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 große Mandala-Malbuch für 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?

Drawing Shadows in Perspective

My daughter created perspective drawings which included shadows in perspective.

Buildings and other objects in artwork follow distinct rules when drawn in perspective. Not surprisingly, the shadows of the objects also follow rules. The video below breaks down the mystery of shadow in perspective in such a simple way. It's fabulous!

This video explains that the vanishing point for the shadow is always on the horizon line just below the light source. In addition, it describes the method of finding the top points of the shadow by creating guide lines from the light source through the top corner of the object.

The video is less than eight minutes long, and after watching, my daughter was able to create her own farm scene with shadows.

Then she tried it again placing the sun in a different location.

To see more of our art projects, please visit our Arts and Crafts Page.

Caldera Volcanoes, Yellowstone, Geyser Activity

Week 29: We made a geyser.

Did you know there is a huge volcano under Yellowstone National Park? It's not just any volcano, but a super volcano. When it erupts it could create major climate change. The last monstrous eruption occurred 640,000 years ago and covered much of North America with ash and global temperatures dropped. It's erupted several times in the past and someday will again.

How the Earth was Made - Yellowstone - Tracks scientists as they search for clues to the volcano's past. We have made extensive use of the video series for our Earth Science unit.

This short video explains what a Caldera Volcano is and gives a brief idea of the destruction it can cause.

Because there are both water and volcanic activity under the ground at Yellowstone National Park, there are geysers. This video explains how geysers work.

Make Your Own Geyser
This video explains how to make your own geyser.

aluminum foil

 Basically, water is boiled and the steam and water bubbles are channeled out through the funnel



This incredibly simple demonstration was a great complement the Caldera Volcano unit study.

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Polish Pottery Poetry Tea Time - Free Verse Poetry

We wrote free verse poetry.

Last April Powol Packets hosted a poetry contest for kids. Throughout the month participating bloggers wrote articles about types of poems and literary elements in poetry. Although the contest is finished, the excellent poetry resources created are great inspiration for poetry tea time.

Not All Poems Rhyme - This article gives simple instructions and explains free verse poetry.

 Step 1 - Write about something that inspires you.

We completed this lesson after just returning from a trip to Boleslawiec, Poland, a town famous for its pottery.

We traveled by tour bus, but got a great tip on a hotel - The Blue Beetroot - should we ever decide to return on our own and stay the night.

I usually write along side the kids and then we all share what we've written. Here's my free verse poem.

Pottery Blue
Pottery Blue
Cups, platters and plates
Stacked to the ceiling
   One - Perfectly Made
   Five - Decoration Only
Customers crowding the shops

Geometric patterns
Perfected line art practiced for hand-writing prep
L's, S's and E's, diamonds and swirls

Peacock tail feather spots
A white circle with dot
A red dot, inside a green ring, inside a white circle, surrounded by blue

Five flower petals
Eight petals and leaves
All stamped in a regular ring around the middle
Hand-made in Poland - Boleslawiec

Perspective Drawings from a Bird's Eye View

My daughter created bird's eye view perspective drawings.

Art is a subject that is actually very related to math. Mechanical drawing, a technique used to create engineering drawings in order to produce parts combines both skills. Looking at great works of art there are obviously mathematical relationships which govern which way lines must be drawn to fade away into the background. With geometric objects these rules are distinct and easily explained. Mastering the rules with simple objects like buildings leads to applying the same rules to irregular objects such as hills and trees. 

This four minute video explains the basics of bird's eye view perspective.

Unfortunately the camera shakes horribly in the video below, but we liked the way the buildings were drawn in many different shapes. It made for an interesting finished drawing.

After watching the above videos, my 12 year old daughter was able to build on her perspective drawing skills and create a bird's eye city view.

Here are links to our previous perspective drawing projects.

First Introduction to One-Point Perspective
Cityscape - One Point Perspective
Drawing People in Perspective
Creating Perspective Drawings from Photos

Check out these great blog hops.

Place Value Activities for Kids

We did two hands-on activities to gain a better understanding of place value.

While beginning the study of decimals, my son was asked to do some rounding. This proved very difficult for him mainly because he had difficulty understanding the meaning of place value on the right-hand side of the decimal point. So we took a step back from rounding and worked on place-value instead.

First I cut 1 cm x 1 cm units from a sheet of paper. I gave them to my son and asked him to write down how many there were. - No problem - 

So I took a fresh 1 cm x 1 cm unit, drew 10 lines and cut of a tenth and asked him to write down how much that one was. He was baffled.

So we got out some money. Money is a great starting point for the decimal system because pennies, dimes, dollars and ten dollar bills are pure examples of the place values.

He was given 1 dollar, 1 dime and 1 penny and asked to write the value. Here's what he wrote.

After reading this it became obvious that he was a bit confused.

After giving him some time to think, he wrote the above which showed his confusion.

Due to his confusion, he was asked to write how many pennies were in each piece of money.

 Then it was back to dollars.

After some thinking it happened. He was able to write the amounts in dollars.

So we went back to the original paper units. After he wrote down .1 for the one-tenth unit, a tenth was cut off from the tenth. The one-hundredth was very hard to see, but the pattern was becoming obvious.

Teaching math to a child who has a strong need to understand application and learns by figuring things out is extremely difficult. If you have suggestions for other place value activities or math activities which encourage kids to figure it out for themselves, please leave me a comment. I would love to hear from you.

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