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Exploring Pi with a Fractal & Pi Activity Round-Up

I really wanted to do something with pi for artwork in my classroom plus would love a good pi activity. I struggled with this one. I have seen the pi skyline like this one over at What Do We Do All Day? It is fun but not quite what I am looking for. There are different pi artworks if you google "pi art" but most is based on the digits of pi. To be honest I do not believe in having kids memorize the digits of pi, so much of the artwork is not my thing. As I was searching for ideas, I came across this YouTube video that intrigued me. I decided to make the "fractal" that has an area of pi! It is a spin from the Sierpinski Carpet, Menger Sponge, and the Wallis Sieve. Now fractals are supposed to be infinite, but I cannot draw them this way. I am working on taking this fractal to the third level. If you were able to go on infinitely the area of this picture would be pi.

One of my goals this year is to bring fractals into my teaching, especially in geometry class. Today I am going to share the fractal tree. It can easily be done on a computer but is also great for practicing measuring with a ruler and protractor. Now a fractal tree is probably one of the most basic fractals and well-known or at least its cousin, the fern is certainly seen as a fractal.

Over the years I have shared my love for fractals with you. I began with my introduction to frozen fractals after Elsa sings about them in "Let It Go" in Disney's Frozen. A fractal is an object that has self-similarity, or each part looks like the whole. It introduces new ideas of symmetry, dimensionality, and more. Fractal geometry often explains some of the irregularities of our world. It can be a very complex topic to understand, but it is an important one. Fractals are making advances in our medical world, entertainment (movies, computer games and more) as well as science. There are some topics that kids even young kids can understand. Since they were introduced in Frozen, many kids have now heard of them. I feel it is important to teach kids about them and give them a true idea of what they are.

Today I am going to share some fun math art looking at a famous fractal--the Sierpinski Gasket or the Sierpinski Triangle. It is a perfect fractal to have kids create and goes well with geometry lessons. A fun way to introduce it and create it is the Chaos Game. Here is a video showing the Chaos Game with a triangle, square, and pentagon. With the triangle the Sierpinski Triangle will appear with enough iterations of the game. The rule as explained in the video is to begin with a random point. Then randomly choose a vertex. Connect your point to the vertex and find the midpoint. (Erase the line.) The midpoint is your new starting point. Repeat. This is a game you could easily play in a class as well. Don't watch the video first though.

Hazel and I LOVE Disney's movie Frozen. We are constantly listening to the soundtrack in our car. One of our favorite songs from the movie is Let It Go. If you have not heard the song or seen the movie you can
check out the song from the actual movie (with movie scenes) from Disney's website.

Last week I gave you an introduction to fractals in response to all the interpretations of frozen fractals from Disney's Frozen movie's song, "Let It Go." Today I thought I would continue my lesson on fractals. But first I wanted to share an easy craft to make an Olaf from the movie. Hazel got her Elsa and Anna dolls this week and she now wants the males so she can re-enact the entire movie. I told her we could make an Olaf. Looking at our supplies I came up with some styrofoam balls, a little bit of white and black Model Magic and some pipe cleaners (black and brown), googly eyes and an orange tear drop shaped foam piece. I cut the biggest and medium styrofoam balls in half and toothpicked them together. Then we used a small styrofoam ball and some of the white clay to make his head. We covered the other two balls as best we could with what we had left of the white clay. We did not have enough, but she didn't care. Then we used the black to form the buttons and mouth. I took a small piece of white for his tooth from the back. We added the brown pipe cleaners for arms and hair and then put the eyes on with tiny black pipe cleaner eye brows. The eyes and eye brows as well as the nose all needed to be glued on to get them to stick well.

Hazel is happy with how he turned out, so we will go with it. I will eventually get us some more white Magic Model to finish his bottom part and add the legs.

Now onto fractals. Last week we looked at the Koch Snowflake since we are talking frozen fractals. But I was thinking I should explain why study fractals besides to know what they are from a line in a song. Fractals are a very new thing in the math world. However they are being used in so many places and have been around forever. Fractals occur in nature and always have. Mathematicians and scientists somewhat ignored them for a long time due to how complex the shapes looked. For years we have simplified our shapes to fit into our cookie cutter basic shapes: circle, square, triangle, rectangle, etc. However things like a fern are not a basic shape and when you simplify it to such you lose some of its elements.

