CONTEST! Just Another "Rate-Time-Distance" Problem?

CONTEST IS OFFICIALLY OVER AND THE WINNER IS ----- NO ONE! Guess I should have offered a 64GB 3G IPad! to be awarded on Black Friday...


The floor is now open for David, Curmudgeon, and my other faithful readers to offer their own solutions.  


And the next contest is...




This is a contest so students must work alone and this needs to be verified by a teacher or parent. No answer will be posted at this time. Deadline is Wed 11-17-10 at 4 PM EST.






Here's a variation on the classic motion-type problems we don't see as often in Algebra I/II but still appear on the SATs. I found this in some long-forgotten source of excellent word problems to challenge NINTH graders! 

Barry walks barefoot in the snow to school in the AM and back over the same route in the PM.  The trip to school first goes uphill for a distance, then on level ground for a distance and finally a distance downhill.  Barry's rate on any uphill slope is 2 mi/hr, any downhill slope is 6 mi/hr and 3 mi/hr on level ground.  If the round trip took 6 hours (hey, these are the old days in the 'outback'), what was the total number of miles walked?


First five correct answers  with complete detailed solutions emailed to me at dmarain@gmail.com will receive a downloaded copy of my new book of Challenge Problems for the SATs and Beyond when it becomes available. Both the student and teacher(s) will receive this.  (Illegal to reproduce or send electronically!). Read further...

Submission by email must include (Number these in your email and copy the validation as well).


1.  Answer and complete detailed solution. If answer is correct but method is sketchy or flawed,      the submission will be rejected.
2.  Full name of student
3.  Grade of student
4.  Math course(s) currently taking
5.  Math teacher's name(s) and parent's name(s)
6.  Name, Complete Address of School; Principal's Name & Email address (if known) 
7.  Email addresses of teacher(s),  parents, student 
8.  Phone number (in case I need to call you) - Optional
9.  How your or your teacher or parent became aware of MathNotations.




VALIDATION


I certify that my student (child) did the work independently.




--------------------------------------------------------------------------------


Name of Teacher or Parent (if work done at home)



"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860)

 "You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear. You've got to be carefully taught." --from South Pacific

RESULTS OF THIRD MATHNOTATIONS CONTEST and OTHER NEWS...

FINALLY -- THE RESULTS ARE IN!!

I apologize for the delay in getting these results out. The participating schools have all been notified.
NOTE: If any participating school did not receive an email from me, the advisor should email me. Also, if I misspelled anyone's name pls let me know and I'll correct it immediately!


INITIAL COMMENTS ON CONTEST, ETC...

• MEAN SCORE: 5.6 PTS OUT OF 12
• TOPICS INCLUDED Number Theory, Geometric Sequences, Function Notation, Geometry, Discrete Math, Quadratic Functions, and Absolute Value Inequalities (advanced level)
• Twenty schools registered from around the world, but only about half were able to actually give the contest.
  
• I will post the open-ended number theory problem later on but I didn't want to take away from recognizing the efforts of these outstanding students and their dedicated advisors.
• The next contest will be announced in a few weeks. Sign up early!
• After the 5th contest, you will be able to purchase all contests and solutions via download.
  

THIS WAS A CHALLENGING CONTEST, PARTICULARLY FOR YOUNGER STUDENTS, ALTHOUGH, AS YOU CAN SEE BELOW, THEY HELD THEIR OWN!! CONGRATULATIONS TO ALL PARTICIPANTS FOR A JOB WELL DONE!

FIRST PLACE - 12 OUT OF 12 POINTS!

