Whiteboard Lesson: Estimating Square Roots (Days 26-27)

Tonight is Back to School Night. With a long evening spent at school, it's a good thing that this is a two-day post, with no scheduled post tomorrow.

In all classes, the kids continue work in the so-called "Student Journals." Then tomorrow, the students will practice on the whiteboards. This should provide adequate preparation for the major test that all students will take on Tuesday. For eighth graders, the test will be on rational approximations to irrational numbers, particularly square roots.

During the music break, I choose a song from Square One TV: "Nine Nine Nine." The reason I chose this song is that this is one of the oldest videos on YouTube -- in fact, Monday, September 26th marks the tenth anniversary of its first posting on the web. I might have sung this song on the anniversary itself (or maybe not, since it's a coding Monday), but I decided that this would be a great song to sing for Back to School Night. (Actually, it would have made more sense to play it on the ninth anniversary since it's a song about the number 9. Well, today is the 9.99th anniversary, so there are your nines!)

Here is that old YouTube video:

Here are the lyrics to this song, courtesy Barry Carter:

http://wordpress.barrycarter.org/index.php/2011/06/07/square-one-tv-more-lyrics/#.V-SYfCgrKUk

Nine Nine Nine

Lead vocals by Reg E. Cathey

Backup vocals by Cynthia Darlow

Nine nine nine
Fantastic number nine
It’s perfectly consistent
It works out every time
Nine nine nine
That crazy number nine
Times any number you can find
It all comes back to nine

Two times nine is eighteen
Eight and one is nine
Three times nine is twenty-seven
Seven and two is nine
Four times nine is thirty-six
Six and three is nine
Five times nine is forty-five
Five and four is nine

Six times nine is fifty-four
Five and four is nine
Seven times nine is sixty-three
Six and three is nine
Eight times nine is seventy-two
Seven and two is nine
Nine times nine is eighty-one
Eight and one is nine

Nine nine nine
Fantastic number nine
It’s perfectly consistent
It works out every time
Nine nine nine
That crazy number nine
Times any number you can find
It all comes back to nine

Nine times ten is ninety
Just drop the zero sign
Nine times eleven is ninety-nine
Makes me rhyme with another line
Then nine and nine is eighteen
And eight and one is nine
Times any number you can find
It all comes back to nine

This work for bigger numbers, too?
Yup.
Let’s try this’un: three thousand four hundred’n eighty seven
Hmm … nine times three thousand four hundred eighty seven is
Thirty-one thousand three hundred eighty-three
Three plus one plus three plus eight plus three is eighteen;
One plus eight is nine.
It always works!

Nine nine nine
Fantastic number nine
It’s perfectly consistent
And it works out every time
Nine nine nine
That crazy number nine
Times any number you can find
It all comes back to nine
It all comes back to nine
It all comes back to nine

As it turns out, a second YouTube video was posted on September 26th, 2006 -- "One Billion Is Big", which I mentioned on the blog around the time of the billion-dollar Powerball jackpot. The reason I favored Nine Nine Nine over One Billion Is Big is that Barry Carter doesn't have the lyrics to the latter song available. I'll have to play and pause the video myself to get the lyrics. I might do so within the next month or so, since there's a lesson coming up in the eighth grade Illinois State text soon about large numbers.

Meanwhile, today's song would be a great song to play around the time of the Dren Quiz for 9's, which will be during the third trimester. In many ways, the hardest digit by which to multiply in base ten is not 9, but 7. The 8's have the advantage of being all even, while the 9's follow the pattern mentioned in the song. (At the Dozenal Forum, it's mentioned that in base 12, it's the 11's times tables that follow the pattern mentioned in the song -- a pattern known as the omega rule.)

At Back to School Night I met several of the parents and sang the song for them. One parent was concerned about our school's lack of a science teacher, but many enjoyed the song. I ended up giving away my old "Meet Me in Pomona, Mona" song to the one parent who volunteered at the fair.

Here is a link to the "A Day in the Life" poster for the 22nd, Jonathan Newman:

hilbertshotel.wordpress.com

Newman is a Maryland middle school teacher -- that's right, many of the participants in the "A Day in the Life" project are middle school teachers! So I definitely want to discuss Newman's blog in much more detail. Here is a link to his September 22nd post:

https://hilbertshotel.wordpress.com/2016/09/22/ditl-september-22nd/

Most of Newman's classes are Common Core Math 8, but he does have one section of Algebra I. He writes that today is the end of the first quaver at his school. Even though he has only one Algebra I class, almost all of the photos in his post are from that class.

Newman writes that he gives his Algebra I students a Three-Act Lesson -- which means that it goes back to the King of the MTBoS, Dan Meyer. This activity is all about taxi fares and ultimately leads to graphing linear functions.

I admit that from my perspective, this is a bit early in Algebra I to be teaching linear functions -- that topic usually appears later in the first quarter or early in the second. Of course, my "Show Me the Numbers" activity is all about graphing what should be a linear function -- but it's more about recording and graphing data and less about the structure of a linear function.

Notice the name of Newman's blog -- Hilbert's Hotel. Back in January, I mentioned the idea of an infinite hotel, dating back to the mathematicians Georg Cantor and David Hilbert.

My next post will be Monday.