is complete.

7. Draw the second web arc. Increase the compass radius to 2 1/4". Place the point in the same location as in step 6. Draw an arc. Repeat around the entire circle.


8. Increase the compass radius to 2 1/2", then 2 3/4" respectively and repeat step 7 drawing the remaining two web arcs.

9. Draw a small circle in the center.

10. Erase all construction lines.

11. Trace desired pencil lines with a black marker.

12. Color.

For similar projects click the links below.
Tutorial - Four Star Mandala
Math-Art Mandala

Tsunami - Earth Science Unit Study

Week 30 - Tsunami
We built sand castles and then noted the percent destruction when damaging them with varying amounts of water.

Our favorite video series this year by far is How the Earth Was Made. Since there's an episode on tsunamis, we watched it.

We also read a few books about tsunamis.

Tsunami! - When the ocean pulls back, the villagers are curious and walk towards it to investigate. Ojisan is a village elder is not fooled. He's scared, but knows what to do when the Tsunami strikes.

Selvakumar Knew Better - This book tells the true story of how a dog helped save a young boy during the 2004 tsunami.

The Big Wave- This book was about so much more than a tsunami. It told the story of how people dealt with the tsunami years afterwards. I happened to read this book while dealing with my own post traumatic stress disorder due to my daughter's Leukemia and it actually really helped me to cope.

Water Volume verses Destruction

One local park has a nice water/sand play area, so our experiment was done there. First, a sand village was constructed.

 Next, one-fourth of a bucket was poured down the channel headed strait for the village.

 The water flowed out of the channel and destroyed the structures on the water side of the sea wall.

The village was rebuilt, and the entire process was repeated several times increasing the amount of water in the tsunami.

Each time the percent of damage was noted, and a graph showing water volume vs damage was created with the results.

There are still a few weeks left in our Earth Science study, so be sure to visit next week for more.

Central America and Caribbean Island Songs for Kids

We learned songs to help us remember the countries of Central America and the Islands of the Caribbean.

Learning geography can be confusing to little kids as names referring to locations such as Michigan, United States, North America, Colorado, Europe, Grand Rapids, Rhineland-Pfalz, Traverse City, Denver, Germany and Littleton are thrown around. What is the difference between a continent, country, state and city?

My six year old was so confused at the beginning of the year and so we took a big step back, and now geography is making more sense.

After coloring a map showing the seven continents we learned the continent song.

Next we discussed and learned the names of the four oceans. After working on other projects for several weeks a European country map was colored. In addition, the GeoPuzzle Europe was completed several times over the course of a few weeks. 

Proceeding onto North America, rather learning the names of each state, a country map was colored. It was noted that three countries make up the majority of the land.

Since singing worked so well for memorizing the continents, two more songs were learned to aid in remembering the names of the countries in Central America and the Islands of the Caribbean.

Central America Song

Caribbean Island Song

That's two continents down and five more to go. I expect this activity to span the entire year.

Check out these great blog hops. They are filled with activity ideas for kids.

Modifying a Crochet Hat Pattern

Do you have difficulty following a pattern?  I like to do things my own way, and with knitting and crochet, that tends to involve a lot of math and logical thinking.

I recently completed this Cross-Over Long DC Hat. However, I never seem to have the yarn called for in the pattern, so modifications are always necessary. This hat was made with Boston chunky yarn on a 5.5 size hook. Since both the hook and yarn were bigger than the pattern called for, the number of stitches and rows needed to be reduced. Using chunky yarn the stitches increased at a faster rate than the pattern specified. Instead of 6, 12, 18, 24, 30 and 36 stitches for rounds 1-6, 9, 18, 27, 36, 43, and 52 were used instead. The initial 14 rounds of stitches which defined the top of the hat were reduced to only six rounds.

The next step was the cross-over stitch. Instead of doing the cross-over stitch for rounds 16-23, it was done for rounds 7-14 before moving onto the rim of the hat. Again, more modifications were required at the brim, because I did not want a brim, and only wanted a rim. After six rounds of single crochet at the bottom the hat was finished.

Who said crafts didn't count as math?

Krakow, Poland - Things to See and Do

History from early medieval times through the post World War II period has left its mark on the architecture of Krakow, Poland. The castle area, Jewish quarter and historic district are compact, laid out in a grid and easy to navigate on foot. The people are friendly, the food is good, there's lots to see making Krakow a very affordable and worthwhile place to visit.

Nikolaus Copernicus

Krakow was home to the famous astronomer Nikolaus Copernicus. During his lifetime, astronomers who developed theories of the universe which were contrary to the teachings of the church were severely punished. Copernicus developed a model of the universe which placed the sun in the center, but didn't have his work published until the last days of his life. The University area of Krakow contains a monument memorial to Nikolaus Copernicus.