CHILES HIGH SCHOOL
TALLAHASSEE, FL

Marshall Jiang - 11th
William Dunn - 12th
Wayne Zhao - 9th
Andrew Young - 11th
Jack Findley - 12th
Danielo Hoekman - 11th

Advisor, Steve Friedlander

SECOND PLACE - 11 OUT OF 12 PTS

HARVEST PARK MIDDLE SCHOOL
PLEASANTON, CA

Eugene Chen - 8th
Jerry Li - 8th
Brian Shimanuki - 8th
Christine Xu - 8th
Jeffrey Zhang - 8th
Ian Zhou - 8th

Advisor, Randall S. Lomas


THIRD PLACE - 9 OUT OF 12 PTS

CANADIAN ACADEMY - PINK PANDA TEAM
KOBE, JAPAN

Kevin Chen - 11th
Sean Qiao - 11th
Alice Fujita - 11th
Cathy Xu - 11th
Steven Jang - 11th
Sooyeon Chung - 10th

Advisor, Ms. Elizabeth Durkin


FOURTH PLACE - 7 OUT OF 12 PTS

CANADIAN ACADEMY - BLACK SWAN TEAM
KOBE, JAPAN

Hyun Song - 11th
Max Mottin - 11th
Ron Lee - 10th
Kyoko Yumura - 10th
Selim Lee - 10th
Evangel Jung - 10th

Advisor, Ms. Elizabeth Durkin


FIFTH PLACE - 4 OUT OF 12 POINTS

MEMORIAL MIDDLE SCHOOL - TEAM DAVID
FAIR LAWN, NJ

David Bates - 8th
Isaiah Chen - 8th
Kajan Jani - 8th
Thomas Koike - 8th
Priya Mehta - 8th
Joseph Nooger - 8th

Advisor, Ms. Karen Kasyan


SIXTH PLACE TIE

WALLINGTON JR/SR HS - SENIOR TEAM
WALLINGTON , NJ

Nicole Bacza - 12th
Tomasz Hajduk - 12th
Martyna Jezewska - 12th
Thomas Minieri - 12th
Urszula Nieznelska - 12th
Damian Niedzielski - 12th

Advisor, Stephanie Regetz


FAIR LAWN HS - TEAMS A & B
FAIR LAWN, NJ

Team A
Egor Buharin - 12th
Kelly Cunningham - 12th
Elizabeth Manzi - 12th
Gurteg Singh - 12th
Daniel Auld - 12th
Richard Gaugler - 12th

Team B
David Rosenfeld - 12th
Gil Rozensher - 12th
Roger Blumin - 9th
Mike Park - 9th
Jason Bandutia - 9th
Alexander Lankianov - 9th

Advisor, Victoria Velasco


SEVENTH PLACE TIE

WALLINGTON JR/SN HS
WALLINGTON, NJ

Junior Team
Konrad Plewa - 11th
Matthew Kmetz - 11th
Eman Elhadad - 11th
Patrick Sudol - 10th
Marek Kwasnica - 10th
Anna Jezewska - 10th

Advisor, Stephanie Regetz

MEMORIAL MIDDLE SCHOOL - TEAM SIMRAN
FAIR LAWN, NJ

Simran Arjani - 8th
Aramis Bermudez - 8th
Allan Chen - 8th
Kateryna Kaplun - 8th
Harsh Patel - 8th

Advisor, Ms. Karen Kasyan

Updates, ODDS AND EVENS and some Geometry Packing Problems

Enjoying your summer hiatus or as busy as ever? I know that feeling!

1. MathNotations' Third Online Math Contest is tentatively scheduled for the week of Oct 12-16, a 5-day window to administer the 45-min contest and email the results. As with the previous contest, it will be FREE, up to two teams from a school may register and the focus for now will be on Geometry, Algebra II and Precalculus. Several other ideas are running through my head but I need the time to bring them to fruition. If any public, charter, prep, parochial or homeschool (including international school) is interested, send me an email ASAP to receive registration materials: "dmarain 'at' geeeemail dot com."

2. CNNMoney.com Article - Something to tell your students in September!
Here is the link. The 2nd paragraph says it all:

The top 15 highest-earning college degrees all have one thing in common -- math skills.