"Barnsley fern plotted with VisSim" by DSP-user - Own work, using model written by Mike Borrello This chart was created with VisSim.. Licensed under CC BY-SA 3.0 via Wikimedia Commons.

As we learn more about fractals we are finding more uses for them. For those who remember Encyclopedia Encarta, the pictures on this CD were developed by programs written to make fractals similar to the wanted picture. Fractals are used in making movie backgrounds, video games as well as being explored in medicine. The lungs are now realized to be fractals as well as our blood vessels (veins and arteries). The more we learn about fractals in the human body the better our medical science will be.

"Thorax Lung 3d (2)" by AndreasHeinemann at Zeppelinzentrum Karlsruhe, Germany http://www.rad-zep.de - http://www.rad-zep.de. Licensed under CC BY-SA 3.0 via Wikimedia Commons.

We will talk today about one of the more basic fractals and one that is easy to create. I often had my geometry students create this fractal in different ways. It is a wonderful way to teach about measuring, as well as midsegments of triangles. We are going to make a Sierpinski Triangle or sometimes called the Sierpinski Gasket. To start you need a triangle. You can use any triangle. Most commonly used are equilateral triangles, but any will work.

Now the rule is to draw the three midsegments of the triangle. A midsegment is a line segment that connects the midpoints of two sides of triangle. Its properties are that it is parallel to the third side and its length is equal to half the length of the third side.

The final part of the rule is to remove the triangle formed by the midsegments. To remove it, we will color it in.

Now we continue to the next stage by doing the same thing for all the non-colored in (nonremoved) triangles.

Sorry for some reason I did not take a picture of Stage 2 with the triangles removed. We continue our rule for Stage 3.

Finally we have Stage 3 which is where I stopped since I was not feeling well and I was getting a bit of a headache. However you can see how the rule can be applied infinitely as with all fractals.

The Sierpinski Triangle is also a great fractal to explore self-similarity. In the one below you can see how each color represents a shape that looks like the whole.

"Sierpinski-rgb". Licensed under CC BY-SA 3.0 via Wikimedia Commons.

The one below is zooming into magnify the smaller parts of the Sierpinski Triangle to show its infinite range.

"Sierpinski zoom" by Mariko GODA - Own work.
Licensed under CC BY-SA 3.0 via Wikimedia Commons.

Finally I want to share with you a Sierpinski Pyramid that we made in one of the summer classes I took at Yale. We made it by forming regular tetrahedrons from envelopes. I do not totally remember how now, but thought it was neat to share.

A true Sierpinski Pyramid would have a hole in the middle, but that is not easy to construct in actual life. Here is one I found on-line.

"Sierpinski pyramid". Licensed under Public domain
via Wikimedia Commons.

Finally if you want to learn more about fractals in nature and the importance of them, check out this video of the Yale professor, Michael Frame, who taught the courses I took on fractals. He ends it with a story about the amazing late Benoit Mandelbrot (last week I shared a picture of myself with Mandelbrot) and about how fractals are about storytelling as is most math and science. It is really worth watching. On that note a talk about fractals is not complete without looking at the Mandelbrot Set. The math involved is more advanced, however it is beautiful to look at.

Mandelbrot set with coloured environment.png

"Mandelbrot set with coloured environment". Licensed under
CC BY-SA 3.0 via Wikimedia Commons.

For some more on fractals check out:

Pi Day Activities for Different Ages

On March 14, mathematicians and much of the world celebrate Pi Day. Since the approximation of the number pi is 3.14, March 14th was picked for the day. It was first celebrated in 1988 in San Francisco. As a math teacher I get excited for Pi Day, however our school is always on spring break on March 14th so I don't get to celebrate it with my students. This year I thought I would do a round-up of Pi Day activities and try to share ones for different age groups since much of what I see are for younger kids and I teach high school. Be sure to start your celebration with some pi jokes and riddles like these. Some of the Best Things in Life Are Mistakes shares a round-up of free Pi Day decorations! By the way Pi Day is also Albert Einstein's birthday. You can also have a birthday celebration for Albert!

Today we are walking in a winter wonderland with Penguin Kids. They asked us to share some winter fun and we chose some fun facts about snowflakes. Plus we are doing a snowflake craft round-up and sharing a winter wonderland book.

