Sewing

This past weekend, I attended something called Costume College, held in Woodland Hills, California.  For those not familiar with the area, its basically the Los Angeles Area.

That is why I didn't get my usual weekend warm-ups posted.  I got absolutely busy and did not get a chance to post.  The picture is of me, in my attire for the ball.  Everyone shows their work by wearing costumes.

I costume in my spare time.  Anyway, during one of the conversations, math came up.  The lady I spoke with explained the pattern for her current outfit was only available in a smaller size.  The store had sold out of the larger sizes, so she had to add 3/8th of an inch all around to make it fit.

I've had to do it but the other way.  I've had to subtract 1/2 inch to make everything fit properly. Many costumers write down tons of different measurements such as the length from the back of your neck to your waist, distance across the shoulders, etc because most patterns are designed for specific measurements.  I have one shoulder that is slightly lower than the other due to playing French Horn for over half my life.  I know a female who has larger upper arms due to heaving batteries.

In addition, many pieces of clothing are designed using some basic shapes.  For instance, those circular poodle skirts from the 1950's are based on a circle with a place for the waist.  Unfortunately, most fabric is not wide enough to cut out a single circle.  I use circular skirts when I belly dance so I've had a lot of experience. I am lazy so I use a string and piece of chalk to draw a fourth of a circle on a folded piece of cloth to get half the skirt. I do it twice, cut out the wait area, sew, put in zipper, and hem. 

Another type of skirt can be made out of two rectangles the width of the hips for the front and back.  This straight skirt uses elastic to gather the extra material around the waist while the rest of the skirt falls straight down.  I often leave slits in each side to make walking easier.

Furthermore, I use two rectangles as a starting point for making harem pants or loose hang about pants.  I use two wide rectangles, one for each leg, cut out the crotch part, sew it, put in some elastic and I am set. 

Ethnic clothing is often put together using rectangles, squares and other shapes to create the dresses, shirts, skirts etc because cloth was woven on narrow looms.  Japanese kimonos originally used material that was no more than 18 inches wide so the clothing created had to take this into account and the most efficient way of doing this was through the use of shapes.

Tomorrow, I'm going to look at the use of shapes and clothing from a different point of view.  I hope you liked today's material.  Let me know what you think.

Busy weekend

I am at an educational conference. The internet signal is up and down. I found out about something new I will share with everyone on Monday. I do not think I will be tomorrow so if I am not, it is because I just ran out of time.

Model Railroads.

  If you are old enough, there was always someone in the family who built a huge 4 by 8 railroad using models.   I remember seeing one in the family with a town, forest, bridge and a lake as part of the journey.

If the builder did things correctly,  everything looked perfect because the scales remained the same for everything.  If not, the trees might be a bit too small and the lake more like an ocean.

Did you know the scales for model railroads were not always the same?  I didn't until I researched this topic.  The National Model Railroad Association has some excellent information if you want to read about this topic in more detail. 

In model railroading, scale means it is a smaller version of the real thing. O scale is also known as 1/4th inch scale which is a ratio of 1 to 48 while the HO scale is 1/8th inch scale with a ratio of 1 to 86 or 1 to 87.  The N scale made its appearance in the 1970's and  has a ratio of 1 to 160 while the Z scale has a ratio of 1 to 220.  This means the O scale is the largest while the Z scale is the smallest.
Another one, the S scale as defined in 1943 is  3/16th inch or a scale of 1 to 64.  At one point this scale almost disappeared but has undergone a Renaissance. 

There are a few others but these are the main ones. Now to add to the confusion, one has to keep in mind, one has to keep in mind the gauge or distance between the rails.  For instance, the distance between the rails for the O scale is a bit more complex because it normally requires 3 rails instead of two and the distance represented is 5 feet.

Its all a bit confusing if you are not familiar with this topic because the distance between the rails must also be done properly so everything looks proper.  So what do you do with this information?  It makes a good project involving research and drawings which are properly scaled.  As part of the research, students can determine which scale is used with which manufacturers or the train such as American Flyer or Lionel. 

I have been traveling and this is being written in an airport between Fairbanks, AK and Burbank, CA.  I'm at a conference till Monday when I head home.

Creating Escher Tessellations in Class

  M.C. Esher born 1898 and died in 1972.  He is best known for his use of tessellations in his art work.    You've seen his work even if you don't know it.  Among other things, he did several drawings where stairs seem to go back upon itself.

