Problem of the Week! Creating knowledge, Escaping Rooms, and Yes we Catan!

Problem of the Week!
I will be posting my favorite problem from each week!  Here are the problems from the first two weeks that I felt were the most interesting and engaging: (From Discovery Learning: The Posa Method, and Problem Solving in Secondary School Mathematics respectively)

1. A safe is protected by a combination lock.  The code is a one-digit number.  The lock has two properties: if you enter a wrong code on the keypad then the code increases by 1 modulo 10; if you enter a number for the second time and it proved to be wrong, the whole safe explodes.  Is it possible to unlock the safe?
2. a. In an 8×8 grid, is it possible to fill the grid with 1×2 tiles so that there can be no horizontal or vertical cut that splits a tile in two?
b. In an 8×8 grid, a pair of opposite corners are removed.  Is it possible to cover the entire grid with 1×2 tiles?

Creating Knowledge:
One of the many reasons I came to Budapest for the BSME program was to see how secondary school students created their own knowledge about mathematics.  Whether it is in the field of Mathematics or students just playing a game, the act of creating is, to me, an integral part of learning.  In one particular Hungarian class I observed this week (Grade 7), the goal of the lesson was to explore the largest shape that could be built with only triangle faces.  To help with the lesson, triangular manipulatives were used that snapped together to form new shapes.  Most students (and us, the students in BSME) first built a tetrahedron.  Many students expanded on this and built larger and larger constructions.  After reaching a new number of triangular faces, a student would put that number up on the board.  About halfway through the lesson, the teacher had the students ask questions.  This was my favorite part of the lesson since it really made the students think hard about what they wanted to know and what they could prove, and the students asked very good questions:  “Can we have an odd number of sides?”, “Is there a smallest number of sides”?, “Largest number of sides?”.  The teacher had students continue to work on these problems and if a student figured out a solution, she had them tell her in secret what the solution was.  At the end of the lesson, students shared their solutions.  Relating this back to my experiences at Stony Brook University, this lesson shared many of the characteristics of constructivism, with students creating their own knowledge, and reflecting on their discoveries.  I am excited for more observations in Budapest!

Escaping Rooms!
My friends and I have now escaped four rooms.  Room escapes are quite popular in Budapest.  Here’s the gist of what a room escape game is like: You and four to five other people are locked in a room and must solve a series of logical puzzles to unlock chests, find keys, and ultimately, escape the room.  Though we cut it down to the wire in the last room we escaped from, we made it, and it has lead to the perfect saying:  “Five Mathematicians walk into a room escape…they get out.”  Escaping rooms has become a fun, weekly activity for us, and anyone that comes to Budapest should try it!

Yes we Catan!
Settlers of Catan is one of the most famous board games of the last twenty years and the best way to destroy friendships.  Such friendships that have been built through the first month of BSM/BSME have been put to the test while playing the Hungarian version of the game, Catan Telepesei.  With six games in the bag, and Jake still not having won a game, tensions are running high.  Many of the games are close though, with the best game ending in a 10-9-9-9 distribution, as close as a game can possibly get.  If you are a player of Catan, then you will certainly understand the descriptions of each participants’ playing style:

Krista – The city-maker:  Krista is in the lead with three games won.  She tends to go for rock and wheat, but since she is currently the game leader, she gets attacked quite often.

Zoe – The sheep master:  Baaaa.  She likes sheep…a lot, and used the power of her sheep port to march to victory this past Tuesday.

Jake – Gets cut off: Always.

Sean – All the numbers: I like to use the Krista approach of rock and wheat, though if I can’t do that, I will try to settle on every number so that I always get a resource.  I am also a big fan of development cards. (Note: Playing the Monopoly card is a great way to alienate you from every other player in the game).

The Distribution so Far:
K-3 | S-2 | Z-1 | J-Sad