What is the sum of 4×1 + 3×2 + 2×3 + 1×4?
Problem 5: Summing Rectangles
Problem 2: Triangles in a Hexagon
In hexagon ABCDEF, how many triangles can be formed by connecting three vertices?
Example ∆BCE.
Problem 3: Walking to the Playground
How many ways can Pascal walk from home to the playground, walking 6 blocks?
Problem 1: Jelly Beans
Bertie has six jelly beans left: one each of Avocado, Buttermilk, Centipede, Dirt, Earwax and Fried Beans flavors. Harry reaches into the bag and takes out three jelly beans.
What possible groups of three jelly beans could Harry take? For example, Harry might take the Buttermilk, Dirt and Earwax jelly beans.
Math Circle Poster and Activity Session
The Bard Math Circle is traveling to Boston next week for the Math Circle Poster and Activity Session at the Joint Math Meeting 2012. This poster session brings together math circles from around the country to share some of their math circle activities.
Our activity Six Choose Three was used in our Spring 2011 circles, and features several problems that are surprisingly related. We invite you to share your solutions and comments in later posts.
The Reel Math Challenge
One of the Bard Math Circle parents sent us this link: The Reel Math Challenge, which is a contest sponsored by MATHCOUNTS. For those who don’t know, MATHCOUNTS is a national, middle school level math competition that promotes excellence in math education through problem-solving. More on that later.
The Reel Math Challenge is a team competition, and the goal is to make the best teaching video that explains a solution to one of the 270 problems in the MATHCOUNTS School Handbook. Each team consists of 4 student Team Members and 1 Team Advisor (an adult).
Interested? This could be a great Bard Math Circle activity, but time is running out. Send a friendly email to bardmathcircle@gmail.com if you’d like to volunteer to be a Team Advisor, and we’ll try to connect you with a team.
Now, more about excellence in math education through problem-solving. Each month we offer an engaging sheet of math problems. Math competitions such as
- Purple Comet (purplecomet.org)
- MOEMS (moems.org)
- MATHCOUNTS (www.mathcounts.org)
- Math Meets (www.mathmeets.com)
- AMC8 (amc.maa.org/amc8/)
all publish similar problems. While the Bard Math Circle is not about competition, we value problem-solving as an entry way into learning mathematics. The Reel Math Challenge is one of the fun ways to solving problems in a math circle environment.
Rubix Cubes at Rhinebeck
I both appreciate and enjoy it when parents get involved with Math Circle. Today at Rhinebeck, Michelle came in with her son Alan, and they both had a great time. Alan played Chicky-Boom and learned about balancing objects while Michelle solved a Rubix Cube! Here’s a picture of the result:
We have three more Math Circles before the New Year! Check us out at the Tivoli Library on December 2nd, the Milton Library on December 3rd, at in Kingston on December 10th. See you there!
December Problem and Solution!!!
Hello once again!!! Have you ever wondered why patterns occur? Well… we don’t have the answer for all patterns in the world, but we can explain one pattern that occurs in the math world. The following problem is based on the multiplication of “repunits” whose digits are compromised of the number 1.
Compute the following:
1 × 1 =
11 × 11 =
111 × 111 =
1111 × 1111 =
How far does this pattern go?
If we multiply out the four expressions above we get the following results:
1
121
12321
1234321
As we can see the number in the center is the number of 1’s that exist in the original number of the original equation. For example, 121 has two as its middle number because 11 has two 1’s. Also, as the number of 1’s increases in the equation, so does the pyramid that occurs in each line. For instance, 11 × 11 is 121 and when we multiply 111 × 111, we get 12321, an up and down pyramid that goes forward until it gets to three and then back down after three. It is a symmetric pyramid of numbers.
If you would like to see this pattern as it develops, watch it here in a video posted by James Sousa: http://www.youtube.com/watch?v=k1X1JCNHjRw
James’ YouTube channel and webpage mathispower4u offer more mathematical resources, including short video explanations (similar to Khan Academy) and free downloadable open source textbooks.
Look out for patterns, they are everywhere!!
Bit-Strings at Bailey Middle School
The Bard Math Circle traveled to Bailey Middle School on Kingston this past Friday; students worked on challenge problems based on a set done in Rhinebeck last April. For one of the problams, students were asked to find how many bit-strings of length n (n-bit strings) there are, given that a single bit is either a 0 or a 1. For example, there are four 2-bit strings (00, 01, 10, 11) and eight 3-bit strings (000, 001, 010, 011, 100, 101, 110, 111).
There are two strategies (maybe more!) that can be used to solve this problem. The first is to write out all of the bit-strings of length 2, 3, 4, etc, and try to find a pattern. The other is to create an algorithm for finding all bit-strings of length m from bit-strings of length m-1, and then write a formula using this information. Can you do it?
Math Mama Rocks
Here’s a great youtube video of a math circle in Richmond, CA, run by Sue VanHattum, called the Math Salon. Sue has set up her event in many ways similar to what we have done at the Bard Math Circle – a great selection of mathematical activities with enough structure to support curious children and their parents, but not so much to make it overly regimented.
Sue also writes the blog Math Mama Writes…, which besides regular reflections, offers lists of Math Education Books, Games and Math Books. What a great math resource!