3. Silly Instruments for Math Teachers to Play
I always told my students that I'm predominantly left-brained -- analytical, organized, detailed, process-oriented, algebraic -- as opposed to most of my children and my wife who are creative, spatial, mechanical, who see the forest more than the trees. One of my sons is a musician and another is a dancer so we are not always on the same wavelength! So I mentioned to my SAT students that I wish I had a more creative side and perhaps be able to play an instrument, but, in fact, the only thing I can "play" is my iPod! One of my students in the front row immediately responded, "I know an instrument you can play, Mr. M -- the triangle! I congratulated her for the cleverness and told her that maybe I will learn how to play the "cymbals." (the class actually applauded that lame attempt at word play!). In fact, I've read that many famous mathematicians were also musicians, so let us know: Do you play an instrument or are passionate about music or do you have a silly instrument for a mathematician to play?

4. Circle Packing Problems
Even though I am dominantly left-brained, I still enjoy challenging spatial geometry problems. I find these questions have improved my creativity and my spatial sense and they often involve multi-faceted thinking. Here are a couple of famous 'packing' problems which are accessible to geometry students. More important than solving these is to give our students a sense of the importance of packing problems and the ongoing research in this area. There are still unsolved problems here!

Although you can easily research packing problems on MathWorld and Wikipedia, the diagrams below come from an exceptional website I discovered. The author, Peter Szabo (missing accents), provides diagrams for packing 2-100 circles with accompanying data (radii, density, etc).


PROBLEM I


The two congruent circles at the left are actually enclosed in a unit square which is not shown.The circles are tangent to each other and to the sides of the square. If these circles have the maximum radius possible, determine the radius.
Note: The indicated square (assume it is a square) is helpful in solving the problem. Trig is not necessary here.

Answer (Yes, I'm providing this since the objective is to discuss the method):
[The following is the diameter, not the radius, of each circle. Thanks to watchmath for correcting this error].









PROBLEM II



Again, imagine that the three congruent circles at the left are enclosed in a unit square and are tangent to each other and to the sides of the square. If the circles have the maximum radius possible, determine this radius.
Notes: The indicated square again may be helpful to solve this problem. Trig can be used but clever use of special right triangles is preferred.

Answer:
[The diameter is given below, not the radius. Thanks to watchmatch for correcting this]

Odds and Evens: 1-8-09...An online math contest and other passing thoughts...

Many thoughts are running through my mind right now...

Projects I'd like to move forward, some changes in this blog, perhaps a different website altogether...

Working on the MathAnagram for the first quarter of 2009...
I've already selected the mathematician. Writing an anagram that has embedded clues is labor-intensive...

My reactions to a Commentary in this week's Education Week authored by the esteemed Steven Leinwand who is calling for a fascinating new concept heretofore unheard of -- a national K-12 Math Curriculum. I wish I had thought of that!

Thoughts about an online math competition for high schools...
Yes, that's right, I've already written the rough draft of the first six questions. I need to get the word out to high schools who might want to pilot this a few weeks from now. No cost for this first contest, but I would like to have at least a dozen schools express some interest in this before I formally announce it. If any of you reading this might be interested or know the math supervisor in your district, please spread the word. High schools can field one team of up to 6 students and will have a short window of time (from the moment I publish the questions) to submit their answers/solutions electronically. The contest will differ from others in that some questions may be multi-part and some parts will require explanation. Not just short answer! In other words, while there will be traditional contest problems, there will also be questions that reflect the investigations on this blog. Calculators will be permitted and a faculty sponsor would be needed to proctor the contest. Clearly there are major logistic problems (registering teams, different time zones, international participation, etc.). I need to work out many issues here. Questions will not at this time go past precalculus.
I might need to have my head examined for considering this since I will have to read and evaluate every one of the responses!
I may also need a separate website for all of this but I need to get a sense of interest out there before I jump in deeply. If this blog elicits few responses, I will probably have to disseminate this in some other way. I'd really appreciate suggestions/reactions to this both in the comments section and via email. As always you can email me at dmarain at geeeeemaillll dot com...

Have embarked on a collaboration with a University math professor who is developing problem-solving experiences for his students. Some of these problems will be based on investigations published in MathNotations...

So many wonderful math blogs out there not only from our regulars but new ones entering the math blogosphere every day. Exciting stuff...