Category: Kingston

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2013-2014 Kingston Schedule, AMC 8

We’re planning out events for the next school year, and here are two programs that will be running, starting this fall:

Event: Monthly math circle in Kingston, NY
Location: Kingston Library, 55 Franklin Street
Dates: We will meet on the following Saturdays, 1pm – 3pm:
     2013: September 28, October 26, November 23, December 21 
     2014: February 8, March 8, April 12, May 10, June 14
Audience: Geared toward middle school and upper elementary students
Interested? Email bardmathcircle@gmail.com and ask to join our Kingston email list.

Educators: Sign up on My Learning Plan to participate and earn credit.

Program: We feature puzzles and games, challenging problems, and hands-on projects. We help students strengthen their critical thinking skills and make math more fun. 

 

Event: American Math Contest 8 (AMC 8)

Location: Bard College, Annandale-on-Hudson

Date: Tuesday, November 19, 2013, 4pm-6pm.
Audience: Top math students in grades 5-8.
Interested? Email bardmathcircle@gmail.com and ask to join our AMC 8  email list. We’ll provide more information this fall.
Contest: The 25 question, 40 minute AMC 8 Contest contains engaging math problems that are challenging at the middle school level. The exam is intended to inspire, promote enthusiasm, and a healthy attitude towards mathematics. Students will be exposed to the richness of middle school level mathematics at a deeper level than ordinarily encountered in the schools.

 

Program: Students and their families will be welcomed with refreshments before the exam. Afterwards, everyone will be treated to an engaging math talk, courtesy of the Bard Math Department.
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AMC 8 Solutions

The AMC 8 Solutions have been published on the AMC website. But the real fun is happening at the Art of Problem Solving resource wiki, where you can already read nicely written solutions.
If you kept a record of the answers you submitted, you can calculate your informal score (out of 25). How did you do?
My informal score is 23. I had a lot of fun working on these problems (without a time constraint) during the week after the AMC 8, while riding around on the NYC subway, shuttling between appointments. I missed problems 21 and 22, mainly because I didn’t read carefully what was being asked. On the other hand, it’s been a long time since I was in middle school. I think I would also have really enjoyed them way back then!
Please leave a comment about your experience with the AMC 8. What were your favorite problems? Do you have a solution you’re proud of? What did you miss, and why? If you can join us on Saturday, December 8th, we’ll share some solutions at the math circle meeting at the Kingston Library, 1pm-3pm.
See you there!

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Instant Insanity

Dear Math Lovers,

It’s that time of month again – the Bard Math Circle will meet on Saturday, November 10th, 1-3pm in the Kingston Library (upstairs in the Community Room). Middle school-aged students will engage in our math puzzles and logic games, work on a sheet of challenging problems, and build a math artifact to take home.

The problems this month are sample problems from the AMC-8 contest. In part, this is preparation for those students who will visit us at Bard College next Tuesday, November 13th to face the AMC-8 contest. But the real reason that we focus on a few challenging problems each month is as an entry point into beautiful mathematics, and seeing unusual and creative ways in which the mathematics we already know can be used to solve problems in ways we don’t expect. We still have room, so if you’re interested, please visit our AMC-8 Page for instructions on how to register.

The hands-on project this month is constructing a challenging puzzle known affectionately as Instant Insanity. It’s a simple-looking puzzle built of three wooden cubes and colored stickers, but as the name suggests, it’s insanely difficult. As a bonus, we’ll see a different way of considering the problem that makes the solution quite simple. And then you get to take the puzzle home to your family…

See you in Kingston this Saturday!

Mathematically,
                             Japheth

—
Bard Math Circle
bardmathcircle@gmail.com
http://bardmathcircle.blogspot.com/

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Kingston Library Circle has begun

The 2012-2013 Math Circle season is now fully underway, with the first math circle at the Kingston Library of the season. Participants enjoyed our math circle puzzles and games, a sheet of challenging math problems at the middle school level, and especially our hands-on project, which this month involved wooden cubes and masking tape!

Please join us for the remaining 8 math circles in Kingston!

Location: Kingston Library, 55 Franklin Street, Kingston, NY
Date and Time: 2nd Saturdays, 1-3pm. Upstairs in the Community Room
     Fall 2012: September 8, October 13, November 10, December 8
          (No meeting in January)
     Spring 2013: February 9, March 9, April 13, May 11, June 8

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Chalk Walk and Tessellations at the Kingston Library

This weekend marked the last meeting of the Bard Math Circle at the Kingston Library for the spring 2012 semester. Bard undergraduates are preparing for finals, seniors will soon be graduating, and Bardians retreat for the summer.

The circle coincided with the Kingston Library’s Chalk Walk, so we planned out a chalk tessellation activity as our hands-on project. We started by learning about symmetries and transformations using Scott Kim’s Half Words activity in pairs, and then everyone designed their own tessellation, based on a square grid.

