This workshop featured the Community Math Circle. Faculty from this program include Gabriella Pinter, Asmita Sodhi, and Steve Heller. In addition, the entire team (see below) was there to help facilitate.

Professional development credit certificates and stipends will be offered for this workshop. Full details will be posted by mid Feb. If you have questions reach out to us at navajomath@gmail.com or 785 473 0273 (call or text).

Funding for this workshop was provided by Math for America, MIT, Duke, and the Kansas State University Foundation.

The workshop featured mathematical activities/explorations led by a team including

Asmita Sodhi

Steve Heller

Peter Petto

Marina Kopylova

Sayonita Ghosh Hajra

Fred Gluck

Daniel Hodgins

Skona Brittain

Gabriella Pinter

Full session videos are posted below.

## Schedule

(All times valid for Crownpoint, NM.)

9:00 Welcome.

9:15 – 10:30 (Gabriella Pinter) Math Circle Session 1

Title: Apple Picking

10:30 – 10:50 Introductions/Discussion

10:50 – 12:05 (Asmita Sodhi) Math Circle Session 2

Title: Pentominoes

12:05 – 12:30 Sanity Break

12:30 – 1:45 (Steve Heller) Math Circle Session 3

Title: Colored Loops

1:45 – Whenever math circle discussion/suggested resources

## Sessions

Apple Picking:

This is a Nim-style game. It is a nice way to understand the fundamental “copycat” strategy. The JRMF app provides a nice way to play the game on-line:

Apple Picking App

Pentominoes:

The session started by describing what a polynomial is and then enumerating (listing all) pentominoes.

It then gave three challenges:

Use four different pentominoes to create a 4 x 5 rectangle in at least four different ways.

Find one where one pentomino does not meet the exterior.

Find one so that all four meet at a common point (like four corners.)

A wealth of information about Pentominos may be found on

Jim Storer’s Pentominos page.

One online tool that helps explorations is

Polypad

Here are some more specific Polypad links:

4×5 rectangles

Making Rectangles: Structured

Making Rectangles: Free Play

Making Rectangles: Solutions (to Structured)

Monotiling: Plane

Monotiling: Rectangle

Replicating (provided by Steve): Double Trouble

Replicating (provided by Steve): Double Trouble Parts

Replicating (provided by Steve): Triple Trouble

Replicating (provided by Steve): Double & Triple Answers

Scroll to the end to see some connections to the common core.

Colored Loops:

Steve shared his math website:

Math Explorations

You can download the following PDF slides for the Stirring Paint Puzzle

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

–>

3.M.G.A.01:

Understand that shapes in different categories (rhombuses, rectangles, & others) may share attributes (having 4 sides), & that the shared attributes can define a larger category (quadrilaterals). Recognize rhombuses, rectangles, & squares as examples of quadrilaterals, & draw examples of quadrilaterals that do not belong to any of these subcategories.

Students used the pentominoes to identify and create quadrilaterals.

3.M.MD.C.07:

Relate area to the operations of multiplication and addition.

a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

c. Use tiling to show that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

d. Understand that rectilinear figures can be decomposed into non-overlapping rectangles and that the sum of the areas of these rectangles is identical to the area of the original rectilinear figure. Apply this technique to solve problems in real-world contexts.

Students used the pentominoes to determine the area of composite figures.