How to Fold or Split Things into Thirds - from a Math Guy James Tanton 2026-09-20 | How to Fold or Split Things into Thirds - from a Math Guy
What is Addition - Philosophically? James Tanton 2024-10-08 | I was asked to make a video on what addition is ... really.Here is my response.
THREE SCHOOL WAYS TO INTERPRET DIVISION: Why, philosophically, are they equivalent? James Tanton 2024-10-07 | In elementary school there's division by groups (quotative division), division by sharing (partitive division), and reverse multiplication. Is it actually obvious that these three interpretations are the same? Let's explore this question!
THE ARITHMETIC OF FRACTIONS: Are you game for the mathematical truth and nothing but the math truth? James Tanton 2024-10-07 | The school curriculum is troubled by a fundamental paradox. Although much of math is motivated by real-world contexts, in the end, math is bigger and bolder than any one real-world context. This video is not for the faint hearted. It reveals the mathematical basis of all the fraction arithmetic you were taught in school, purely as a math story, without absolute avoidance of supposed real-world "explanations." Math is fully capable of explaining itself, and that is what we show here.This video is at an advanced high-school/college level. Proceed with this warning. There's a PDF to accompany this work, a "Thinking Worksheet" of sorts. Go to CHAPTER 5 here: gdaymath.com/lessons/gmp/9-1-chapter-content
Three Oft-Overlooked Principles of Curriculum Design James Tanton 2024-07-25 | As I've been working to bring together, rewrite, and tighten up my various musings and ponderings on Arithmetic and Algebra through the K-12 (and college) curriculum, I've identified some principles I think are very important. I share and briefly discuss three big ones here. Enjoy! [[ The link to Arithmetic & Algebra: gdaymath.com/lessons/gmp/9-1-chapter-content ]]
A BORING PARTY TRICK with infinite consequences James Tanton 2024-01-07 | In this (stand alone) PART 2 video on infinity we find that there are infinitely many sets each genuinely infinitely bigger than the the previous one in the list. Figuring out what these infinities actually mean and whether or not there are infinities between the ones we found is a matter of extreme brain-hurty-ness. We should get into that in a PART 3 video.
SQUARE ROOTS and the AREA MODEL James Tanton 2024-01-04 | A few quick little thoughts on square roots and on the word "simplify."
Multiplication Facts and the Area Model James Tanton 2024-01-01 | A little piece on using the AREA MODEL to help with multiplication facts to be memorized.
Graphing Something Horrible with the Power of Common Sense James Tanton 2024-01-01 | In a recent video I shared my personal worries about factoring algebraic expressions is often presented to students in an algebra class. This not to say one shouldn't teach factoring -- it has purpose and a power. This video gives an extreme example of its power.
There is more than one type of Infinity! (INFINITY: Part 1) James Tanton 2023-12-31 | Let's play with the infinite today and see where it takes us.
POLYNOMIAL DIVISION via the Area Model James Tanton 2023-12-31 | The Area Model many learn in grade school for multiplication is beautiful and powerful and applies to high-school algebra too! (And let's push it beyond what people usually do too and create some infinite series!)
On FACTORING QUADRATIC EXPRESSIONS if you must James Tanton 2023-12-30 | I have a bad attitude towards this topic! The algebra curriculum has students factor quadratic expressions for what purpose -- to quickly recognize the zeros of carefully crafted quadratic functions? to factor because the author spent some time crafting examples that factor nicely? If one is forced to play the factoring game, then this is how I personally play it. Enjoy(?)
Some Quick Fun with the Fourth Dimension James Tanton 2023-12-30 | Let's play! Here are some impromptu thoughts on playing with the fourth-dimension.
The Area Model for Long Division an approach I do NOT recommend (and then one I do!) James Tanton 2023-12-29 | The area model provides a natural and beautiful means for conducting long multiplication. It is natural to explore then if we can conduct the process backwards. Let's explore!
Negative times Negative: A Deep Dive into Understanding It James Tanton 2023-12-28 | It's an age-old question: Why is negative times negative positive? And school mathematics is not prepared to give a proper justification as the proclivity there, for fine reasons perhaps, is to seek real world models that "explain" math. (Where in the real world do you actually multiply two negative numbers together? "If I am traveling at a negative velocity and go backwards in time, then I've moved a positive distance forwards." Got that?) Here's the math that leads us to say that negative times negative is positive. It all just hinges on one belief about how numbers work.
Line Multiplication Explored and Explained James Tanton 2023-12-27 | Every few years "Line Multiplication" or "Japanese Multiplication" (or some other name for the method) makes the internet rounds. It is a curious approach to conducting long multiplication and it is fun to try to make sense of this beautifully quirky--and not exactly efficient (but who cares?)--method.
Long Multiplication is Weird James Tanton 2023-12-27 | It is so very easy to equate familiarity with understanding, and the long multiplication algorithm is a mighty fine example of this!