He is perfect for using in a math class during tessellations and  transformations because he uses both in his artwork. This YouTube video does a lovely job of introducing M.C. Escher's work while discussing the mathematics of it.

The question becomes how did he create it?  Well there is a wonderful 32 page teachers guide from the Akron Art museum on it.

The guide includes the mathematics behind the topic.  After introducing M.C. Escher, the first lesson begins  by discussing different types of symmetry.  Next students are expected to identify the type of symmetry used in the examples.

Lesson 2 focuses on three dimensional shapes such as those found in crystals. The lesson includes information on faces, vertices, and edges so they get the vocabulary.    Lesson 3 goes on to look at architecture, parallel and perpendicular lines, and creating cubes out of isometric paper.  Lesson 4's topic is reasoning through the use of a Mobius strip and includes real life uses.   All four lessons focus on the mathematics involved.  The remaining part of the pdf focuses on art. I like the way the math lessons are created.

You Tube has several nice videos on creating general tessellations in the Escher method including this 11 minute one which is slow and takes things step by step.  At the end students have one but the form is not specific.  If students want to create a more specific shaped tessellations check this video shows how to create a Escher Bird Tessellation step by step on sketchpad.

In addition Tessellations.org has some great instructions using tracing paper and equilateral triangles. In fact the whole site is devoted to tessellations.  They even have a version of Angry Birds in a tessellation form.

I'm finishing this up for two reasons.  First, there have been two power outages already this afternoon in the last 15 minutes and second, I have to finish packing for a trip I am taking to Los Angeles.  I needed to get ahead so I do not miss anything. 

Let me now what you think.  I love hearing from people.

First Day of School.

For most people, the first day of school should be happening sometime within the next 6 weeks.  My students have their first day of school on August 15th.

By the time students hit high school, teachers tend to pass out syllabus, go over the grading policy, talk about attendance, or give a test to see what students remember.

That first day of school can be a bit hard for students who may have spent the summer going to bed late and sleeping equally late in the morning.  Its a sudden readjustment for both them and us.

I've read things which suggest a teacher can put off all of the usual business until the second or third day

I usually start the first day by having students work on remembering math terms. All they need is a piece of paper, a white board, a tablet, and something to write with. They need to write the alphabet vertically so A is at the top of the paper and Z is at the bottom.  I give them 10 minutes to write down mathematical terms for as many letters as they can.  At the end of 10 minutes, I have them place their list on the desk right in front of them. 

I have everyone get up and check out everyone else's answers.  They may not touch but they may look. At the end of 2 minutes, I have them sit down before giving them 2 more minutes to add to their lists.

At this point, I ask for suggestions for each letter.  I always write down several choices and if someone gives a suggestion that is boarder line, I ask them for their justification before students vote to decide if its acceptable.  I often run out of time before we get through the whole list.

My students enjoy it.  I tell them it is a way to get their brains back into thinking about math.  I never grade this activity.

One suggestion I've seen is to have students do a self portrait or write an auto biography so the teacher can learn more about them. Along the same line , have students write four clues about themselves on an index card and sign it with a code name.  Gather these cards up, shuffle, and pass the cards out to the students. Challenge them to find the person whose clues they have.  They become the detectives.  Students will have to question each other in order to gain information.

Let the students brainstorm ideas for new years resolutions for the classroom.  Resolutions should be positive and can be recorded on cloud shaped papers which are pinned to the bulletin board with the words We Resolve: What about organizing a scavenger hunt where students look for the pencil sharpener, paper, hall passes, etc so they get to know where you keep things.

Keep your eyes open for the next list of suggestions for the first day of school but it won't happen for at least a week.  Let me know what you think.

iTunes University Part 2

  I had so much fun exploring this site for more math based materials one can easily integrate into the classroom.

Check out the Math of Design, a series of podcasts by Professor Jay Kapraff on 11 different topics such as the structure behind structures, and from tangrams to Amish Quilts.  These podcasts are about half an hour long.

Queen Mary, University of London has the Mathematical Magic with 16 short videos on how mathematics relates to magic including two calculator tricks, dicing with destiny, and a short piece on jokers.

 If you only have time for shorts, take a look at Math Snacks by New Mexico State Learning Lab.  The animation shorts run anywhere from 2 to 6 minutes and address ratios in a variety of situations.  The shorts are in both English and Spanish.  I watched one on dating where the girl compared the number of words she spoke to the number her date spoke.  It took her three dates to finally find someone who spoke the same number of words for a 1:1 ratio.  The shorts are cute.

