… makes sense
… is more than just arithmetic
… is joyous
… makes them strong
… is meaningful
… is creative
… is full of fascinating questions
… opens up many paths to solutions
… is friendly
… solves big problems and makes the world better
… is a powerful tool they can master
… is beautiful
… lets them learn in their own ways
… is connected to their lives
… asks “why” and not just “how”
… opens the world
From the upcoming new book Avoid Hard Work by James Tanton and the Natural Math team.
Did you know 97 is an emirp? It’s prime both forward and backward! What other emirps can you find?
Welcome to the 97th edition of the Math Teachers At Play math education blog carnival: a monthly smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.
A few articles were submitted by their authors, but most were drawn from the immense backlog in my rss reader. If you’d like to see your blog post featured next month, be sure to send it in yourself. Our hosts are busy parents and teachers who have limited time to scour the Internet for goodies.
To add a bit of color, I’ve thrown in several favorites from my newly updated Math with Living Books pages. Some (affiliate) links go to Amazon.com, where you can read descriptions and reviews — but there’s no need to buy. Most of these books should be available through your local library.
Table of Contents
If you’d like to skip directly to your area of interest, click here:
Please: If you enjoy the carnival, would you consider volunteering to host sometime this year? Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn, please speak up!
And now, let the mathematical fun begin!
When the queen of her bugs demands that her army march in even lines, Private Joe divides the marchers into more and more lines so that he will not be left out of the parade.
David Wees (@DavidWees) and his son explore Inductive Reasoning: “You know, Dad. There are an infinite number of solutions…”
Joshua Greene (@JoshuaGreene19) writes Ode to a bead string (a non-poem poem): “One of the cool things about open play with math manipulatives is that it provides a lot of easy entry points into short math chats.”
Crystal Wagner (@Tri_Learning) shares several Math Games to Play in the Car: “Or maybe you are waiting in line at the grocery store or doctor’s appointment. Turn these times of waiting into learning opportunities.”
Christopher Danielson (@Trianglemancsd) shows how The sequence machine can launch math conversations with older students: “Now you can generate number sequences, without being distracted by the multiplication facts.”
Help inspire your kids to try writing their own unique problems. Includes a wide range of math topics and concepts: money and time, fractions, percentages, geometry, logic, and multi-step problem solving.
I’ll let you in on a secret about teaching: there is no place in the world where it rolls along smoothly without problems. Only in articles and books can that happen.
Learning math is an adventure into the unknown. The ideas we adults take for granted are a wild, unexplored country to our children. Like any traveler in a strange land, they will stumble over rocky places and meet with unexpected detours.
Whenever I visit a parenting forum, I feel compassion for the families who are struggling with math. No other school subject elicits such depths of frustration and despair.
You could say that Tessalation is a book about tessellations (repeating tiled patterns), but it is really a children’s picture book about discovering order in a chaotic world.
— Emily Grosvenor
Seeing Math in the World
In taking a playful approach to mathematics, I hope to open children’s eyes to math in their world. Schooly math lessons have led many of my math group kids to think a “pattern” has to be a strictly repeating (and rather boring) series of shapes or colors.
But in the real world, patterns are so important that American mathematician Lynn Arthur Steen defined mathematics as the science of patterns.
“As biology is the science of life and physics the science of energy and matter, so mathematics is the science of patterns,” Steen wrote. “We live in an environment steeped in patterns — patterns of numbers and space, of science and art, of computation and imagination. Patterns permeate the learning of mathematics, beginning when children learn the rhythm of counting and continuing through times tables all the way to fractals and binomial coefficients.”
Tessa Truman-Ling’s delight in patterns is contagious. And it will provide a wonderful jumping-off point for a variety of math activities.
Visit Grosvenor’s Kickstarter page to find out more about her lovely book:
Tova Brown concludes her exploration of the Hilbert’s Hotel Paradox with a look at the cardinality of the real numbers.
You run a hotel with an infinite number of rooms. You pride yourself on accommodating everyone, even guests arriving in infinitely large groups — but some infinities are more infinite than others, as it turns out.
Tova Brown dives deeper into Hilbert’s Hotel Paradox, considering the difference between rational numbers and reals.
You run an infinitely large hotel, and are happy to realize that you can accommodate an infinite number of infinite groups of guests.
However, a delicate diplomatic situation arises when a portal to another universe opens, introducing a different kind of guest, in a different kind of group.
Tova Brown continues to examine Hilbert’s Hotel Paradox, pondering infinite sets of infinite sets.
As the proprietor of an infinitely large hotel, you pride yourself on welcoming everyone, even when the rooms are full. Your hotel becomes very popular among infinite sports teams, as a result.
Recruitment season presents a challenge, however, when many infinite teams arrive at once. How many infinite teams can stay in a single infinite hotel?
Tova Brown explores the second part of Hilbert’s Hotel Paradox. What’s infinity plus infinity?
Running an infinite hotel has its perks. Even when the rooms are full you can always find space for new guests, so you proudly welcome everyone who appears at your door.
When two guests arrive at once, you make room. When ten guests arrive, you accommodate them easily. When a crowd of hundreds appears, you welcome them all.
Tova Brown’s introduction to Hilbert’s Hotel Paradox, a riddle about the nature of infinity…
Once upon a time, there was a hotel with an infinite number of rooms. You might be thinking this is impossible, and if so you’re right. A hotel like this could never exist in the real world.
But fortunately we’re not talking about the real world, we’re talking about math. And when we do math we can make up whatever rules we want, just to see what happens.
From the upcoming new book Avoid Hard Work by James Tanton and the Natural Math team.
Tova Brown concludes her exploration of the Hilbert’s Hotel Paradox with a look at the cardinality of the real numbers.
Denise Gaskins' Let's Play Math 