This workshop featured Gordon Hamilton, Matthias Kawski, and Dave Auckly.
Professional development credit certificates and $100 stipends were offered for this workshop. If you have questions reach out to us at navajomath@gmail.com or 785 473 0273 (call or text).
The workshop was held at Page High School, in Page, AZ.
Funding for this workshop was provided by MIT, the Kansas State University Foundation, Duke University, the Arizona Community Foundation, and Math for America.
Full session descriptions are posted below.
Schedule
(All times valid for Page, AZ.)
8:15 – 9:00 Light Breakfast.
9:15 – 10:30 (Gordon Hamilton) Math Circle Session 1
Title: Glue & QR Code Mazes
10:30 – 10:50 Introductions/Discussion
10:50 – 12:05 (Matthias Kawski) Math Circle Session 2
Title: The Permutahedron — exploring something big with students.
12:05 – 1:00 Lunch
1:30 – 2:15 (Dave) Math Circle Session 3
Title: Cube Coloring
2:15 – Whenever math circle discussion/requests
Sessions
Glue & QR Code Mazes —
Join others to create some elementary school art puzzles. We won’t start with the rules.
Rules are boring. Instead, we’ll pretend that you’re part of an elementary school classroom, and
we’ll playfully explore the puzzles together.
It will be a fun, puzzling experience with lots of pedagogy.
Gord shared activities from The Math Pickle.
One activity was a version of “Liar’s Dice.” In this game, 3 – 5 teams are each given 5 regular dice. The teams roll
all the dice, keeping the result secret from the other teams. The teams then take turns bidding, or calling bluff. A
bid is there are X copies of Y with all of the dice that have been rolled by all teams. For example, there are 3 fours, (34). Each successive bid has to be higher. Here 35 and 41 are higher than 34, but 33 is not. If a team does not bit, it must call bluff. Once bluff is called, they count the dice. If the bid is made, i.e. for 34 one would need 3, 4, 5, or 6 fours, the team that calls bluff loses one die. If the bid is not made the team that made the bid loses one die.
Another activity was the tumbleweed puzzle. The name was given to the puzzle by Zeke Chee, and Gord invented the puzzle
during the camp. The rules of this puzzle are to start with a finite collection of vectors in the plane, each having integer coordinates. One then places the vectors tail to head in cyclic order skipping any vector that would collide with any vector already placed. The puzzle is to predict what will happen. Dave suggested that this could be played as a game, where each of two players picked a fixed number of vectors and then took turns placing their vectors in cyclic order skipping ones that would collide. The last player to make a legal move wins.
There is the description of Pinocchio’s Playmates. Here are Pinocchios Playmates Puzzle Sheets.
Here is a description of Diversity City.
Here is the handout for Diversity City.
Here is a description of Glue
Here is a bonus called QR code mazes.
The Permutahedron — exploring something big with students.
The permutahedron is a remarkable 3D object. We will understand some properties of it and several ways to describe it and then build a big model of it. This is one of our “Big Math” projects. You can read more about these on our PVC Math page. You should also see the
Permutohedron handout.
Cube coloring —
We will explore several cube coloring challenges.
This is a first generation Julia Robinson Mathematics Festival Activity.
The hand-out explains what happened. We used plastic cubes and markers to help explore.
Coloring Cubes
There are many ideas related to this. Dave took a bit too long trying to hint at all of them. The challenge of coloring
27 cubes so that they could be assembled into a red 3 x 3 x 3 cube, or a green 3 x 3 x 3 cube, or a blue 3 x 3 x 3 cube is a good problem to shoot for. The 2 x 2 x 2 case with two colors is much easier and can serve as a good warm-up problem.
The first problem would easily fill a pair of class periods. Other problems are counting the number of red faces and the number of other faces in the 3 x 3 x 3 cube, or counting the number of cubes with no red faces, just 1 red face, just 2 red faces, or 3 red faces. The same questions may be asked about the N x N x N cube. One could even work in higher dimensions.
A fancy solution to this problem entails overlapping three different tilings of space with cubes. This process is similar to one of three ways to design dissection puzzles. You can check out our Dissection Puzzle page or ask for more information about this.
Can be e-mailed navajomath@gmail.com, sent via text (785) 473-0273, or mailed to:
Dave Auckly
Math Department
Kansas State University
Cardewll 138
1228 N MLK Drive
Manhattan, KS 66505