Welcome to the 158th edition of Math Teachers at Play, AKA The Playful Math Carnival. For my regular readers who are new to MTaP, you can find out more about it on Denise Gaskin’s website. It’s a monthly roundup of playful and educational math blogs (and whatnot), hosted by a different blogger each month. Check out Carnival #157 over on Math Mama Writes. Also check out our friends, the Carnival of Mathematics, for some more mathy, bloggy fun. The current edition, #207, over at Sam Hartburn’s blog, is particularly playful.
And for regular MTaP readers who are new to The Montessori Cosmos, welcome! I blog about Montessori, math, and deschooling (in or out of school). For a really good picture of my thinking, read my Montessori Unschool Manifesto here.
Fun Facts about 158
There are exactly 158 digits in 100!. (100! is 100 x 99 x 98 x … x 2 x 1).
There are no numbers that have 158 coprimes smaller than it, which means 158 is nontotient. Two numbers are coprime or relatively prime if they have no factors in common besides 1, or in other words, if their greatest common factor is 1.
The sum of the digits of 158 is 14, so it is not divisible by 3 or 9. In fact, 158 has only four factors: 1, 2, 79, and 158.
Articles with Activity ideas
Fraction Dominoes Puzzle: I’m excited to try this puzzle with my students. I’m even more excited to get them to make their own puzzles for each other or their younger colleagues. I’ve never thought of using dominoes as fractions before. I’m not sure it’s really necessary to use dominoes, but it’s a fun idea.
Five Fun Things To Do With 21st Century Pattern Blocks: Oh boy do I want a set of these 21st Century Pattern Blocks made by Math4Love. I want their Upscale Pattern Blocks, too, and I don’t even have a classroom right now! Christopher Danielson of Talking Math With Your Kids has put together a wonderful collection of activities/prompts for the pattern blocks. I especially want to try the mirror reflections. [Elementary Montessorians: I think the proportions of the blue magic triangles are the same as the red triangles in these pattern blocks, so you may be able to do most of these with materials you already have.]
Things to do with Math4Love 21st Century Pattern Blocks and Upscale Pattern Blocks
H/T: Hana Murray, @MurrayH83 over on Twitter.
Pattern Machines: What They Are And Why You Need One: Christopher Danielson has also figured out what to do with those silly pop-up multiplication machines from Lakeshore Learning—turn them into something else. I can imagine these being hugely engaging for those 6- and 7-year-olds who need to fidget. And I can envision some wonderful conversations about multiples and the patterns they make.
Speaking of multiples, I wrote about a wonderful conversation I had with some children about the patterns we saw in a 100 chart (and why I’ve switched from the traditional Montessori Multiples of Numbers paper to a 100 chart).
Here’s another great example of a simple question leading to wonderful mathematical debate: “It Depends on The Meaning of Almost.”
The Powers of The Multiplication Table: And here’s a great article from Plus with more multiplication table patterns.
Just One Cut: This is one of my favorite activities to do early in the year. Fold paper so you can cut a square out of the middle with only one cut. What other shapes can you make?
Math for Love has a review of Ben Orlin’s new book Math Games with Bad Drawings. I’ll add my vote for this book. It was hugely popular in my elementary classroom last year, even though I only taught two or three games from it. The children were constantly asking to borrow it to teach themselves new games. Now it’s sitting on my bedside table waiting for me to clear out some time to read it straight through.
Math in Nature: 5 Stunning Ways We See Math in The World: Math Geek Mama has a nice article about math in nature.
If you want to dig deeper into math in nature, check out this 3-part oldie but goody from Vi Hart on why plants love Fibonacci Numbers:
There is also lots of math to be found in the kitchen. Here are Three Ways to See Mathematical Structure in The Kitchen (with young children).
Denise Gaskins is writing a new book called Math Word Problems from Literature, and she has written a three-part blog series about some of the resources and ideas she mentions in the book. You can find them here:
Numberless Word Problems: I have never tried numberless word problems, but I’ve wanted to for a while, and I’m excited to try them with my middle schoolers this year.
Playful Math: Getting Students to Write Their Own [Problems]
Something Fun
Grant Sanderson over at 3blue1brown hosts one of my favorite YouTube channels. (If I call it a vlog, is it legit on a blog roundup?) This is a great video about lying with visual proofs.
Practical Theory—Stuff You should know
Math Beyond The School Mindset: An excellent article that explores a broader view of math. The article makes two key points that I think are crucial: 1) It may be cognitively and academically beneficial to delay the introduction of formalism/symbols for most children, and 2) Math needs stories. In fact, this article argues that we math teachers may be doing more harm than good, and I believe it. (To be fair, math teachers aren’t really the guilty party here; until we can get politicians, school boards, standardized testing companies, Bill Gates, and probably parents on board, most math teachers have little say in what they teach.)
Racks and Tubes: The Legend: Speaking of stories, here is my attempt at a story for the Montessori Racks and Tubes material. It works if you need to teach formal long division, although I’m still not wildly pleased with it, because it’s a story meant to teach a particular algorithm, rather than a story meant to provoke thought.
Why Kids Should Use Their Fingers In Math Class: In this article from The Atlantic, Jo Boaler writes about the importance of letting children use their fingers to count. As Montessorians like to say, “The hand is the prehensile instrument of the mind”. This applies as much to counting on our fingers as it does to using manipulatives to learn math.
Dehumanizing Math Educators: Jo Boaler has been the target of unrelenting attacks, primarily by white men, for years and years. Sunil Singh has a behind-the-scenes look at what Boaler has been going through. She has worked so hard to bring the beauty and humanity of mathematics to classrooms, but there are so many people who believe that math facts are the most important thing to learn in math class.
Cool Applications
Geometric Analysis Reveals How Birds Mastered Flight: Here’s a super fun article about using geometry to understand how birds fly.
Can Maths Help Improve The Communities of The Future? This article from Plus magazine explores different ways that mathematical models can be used to help local governments plan solve pressing problems. It’s got great examples of math applications that definitely don’t have one right answer, because the math is a tool used by humans to help organize and weigh human judgements.
The mathematics of gerrymandering got some big play this week in The Washington Post. I’m glad to see this issue going mainstream, and this article does a good job explaining the basics of the math, as well as the pros and cons of Monte Carlo simulation (basically solving problems by getting a computer to simulate lots of solutions to the problem using probability).
Mike’s Math Page has a nice article on exploring the mathematics of gerrymandering with kids. Unfortunately, the actual curriculum materials aren’t public, but you might be able to get them if you request them. If you’re an NCTM member, you can get a different set of resources here: Gerrymandering: When Equivalent is Not Equal!