Common Core Math

My understanding of the Common Core State Standard Initiative is that it is a set of guidelines as to what students are supposed to learn at various grade levels. How those guidelines are met is left to the individual states that adopt the CCSSI. You can read more here and judge for yourself. I’m not here to argue whether the CCSSI is good or bad, or if it impinges on “States Rights” or if it’s a tool of Satan. I just want to address one REALLY BAD piece of pedagogy.

I recently ran across the following image in a Facebook posting complaining about the Common Core Math requirements.

Common-Core-Math

I can’t find the original, full image so I’m going to interpret the missing text this way:

“Add 26+17 by breaking up the numbers to make a tens group. Use a number that adds to the 6 in 26 to make a 10’s. Since 6+4=10, use 4.”

I’m also assuming that this is the entirety of the problem. The rest is (not so) obvious. In fact it’s mind swivelingly hard to interpret. So for all you parents suffering through addition problems like this here’s my explanation.

For all of us who learned addition between the beginning of time through the “New Math” of the 1960’s the problem can be solved thusly:

Six plus seven is thirteen. Write down the three and carry the one to
the tens place. One plus two plus one is four. Write down the four
giving forty three.

The method in the image is basically asking what number can we add to 26 to force the carry of a one. Well, that would be four. That gets us to thirty but what about the 17? Since we already added four to 26 we have to adjust the 17 down by four before adding it to the 30. That’s where the “17 = 4 + 13” comes from.

Still a little fuzzy? Can you imagine asking a first or second grader, “Use a number that adds to the 6 in 26 to make a 10’s”? I was the little turkey that would always ask, “Why?” That hopefully would lead to a discussion of the carry operation. But this example doesn’t go there. It states, “Think: 17=4+13.” This is a complete non sequitur and doesn’t engage the student in any sort of problem solving activity. It commands “Think” and doesn’t address rational stepwise solution. So, if you’re fuzzy don’t worry.

This is how I would break the problem down (if for some completely twisted reason I was going to teach addition this way . . . which I wouldn’t).

We are going to use a non-traditional method to add the two digit numbers 26 and 17.

  1. First we’re going to find a number that when added to 26 causes a carry into the ten’s place.
  2. Isolate the 6 and solve the following equation:
    6+x=10
    x=10-6
    x=4
  3. Add 4 to 26. Using the “Old Math”, six plus four is ten, write down the zero and carry the one. One plus two is three giving thirty.
  4. Because we adjusted 26 up by 4 (forcing the carry) we must adjust the 17 down by 4. This is where the “17=4+13” comes from. In fact this should be “17-4=13” since that’s the actual computation we need to do . . . but I guess subtraction isn’t covered until next week so we have to “Think” our way around it.
  5. Now we can add the 13 to the 30 and get 43.

So actually all we’re doing is adjusting one number up to the next multiple of 10 and adjusting the second number down by the same factor before adding. Reverse the above problem: 17+26. You can almost do it in your head. (17+3)+(26-3) = 20+23 = 43.

I have several issues with the method.

  1. It only works for two digit numbers. Since it only addresses the carry from the units place this method fails to accurately add three, four, or five digit numbers. It’s not general. Want to make a kid cry? Tell them to use this method to add 998+427.
  2. It works for negative numbers but is potentially very confusing due to the adding of negative numbers. (I forget when I learned about adding negatives – I doubt it was first grade.)
  3. I’m being a stickler here but you just can’t pull the six out of 26 and operate on it. Intuitively you can but formally you have to isolate it with a modulo operation.

Since I spent the time pulling the method out of this horrid bit of pedagogy I might as well formalize it a bit. Here goes.

If x and y are two, two digit integers to be added together the following equation will produce satisfactory answers.

sum = (10 - x mod 10) + x + y - (10 - x mod 10)
where x mod 10 is the remainder after division, e.g. 17 mod 10 = 7.

Ok, need a laugh? Think things are tough now? Here’s a song from the 1960’s by Tom Lehrer. Click here to enjoy.

NCSE/UNC Spectrum Concert

The North Carolina Saxophone Ensemble and the UNC Saxophone Studio will perform on 11Apr2014 in the Kenan Music building rehearsal hall. The program notes for the concert will be projected on a large screen rather than printed, saving paper and allowing people to review the program both before and after the performance. To see the program notes click here.

Here are short descriptions of each piece.

Four5 – The fifth in a series of pieces for four players by John Cage. Cage wrote the “Number Pieces” later in his career. Click here for more information.

Melodies for Saxophone – Thirteen melodies written by Philip Glass for Jean Genet’s play “Prisoner Of Love” adapted by Joanne Akalaitis for the New York Theater Workshop.

The Difficulties – Electronica by Mark Engebretson and poetry by Brian Lampkin. For this performance a jazz baritone saxophone improvisation triggers electronic sounds to compliment the reading of Lampkin’s poem “The Difficulties”.

Far Away – Takatsugu Muramatsu is most noted for his work in film and television but “Far Away” was originally written for the Libera boys choir.

Last Tango in Bayreuth – Peter Schickele originally played this on piano as something of a party trick, eventually completing it as a quartet for four bassoons. It’s a tongue-in cheek tribute to Richard Wagner based on the “Tristan” chord from Tristan ind Isolde and a theme from “Overture to Act III” of Loehengrin.

