Next Meeting: September 19, Stone Middle School

Special thanks to Emily Altodonna and Stone Middle School for agreeing to host the next Northern Virginia Math Teachers’ Circle meeting. This is a chance for teachers to engage in mathematical problem-solving in a laid-back collegial environment. Food will be provided! All middle school math teachers in Northern Virginia are welcome to join us.

Topic: Grid Luck
We’ll explore problems on grid paper — some geometric, some not. Led by Dr. Padhu Seshaiyer from George Mason University, this session will use a hands-on approach and demonstrate multiple representations for each problem. Get ready to get griddy!

Wednesday, September 19, 4:00-5:30pm
Stone Middle  School
5500 Sully Park Drive
Centreville, VA 20120

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Spring NoVaMTC Events

We had taken an unexpected hiatus, but we’re back on track! There are three upcoming events (details below), and we’re working to finalize a fall schedule. Hope to see you at a NoVaMTC event soon!

Please let us know if you’re coming! RSVP to novamtc@verizon.net.

  • The Oldest Interesting Math Artifact (Bob Sachs)
    May 30 (Wed), 5:00 – 6:30 p.m. — NCTM Headquarters
    1906 Association Drive, Reston, VA
    One of the oldest interesting math artifacts is the Babylonian tablet YBC 7289, which has an amazingly accurate approximation to the square root of 2. This session will explore the interesting math behind this tablet: Base 60 Babylonian math; how the computation might have come to be; the square root of 2 approximations; the Pythagorean theorem; and algorithms.  Since there is no written record of how the tablet was created, our group session will speculate and we can’t be proven wrong!
  • Game Night (Patrick Vennebush)
    June 12 (Tue), 6:00 – 8:00 p.m. — NCTM Headquarters
    1906 Association Drive, Reston, VA
    I’m afraid that sometimes you’ll play lonely games, too;
    games you can’t win, ‘cause you’ll play against you. – Dr. Seuss
    Explore some solitaire games that you CAN win, with a little investigation. Then try your luck at some two‑player extensions. Games will happen all night… if you can’t arrive at 6:00, show up at 6:30 or 7:00… we’ll still be playing, enjoying snacks and beverages, and socializing! This is a fun, mathy way to end the school year!
  • Advanced Problem Solving (Padhu Seshaiyer, Bob Sachs, and Patrick Vennebush)
    June 25-26, Afternoon Sessions – Fairfax County Public Schools Advanced Academic Institute
    These sessions will introduce grades 4-6 teachers (June 25) and grades 6-8 teachers (June 26)  to NoVaMTC. It will help them to engage in open-ended math problem solving and learn how to initiate more student-centered and inquiry-based pedagogies in their classrooms.

Tonight’s Fun, and Next Meeting Info

Padhu led an excellent geometry session tonight. If you weren’t able to join us, here’s a question for you to ponder:

Consider a triangle with vertices at (0,2), (3,4) and (4,1).

  • What is the area of this triangle?
  • Show that the area of the triangle is equal to the following expression. (The expression is plus/minus one-half the determinant of the matrix formed by using the x-coordinates of the points in the first column, using the y-coordinates of the points in the second column, and using a value of 1 for each entry in the third column.)

Area Determinant

  • Why does the determinant formula work?

We spent a fair amount of time discussing the third question, and Padhu did an excellent job of connecting this topic from Algebra II to topics in the middle school math curriculum.

Next Meeting
Our next meeting will be Tuesday, December 13, 5:00-6:30pm, at the NCTM Headquarters in Reston, VA.

Will you be there? Please fill out this super-quick, one-question poll: NoVaMTC December Meeting.

First Fall Meeting, October 25

Our first meeting for 2011 will be held next Tuesday, October 25, at NCTM Headquarters in Reston, VA.

Date: Tuesday, October 25
Time: TBD, based on your input (please complete this Doodle poll)
Topic: Fun with Polynomials
Location: 1906 Association Drive, Reston, VA 20191 (NCTM)

Details about the schedule are available here.

For future meetings, we need your input! What days and times are best for you? Help us accommodate maximum participation by indicating your preferences on this Google poll.

We hope to see you next Tuesday!

Solution to May Problem

As I mentioned in the last post, at the end of the May meeting, Bob Sachs left us with the following problem:

Can you find a general formula for the following sum?
1 × 2 + 2 × 3 + 3 × 4 + … + n(n + 1)

I don’t know if we actually have a solution, but Margaret Coffey put a lot of effort into trying to find one! Her attempt at a solution is here:
https://novamtc.files.wordpress.com/2011/05/mathcircleproblem-mcoffey-110530.docx

Feel free to send me a file if you have a different approach, and I’ll post it. Or simply write up your thoughts as a reply to this post.

May Meeting Follow-Up

We had a splendid time this past Tuesday. Bob Sachs led us through some great problems involving sums of series. We first examined triangular numbers in depth, and then we tried to determine the value of the sums 12 + 22 + 32 + … + n2 and 13 + 23 + 33 + … + n3.

The last problem we explored was a cliffhanger — we didn’t find a general formula for the sum before we left, and perhaps you’ll enjoy playing with it. Can you find a general formula for the following sum?

1 × 2 + 2 × 3 + 3 × 4 + … + n(n + 1)

Although our meetings are on hiatus for the summer, be sure to subscribe to this blog! We’ll post problems throughout the summer, to give you some things to think about while relaxing at the beach.

NoVaMTC meetings will resume in the fall. Please complete the two surveys below so that we know your preferences for when to meet. (Check all that apply.)