Hand Tricks!
Using one’s hands is practically intuitive in the math world. Counting on one’s fingers is the most basic mathematical practice one could think of. But there is other more complex math you and your kid can do with your hands!
For example, you are hardly limited to counting to 10. If you bring the binary system into the equation, your kid can count all the way to 1,023 using their hands. It’s pretty simple: 0 is your right fist, 1 is your right thumb, 2 is your right index finger, and 4 is your right middle finger. Do you see a pattern? Each finger number is the double of the one before it. So, if you want to count 6, you hold up your index and middle finger (2 and 4). A more thorough explanation is in comic form at Instructables.
In addition to counting on your hands, you can also use them as multiplication tables. Ms. K at Teacher Blog Spot explains how your kid can divide each finger into sections of 3 or 4 and multiply by the number of fingers, with a maximum of either 15 or 20.
A similar method of multiplying on your fingers is called finger reckoning. Finger reckoning has been used since at least the 15th century, when merchants would use it to calculate numbers out of the sight of competitors eyes. While Ms. K’s method is based primarily on counting, finger reckoning uses multiples of ten. It is more complex but you get the answer faster and more efficiently. You can read more about finger reckoning in our blog post about it.
There’s no need to limit you or your kid to computing multiplication and addition, however. An easy and useful trick for remembering how many days are in each month is to count out the months on your knuckles and the spaces in between. Make sure to remember that each knuckle is 31 days and each space is 30 days, except February, which is 28 or 29.
Hand tricks aren’t limited to computation either. One of the most common practices in kid art is tracing hands for drawings, and that can be used to teach symmetry. While we didn’t come up with this particular example, the Moebius Noodles book has a symmetry game called Double Doodle Zoo which demonstrates how one shape (like the hands) can turn into another (the heart).
An easy three-dimensional example of a hand shape is getting a few people together and having them recreate a fibonacci spiral with their hands. This is a great example of shapes in math and how they can transcend two dimensions.
You can do even more geometry with your body than making a Fibonacci spiral with your hands. In this video, mathemetician James Tanton explains how to do the National Math Salute. Using knot theory, you create a simple knot with your hands and undo it. The hand salute also uses elements of topology: the study of insides and outsides, and the orientation of surfaces. It’s simple to watch, but it’s easy to do it wrong. See if you and your kid can figure it out!
Posted in Make
Who am I? A guessing game
“Math is not linear.”
People say that, but do you believe it?
Here is the history of one person’s interaction with Khan Academy. Answer this person’s riddle: WHO AM I?
Judging by this historical document, how old do you think the person is? What is the grade level? Anything else you care to guess?
Yes, all these are trick questions. I will post the answer in comments on August 10th. Leave your guess as a comment and subscribe, to see the surprising answer.
Update: the mystery person revealed (see comments).
Posted in Grow
Infinity Is Farther Than You Think
What’s bigger, a fillion or a cometallion? These are the two big numbers my son and his friend made up one day. They couldn’t give me any more details other than “these are huge numbers” and “but smaller than a googol”. To them, all numbers went to googol, after which was the infinity. My idea of how big numbers could get was actually pretty much the same. And then we read the Really Big Numbers book by Richard Evan Schwartz.
Although reading is probably not the best word to describe it. The author himself likens the book to “the game of bucking bronco”. You follow the text for a while until it gets to be too much. But it’s perfectly okay because, as the introduction explains, “This book isn’t something that you have to read all at once… Just read as far as it makes sense and then save the parts you don’t understand for later.”
And just like any good bucking bronco ride, the book starts off slowly, counting by 1, then by 10, then by 100… It’s a gentle ride and you begin to wonder how is this book any different from other children’s books about big numbers.
So we get to count by millions, then – billions. Exponents enter the scene. Well, for adult readers this is a familiar and fairly comfortable territory. And we are heading safely to googol! Which is unimaginably huge, bigger than the number of atoms in the observable universe, but it is still comfortable and familiar.
And that’s where you get kicked off your high horse of “I know all about really big numbers” (well, I did anyway). Because next comes googol-plex. And it is an even more enormously big number than googol. You are barely hanging on now. And then, just as you think it won’t get any crazier, come Fred and Big Jim. And “Fred” is a number so huge that it dwarfs googol-plex. And “Big Jim” is way way way bigger than “Fred”. And more and more incomprehensibly, stupendously, mind-bogglingly huge numbers follow. The numbers get to be so ridiculously ginormous that the exponential notation fails. A different way of writing numbers is introduced. The bronco bucks and we are, once again, off of it (well, I am anyway).
The comforting familiarity of millions, billions and other big numbers disappears when you get to REALLY BIG numbers. Instead, you face something that is hard, seemingly impossible to comprehend. These numbers just don’t make sense! And then you realize that this is what young kids feel like when first learning counting past ten, facing the abstractions outside the range of their experiences. And you realize that you’ve already felt this way before, long time ago, when you were a child just learning to count. And you get a chance to empathize with your kids.
