## Playful Math Education Carnival 106

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 106th edition of the Math Teachers At Play math education blog carnival — a 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. Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle in honor of our 106th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

## Try This Puzzle

If you slice a pizza with a lightsaber, you’ll make straight cuts all the way across. Slice it once, and you get two pieces.

If you slice it five times, you’ll get a maximum of sixteen pieces. (And if you’re lucky you might get a star!)

• How many times would you have to slice the pizza to get 106 pieces?

## How To Break In Your New Math Journal

I love my new paperback math journal series. The books are sturdy, inexpensive, and fit nicely in my purse.

But as with any paperback book, these have one problem. How do I use them without cracking the spine?

When we exercise, we need to warm up our bodies with a bit of stretching to prevent injury. In the same way, we need to warm up a new book to protect it. The process is called “breaking it in.”

It only takes a few minutes to break in a paperback book:

### Step by Step

Never force the book but help it limber up gradually, and it will serve you well.

Because my journals are working books, I take the breaking-in process a bit further than shown in the video:

(1) Set the book on its back and follow the process above. Press down each cover, but not completely flat — let it bend at the fold line, about 1 cm from the actual spine. Then press a couple pages at a time, alternating front and back, down flat on each cover.

(2) Flip through the pages of the book forward and backward to limber them up.

(3) Repeat the steps of the video. This time, gently lean the main part of the book away from the part you are pressing down. Aim for a 130–140 degree angle.

(4) Flip through the pages again. For paperbacks, you can even roll the whole book back and forth a bit — gently curving the cover and pages almost as if you’re trying to fold the book in half — to encourage flexibility.

(5) Optional: Repeat the breaking-in process one more time. This time, fold each section back as close to 180 degrees as it will go.

And you’re done!

The pages will still curve in at the fold line, where they connect to the spine of the book. You want that because it makes the book strong. But now they’ll also open up to provide a nice, wide area for writing or math doodling.

## Dot Grid Doodling

### What can you DO with a page full of dots?

Yesterday, I mentioned my new series of paperback dot grid notebooks, and I promised to share a few ideas for mathematical doodling.

But first, let me share my new dot-grid journals for kids. Aren’t they pretty?

Doodling gives our minds a chance to relax, wander, and come back to our work refreshed. And though it goes against intuition, doodling can help us remember more of what we learn.

Math doodles let us experiment with geometric shapes and symmetries. We can feel our way into math ideas gradually, through informal play. Through doodles, our students will explore a wide range of mathematical structures and relationships.

Our own school experiences can make it hard for us to teach. What we never learned in school was the concept of playing around with math, allowing ideas to “percolate,” so to speak, before mastery occurs, and that process may take time.

—Julie Brennan

I like to doodle on dotty grid paper, like the pages in my math journals, but there’s No Purchase Necessary! You can design your own printable dot page at Incompetech’s PDF generator, or download my free coloring book (which includes several pages of printable dot and graph paper).

### Patterns in Shape and Angle

To make a faceted mathematical gemstone, start with any shape you like. Then build other shapes around it. What do you notice? Does your pattern grow outward from its center? Or flow around the corner of your page? How is each layer similar, and how is it different?

Arbitrary constraints can lead to mathematically interesting doodles. For instance, create a design out of 45-45-90 triangles by coloring exactly half of every grid square. How many variations can you find?

### Symmetry Challenge

Play a symmetry puzzle game. Draw a line of symmetry and fill in part of the design. Then trade with a partner to finish each other’s doodles.

Make more complex symmetry puzzles with additional reflection lines.

• Who can talk about mathematical doodling without mentioning Vi Hart? If you’ve never seen her “Doodling in Math Class” video series, you’re in for a treat!
• See if you can draw a rotational-symmetry design, like Don’s “Order 4” graphs.
• Or experiment with the more flexible rules in John’s “Knot Fun” lesson.
• And my latest obsession: the “ultimate” tutorial series on Celtic Knotwork, which explores the link between knots and their underlying graphs.

Before you start doodling: How to Break In Your New Math Journal.

Feature photo (top): Sommermorgen (Alte Holzbrücke in Pretzfeld) by Curt Herrmann, via Wikimedia Commons. [Public domain]

## Dot Grid Journals with Coloring Pages

My newest book project began with a few simple coloring pages for my homeschool co-op kids. You may recall when I collected those into a downloadable coloring book last December. Well, I kept tinkering with the designs into January. And then it was time to buy a new planner…

The problem is, I’m not a naturally organized person. I like making lists and plans, but sticking to them is tougher. And I’ve never found a planner or organizational system that I could follow for longer than two weeks at a go. That is until I heard of bullet journaling.

But journaling requires a journal — a notebook of some sort. And I couldn’t find any that I liked. Either the pages were too narrow and felt cramped, or the thing didn’t fit even in my oversized purse. Or the fancy, hardcover binding made it heavy to lug around. Or there weren’t enough pages to last more than a few weeks. Or the lines were too dark, or too widely spaced.

Never quite what I wanted.

So I decided to make my own.

I started with dot-grid pages for flexible layouts and for doodling. I scattered some of my favorite math and education quotations through each book. And then I added several of my most flexible geometric coloring pages (loosely based on Islamic tessellation designs).

And I had so much fun I couldn’t stop with just one. So let me introduce my Dot Grid Notebook with Coloring Pages series:

With 170 roomy pages, each book gives you plenty of space to record memories, plan projects, and keep track of tasks. The dot grid makes it easy to draw graphs or diagrams. Take notes, jot down ideas, copy your favorite quotations, or doodle to your heart’s content.

