Gingerbread Houses

On the day before Christmas break, the 8th grade made gingerbread houses. It was a fun class (even if it did not have too much to do with math!). We could have calculated the volume of each house, but we ran out of time. Good memories!

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Crocheting a Coral Reef

Nearly four years ago I posted a story about knitting Escher inspired shapes and hyperbolic planes. Today in my mailbox I found a post from Let’s Play Math about a Hyperbolic Crochet Coral Reef. I immediately knew I had to share the information. If you don’t know much math, don’t worry — you can still crochet these mathematical objects and be a part of this wonderful project. Watch the video. Margaret Wertheim connects the crochet pieces to the evolution of life on earth, mathematics, history and traditional feminine arts. Through crochet, women have been able to model shapes in nature that have been ignored by mathematicians. This could even be a great after school project for suitably motivated people. If you are interested, I suggest you read all of the links in this post.

Let's Play Math gives simplified directions for crocheting the hyperbolic planes. Here is a link to a pdf file that gives more detailed directions on how to crochet these shapes: http://crochetcoralreef.org/Content/makeyourown/IFF-CrochetReef-HowToHandout.pdf You can even buy a book of instructions at http://theiff.org/publications/index.html

Some fascinating articles about the coral reef project can be found in this article at http://www.math.cornell.edu/~dtaimina/hypplanes.htm

Finally, here is a slide show of the crocheted coral reef:

The Coral Reef Project is from the Institute for Figuring. It is a fascinating group and worth browsing their site.

Happy crocheting!

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Mode, Median and Mean

I found this great activity at BBC: Bitesize with the code for the blog. It took me, regrettably, awhile to learn how to manipulate the buildings. Now I'm off to find more more!

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The Revised Common Lectionary on Many Eyes

If you click on the image, you will see it full size in a new window.

Apparantly this word cloud visualization of the RCL is based on only one Sunday's reading of Year B (we are now in Year C). I am working on a way to easily create a text file of all of the readings for one year and create another word cloud. Would it be too big? I did a word cloud for this Sunday's readings (you can see it here and play with it yourself). It is fun to compare the two:

Many Eyes is a site I have watched for years and even played with a bit. This is my first attempt making a visualization. It is a fantastic classroom resource and activity. Here is an excerpt from the Many Eyes About page:

Many Eyes is a bet on the power of human visual intelligence to find patterns. Our goal is to "democratize" visualization and to enable a new social kind of data analysis. Jump right to our visualizations now, take a tour, or read on for a leisurely explanation of the project.

All of us in CUE's Visual Communication Lab are passionate about the potential of data visualization to spark insight. It is that magical moment we live for: an unwieldy, unyielding data set is transformed into an image on the screen, and suddenly the user can perceive an unexpected pattern. As visualization designers we have witnessed and experienced many of those wondrous sparks. But in recent years, we have become acutely aware that the visualizations and the sparks they generate, take on new value in a social setting. Visualization is a catalyst for discussion and collective insight about data.

We all deal with data that we'd like to understand better. It may be as straightforward as a sales spreadsheet or fantasy football stats chart, or as vague as a cluttered email inbox. But a remarkable amount of it has social meaning beyond ourselves. When we share it and discuss it, we understand it in new ways.

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Geometric Solids in Art Class

My American Beech stamp

I was taking an art class. I have simply horrible art skills. I wanted to improve them to the point that I could create my own nature sketch book. Nature sketch books are a centuries old tradition for women. Beatrix Potter kept nature sketchbooks and was extremely talented. Another artist, Mary, has a nature sketchbook. Mary's sketchbook was the inspiration for me to take this art class. When you look at her sketches (by clicking the link or her image on the left) you will see why I want to learn how to draw and paint. Summer is coming. My goal was to learn enough about drawing to begin my sketchbook this year.