A Combinatorial Geometry puzzle that leads to Picks Theorem and beyond! James Tanton 2023-11-27 | A recent round of Twitter puzzles (sorry, X puzzles) led me to an entry point into Pick's famous theorem that I knew about, but never truly understood. So, I decided to figure out for myself, once and for all, what's really afoot here. This video shows the result of my brain's meanderings!
A Lovely Geometry Puzzle James Tanton 2023-06-25 | I recently posted a puzzle on twitter and folk answered it in a number of lovely ways. Can you come up withy your own novel solution?
The Bee Numbers! James Tanton 2022-11-23 | Can you explain why the count of bees in any one generation is the sum of the counts of bees in its two previous generations?
Friends of Muzology teach us how they say the number 175487. James Tanton 2022-10-11 | Teach us too! Send a picture, or a text, or a video to ** info@globalmathproject.org. **Tell us: 1) The language you are sharing 2) How what you share translates literally, word-for-word, into English.
How do you say the number 175487 in your language? James Tanton 2022-09-15 | Earlier this year, we at the Global Math Project asked "How do you say the number 87 in your native language?" We received hundreds of responses and the discussions were fascinating! (See section 7 of our Classroom Guide at gdaymath.com/courses/exploding-dots to see the results.) Now we're asking a bigger question as part of Global Math Week 2022 (Oct 10-17). Watch the video and share your answer at info@globalmathproject.org.
9. If English is Weird, We Can be Weird Too! ADDITION (Exploding Dots) James Tanton 2022-08-26 | This is video number 9 of the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
8. English is Weird James Tanton 2022-08-26 | This is video number 8 of the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
7. Number Bases in Society (Exploding Dots) James Tanton 2022-08-26 | This is video number 7 in the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
6. Explaining the Machines (Exploding Dots) James Tanton 2022-08-26 | This is video number 6 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
QUICK OVERVIEW (Optional) James Tanton 2022-08-26 | The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
20. Advanced Algebra is not the Advanced, Really (Exploding Dots) James Tanton 2022-08-26 | This video number 20 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
3. Having Fun with Binary (Exploding Dots) James Tanton 2022-08-25 | This is video number 3 in the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
5. The ten-one Machine (Exploding Dots) James Tanton 2022-08-25 | This is video number 5 in the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
4. More Machines (Exploding Dots) James Tanton 2022-08-25 | This is video number 4 in the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
2. Explaining the two-one machine (Exploding Dots) James Tanton 2022-08-25 | This is video number 2 in the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
24. Fractions and Division (Exploding Dots) James Tanton 2022-08-25 | This is video number 24 in the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
25. Every Fraction is a Repeating Decimal (Exploding Dots) James Tanton 2022-08-25 | This is video number 25 in the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
17. Long Division (Exploding Dots) James Tanton 2022-08-25 | This is video number 17 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
0. What is a Prime Number? James Tanton 2022-08-25 | This is a video to go with the introduction to a booklet on Exploding Dots. It explains a concept that is briefly -- and tangentially -- mentioned.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
15. Subtraction (Exploding Dots) James Tanton 2022-08-25 | This is video number 15 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
29. Division in Any Base (Exploding Dots) James Tanton 2022-08-25 | This is video number 29 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
13. NEW NUMBERS: The Opposites of the Counting Numbers (Exploding Dots) James Tanton 2022-08-25 | This is video number 13 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
1. A Story that is Not True James Tanton 2022-08-25 | This is video number 1 in the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
26. A Decimal that does not Repeat is not a Fraction (Exploding Dots) James Tanton 2022-08-25 | This is video number 26 in the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
16. Division (Exploding Dots) James Tanton 2022-08-25 | This is video number 16 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
18. The Traditional Algorithm (Exploding Dots) James Tanton 2022-08-25 | This is video number 18 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
23. Fractions as Sharing (Exploding Dots) James Tanton 2022-08-25 | This is video number 23 in the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
32. Bonus: Some Infinite Series (Exploding Dots) James Tanton 2022-08-25 | This is video number 32 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
31. Resolution (Exploding Dots) James Tanton 2022-08-25 | This is video number 31 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
21. Discovering Decimals (Exploding Dots) James Tanton 2022-08-25 | This is video number 21 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
22. Multiplying Decimals by Ten (Exploding Dots) James Tanton 2022-08-25 | This is video number 22 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
14. Dots and Tods James Tanton 2022-08-25 | This is video number 14 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
19. Remainders James Tanton 2022-08-25 | This is video number 19 in the Exploding Dots story.The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
11. To Multiply by Ten, Add a Zero. HUH? (Exploding Dots) James Tanton 2022-08-25 | This is video number 11 in the Exploding Dots story. The written guide to go with these videos and access to the full playlist is here: gdaymath.com/courses/exploding-dotsAlso see ** www.globalmathproject.org ** for the global math phenomenon afoot.