• Light gray dots at 5 mm spacing provide guidance for flexible page layouts.
• 11 geometric coloring pages allow a multitude of artistic possibilities.
• 31 favorite quotes offer a vision for creative math education.
• 6 × 9 inch (about 15 × 23 cm) pages are wider than many journals, yet still fit comfortably into a large purse or bag.
• Paperback binding makes the journal sturdy but lightweight. Carry it anywhere!

Prevent cracked spines: How to Break In Your New Math Journal.

The ebook edition features all 124 quotations (31 from each journal) about mathematics, education, and problem solving. Read through for your own pleasure, post them by your workspace, or use them as writing prompts for yourself or your students. [Yes, all of the ebooks are the same.]

### But, what can you DO with all those nice, dotty pages?

Of course, you can use them for bullet journaling. That’s why I originally created the books, because I couldn’t find planners that fit my personal style. My bullet journal is basically an anthology of To-Do lists, bound together so they don’t get lost in the clutter. It’s the only planner system I’ve been able to stick with for more than two weeks at a go.

Or you could use the dotty pages for a commonplace book. That’s my favorite kind of journaling. Like a magpie, I collect shiny tidbits from books, websites, conversations overheard, and more. Passages. Definitions. Poems. Recipes. Proverbs. Things I’m wondering about. Cute kid sayings. It all goes into the mix.

And math puzzles, of course! Below, I’m playing my way through Paul Lockhart’s Measurement. I use the cloud-like labels in the outer margins of each page for keywords that identify what I’m writing, because someday I’ll need to skim back and find an old note.

But where dot grid pages really excel is at doodling — I’m sure you noticed the faceted design filling the lower half of my journal page above and the gem almost overrunning my February calendar. So watch for tomorrow’s blog post featuring a variety of ways to create your own mathematical doodles.

Best wishes, and happy mathing!

P.S.: Do you have a blog? If you’d like to feature a Dot Grid Journal review and giveaway, I’ll provide the prize. Leave a comment below, and we’ll work out the details.

## Beauty in Math: A Fable

Have you ever wondered what mathematicians mean when they talk about a “beautiful” math proof?

“Beauty in mathematics is seeing the truth without effort.”

“There’s something striking about the economy of the counselor’s construction. He drew a single line, and that totally changed one’s vision of the geometry involved.

“Very often, there’s a simple introduction of something that’s not logically within the framework of the question — and it can be very simple — and it utterly changes your view of what the question really is about.”

CREDITS: Castle photo (top) by Rachel Davis via Unsplash. “A Mathematical Fable” via YouTube. Story told by Barry Mazur. Animation by Pete McPartlan. Video by Brady Haran for Numberphile.

## FAQ: Homeschool Burnout

“Spring cleaning has made my desk look worse than before. Nobody feels like studying. The kids would rather be outside, and their mom would rather take a nap. If I line everyone up on the curb in the morning, do you think the yellow bus will take them?”

Homeschool burnout — it’s a perennial problem. If you’re suffering from lethargy and can’t face another day of school work, here are some ideas that kept me going long enough to graduate almost-five kids (my “baby” finishes homeschooling this spring!):

(2) Connect with other homeschoolers. Meet with friends for tea, or have a Mom’s Night Out while Dad babysits. Talk about substantive things, like educational philosophy — what you like about homeschooling, and what you’d like to change. Share your dreams for your children. Remind each other why you’re doing this.

(3) Attend support group meetings. I find that after so many years, I let the meetings slide. I think, I already know everything they are going to say. But being with other homeschoolers is encouraging. And if you find out that you can help a new homeschooler with advice, that gives you a boost, too.

(4) Find one or two forums where you can become one of the resident experts, and answer posts as often as you can. As with number 3 above, being able to give advice (and being appreciated for it) can give you the energy to keep on going.

(5) Go to a homeschooling convention, if you get the chance. The speakers are stimulating, and you may find some new book or tool that sparks your imagination.

(6) Do school anyway. It may seem impossible when you’re stuck in the doldrums, but once you get going, you may find it easier. The light of understanding in a child’s eyes can give Mom quite a lift!

(7) Try something completely different. If you have always used a textbook program, then set it aside for a month and just read library books. If you have read lots of great literature, then try some hands-on projects, or get out those science experiments you keep putting off, or visit all the museums within a two-hour radius, or… I’m sure you can think of something that has been lingering on your good-intentions list. I never could stand to teach the same old thing every year, and none of my five kids got exactly the same education. Happily, there is always another way to approach any homeschooling topic. How about Gameschooling?

(8) Figure out what your students are able to do on their own, and let them do it. Encourage them to develop as much independence as possible.

(9) Use some of your children’s independent time to learn something new for yourself. Have you always wanted to try painting, or crochet, or woodworking? Be an example of life-long learning.

(10) Start (or join in progress) a group class or co-op. You may be able to trade around with some other families: you teach history and others teach math or cooking, or whatever arrangement fits for you. This is especially helpful for those time-consuming projects that always seem to get put off, like art or science experiments.

(11) Try some of these intensely practical Tips For Coping With Homeschool Burnout.

(12) And are you a Christian homeschooler? Then pray! Your Father knows what you need, and Immanuel is with you always. Try praying your way through 1 Corinthians 13 (or this homeschooling version).

If you have any other ideas for beating the burnout blues, please share!

Homeschooling is not always peaches and cream. If anyone promised you that, they lied. But be assured that it homeschool burnout is not a terminal condition. You will recover your joy in sharing your children’s education.

I learned one thing from every story I’ve ever read: adventures never run smoothly.

And what greater adventure could there be than to introduce your child to all the wonderful things in God’s world?

CREDITS: “Scream” photo (top) by greg westfall via Flickr (CC BY 2.0).