Pi, Pi, Mathematical Pi

Every day this week we took a look at Pi.  On Monday and again later in the week we listened to the Mathematical Pi Song (to the tune of American Pie). I gave each student a paper plate and assigned them a number.  They were to write that number on the plate and decorate.  We hung the plates in a “Pi Number Line” down the hall.  That way we could think about this irrational number all week!  I gave each student a copy of the Greek Alphabet and we practiced reciting it.  I wanted them to see the letter Π and know where it came from.

On Tuesday we reviewed the words <radius>, <circumference>, and <diameter>.  Earlier in the year we had discovered that the word sum for <circumference> is  <circum> + <fer> + <ence>.  The prefix <circum> means around and the base <fer> means to carry.  The circumference is the distance carried around the outside of the circle.  The word sum for <diameter> is <dia> + <meter>.  The prefix <dia> means through and the base <meter> means to measure.  You measure the distance through the circle to find the diameter.    The word sum for <radius> is <radi> + <us>.  The base <radi> means rod, spoke of wheel, and ray of light.  I like to picture the radius of a circle as a spoke of a wheel.  I brought miniature donuts.  We multiplied the diameter of a donut by Pi, and in doing so calculated the circumference of the donut.  We watched another video having to do with Pi.  This one was the  ‘The Dance of the Sugar Pi Fairy’!  How fun to find creative ways to memorize digits of Pi.  (Certainly not a necessary thing to do, but certainly a tempting thing to do)

On Wednesday I brought cookies.  We measured the circumference and divided that by Pi to calculate the diameter of the cookie.  We also listened to some very creative math/musicians who put digits of Pi to music!  The first one is called Song from Π.  It is an enchanting piano piece with interesting facts about the number Pi.  The digits of Pi float by as they are being played on the piano.  Quite honestly, we loved the music, but found it difficult to follow the digits.  The second one was fascinating for other reasons.  The artist repeats the first 31 digits of Pi.  He uses different instruments and different tempos.  It’s called What Pi Sounds Like.

On Thursday I brought peanut butter cups and we measured both the circumference and the diameter.  We then found Pi by dividing the circumference by the diameter.  Several students came up with 3.166.  That’s pretty close!  We watched a video about art created from the digits of Pi.  It is called Pi is Beautiful.   We were inspired to see what kind of art we could create using the digits of Pi.  I found a circular graph.  We numbered around the outside using the digits of Pi.  If the number was a 3, then 3 squares toward the center were colored in.  Some students assigned a specific color to each number 1-9 to see what that would look like.  Some students stuck to using 1, 2, or 3 colors.  We were very pleased with the results and hung them in the hall above our Pi number line.

Then came Friday – March 14!  Students brought in pies – 17 in all!  We ate pie several times throughout the day and shared with adults around the school.  We held a contest to see who had been able to memorize the most digits of Pi throughout the week.  Our winner memorized 100 digits of Pi!  We were amazed!  Our second place winner memorized 61 digits and our third place winner memorized 24 digits!  Wow!  What fun.  Enjoy the following video.  It’s kind of a medley of our day!



A Lesson With Third Graders … The ‘ed’ Suffix!

It’s not unusual to see students coming into fifth grade making the following spelling errors:  <workt>  instead of <worked> and <happend> instead of <happened>.  I asked my students if they would be interested in teaching a lesson on this important suffix to third graders.   They were enthusiastic!  (I was glad because this opportunity would also solidify an understanding for MY students)   We wanted the students to notice two things about this special suffix.

First we wanted them to notice that when adding the <ed> suffix, three things can happen. 

1)  Sometimes the single silent <e> on the end of the base is dropped.  An example of this is the word <like>.  A word sum looks like this:  <like/> + <ed> –> <liked>.  The <e> on the based is dropped.

2)  Sometimes the final consonant is doubled.  An example of this is the word <stop>.  A word sum looks like this:  <stop(p)> + <ed> –>  <stopped>.  The <p> is the final consonant of the base word <stop> and is doubled when adding the <ed> suffix.

3)  Sometimes there is no change to the base word when adding the <ed> suffix.  An example of this is the word <wish>.  A word sum looks like this:  <wish> + <ed> –> <wished>.

Secondly we wanted them to notice that we don’t know how to pronounce the <ed> suffix until we see it in a word.

1)  It could be represented by the phoneme /t/ as in the word <jumped>.

2)  It could be represented by the phoneme /Id/ as in the word <painted>.

3)  It could be represented by the phoneme /d/ as in the word <grilled>.