Barbican

A barbican is a fortified structure which lies just outside a city boundary. Barbicans were built during the middle ages and served as a front line of defense for the city. The city of Krakow has a well preserved barbican which is a rarity as not many are left.

Wawel Castle

 The country of Poland and the city of Krakow have a history riddled with occupation by outsiders. The Wawel Castle reflects this history in its architecture. Just looking at the above photo, it is evident from the exterior construction materials and styles that the castle was constructed over a long period of time. The most recent portion, on the right hand side of the photo, was constructed during World War II and severed as a headquarters during the war.

The courtyard portion of the castle dates to the Renaissance period. Tours of the staterooms begin in the courtyard and proceed around the rooms inside this portion of the castle.

St. Mary's Cathedral

The trumpeter still plays every hour from the peak of St. Mary's Gothic Cathedral as a signal that all is well.

The Trumpeter of Krakow is a historical fiction children's book set in the middle ages. After a young boy and his family seek refuge within the city of Krakow after fleeing from the Tarters, he becomes the trumpeter.

The amazingly carved alter within the church stands much higher than this photo indicates. The figures in one of the panels are over 3 feet tall.

Inside, the walls and ceilings are covered with bright and beautiful decoration.

Church of Saints Peter and Paul

Krakow contains many churches including the Renaissance style church of Saints Peter and Paul shown above. This church is most famous for the statues of the apostles in the front and it occasionally gives nighttime orchestral concerts.

Franciscan Church
Pope John Paul is from Poland and spent lots of time in Krakow. His image is visible all over the city; as a statue outside the cathedral at the Wawel castle, as a statue inside the salt mine a 20 minute drive from the city, and on banners, plaques and postcards within the city.

The Franciscan Church contains a plaque on one of the pews stating that John Paul once sat here. Inside the walls were painted with large, bright geometric and floral designs in the Art Nouveau style.

Jewish Quarter

Long before World War II Krakow was a safe haven for Jewish people. When Jews were persecuted in other locations, they not only sought refuge in Krakow, but thrived.

Unfortunately we are all too aware of how that all changed during World War II. The Jewish population of Krakow was virtually wiped off the map. Concentration camps were too close and the horrors of war descended upon the city.

The photo above was taken outside the gates of Oscar Schlinder's factory. Schlinder was a German member of the Nazi party who ran a ceramics factory in Krakow during the war. Once he understood the horrific nature of what was happening around him, he went on a mission to hire and thereby protect as many Jewish people as possible. In comparison to the death toll his efforts were futile. However, he was able to save hundreds of lives and his efforts had lasting impacts on many generations of people. His story is told in the Hollywood movie Schindler's List. (Recommended for adults.)

The Jewish people of Krakow were imprisoned in an area of the city by a concrete wall. The rounded edges of top of the wall were built to resemble the tombstones found in Jewish cemeteries; an especially cruel mental tactic.

Today there is a small Jewish population living in Krakow. The area of the city contains many decorative wrought iron fences featuring Jewish symbols.


Sukiennice (Cloth Hall)

 The Sukiennice was built in the Renaissance style in the main square as a place for merchants to sell cloth.

Today the building is still used for sales; only the products now sold are items desired by tourists.

Polish Food
Poland is a northern country and therefore, potatoes, beets, cabbage, pork, and wheat (foods which grow in cold climates) were ingredients in many dishes.
 

 This beet root soup contained beets and dumplings filled with pork.

Stir-fried potatoes and pork were sold in the village square as fast food. In the background, a plate of pierogis is visible. Pierogis are the Polish version of ravioli. Basically they are stuffed with cheese, spinach, or pork and served without tomato sauce.

The city was filled with street vendors selling pretzels. Although they were in rings, they still tasted like pretzels.

Polish Folk Art

Much of Polish folk art and traditions are linked to Christianity. The images contained many bright colors and both orange and blue were prominent in many paintings.

Traditional Polish clothing consisted of a vest, skirt and jacket. Depending on the time frame and region of Poland, the styles were quite different. Some used embroidery, others lace, sequence, beads, or a combination. All were extensively adorned like the beaded vest in the above photo and the hat below.

Hand painting of eggs was perfected in Poland and the Folk Art museum contained a large display.

Wieliczka Salt Mine

About 20 minutes drive outside the city of Krakow there is a salt mine. Inside miners carved over 100 figures and panels into the salt rock.

This figure shows a miner burning off hazardous gas in the morning before other miners arrive for work. As you can imagine, this was the most dangerous job in the mine.

This child-sized elf is one of several which can be found in the mine.

This Bible scene is carved into the wall of one of the three underground cathedrals. The mine contains rooms large enough for banquets and each year it hosts special events such as bungee jumping and weddings.

Traveling is hands-on way to learn. One weekend trip can be packed with enough reading (signs and displays), history, science and PE to easily count as a week of school..... and when it's over, writing about it in a journal makes a nice keepsake.