Heading outside, we grabbed chalk and claimed sidewalk squares on Franklin Street and chalked out our designs. Here’s a gallery of the sidewalk surrounding the library, including our designs.

After tessellating, we solved the interesting problems and the Bard math majors presented solutions. I’m excited how they’re developing as teachers! They’re learning to engage the students, share multiple strategies, and connect the problems to other contexts. One Bardian is graduating, and will head off to earn her masters in teaching degree and become a math teacher. Next year looks like it will be in good hands with the Bardians who return as seniors.

Check out the last photo, as we celebrated the end of the semester at Boice Brothers Dairy for some delicious ice cream!

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Problems and Solutions for Kingston Math Circle 3/10/12

Solutions

1. In the correctly worked out addition problem below, different letters represent different digits. What digit does A represent?

A4+4A=BCB

First, look at how big the sum can be, and deduce that B must be 1, since the sum of two 2-digit numbers can’t be more than 198 (which is 99+99). Second, consider the units digits. Since A + 4 ends with B = 1, A must be 7.

Check: 47 + 74 = 121.

2. What is the first year in the 21st century (2001 through 2100) that is divisible by 11?

Divide: 2000 ÷ 11 = 181 with remainder 9. Add 2 years to get the next multiple of 11, which is 2002.

Alternate solution: Find a nearby multiple of 11, for example 2200, and count back by 99. Counting backwards, 2200, 2200 – 99 and 2200 – 99 – 99 are all multiples of 11. The last one is 2200 – 99 – 99 = 2002.

3. 9 apes weigh as much as 4 bears. 8 bears weigh as much as 15 cougars. 10 cougars weigh as much as 27 deer. How many deer weigh the same as 4 apes?

Let’s scale up! If 9 apes weigh as much as 4 bears, then doubling, 18 apes weigh as much as 8 bears, and so 18 apes weigh as much as 15 cougars. Let’s double that to find that 36 apes weigh as much as 30 cougars, and so 36 apes weigh as much as 3 times 27, or 81 deer. Now scale down by a factor of 9 to find that 4 apes weigh as much as 9 deer.

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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!!
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Bard Math Circle at Kingston Library – more highlights

We had our first math circle of the year yesterday at the Kingston Library. This circle meets on the 2nd Saturday of each month, so:

Second Saturdays, 1-3pm at the Kingston Library, 55 Franklin Street, Kingston NY 12401
2011: September 10, October 8, November 12, December 17
2012: January 14, February 11, March 10, April 14, May 12

Here are some of the mathematical highlights:

Area Puzzles

The problem sheet this month had dissection problems. Goal: cut each shape into pieces and rearrange them into a square. How few pieces can you use?

Dragon Illusion

The hands-on math take-away was a dragon illusion. Here’s a video that I made of the one I assembled:

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As you can see, the dragon’s head appears to follow you as you move from side-to-side. This illusion was designed by Jerry Andrus, and you can download your copy here: http://www.g4g-com.org/storage/Dragon-Illusion-GG2010.pdf. If you’re interested in a mathematical adventure, find out who Jerry Andrus is, and what is “GG2010”, which is short for Gathering for Gardner 2010!

The Game of 21-Nim

Jeannette taught us all how to play a game called 21-Nim. This is a game for two players, played with a pile of 21 counters. On your move you can remove 1, 2 or 3 counters, and whoever takes the last counter wins. After explaining the rules, Jeannette gave everyone a chance to play, and finished by analyzing strategies.

We’ll be playing 21-Nim at several of our circles this month, so come out and play!

 

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Kingston Library Circle: 2nd Saturdays this year!

The Bard Math Circle at the Kingston Public Library starts again on Saturday, September 10th, and continues through May on the 2nd Saturday of each month.

This math circle is targeted towards middle-school aged students, but everyone (especially families and math teachers) is welcome! Our goals include building mathematical intuition, insight, involvement and engagement. We encourage students to work together, to develop their mathematical communication skills, and to become part of a mathematical community.

We’ll continue our focus this year on:

  • Math Games and Logic Puzzles
  • Insightful Problems
  • Hands-on Math Takeaways

And new this year, we’ll have a special double-focus:

  • Solve the Rubik’s Cube: Bring your cube or borrow one of ours. We’ll learn an efficient solving method and then explore the mathematics behind the cube.
  • Game Theory: Starting with the classic game of Nim, we’ll explore game theory through this and other delightful games.

The Bard Math Circle at the Kingston Library is organized by Bard math professor Japheth Wood, and facilitated by Bard Math Majors. If you’re interested in assisting, contact Japheth: jwood@bard.edu.

Second Saturdays, 1-3pm at the Kingston Library, 55 Franklin Street, Kingston NY 12401
2011: September 10, October 8, November 12, December 17
2012: January 14, February 11, March 10, April 14, May 12