Exploding Dots

I must admit, I have become a bit obsessed with exploding dots brought to you by Dr. James Tanton of the Global Math Project.

Audience

I began my journey to explosions after a recommendation for the premier workshop of Coastal Carolina University's Math Teachers' Circle in August, 2016. Since then, I have incorporated exploding dots into a variety of curricula from working with pre-service middle school teachers to discover innovative algorithms for multiplication (i.e. lattice method, Japanese method, area method) to taking an in-depth look at division, decimal expansion, polynomial division, and geometric series in my upper-division Functions, Applications, and Chaos course.

Exploding Dots (Multiplication) Outline

The objective of this exploration is to develop a more robust understanding of number systems and operations. The main focus is on addition, multiplication, and subtraction and converting between decimal and other base number systems.

1. Students learn about an 'alien machine' that takes dots as inputs and converts them to an output codes (i.e. converting between decimal and other number systems.
2. Students come up with methods for determining the output codes of different base machines.
3. Students try to expand the machine to model basic operations such as multiplication, addition, and subtracting.
4. Facilitator connects the students' methods to different multiplication algorithms.

Exploding Dots (Division) Outline

The objective of this exploration

1. Students learn about an 'alien machine' that takes dots as inputs and converts them to an output codes (i.e. converting between decimal and other number systems.
2. Students come up with methods for determining the output codes of different base machines.
3. Students try to expand the machine to model basic operations such as multiplication, addition, and subtracting.
4. Facilitator connects the students' methods to different multiplication algorithms.