Shetland Sequence – An arrangement of Shetland jigs by the British saxophonist Jan Steele. The jigs included are “Jack broke da prison door”, “Donald Blue”, “Sleep sound ida morning'”, “Lassies trust in providence”, and “Bonnie Isle o’Whaljay”.

Ecstatic Fanfare – An arrangement of the brass fanfare from the first movement of Steven Bryant’s “Ecstatic Waters” for wind ensemble.

Smiles and Chuckles / Beautiful Ohio Blues – These two pieces date from the early 20th century and were written for the Columbia Saxophone Sextet and The Six Brown Brothers. The arranger, David Lovrien, transcribed the pieces from recordings made on wax cylinders making these truly authentic saxophone pieces.

Capriol Suite – A collection of six dances with a Renaissance flavor written in 1926 by Peter Warlock. Originally written as a piano duet, Warlock re-scored the work for orchestra.

Festive Overture, Opus 96 –  Dmitri Shostakovich wrote this work in three days for the 37th anniversary of the October Revolution in 1954. Stylistically it is based on Glinka‘s Russlan and Ludmilla overture written in 1842.

Trilogy – A transcription of the opening vocal section of the larger work of the same name by Keith Emerson and Greg Lake with the tenor sax taking the vocal solo and the ensemble covering the piano parts.

 

 

Complete the Cone – Fact or Myth

I attended the U.S. Navy International Saxophone Symposium at George Mason University earlier this month. Along with all the great recitals and concerts, I attended an excellent  presentation titled “Working With Your Repair Technician” by Shelly Tanabe, owner of  Wind Player Services in NYC. One of the last slides of the presentation addressed the idea that the sax is a conical instrument and that the volume of the mouthpiece completes the cone.

Deep down, I’ve always been suspicious of this idea and seeing it again in the presentation made me decide to investigate it a little deeper. Since it’ll probably take more than one post I’ll add a menu item on the banner titled “Complete the Cone Series” that will link to everything.

Those of you who know me and my background are probably groaning right now. Yes, there will be geometry, trigonometry, and even some 9th grade physical science. Come on, it’ll be fun!!

Electric Flying Wing Mashup

Here’s a little project that came from a couple of different directions and turned into quite a nice little flying machine. It’s a complete hack but that’s just how it happened. The oldest bit of the project is a molded white foam “walk along” glider. It was developed by Tyler MacCready, the son of Paul MacCready the founder of AeroVironment. If you want to see one in a action check out this youTube video:

I’ve flown this around hallways at work and the local parking lots for over 8 years now and I’m not even sure you can buy them from Tyler any more. There are lots of pictures and plans on the web though so you shouldn’t have any problems coming up with you own plane if you wanted to try to duplicate what I’ve done.

The second bit of the mashup is the PowerUp™ Electric Paper Airplane Conversion Kit  from Tailor Toys. You can find it here at Think Geek:

http://www.thinkgeek.com/product/e9e7/

It’s a very cool unit comprised of a 2.7V, 10F (yes FARAD, not microfarad) ultra capacitor and a 14mm X 5mm electric motor mounted on a very thin, square, carbon fiber “pulltrusion” tube. You clip it onto your favorite paper airplane, charge up the capacitor with the hand held battery pack (3-AA batteries) and let fly. I flew a lot of paper airplanes before it hit me . . . the walk along glider!

Initially, I epoxied a balsa keel to the bottom of the wing and tacked the PowerUp unit to it. This setup made it hard to change the thrust line and gave only OK performance – it was a bit heavy. After messing with it for several weeks I bit the bullet and went on a weight reduction spree. A set of small diagonal cutters made quick work of freeing the motor and capacitor from their plastic mounts. I then cut the wires – making sure to leave enough lead length for later soldering – and extracted them from the tube. Keep the tube, it’s incredibly stiff and makes a great stabilizer or fin spar.

I trimmed the keel level with the bottom of the wing, notched out the trailing edge to accept the motor that was now mounted in some packing foam, routed and re-soldered the leads from the capacitor to the motor, and tacked the whole thing together with a minimal amount of 5 minute epoxy applied from the tip of a toothpick. Note that the motor is tacked into its slot with a tiny amount of epoxy but that the block itself is only glued at its leading edge. This allows the block to flex up and down slightly for thrust line adjustments.

No sophisticated charging jack is needed just apply the metal contacts to the leads of the capacitor and count to twenty. The capacitor isn’t polarized so it’s possible to accidentally reverse the charger and get the motor to run backwards. Just let it run down and recharge with the correct orientation.

I’ve only flown this in large rooms and outside in a parking lot in absolutely dead air (one time at 1:00AM I amused a local police officer with several flights). Adjust the thrust line for a gentle climb and tweak a wingtip for a wide left turn. I can easily get 30-45 second flights from it and have had a couple of 60-90 second flights.

Here are some pictures and if I can get someone to video a flight I’ll post it. By the way, that’s 10 grams showing on the scale.

Birthday Flight

So, what do you get 85 year old twins for their birthday? Why not a ride in a 1988 Waco biplane? Shirley Martin’s and Jane Gerchman’s children bought them a tour ride with Ocean City Sky Tours based at Ocean City Municipal Airport, Ocean City, MD. The 30 minute flight took them from Assateague Island (where they spotted several of the famous ponies) to the Maryland/Delaware state line. Relatives near the state line caught the flight on video as the plane circled several times.

Shirley and Jane’s big flying adventure!