April 22, 2017 Teacher Workshop

April 22 Teacher Workshop

Math Activities

Dave Auckly, Remi Molinier, Tatiana Shubin, Amanda Serenevy and Bob Klein led a teacher workshop at the Tsaile campus of Diné College on Saturday, April 22, 2017. The event was held in the classroom building on the Tsaile campus of Diné College. Professional development credit certificates will be available for this workshop.

The full schedule and list of sessions is posted below. We had parallel sessions.
We ran an event called Girls’ Adventures in Math concurrently with the teachers’ workshop. This adventure included visually striking cartoons featuring positive female role models presenting math puzzles, games and fun. We ask teachers that attend this workshop to consider bringing a group of girls to participate. More information about this event for girls may be found at:
Girls’ Adventures in Math at Dine College.

If you are interested in attending please register below.


8:00 – 8:55 Breakfast (and intros)

9:00 – 10:30 Session 1A Dave Auckly/Remi Molinier – Cube Slicing (Middle level)
Session 1B Amanda Serenevy – Queen Dido’s Problem (Upper Level)

10:30 – noon Session 2A Tatiana Shubin – Parity and Invariants (6th – 12th)
Session 2B Bob Klein – Pancake Math (Upper Level)

12:00 – 1:00 lunch and group discussion

1:00 – 2:30 Session 3A Amanda Serenevy – Area Enigmas (Middle level)
Session 3B Tatiana Shubin – Grid Power (Upper level)

2:30 – 3:00 Final discussion.


Detailed Session Descriptions:

Cube Slicing
The Big Cheese said, “Let them eat carrots,” and the veggies went into full revolt.
Many cheese cubes were sliced and mathematical havoc reigned.

Queen Dido’s Problem
According to Greek and Roman legends, Queen Dido founded Carthage by persuading a North African king to give a small piece of land to her followers, all of whom were refugees from the tyranny of her evil brother. The king agreed to give her as much land as could be encompassed by the hide of an ox. Queen Dido was clever and cut the hide into thin strips, which she then sewed together to form a loop. She then needed to place this loop on the ground and would be given the area inside of it. The question is, what shape should she form using the loop so that the area is as large as possible? During this session, we will follow in the footsteps of Jakob Steiner to discover several elegant proofs relating to Queen Dido’s problem. This session will be ideal for high school math teachers.

Area Enigmas
During this session, we will explore a variety of enigmas relating to fractions and areas. These explorations are intended primarily for 3rd through 8th grade teachers. Topics will include working with physical models of fractional areas and perimeters, Dan Finkel’s Half-Area Quadrilateral lesson (which motivates the discovery of formulas for quadrilateral areas), and an assortment of fun area and fraction questions from Tatiana Shubin.

Parity and Invariants
Invariants are extremely useful in mathematics, computer science, and natural sciences.

In this session, we will investigate how a simple idea of parity – evenness, and oddness – helps to solve challenging problems. This will lead us to discover a much more general and powerful problem-solving tool, that of an invariant, and to apply it to solving many delightful problems.

Grid Power
One important goal of a math teacher is to make students ask and answer their own – sometimes deep and always exciting – questions. In this session, we will see examples of some such questions with unexpected ramifications that spring up from observing grid paper. These natural questions will lead us into discovering important facts in geometry, algebra, and number theory, and underlying connections between these parts of mathematics.

Pancake Math
The cook is often in a hurry but the server still wants the customer to appreciate the way their breakfast looks. Math will help the folks at Diné Dinér serve it up right.

Math Activities

Cube Slices PDF

Parity Lesson Plan PDF

The following video shows some math circle leaders running the parity lesson at a Circle on the road in DC:

Link to parity video

Area-Perimeter Problems