Monthly Archives: March 2010
On the Path of the Elders
Please take a moment to explore this expansive website:
On the Path of the Elders
March Madness Math
March Madness, the annual NCAA basketball playoff spectacle in which millions of us, firmly docked in front of the TV screen, consume 1,000 calories an hour while watching young athletes burn 12 calories a minute, began this week.
If you’re planning to participate in this national sitin, you can drastically enhance the viewing experience by pondering the parabola.
It’s the elegant arched trajectory naturally formed by any projectile, from an artillery round to a tomato, moving in a gravitational field. Parabolas have been extensively studied since people started throwing stuff at each other, and they shape the outcome of many ballistic sports, such as baseball, golf, football, shot put and more. But they reach their apex in basketball, where field goals and free throws demand precision control of parabolas.
But not just any parabola. Success favours a fairly high arch. The ball must pass through the hoop with a little room to spare, and that limits the possibilities. The hoop is roughly 48 centimetres in diameter, and the men’s ball is about 24 centimetres wide (women’s about 23.5). So if the men’s ball were thrown straight down from above that is, at an angle of 90 degrees to the horizontal hoop rim, as in the classic Michael Jordan airborne dunk, there would be just under 11 centimetres of free space all around, a comfy margin.
But as the angle decreases and approaches the horizontal, the free space for a “nothing but net” shot gets much smaller. At 55 degrees, it’s about 6.4 centimetres. At 45 degrees, it’s down to 3.8 centimetres. And at 30 degrees, it’s basically impossible to get the ball straight into the basket, even with a full scholarship and more tattoos than a Hell’s Angels convention.
Not surprisingly, increasing the height at which the player launches the ball not only reduces the distance to the basket, but raises the entry angle of the ball’s parabolic arch, allowing more free space.
In a 1980s study, Peter Brancazio, a Brooklyn College physics professor, determined that adding two feet to the height at which a shot leaves the player’s fingers increases success by a whopping 17 per cent. No wonder you see so many jump shots.
But is there a launch angle that gives the maximum probability of a perfect telegenic swish? Well, there are many different parabolas that will do the job, and the choice varies according to player height, personal preference and court position.
But one way to decide, Brancazio wrote 25 years ago in Sport Science: Physical Laws and Optimum Performance, is to “consider the amount of force needed to launch the shot.
“It is to the shooter’s advantage to use as little force as possible,” he reasoned, because the less the force, “the more quickly and effortlessly (the ball) can be released.”
Okay, fine, but how do we know what takes the least force?
Here, physics comes literally into play.
We know from theory and experiment that you get the most distance with the least effort by firing a projectile at 45 degrees, exactly midway between vertical and horizontal. And we can assume that leasteffort shooting is really important for a player taking a jump shot, because he or she can’t push against the floor for power, especially in heavy defensive traffic. So the fastest and easiest angle would seem to be 45 degrees.
Except when it isn’t, which is a lot of the time. The reason is that 45 degrees is the ideal leasteffort angle only if the ball is shot from the same height as the basket, which is 10 feet above the floor. So it’s perfect for a 7foot player whose arms reach two feet over his or her head, and who jumps a foot off the floor to shoot.
The rest of us will be launching the ball “uphill” (that is, as if we were firing a cannon at a target on a higher elevation). So we’ll need larger angles.
How much larger? Again, science comes to the rescue. Brancazio explains that you need 45 degrees, plus half the angle formed by a straight line between the position of the ball at launch and the basket. Depending on your height and where you are on the court, that typically ranges from 7 to 14 degrees.
Thus, for a shot leaving your hands at eight feet above the floor from 18 feet out, you’ll want to launch the ball at a bit more than 48 degrees. For most players at a distance of 10 to 25 feet, the leasteffort angle ranges between 47 and 52 degrees.
Using that system, you can calculate the ideal freethrow angle. It’s 13.75 feet from the freethrow line to the centre of the basket, and a 6foot player launches the ball from about seven feet above the hardwood. That works out to a shooting angle of 51 degrees.
Of course, Brancazio did his calculations long before the advent of the modern computer. But a new stateoftheart study gives basically the same result. Last November, engineers at North Carolina State University published an analysis of hundreds of thousands of 3D computer simulations of free throws. Their optimal angle: 52 degrees. (Check it out during the playoffs. Seen from the side, a 52degree freethrow parabola has its highest point just about even with the top of the backboard.)
Freethrow success is also improved by adding a little backspin, which pushes the ball downward if it hits the back of the rim.
The North Carolina State engineers calculated the ideal rate of freethrow backspin at three cycles per second. That is, a shot that takes one second to reach the basket will make three full revolutions counterclockwise as seen from the stands on the player’s right side.
While you’re at it, stop to remember Menaechmus, the geometer who first described the parabola in the 4th century B.C. He never made a layup, but he had game.
Some Fun For March Break
Creative Puns for Educated Minds
1. The roundest knight at King Arthur’s round table was Sir Cumference. He acquired his size from too much pi.
2. I thought I saw an eye doctor on an Alaskan island, but it turned out to be an optical Aleutian
3. She was only a whiskey maker, but he loved her still.
4. A rubber band pistol was confiscated from algebra class because it was a weapon of math disruption.
5. The butcher backed into the meat grinder and got a little behind in his work.
6. No matter how much you push the envelope, it’ll still be stationery.
7. A dog gave birth to puppies near the road and was cited for littering.
8. A grenade thrown into a kitchen in France would result in Linoleum Blownapart.
9. Two silk worms had a race. They ended up in a tie.
10. Time flies like an arrow. Fruit flies like a banana.
11. A hole has been found in the nudist camp wall. The police are looking into it.
12. Atheism is a nonprophet organization
13. Two hats were hanging on a hat rack in the hallway. One hat said to the other, “You stay here; I’ll go on a head.”
14. I wondered why the baseball kept getting bigger. Then it hit me.
15. A sign on the lawn at a drug rehab center said: “Keep off the Grass.”
16. A small boy swallowed some coins and was taken to a hospital. When his grandmother telephoned to ask how he was, a nurse said, “No change yet.”
17. A chicken crossing the road is poultry in motion.
19. The short fortuneteller who escaped from prison was a small medium at large.
20. The man who survived mustard gas and pepper spray is now a seasoned veteran.
21. A backward poet writes inverse.
22. In democracy it’s your vote that counts. In feudalism it’s your count that votes.
23. When cannibals ate a missionary, they got a taste of religion.
24. Don’t join dangerous cults: Practice safe sects!
Canadian schools got results with more teachers – Times Online
Canadian schools got results with more teachers
January Numeracy Committee Meeting Minutes
Six Nations District Numeracy Committee Meeting Minutes
Thursday, January 21^{st}, 2010
JC Hill (2:30 – 4:00)
Agenda Items 
Present: Alice Anderson, Carrie Froman, Janis Thomas, Judy McNaughton, Joe Restoule General
Absent: Sandy Hill

