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Patterns - Even in Sound!

Resonance Sound Experiment
As you know, all math is based on patterns.  In fact, patterns are everywhere.  This year, my husband is going to do an experiment with his students on sound and vibration.  He was looking for some ideas on You Tube, and came across The Amazing Resonance Experiment.

If you click under the picture on the left, you will see an incredible thing happen when salt is put on the surface of a metal plate connected to a tone generator and then vibrated with different sound frequencies. Different patterns emerge in a seemingly graceful dance.  As the plate vibrates at different frequencies, the salt particles fall into different resonant patterns.  It is mind-boggling how the frequencies create such detailed and meticulous patterns of the salt grains. When the video began, I expected all of the patterns to be symmetrical, but many were not (although, as a mathematician, I thought they were trying!).  I do think it is beautiful how one pattern morphs into the next. Notice how the patterns become more complex as the tone increases in frequency.  Also take note of how the individual shapes (circles, squares, etc.) that form the patterns keep getting smaller and smaller as the frequency becomes higher.

According to physics, everything is frequency and vibration. "These salt patterns are a result of micro bendings in the material due to the vibration waves going through it. The salt gathers at stationary points on the plate where there is the energetic most convenient place. In other words, the salt gathering results from vibrating the plate at different frequencies.  However, the patterns are not connected solely to the frequency, but rather to the frequency combined with the shape of the metal plate.  Using the same frequencies on differently shaped plates (round, triangular, etc.) would produce different patterns. Even changing the material would affect the result." The experiment has been tried with flour, sand and sugar with the flour forming clumps (not a desired result). 

So take five minutes to watch the video and see the shape of sound which is beautiful, remarkable as well as fascinating !  Don't you love science?  It's just as amazing as math!! 

Dinner Dilemma and the Roll of a Die

Being a grandparent lets you try some new discipline methods that you never thought of as a parent. My grandchildren don't always like what I serve for dinner (Unbelievable, isn't it?); so, many times food is left on their plates. My children want their children to at least take a bite of everything on their plate which often times feels like a monumental task for our grandchildren. The Solution? I have an oversized sponge die on hand for such occasions. The child who doesn't want to eat rolls the die, and the number that comes up is how many bites they must take before dessert is served. Now, the child must argue with the die and not the parent or me! (It's difficult to argue with an inanimate object.)

Besides taking care of a dinner dilemma, my grandchildren are learning to conserve sets. (Oh, there's the math part of this article!) Since there are no numbers on the die, only dots, the child must count the dots to find out the number. Surprisingly, even the youngest are learning to recognize the dot patterns and can state the number of dots without counting. This indicates they are learning to conserve sets, a necessary prerequisite to memorizing the math facts. If you aren't sure what conserving sets means, go back and read my blog posting entitled Can't Memorize Those Dreaded Math Facts. In the meantime, enjoy a new way to enjoy dinner because it is pretty dicey!

You might like a math game that uses dice. It is called Bug Ya and can be purchased at my store. Three games are included in the four page resource packet. One is for addition and subtraction; the second is for multiplication, and the third game involves the use of money. The second and third games may involve subtraction with renaming and addition with regrouping based on the numbers that are used. All the games have been developed to extend the recall of facts through playful and intelligent practice. Be sure and download the preview.

Getting to Know You...

School is beginning for most of us.  I teach on the college level, but I still feel the most important thing I can do is to make the students feel connected to one another so that they at least know one other person in the class.  I always start each new class by playing a true/false game.  I start off the first class by listing four items about myself, three that are true and one that is false.  The students try to discover the false one.  On a 3” × 5” card, I then have the students write four things about themselves, three true and one false from which we, as a class, try to find the false one.  I then collect and save the cards.
At the next class meeting, I will choose 3-4 cards from which to read the true statements. As a class, we try to match the student to the card.  It really helps the students to relax and have fun at the same time plus they get to know each other. I usually do this activity for a couple of weeks until I sense that the students are comfortable being in the group.
By the way, here are my four statements.  Can you choose the false one?
  1. I have eight grandchildren, five of whom are adopted.
  2. My husband asked me to marry me on our first date.
  3. I am a big Jayhawk (Kansas University) fan.  (We live in Kansas.)
  4. I have been teaching for over 30 years.
Give up?  You can find the answer on the page entitled Answers to Questions.


You might be interested in two other back to school items.  First is the Back to School Glyph for grades K-3.

Secondly, for new teachers, there is a Beginning of the Year Checklist. This four page comprehensive checklist walks you through 88 items which should to be established before the first day of school.

Not on the Test

Not on the Test
While watching my granddaughter at her tennis lesson, I was visiting with two teachers.  One was a retired fourth grade teacher and the other currently taught Algebra in middle school.  Both we decrying the fact that each year the students come with knowledge that is more narrow than broad.  They both felt this was because more and more time is now spent on testing or getting ready for testing.  As I stated in my January 25, 2012 posting entitled The Pros and Cons of Testing, "High stakes tests have become the “Big Brother” of education, always there watching, waiting, and demanding our time. As preparing for tests, taking pre-tests, reliably filling in bubbles, and then taking the actual assessments skulk into our classroom, something else of value is replaced since there are only so many hours in a day.  In my opinion, tests are replacing high quality teaching and much needed programs such as music and art."

A long time ago, a friend sent me a song written by Tom Chapin with John Forster called Not on the Test. I saved it, and I listen to it often, especially when I am having a "down" day.  Tom and John wrote the song to express their disappointment in the lack of arts education in many public schools.  Even though the song refers to No Child Left Behind, with Common Core approaching with its own set of tests, I think you might get a much needed laugh from the song.  Just click on the link under the picture, and let me know what you think!