Here’s something else Really Big Numbers helps with as it takes adults out of the realm of familiar. It gives a chance to become an explorer. Most of the time when we talk about math and read math books to our kids, the math in them is well-known to us. So we assume a kind of tour guide attitude and expect the kids to be these well-mannered and appreciative tourists. Richard Schwartz, by contrast, invites us to an unfamiliar, counter-intuitive, “there be dragons” math where both tour guides and tourists become explorers and adventurers.
Really Big Numbers is a small book that can take a long time to read or even look through. It is a chance to learn something new about the really big numbers. But it is also a chance to experience the awe, the mystery and the playfulness of math with your child and as a child.
Posted in Grow
Summer math and circle leaders incubator: Newsletter July 16, 2014
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Hi, I am Moby Snoodles, and this is news about Natural Math.
Send me your questions, comments, and stories of math adventures at moby@moebiusnoodles.com
In this newsletter:
- Summer math: grind or adventure?
- Volunteer or business opportunities for you
- Will 3D printers change the world… of mathematics?
- Quick bits: 12x spiral, Playing With Math in Spanish, shapes out of shapes, jobs for kids
Summer Math – Grind or Adventure?
What does your child’s summer math time look like? Perhaps it is filled with worksheets and arithmetic drills similar to what they get to do the rest of the year. If that’s the case, it is time to get outside, and try mathematics that is playful, adventurous, creative, and lively.
Instead of giving your kid a beach-themed worksheet for counting shells or adding fish, do some beach combing first and then create mandalas with the found objects. Along the way your child can explore rotational symmetry, patterns, and even integration.
Going to a park instead? Pick up a few sticks and have a game of “how many triangles can you build with these sticks?” or challenge your child to create a circle out of the straight sticks.
Use pool noodles to build giant geometric solids. Go berry picking and invite kids to create complex shapes out of simple blueberries – for a tasty introduction to integration. Having a picnic? Pack some tangramwiches.
If you are worried that your child will experience a “brain drain” without the worksheets and won’t do well in math come the new school year, keep in mind that arithmetic is just a tiny part of mathematics. Treat summer break as a chance to develop your child’s mathematical mindset, not just the ability to manipulate numbers.
1001 circles: Opportunities for leaders
We often get calls for help from people who want their kids to be in a math circle, but can’t find one nearby. We hear you! This lack of circles means a lot of opportunities for growth and leadership – for teens, parents, grandparents, teachers, and anyone who loves math and cares about kids. If you are already leading a math circle, tell us about your experience. If not, have you ever thought of leading math circles?
This Fall, we are starting a training program for new math circle leaders. It will focus not only on content, but also on time planning, building healthy communities, money, logistics, psychology of learning, and any other support that leaders of math circles need to succeed. We will work with this group of leaders very closely to determine and address their needs. As a result, members of the program will prepare and run their first math circles, either as volunteers, or as a paid service. Unlike our open online courses, this program will be for a small group of people, because of the high amount of individual interaction with each participant.
Is this a good fit for you? It is if you are:
- A parent or grandparent who puts together playgroups, clubs, teams, or homeschool co-ops, and develops experience organizing groups for their kids
- A teen who organizes teams and clubs for yourself, or works as a tutor or camp counselor
- A tutor who is looking for better math content
- A math enthusiast who wants to try your designs and inventions with kids
- A teacher who wants to have more teaching freedom
- A mathematics, science, and technology professional who wants to do more teaching
If you want to participate, let me know by email at moby@moebiusnoodles.com
3D Printers for Math
Finally, 3D printers are becoming truly mainstream as Home Depot, the world’s largest home-improvement chain, starts selling them in some of their stores. Okay, only twelve stores, but it’s a good start. In a few years, having a 3D printer at home will be just as ordinary as having a regular printer is now. Which makes me wonder about math education, of course.
Printables of all sorts, including thousands of dull math worksheets, were made possible by cheap and ubiquitous paper printers and copiers. Will something similar happen with 3D printing? Will our kids end up having to work through some version of 3D math worksheets? Hopefully not! What math will you and your kids print when you get a 3D printer?
Meta-Mobius by joabaldwin
Blogs and networks: quick bits
Children are weird, like little space aliens, but they are better at some tasks than adults. They break all records on originality, provide deep insights, and rock divergent thinking tests. Want to imagine a world where children’s strangeness is recognized and used in professional settings? Check out our new collection, Jobs for Kids.
Our crowdfunding campaign for the book Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers has reached its main goal. Big thanks to all who contributed! The first stretch goal is Spanish translation. We have 3 days left – will we make that goal? Help us reach Spanish-speaking people: tell your friends and colleagues about the campaign.
From squash that looks like a duck to 3D modeling, making shapes out of shapes is a traditional bridge into mathematics. Check out this collection of geometry to calculus activities for toddlers, kids, and adults.
1001 Circles is a series of stories that show what a math circle might be like, from the point of view of circle leaders. Last week, our guest was Joey Grether, whose journey to math play with kids started with designing tools and devices. Want to play with a totally different way to build times tables? This story of Joel’s 12x Spiral is for you!
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Talk to you soon! Moby Snoodles, aka Yelena McManaman and Dr. Maria Droujkova
Posted in Newsletter