Review minutes from last meeting 
In order to accommodate time for the guest speaker, minutes were emailed out for approval in advance of the meeting. No amendments were requested so minutes are considered approved.

Special Guest Presentation by Understanding Math personnel 
Cynthia Rutledge from Neufeld Math presented on the Understanding Numeration (K3) and Understanding Math (410) software. Approximately 10 other Six Nations staff members were also able to attend. Cynthia spoke at length about the program and demonstrated several lessons across different strands/grades. The following are a few pieces of information she shared:
training is sold along with the software, and is a key element to its success the software includes over 3000 lessons there is the ability to track progress of students it does not need to be used on SMARTboard (though this enhances it); a data projector is sufficient for classroom instruction use the software includes word banks for student/teacher use, as well as a search engine many lessons explore different approaches to a mathematical concept (for example, five different ways to approach multiplication) the entire Thames Valley District School Board has a license Neufeld math prefers to sell licenses at a district level (it works out to roughly $25 per student) licenses are lifetime, with upgrading included when available students are recommended to work in triads, using the “flight plan” method of 1 driver, 1 recorder, and 1 task manager (pilot, navigator, copilot); also a student driver at the front of the room to allow teacher to circulate amongst students Neufeld is working on other strands besides Numeration for grades K3 Cynthia’s email is crutledge@neufeldmath.com and she recommended going to www.corr.neufeldmath.com to see how the software matches up with the curriculum (correlations). 
Math Assessment Tools 
Due to the length of the Understanding Math presentation, all other agenda items were moved forward to the next Numeracy Committee meeting. Members did stay after the presentation to discuss a few items, as reported below.
PD planning for Numeracy Nets: Webinar is scheduled for Feb. 25th or March 11^{th}, as Pearson will not be supporting Numeracy Nets with inperson PD, only webinars.
Teacher use?:
Ideas for ONAP implementation:

CAT/Insight Testing Opportunity 
Follow up on participation:

Math contest (Caribou) 
Upcoming dates/Classes involved:
Yesterday’s results: Teachers were given copies of their school’s Caribou results, as well as certificates to share with the students who participated in the contest.

ILT Literacy/Math Night on November 26th 
Report on how it went:

ECG Math Night 
There was no information to share about this.

Explore Learning Teacher Passwords 
Comments/concerns/feedback:
PD opportunity update: Explore Learning has been contacted and are available for a half day or after school PD session.

Mathville 1

Comments/concerns/feedback?:

Math Trek 4,5,6 
Mr. Hickey handed out copies of this software for each school to have.

Explore Learning Newsletter
i sent this out via email, but since we can’t access email from home, i thought i would add the same link here for viewing from home.
Mimio Math Packs
Here is a site where you can download lesson plans and activities, flash animations and images of math figures and shapes. If you need help downloading the files, just scroll down the page to where the teacher has responded with stepbystep instructions for saving the files to your computer.
MS Society of Canada
SMART Webinar Cancelled
For those who signed up or were interested in signing up, the Webinar with Marian Small on measurement, scheduled for this Wednesday has been cancelled. i received an email, and i am assuming those of you that registered received the same email. Just wanted to post it on here, just in case anyone was making plans and hadn’t registered yet.
In a word, Brilliant.
Check out the 5 “A”s, the 4 “D”s, and all the fluencies required of the digital citizen at the 21st Century Fluency Project. Then think about the skills we hope to develop in our students.