I found an hour long segment on the Mathematics of Juggling in Physical Sciences and Mathematics by Cornell University.  It is one hour long and explores the mathematics involved with juggling.  I have a few students who are trying to learn to juggle and they just might.

On the other hand, Open University has Mathematical Models: from Sundials to Number Engines.  I watched the video on sundials which explained in detail how it works.  The particular sundial used as an example showed both the time of day and time of year. I found how they used certain paths to show the time of year.  It was cool.  In addition, I checked out the video which discussed recording sales on clay tablets in Babylonia.  Apparently, they used a base 60 system.  The spokesperson indicated writing was developed for mathematical modeling.  This site is more of a history of models but it was quite interesting.

Spice up a day by showing students one of three videos in Rollercoaster Design by Open University.  The three videos discuss the designing of a ride called Nemesis in England from a mathematical point of view including showing a graph of the ride if you stretched it out completely.  Each video has a transcript in case its needed.

For those days your students need a bit more of a challenge, check out Math Challenges by the University of Warwick which has 6 problems for students to solve.  Solutions are provided so the teacher knows what to do.  I looked at a problem which showed 5 glasses.  The first three were filled and the last two were empty.  You can only make one move so the classes are alternating, full, empty, full, empty, full.  How do you do it.

These are only a few of the collections and courses offered via iTunes University.  There are actual math classes such as geometry, algebra, string theory but there are also interesting ones on gliding, etc.  There are even some iBooks available.  Go look, check things out to decide which ones you want to spice up your class with.

Let me know what you think.

iTunes University Part 1.

  When I plan a lesson, I often forget to check iTunes University for offerings to incorporate in my math classes.  There are always courses and classes being added so its worth checking out.

Over the next two days, I'm going to suggest several with interesting activities or topics for the classroom.

The first is  Curious Math: Foundations of Math by Orr and Kyle Pearce.  The class was designed to bridge two different math classes in Ontario.  It is a combination of iBooks, 3 Act tasks, and some have a teachers manual to accompany them.  This course covers measurement, proportional reasoning, graphing, linear relationships, and algebraic representations.

Some of the activities are only for iPads but most can be downloaded onto a computer so if your school has bandwidth issues, you can download many of the videos to your computer to show.  I checked out a video showing a young man beating the world record for number of claps per minute.  He set a new record but I cannot believe how fast he was able to clap.  Over 800 claps in one minute.  It was awesome.  This was part of a 3 act task.  I'm wanting to do it with my class.

The second is from the The University of Oxford called The Secrets of Mathematics.  This series of lectures discuss a variety of topics from symmetry to modeling genes, to What maths really do for a total of 38 different lectures.  Each lecture lasts about an hour, some more, some less.  I began listening to one called The Sound of Symmetry which covered symmetry in nature.  For me, I found it fascinating. 

Other lectures like The Mathematics of Visual Illusion, or The History of Mathematics in 300 stamps, along with Maths in Music caught my eye.  I want to watch these myself and learn more.  In fact, I can use these lectures for learning to take visual notes before I try to explain it to my students.  I have a purpose for watching these. 

I will not have more than 45 minutes in a class period for watching these so if I break them in half to show, I can get through a few and expose students to a different perspective on mathematics.  I think we need to do this so students see mathematics is not always solving equations per-say.

Check out the first lecture in the Beauty of Mathematics from Aspen Ideas Festival called A Mathematician Reads the newspaper. It is an hour long lecture where a mathematician shows all the ways math is used in newspapers.  This might help answer "When will I ever see this?"

Open University has a wonderful class called Exploring Mathematics: A Powerful Tool which explores ways math is used in the real world.  I watched a short introductory video which touched on specialized bamboo scaffolding in Hong Kong and predicting climate change.  The bamboo scaffolding caught me right there.  Other topics include How Math Helps Dolphins, a five minute video examining the use of statistical modeling to determine endangered species survival rates.

Open University has a second class in this nature called Exploring Mathematics: Maths in Nature and Art.   Some of the topics include How a sundial works, Manufacturing patterns (designing carpets), spirals in nature, and the Lure of fractals.  Every video comes with a transcript in this and the previous one.  In addition, most videos are under 10 minutes long.

Tomorrow, I'm going to look at a few more classes, collections, and podcasts created to show students that math is related to real life. Let me know what you think.  Have fun exploring these.