My American Beech (above) is pretty good. But I messed up the caption of Fagus grandifolia. I couldn't fix it without making a mess. And I also cheated. I used carbon paper with an image I printed from the Internet. Am I ashamed? Not! My philosophy: with art, for me, anything goes.

My gray scale

So then the art teacher, in preparation for drawing lessons, had us make our own gray scale. I loved this project because it is just like the color scales on computers. I know computers. I did rather well. I just wish the art teacher had made her little boxes properly. It looks messy.

Geometric Still Life
Geometric solids: a right circular cylinder, a right circular cone and a rectangular prism

My favorite work was this still life of geometric solids. With practice I could be excellent with it. Of course, as a mathematics teacher I have drawn geometric solids for years and years and have even instructed children on how to draw them. So what did I do next? I quit art class. The next assignment was to draw these and paint them on canvas with primary colors and blending the colors with white and black for shading. I became overwhelmed and quit. If I were my own student, I would praise, encourage and counsel myself to let this new skill evolve and give myself instruction on relaxation. The art teacher is probably younger than my own daughters, so she didn't counsel me. I wish she had.

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Curve-Stitching a Shamrock Update

Back in 2008 I posted my lesson plan for curve-stitching lesson for St. Patrick's Day. Hundreds of teachers have read that post. I am reposting it today so that I could update it. I'm flattered and proud that so many teachers have enjoyed the lesson. I have posted all the materials needed for this lesson at my static site meeyauw's hideout. You can click that link and then click the St. Patrick's Day Activities link or you can click the image above or here. I found that there was one broken link but I have left you search terms to look for new activities online. Thank you again!

Happy St. Patrick's Day!

A three-leafed clover, the shamrock is the national emblem of Ireland. Although it is widely believed that St. Patrick used the shamrock to illustrate the Christian doctrine of the trinity, this idea cannot be proven. In fact the first written mention of this story did not appear until nearly a thousand years after Patrick's death.

The shamrock, which was also called the "seamroy" by the Celts, was a sacred plant in ancient Ireland because it symbolized the rebirth of spring. By the seventeenth century, the shamrock had become a symbol of emerging Irish nationalism. As the English began to seize Irish land and make laws against the use of the Irish language and the practice of Catholicism, many Irish began to wear the shamrock as a symbol of their pride in their heritage and their displeasure with English rule.

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Happy ∏ Day!

click on the graphic to view it full size in a new window

It's been a rough day in New Hampshire. We lost power most of the day on Saturday because of this big Nor'easter that is going on to the south of us. And today's rain/sleet/ice/snow/wind storm has been wreaking havoc on the Internet connection. Weather like this chills your bones. So I'm making pot roast, watching movies and doing laundry to pass the time while I upload and post material.

I forgot about ∏ Day until this morning (as I also missed church because I never fixed the clocks last night). On this ∏ Day I am presenting an Excel graphing activity I use with older middle school students. All students seem to have a problem grasping the concept that ∏ is a non-repeating, non-terminating decimal. They have an even more difficult time understanding that all of the digits 0-9 occur with the same frequency. Before we do this activity, my students already have a lot of experience with counting occurrences of heads and tails and counting the outcomes of rolling a die. They also have learned how to record their results in a spreadsheet.

I then demonstrate how they can use an Excel spreadsheet to simulate the roll of a die or the toss of a coin and how to count the outcomes using the COUNT function and other formulas. They also learn how to import raw data of a comma- or space-delineated file into Excel.

With all of these new skills, my students are then able to use Excel to count the occurrences of each digit in the decimal portion of ∏, whether it is 1,000 digits or 1 million digits. I encourage them to import different amounts of data. Then they compute the probability of each digit occurring in ∏ and find that the more digits of ∏ that they use, the closer the probabilities of each digit appearing approach 10%. This result is similar to their coin toss experiments.

It took several hours, but I have uploaded the files to my static web pages at meeyauw's hideout. I even included a file that contains the first million digits of ∏. You can study the formulas used in the spreadsheets and see the graphs we created. The graphic above used 10,000 digits of ∏ to find that the probabilities of a digit appearing in the decimal portion of ∏ approach or are at 10%.