While watching myself in this video, I caught myself falling into old habits.  I had asked a student how a word would sound once the suffix was added.  Well, I’m making a big change in the way I talk about letters and words with my students.  The truth I have recently learned is that words and letters don’t make sounds!  The truth is that a single letter,  digraph or trigraph can represent several sounds.  I think that established readers recognize that, but how confusing is it when we teach young children that a letter makes one sound, and then later we expect them to realize that it can represent other sounds as well.  This idea of letters making sounds feeds into the whole idea that our spelling system is crazy and illogical.  We have come to rely too heavily on sounding words out based on the limited letter/sound combinations we have been taught.  This is why students misspell <worked> and <spilled>.  It is time to teach that letters, digraphs and trigraphs can each represent several phonemes and that the phonemes represented by some digraphs need to be flexible within word families (heal and health; real and reality).  This is why I wanted to have my students teach this lesson.  What they teach to others, they will need to understand themselves.

Enjoy the following video excerpt from our lesson.


Move Over Superman! Here comes the Affix Squad!

Enter our superheros … Prefix and Suffix.  What is their mission in life?  To boldly build families of words from a single base!  In this, our latest video, this dynamic duo help out a bystander who is curious about building a word family with <like> as its base.

Thinking that we had that video (and the information therein) tied up into a neat little package, we received a delightfully thoughtful email response from our Canadian friend Skot Caldwell.

He raised a great question: ” The Affix Squad’s wise advice to never blindly follow the rules has me wondering about <likeable>.  Would the existing patterns not suffice to explain the dropping of silent <e> when forming <likable>?   We are not troubled by the spelling of <liking> or <liked> and do not confuse these with <licking> or <licked>?”

Immediately I was drawn in.  It’s true.  I don’t need the <e> in <liking> to know it’s not <licking>, so why need it here?  I took this rather intriguing point to my students today.    They weren’t sure what to say at first.  Falling into past practices for a moment, they were waiting for me to tell them which was right and which was wrong.  Instead I said, “What do you think?  Are we right?  Are we wrong?  Are both spellings right?  What should we do next as we ponder this?”

Danica offered to look at Etymonline.  Cooper looked in the Collins and Gage Canadian Dictionary.  Hannah looked in the Webster’s Dictionary.  While they looked I read more from Skot’s email:

“Perhaps this is a case of a spelling convention that needs to be solidified or altered.  Am I correct in guessing that this is a regional difference like <centre> and <center>?  As with <centre> and <center> the spelling <likable> and <likeable> are both attested and in use, as are <sizable> and <sizeable>.  The Word Searcher includes versions of many similar pairs.  But as with <centre + al> and <center + al>, only one spelling seems to satisfy suffixing conventions.  I am searching for a word that always drops its silent <e> when adding <-able>, but haven’t found one as yet.”
Hmmmmm.  This seemed very logical.  When returning to the group, Danica, Cooper, and Hannah all reported the same thing.  Both spellings were listed in each source.  No matter which was listed first, the other was listed as an alternate spelling.  I also shared what I had found at Word Searcher:  both loveable and lovable, both liveable and livable.  This definitely supports what Skot said.  It seems very sensible that the <e> would be dropped when adding the <able> suffix.  Austin said so in the video, and he was right.  Why then did it look so wrong?

Then I asked the question, ” Before we knew to look at a word’s structure when considering its spelling, how many of you judged whether a word was spelled right by whether or not it looked right?”  All hands went up, including mine.  What did the word that we had worked so hard to memorize look like?  What was the order of the letters?  We wrote down the word and compared it to the picture in our head.  Growing up, I had been taught to keep the <e> in <likeable>.   Because I had written it so many times, it looked right to me and <likable> did not.

More from Skot:  “I expect that the conventions that are not as sensible–whether British or American–are far too commonly used to combat in the countries where they are solidly accepted.”  Boom!  I agree with Skot on this one.  The convention that is the most sensible is to drop the <e> when adding <able> (vowel suffix).  The problem is that it has become common practice to keep the <e>, and since a dictionary is really only a reflection of the people who use it, both spellings are listed and considered alternate spellings.

So!  We decided that <likable> is more sensible when considering the spelling conventions, but that both are considered acceptable spellings by dictionary resources.  We also decided to keep the search on for a word that always drops the silent <e> when adding the suffix <able>.  Who knows if we’ll find one.  We’re still looking for that word in which <tion> is a definite suffix!  We’re also interested in finding out more about the words <mileage> and <acreage> that keep the <e>.  Are there more like that?

See?  What a remarkable day it has been.  And seeing as our school was celebrating the birthday of Dr. Suess today, all we could say was, “Oh! The Thinks You Can Think!”