Last week I shared our first music inspired art/activity post. This week, we are sharing another song inspired art from the same CD, I Have a Dream by Daria. The song this week is among Hazel's favorites. It is called Ride, Horse Ride. First I am going to share with you the song via Daria's video.

Now this song is rather simple and has a fun beat. Daria e-mailed me a wonderful idea of making a Pow-wow Drum to play while listening this song. We have not done this yet, but I hope to. We however worked on mirror image paintings and chalk drawings for the sun and moon beams and then put horse stickers on them.

We started with chalk drawings. We folded a white piece of paper in half and then used sun colors: red, yellow, orange, white and colored on half the page. Then we folded the page and used a rolling pin over the paper to try to transfer the chalk to the other side. It did not transfer as much as we hoped, but we had fun with it. We repeated this activity with black paper using moon colors: blue, white, green, yellow. Then we put small horse stickers on them.

Next we used some paints. We used washable finger paints and a few colors of acrylics. We used too much paint on each picture. They are going to take days to really dry. However Hazel really enjoyed this. Again we folded the paper in half and put paint (drops) on one side. This transferred much better to the other side. (In fact for those looking for a lesson there is a fractal lesson I once did with this type of painting. The transfer process puts lines into the paint and they form a type of fractals.) Next we went and put horse pictures on them. Hazel decided which one got the big stickers and we had horse head stickers for the other ones. Hazel also made one extra painting with all the colors of finger paints.

While making the drawings and paintings we were listening to Daria's CD and Hazel enjoyed singing into the microphones on her portable CD player. She knows all the words to all the songs so she was having a blast.

Origami in the Geometry Classroom

Disclosure: I was sent these packages of origami paper in exchange for an honest review. All opinions are my own.

Last week was a stressful and emotional week at school and home, so I wasn't able to post. I have realized when I'm not in the right mindset my reviews are hard to write. For a while I have wanted to share some ideas I use in my geometry class with origami paper. I will be sharing four new packages of origami paper with you in this post. I keep a box of origami paper in my classroom and students come and get some when they are feeling creative or need to relax. I also use it in my geometry class. I have the kids do a project using geometric terms project using geometric terms, but I also use it for some easy discovery and illustrating properties. I have been wanting to share these ideas with you. May is the perfect time to introduce it since origami is a Japanese art form and ties into Asian American and Pacific Islander Heritage Month.

Thank you to everyone who shared last week. As always it is so inspiring to check out what everyone has been up to. If you have not had a chance to check out the ideas others shared, please do so and remember to leave some comment love! We had a two-way tie for most clicked.

From Crafty Journal: Aluminum Can Dimensional Star

and

From A Bountiful Love: How We Potty Trained Our 2 Year Old in 1 Week

For features I chose two categories. The first is summer/beach themed crafts and the other is some of my favorites!

Summer Features

1) From Kids Activities Blog: DIY Seashell Necklace

2) From Moosewood Connections: Shell Critters

3) From Stella123: The Perfect Free Beach Souvenir

4) From Kids Activities Blog: Butterfly Pasta Watercolor Art

A Few of My Favorites

1) From How The Sun Rose: Around the Sun and DIY Birthday Ring

2) From The Chaos and The Clutter: Create Your Own Babysitting Kit

3) From Jewelry Making Journal: Wire Angel Pendant Tutorial

4) From Felt with Love Designs: Reader Requested: Monkey with Blanket Stuffed Animal with Free Pattern

5) From Craft Ideas for Kids: Making Rain

6) From Mini Monets and Mommies: DIY Glow in the Dark Kids' Paint

7) From The Surly Housewife: 10 Everyday Chores Any Kid Can Do

8) From Wesens-Art: Recycling Art

Thank you to everyone who shared last week!! I hope you will join us and share again!! If you are featured here, please feel free to grab a featured button to display proudly on your blog.

Featured Button Code:

From Your Hostess: This week we our Craft Stick Fish, Petrosinella: A Neapolitan Rapunzel, Sock Animals, our second Fractal Lesson and an Olaf craft and our Patriotic Necklaces.This coming week we will be hosting two giveaways, so make sure you come check them out!!

