The original Exploding Dots experience is a set of 12 lesson plans to follow and matching videos to share.
But how have we grown since those early days!
You can follow our original vision of teaching Exploding Dots with the 12 experiences below. (Multiple language versions are available here.)
Or …
1.) Try this new YouTube Playlist for a friendly, classroom tested, middle-school set of videos and matching downloadable workbook.
2.) See how Exploding Dots naturally sit in a high-school and university College Algebra curriculum by checking out Chapters 4, 7, and 8, in particular, of these College Algebra course notes.
3.) Try one of our new various web apps we’re soon to share with the world! (Watch this space for their imminent releases!)
Remember: Once you have experienced the fun and profound enjoyment of Exploding Dots yourself, you can conduct classroom experiences with your students in any way you wish: project videos onto a whiteboard, pause at key moments, and have students fill in what they think James is about to do; follow a lesson plan or guide assiduously and couple it with a web-app experience, or create a style and approach that best suits you and your students style and thinking. Student “aha moments” and “mind-blown” moments are sure to be abundant. Enjoy!
EXPLORATION 1: A MYSTERIOUS MACHINE
Here we introduce and interact with a mysterious machine that sets the scene for the entire Exploding Dots story and a transformational mindset for mathematics.
Topic: Discovering place-value
Grades: All
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Interactive web app for this Experience:
EXPLORATION 2: A MATHEMATICAL INSIGHT
Here we figure out what the mysterious machines are doing and discover the notion of place value. We now have a powerful visual understanding of this subtle concept that profoundly helps us understand so much grade-school, middle-school, and high-school mathematics in brand new light.
Topic: Deeply understanding place-value. Understanding why we humans are drawn to base-ten
Grades: All
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EXPLORATION 3: ADDITION AND MULTIPLICATION
Here we make profound sense of the standard algorithms.
Topic: Long Addition. Multiplication.
Grades: All, but of particular interest to K-6.
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EXPLORATION 4: SUBTRACTION
See subtraction as the addition of the opposite. This insight, coupled with the Exploding Dots machinery, provides natural and deep insight into long subtraction.
Topic: Negative numbers. Long Subtraction.
Grades: All, but of particular interest to K-6.
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EXPLORATION 5: DIVISION
Long division is made exceptionally clear.
Topic: Long Division. Long Division with remainders.
Grades: All, but of particular interest to K-6.
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EXPLORATION 6: ALL BASES, ALL AT ONCE: POLYNOMIALS
Here we discover that K-6 school arithmetic is high-school mathematics in disguise.
Topic: Polynomials. Division of Polynomials. Synthetic division in disguise.
Grades: All, but of particular interest to 7-12
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EXPLORATION 7: INFINITE SUMS
Here we play with “infinitely long polynomials,” discover the geometric series formula, and more!
Topic: The geometric series formula.
Grades: All, but of particular interest to 7-12
EXPLORATION 8: DECIMALS
Another infinite produces more boxes in the machine. We discover decimal numbers.
Topic: Decimals. Converting fractions into decimals. Constructing irrational numbers.
Grades: All, but of particular interest to 7-12
EXPLORATION 9: WEIRD AND WILD MACHINES
Now we are just playing. We discover fractional bases, negative bases, and more. Each discovery often comes with unsolved research questions.
Topic: Base-one-and-a-half and other fractional bases. Negative and other bases.
Grades: All who want to have wild intellectual fun
EXPLORATION 10: UNUSUAL NUMBERS FOR UNUSUAL MATHEMATICS
Is 0.9999…. equal to one or is it not? We explore this question and an even wilder one than that!
Topic: Convergence of infinite processes (limits). p-adic numbers.
Grades: All who want to have wild intellectual fun
EXPLORATION 11: GRAPE CODES AND NAPIER'S CHECKERBOARDS
Making Exploding Dos two dimensional allows you do conduct algebra with polynomials of two variables x and y. Scottish mathematician John Napier of the 1600s did essentially this with his multiplication checkerboard.
Topic: Napier’s historical approach to multiplication and division. Polynomial algebra with two-variables.
Grades: All who want to have wild intellectual fun
Written guide for this Experience:
Interactive web app for this Experience:
Go to this special site for this experience.
EXPLORATION 12: PUZZLES THAT CAN BE SOLVED WITH EXPLODING DOTS
Here is a collection of puzzles—some classic, some not so classic—that can be explained with Exploding Dots. Puzzles of all levels for all ages can be found here.
Topic: Puzzles galore!
Grades: Absolutely everyone.
Written guide for this Experience:
Interactive web app for this Experience:
Go to this special site for this experience.