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Below is my playlist of ∏ Day videos from YouTube. I haven't seen most of them because of the Internet problems.

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My last Pi Day contribution today is the ever so much fun site, the Pi Search Page. When students have done their spreadsheets and charts, they are encouraged to play with this site. Hopefully this site reinforces the concepts that I want them to understand. Today I entered the Apple Computer Store telephone number (1-800-MY-APPLE or 1-800-692-7753). There was no result when I entered the entire phone number. But when I entered 6927753, the results were:

The string 6927753 occurs at position 24,791,273 counting from the first digit after the decimal point. The 3. is not counted.

The string and surrounding digits:
51437113655565872488 6927753 92233691772360083137
this query took 0.007674 seconds

HAPPY PI DAY!

moar funny pictures

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mathrecreation: teachers - born or built?

mathrecreation: teachers - born or built?
Go read this. Really.

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Homemade Playdough Recipe

Rainy day got your kids down? Looking for a quick and easy homemade craft that will get their creative gears turning? Try this homemade playdough. Just 5 basic pantry ingredients and an adult to heat the water, and the world of color, fun and fantasy are just around the corner.

Hands-on time: 5 mins. to 10 mins.
Total time: 5 mins. to 10 mins.

Playdough

2 cups King Arthur Unbleached All Purpose Flour
1 cup salt
1 tablespoon cream of tartar
1 tablespoon vegetable oil
2 cups very hot water
various food coloring (optional but fun)
various scented oils or liquid flavorings (again, optional)

Directions

1) Mix the flour, salt, cream of tartar with a whisk until well blended. Break up any lumps of salt with your fingers.

2) Add the oil to the hot water (a good job for grownups). Mix into the flour blend until a smooth dough forms. The dough will be quite warm to being with, but cools quickly.

3) If using colors and scents, divide the dough into sections and scent and color each. Wearing rubber gloves for the initial kneading will help keep your hands from becoming stained.

4) Once your shapes, critters, and designs are done, they can be dried at room temperature overnight, or longer, and painted with craft paints for lasting treasures. If you are not keeping shapes, etc. the playdough can be stored airtight in the fridge for one week.

© King Arthur Flour, Inc.

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Happy Pi Day!

Math — Gocomics.com: Comics, editorial cartoons, email comics, comic strips

Technorati Tags: Pi Day, GoComics, Non Sequitor
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Puzzler: Kenken Puzzles

Play online at kenken.com or at the New York Times (free but registration required).
Technorati Tags: kenken, Will Shortz
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Friday Fractal: Nova: Hunting the Hidden Dimension

Now that I have the Internet again, I have a lot of blogging to do. That's why there are two Friday Fractal posts tonight. Hunting the Hidden Dimension is the perfect introduction to fractals. You can watch this PBS video online now by clicking the link on the title. There is another PBS site, the Hunting the Hidden Dimension homepage, where you can explore fractals with an interactive applet and even create your own (as I did, above).

If you are a teacher, you will find a teacher's guide with an interesting classroom activity. You can stream the program for free on a projector at school, do the activities, let your students lose with free fractal software and see what happens! I'm going to suggest this as an After School Program at school.

Friday Fractal

Technorati Tags: fractals, Hunting the Hidden Dimension, PBS
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Blogged with the Flock Browser

Friday Fractal: Ron Eglash and African Fractals

Friday Fractal

Technorati Tags: Ron Eglash, African fractals

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Light the Christmas Tree Game

You can find this game at A Kid's Math in the Math Games section. It took me an embarrassingly long time to figure this game out and now I'm addicted. Even though I still don't have the Internet, I can load the web site at school or at the library and then play at home. After I win a game and click "play again," a new game is loaded. Thank goodness for javascript.
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Scratching "meeyauw"

Screenshots of the animation of "meeyauw" that I created in preparation for class on Tuesday. The animation can be seen at http://scratch.mit.edu/projects/meeyauw/308676. The kids in Scratch Club love this stuff! I found an excellent resource at learnscratch.org. Check it out.