Now for This Week's Party
A Few Simple Guidelines:
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2) Link any kid-friendly, child-centered post. Please no etsy shops or giveaways, etc. Remember to link to your actual post.

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5) If you do not have a blog, but want to share an idea you can leave it in the comments or e-mail it to me with a picture (if possible).

Disclaimer: By sharing here, you are giving Crafty Moms Share permission to use your photos for features and to pin your craft at Pinterest.

Bringing Origami to Geometry Class -- Product Reviews

Disclosure: I was sent these products in exchange for an honest review. All opinions are my own.

One thing I love to do is bring origami into my classroom. Whether using the old patty paper methods to discover theorems and such or doing origami and perhaps an origami project to demonstrate using geometric terms or just to have cool geometric shapes around the room, I love adding origami. I actually have a box of origami paper in my room-- a boot box covered with Asian wrapping paper. Students come in all the time to have a piece or two just to create something for a relaxed moment. Today I am sharing a book full of geometry and geometric shapes all created by origami and two different packs of origami paper (which all will be added to my classroom supply). I have a shelf full of origami books and kits as well. The book is The Art & Science of Geometric Origami by Jun Maekawa. The packs of paper are Origami Paper 300 Sheets Vibrant Colors 4" (10 cm) and Origami Paper in a Box Japanese Washi Patterns.

Thank you to everyone who shared with us last week!! There were so many amazing ideas. For features this week I chose two themes: 4th of July/Independence Day and Summer. Since my mind seems to be with both it only seemed right. I picked a few of each, but there are many more from last week! I hope you will go check them and all that was shared out!

Fourth of July Features

1) From Happy Deal- Happy Day: Frugal Craft: 4th of July Centerpiece

2) From Rock-a-Bye Parents: American Flag Bead Pin

3) From Gift of Curiosity: 4th of July Montessori Activities

4) From Stella 123: 4th of July Marshmallow Decorating

5) From ArtClubBlog: Flag Stones

6) From A Little Pinch of Perfect: Patriotic Windsock Kid Craft

Summer Features

1) From Living Montessori Now: Top 10 Summer Themes for Preschoolers

2) From Our Adventure Story: The Ultimate 2014 Summer Adventure List

3) From Play Dr. Mom: ABC's of Summer

4) From Felt with Love Designs: Links with Love: The Ultimate Round-Up of Summer Sewing Projects

5) From The Jenny Evolution: Beach Books for the Summer

6) From Krafts and Kiddos: Handprint Mermaid Painting

7) There's Just One Mommy: 20 Sea Animal Crafts

Thank you to everyone who shared last week!! I hope you will join us and share again!! If you are featured here, please feel free to grab a featured button to display proudly on your blog.

Featured Button Code:

From Your Hostess: This week we explored lemons, shared The Persian Cinderella for our Fairy Tales in Different Cultures, a simple craft to help teach prayer, a starfish and sand dollar wreath, a review of math picture books and a math lesson on fractal (frozen fractals from Disney's Frozen).

Make sure you enter our giveaway!

Now for This Week's Party
A Few Simple Guidelines:
1) Please follow Crafty Moms Share via GFC (or one of the other ways that work for you).

Disclaimer: By sharing here, you are giving Crafty Moms Share permission to use your photos for features and to pin your craft at Pinterest.

Happy Pi Day

Today is the official holiday of Pi Day!! As a former math teacher, I love to celebrate it. Last year I gave you some of the sheets I used with my high school classes to celebrate it and to justify our having pie. This year I thought I would look at a bit of the history of pi.

Exploring Pi with a Fractal & Pi Activity Round-Up

Fractal Tree -- Geometry Class Project

Christmas Fractal Lesson

Sierpinski Gasket -- Math Art -- Fractals

What Are Frozen Fractals? A Lesson on Fractals to Go with Disney's Frozen Movie and Let It Go Song

Frozen Fractals Lesson 2 and Olaf Craft

Pi Day Activities for Different Ages

Fun Facts about Snowflakes -- Walking in a Winter Wonderland

Song Inspired Art: Ride, Horse Ride by Daria

Origami in the Geometry Classroom

Sharing Saturday 14-27

Bringing Origami to Geometry Class -- Product Reviews

Sharing Saturday 14-26

Happy Pi Day

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