# Adventures in Exploding Dots: A six-lesson series

##### by James Tanton

I, James, recently led a Zoom lesson to introduce the topic of Exploding Dots to students, educators, and math enthusiasts across the nation, the first of six lessons to come on the topic. I began with the classic mind-reading trick of sharing on the screen the following five groups of numbers. I asked each participant to look within each group for the day of the month on which they were born. For example, I was born on the first of the month and I see that the number 1 appears only in group E. Someone born on the 25th of the month sees their day number in groups A, B, and E.

I then asked each participant to type into the chat window the groups in which their day number appears. As letters scurried across the window, I shouted out …

“Luc: You wrote groups A and D. Your number is 18.”

“Aba: You typed B, C, E. Your number is 13.”

“Gretta: You typed just D. Your number is 2.”

It was wild and fun, and a lot of “wows” started appearing in the chat window too.

The trick is conducted by looking at the top left numbers in each group mentioned and simply summing these values. Some students cottoned on to this. But why this trick works was left unresolved for a spell. For that moment we were simply marveling at the fact that there seems to be something “magical” about the doubling numbers 1, 2, 4, 8, 16 ….  Moreover, we were now all fired up to learn about the Exploding Dots machine and discover binary numbers.

The number that appears in groups A, B, and E is .

The Global Math Project and Strange Times

The Global Math Project was founded in 2016 with the mission of providing remarkably accessible, powerful, and genuinely joyful entry points into the fundamentals of mathematics thinking. Its favorite—and certainly most popular—topic is Exploding Dots: the powerful story of place-value as it spans the entire K-12 curriculum in arithmetic, algebra, college mathematics, and beyond! Well over six million students and teachers across the planet have played with its stunning visuals and saw mathematics they thought they knew so well in astounding new light. Students and teachers alike regularly describe the experience as “mind blowing,” and the approach is regularly being used in classrooms around the world.

At least in classrooms as we once knew them.

Tanzania, 2019. Photo by Erick Mathew.

These are strange and tricky times. So much has changed and so much keeps changing still for schools. Teachers are at, and often beyond, capacity in handling the unexpected and continually varying parameters of online, in-person, or hybrid teaching.

The Global Math Project realized it can at least give educators some respite and the occasional actual break! We could offer online lessons on curriculum-connected mathematics and let teachers have us take the reins for a spell.

So, we started the Adventures in Exploding Dots series, a sequence of six lessons for grade 4 and up, covering the basics and the adventures of the Exploding Dots story. We transitioned our teaching to online, and we can certainly share our approach to that challenge with one and all. Details about the lessons and registration can be found on the mathcommunities.org page.

The series will repeat all year long, and additional cycles will commence soon with co-founder Dr. Raj Shah and with GMP Ambassadors leading the way.

The Global Math Project is continually inspired and propelled by the world’s beautiful community of educators who simply want to share with their wonderful students the joy, meaning, and human connection mathematics offers. Our hope is that we can indeed provide a modicum of support, respite, and reconnection with the joy of mathematics during these demanding times.

 THE SIX LESSONSLesson 1 The Five-Card Mind-Reading Trick    Setting the scene for deep understanding of place-value. Lesson 2 Wild MachinesA focus on base ten and why we humans are drawn to it.Lesson 3 Weird English … and Addition and MultiplicationA deep understanding of long addition and multiplication. Lesson 4 Dots and Tods … and Subtraction                             An astonishing way to make sense of long subtraction.Lesson 5 Mind-Blowing Division                                         Long division made exceptionally clear. (It’s high-school math too!)  Lesson 6 Fractions as Decimals … and something Irrational                      Fractions as decimals and meeting the infinite.
 To learn more about the Global Math Project see www.globalmathproject.org.To hear why Exploding Dots is relevant to classroom practice in her own personal view, check out co-founder Jill Diniz’ video here. https://youtu.be/itoYGoBRVwQ
 Something to PonderThe original five-card mind-reading trick relies on the fact that each number can be expressed as a sum of the powers of two: 1, 2,4, 8, 16, …. It serves as an entry-point for discovering the base-two numeral system.  Here’s another five-card mind-reading trick. It uses these five cards and asks a participant to think of a number between -10 and 21, and to share in which group(s) their chosen numbers appear. Does this variant of the trick also inspire the discovery of a number base?

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