Technorati Tags: Scratch
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Blog Your Blessings: Extrinsic Motivators

The weather has been beautiful this weekend and I have been stuck inside studying (and moaning about it) — although I did get outside for some great photos yesterday morning; this photo is Sentinel Rock, a glacial erratic in Westmore. I took a class this summer (Teaching Mathematics to ADD/ADHD/LD Students, paid by my contract) and am now taking two six week workshops (Tools for Building Math Concepts and Algebraic Reasoning at the Math Forum, both paid for by the National Science Foundation). Instead of doing my homework during the rainy season in August, I am forced to do it now. I love doing the assignments — so why didn't I? 

This year we are required to write professional goals for ourselves at school. I am going to read Knowing and Teaching Elementary Mathematics by Liping Ma and Fostering Algebraic Thinking by Mark Driscoll. I've had these books for ages and have not read them. Books such as these energize and enrich my teaching and I find them fascinating. So why didn't I read them? 

My final blessing is my camera — an intrinsic motivator. Over the years, the camera has become a comforting companion for me. Behind the view finder I find focus and purpose beyond my professional life. This week I was finally published in Humanities (September/October 2008, page 19) — the magazine of the National Endowment for the Humanities.  The photo is of the round barn at the Shelburne Museum that I took on a school field trip a year and a half ago. The photo is not in the online edition of the magazine, but the print edition has my name on it. I think I want to subscribe to this beautiful magazine out of thanks, but it costs $24 a year. I want to thank Maria Biernik at NEH for finding and using the photo.

My motivators — extrinsic and intrinsic — enrich my life.

My Sentinel Rock State Park Set on Flickr

My Shelburne Museum Set on Flickr

To read more blessings clickBlog Your Blessings
or Blog Your Blessings

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Teacher Potluck Carnival: Earth Day Edition

Welcome to the Earth Day Edition of the Teacher Potluck Carnival! First, let me apologize for this being two days late. Blog Carnival was down, I had classes to teach and appointments to keep. I have made sure that the next carnival will be close to a weekend.

So on to the Teacher Potluck Carnival! There were a lot of submissions this month. There is one recipe that I am so excited about: math cookies! I can't wait to try baking them. Lots of other good food and more great tips for us teachers are here

FOOD

Bobby presents a Chicken Alfredo recipe posted at Free OnlineRecipes. Bobby has convinced me that I can make this. Enjoy!

Theo presents Review of Horizon Organic Fat-Free Plain Organic Yogurt posted at Organic Test Kitchen. This yogurt is not sold in the Northeast Kingdom of Vermont so I can't try it. But Theo has and I found it an interesting review. It taught me what to watch for in yogurts (which are big here with the many organic dairy farms). Organic Test Kitchen looks like a great blog that I'll be checking out more in the future.

Finally, Leena Helttula presents Mathematics and Baking posted at Conceptis addict. I have enjoyed Leena's blog for quite awhile. She is a puzzler and introduces me to great puzzles. And now? She found a recipe for Sierpinski cookies! Can you believe it? Check out her blog! The photo of the cookies is from her site. She includes complete recipes for how to create them.

EDUCATION

Scott Palat presents School Discipline: Effective Strategies for Instilling Successful Classroom Discipline | posted at Colleen Palat. I enjoy articles like this because I believe we all need to be regularly reminded of these strategies.

And finally, Eric Koshinsky presents How to Teach Speaking posted at Teachers Call.

I present Vermont's First Annual Junior Iron Chef Competition. Middle and high school students throughout Vermont competed in an Iron Chef type competition in order to promote using natural and local foods. The video is from Stuck in VT. We are beginning a Farm to School program at our school and at many others in our district. The awful videos about mistreated cattle at slaughter houses helped push this program forward. You may want to check this movement out for your school.

The next edition of Teacher Potluck Carnival will be the Memorial Day Edition on May 25. Be sure to submit early and often!

SUBMIT YOUR TEACHER POTLUCK CARNIVAL POST HERE!

Teacher Potluck Carnival

Technorati Tags: Sierpinski cookies, Farm to School

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WBUR & NPR's On Point : The End of the Math Wars?

WBUR & NPR's On Point : The End of the Math Wars?

For 20-odd years, mathematicians, parents, and teachers have been arguing over the best way to teach your children math. Well, a national panel formed by President Bush two years ago has just issued its findings, and is pushing schools to go back to the basics — memorization, multiplication tables, and less so-called "fuzzy math."

This hour, On Point: we ask experts if it all adds up -- and with their help, we do your kids' math homework.

• John Hechinger, education reporter for The Wall Street Journal
• Mary Eich, a former math teacher, she is the K-8 math coordinator for the Newton, Massachusetts, public schools
• Wilfried Schmid, professor of mathematics at Harvard University and a member of the National Mathematics Advisory Panel, which recently released its report
• Joseph Rosenstein, professor of mathematics at Rutgers University and director of the New Jersey Mathematics and Science Education Coalition

Click here to listen.

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Teacher Potluck Carnival: The Pi Day Edition

Welcome to the Irrational Teacher Potluck Carnival for Pi Day 2008!

Pi Day and Pi Approximation Day are two holidays held to celebrate the mathematical constant π (pi). Pi Day is observed on March 14 (3/14 in American date format), due to π being equal to roughly 3.14. Sometimes it is celebrated on March 14 at 1:59 p.m. (commonly known as Pi Minute). If π is truncated to seven decimal places, it becomes 3.1415926, making March 14 at 1:59:26 p.m., Pi Second (or sometimes March 14, 1592 at 6:53:58 a.m.). Pi Approximation Day may be observed on any of several dates, most often July 22 (22/7 (European date format) is a popular approximation of π). March 14 also happens to be Albert Einstein's birthday.

The first Pi Day celebration was held at the San Francisco Exploratorium in 1988, with staff and public marching around one of its circular spaces, and then consuming fruit pies; the museum has since added pizza pies to its Pi Day menu.[1] The founder of Pi Day, the "Prince of Pi", is Larry Shaw,[2] now retired from the Exploratorium, but still helping out with the celebrations. They have also recently added the first Pi Day celebrations in Second Life.

The Massachusetts Institute of Technology often mails out its acceptance letters to be delivered to prospective students on Pi Day.

See Wikipedia, Pi Day, http://en.wikipedia.org/wiki/Pi_Day (as of Mar. 14, 2008, 00:26 GMT).

Tomorrow we are celebrating ∏ Day with our ∏ Memorization Contest, a ∏ Day Sudoku, and, of course, pies! Chocolate pudding pie seems to be the kids' favorite, with blueberry and pumpkin coming in second.

But don't worry! Our recipes and education links are very rational. In fact, at least one is green for St. Patrick's Day. All our recipes are circular. Happy Pi Day!

FOOD

Let's start off with St. Pat's Pistachio Cookies. I got this recipe from my weekly mailing from King Arthur Flour. You get green cookies, which is fun! They suggest you use the Jell-o brand of Pistachio pudding for the best color.

I spent this past Saturday making my Apple Crumble Pie from cooks.com. I love pies. They are my favorite breakfast food. But making them? A mess! The crust I make is terrific but makes me too tense. Luckily, our store in the village now has a local frozen organic pie crust available. Amy has used two shells for a two crust pie. Still too much work for me. This apple pie has an easy crumble topping that works beautifully just as the recipe says it will. The crumble topping feels skimpy but trust the recipe and it will work. I love the sheen that the raw apples have with the flour and lemon water mixture. The last photo is of the first piece of pie from the pie tin. The flour and lemon juice mixture made a beautiful gel that was completely natural. Click on the image to see it full size.

Finally, my Amy has granted me permission to publish her "perfected" chocolate chip cookies. What does "perfected" mean? I don't get anymore cookies because she has no need to further test her recipe. She is in search of another recipe to perfect. It had better be something chocolate. Sorry, no photos. I ate the cookies.

2 sticks unsalted butter
2 cups flour
1 cup whole wheat flour (or just use all regular flour)
1 teaspoon salt
1 teaspoon baking soda
1 teaspoon baking powder
1/4 cup sugar
1 1/4 cups brown sugar
1 egg
1 egg yolk
2 tablespoons milk
1 1/2 teaspoons vanilla extract
2 cups semisweet chocolate chips
about 2 cups of toasted walnuts or pecans

Hardware:
Ice cream scooper (#20 disher, to be exact)
Parchment paper
Baking sheets
Mixer

Heat oven to 375° F.
Melt the butter in a heavy-bottom medium saucepan over low heat. Sift together the flour, salt, and baking soda and set aside.
Pour the melted butter in the mixer's work bowl. Add the sugar and brown sugar. Cream the butter and sugars on medium speed. Add the egg, yolk, 2 tablespoons milk and vanilla extract and mix until well combined. Slowly incorporate the flour mixture until thoroughly combined.
Stir in the chocolate chips and nuts.
Chill the dough, (I did not do this.)

Scoop cookie onto parchment-lined baking sheets, 6 cookies per sheet. Bake for 14 minutes or until golden brown, checking the cookies after 5 minutes. Rotate the baking sheet for even browning. Cool completely and store in an airtight container.

EDUCATION

Jean Mosher presents More American Children Educated Online posted at Always in Motion. I read the article and it raises important questions about public funding, for-profit educational corporations, credentials and regulation. We have to be aware of the issues because they could affect us sooner than we know.

With that in mind, consider Mark Monaghan's post The need for eLearning posted at eLearning. If you have not seen this video, you must. It will put the eLearning debate into focus.

Despite a district-wide rule prohibiting cell phones in our schools, students have them. Cell phones have audio, still photo and video capabilities. What would you do if suddenly you appeared on YouTube in a cell phone video? Greg Laden presents Greg Laden's Blog : Teachers Gone Wild posted at Greg Laden's Blog. I think this is another article that you must read.

Are you planning on buying pronunciation software for your students? Eric Koshinsky presents Pronunciation Software to Improve English Pronunciation posted at Teachers Call. There are more criteria to consider than I had ever realized.

That's it for this edition of the Potluck Carnival. Please submit your recipe, story or article for the next carnival here.

HAPPY PI DAY!

moar funny pictures

Teacher Potluck Carnival

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Heads or Tails: Curve-Stitching The Green

St. Patrick's Day Mathematics Lesson

Suggested to me by Multicultural Mathematics: Teaching Mathematics from a Global Perspective by David Nelson, George Gheverghese Joseph and Julian Williams

OBJECTIVES:
Develop number sense
Introduce number theory
Practice sums of ten

MATERIALS:
Worksheets
History of the Shamrock
pencils
markers
video about the history of St. Patrick's Day
Richard Phillips: Numbers: Facts, Figures and Fiction
D. G. Wells: The Penguin Dictionary of Curious and Interesting Numbers

LESSON:
Read History of the Shamrock
Watch "The Story of St. Patrick's Day" video
Curve-stitch a shamrock (St. Patrick's Day worksheet).
Investigate the number 3 with information from Phillips and Wells.

EXTENSION:
What other shapes might you get by using other sums?

LINKS:
Search The Math Forum and enter "curve stitching" in the text field.
Google for more info about: Lissajous Figures, String Art Lissajous. JAVA sites.

To see more Heads or Tails participants, visit Skittles

or click Heads or Tails.
Thank you so much for visiting.

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