The free 50-page PDF *Hundred Charts Galore!* file features 1–100 charts, 0–99 charts, bottom’s-up versions, multiple-chart pages, blank charts, game boards, and more. Everything you need to play the activities in my *70+ Things to Do with a Hundred Chart* book (coming soon from Tabletop Academy Press).

Download Hundred Charts Galore

If all goes well, the hundred chart book should be out (at least in ebook format) by the end of this month. While you’re waiting, you can try some of the activities in my all-time most popular blog post:

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

]]>Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up through first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

Click here to submit your blog post

**Don’t procrastinate: The deadline for entries is Sunday, November 25.** But if you wait that long, you’ll forget. So send in your submission today!

Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers.

If you haven’t written anything about math lately, here are some ideas to get your creative juices flowing…

**Talking Math with Kids:**Children often have surprising insight. Even when they’re confused about math, their point of view can open our adult eyes to new understanding. Share your kids’ stories.

**Games or Activities:**Do you have a game, activity, or anecdote about teaching math to young students? We’d love to play along.

**Lesson Ideas:**This section is for arithmetic explorations, geometry puzzles, trig investigations, contest-preparation tips, and more. Can you make math topics come alive, so they will stick in a student’s mind?

**Teaching Tips:**Other teachers’ blogs are an important factor in my continuing education. The more I read about the theory and practice of teaching math, the more I realize how much I have yet to learn. So please, fellow teachers, don’t be shy — share your insights!

**Mathematical Recreations:**What kind of math do you do, just for fun?

While you’re waiting for next week’s carnival, you may enjoy:

- Browsing past editions of the Playful Math Blog Carnival
- Or visiting the latest Carnival of Mathematics

CREDITS: “Two Bloggers, after Norman Rockwell” sketch (top) by Mike Licht (CC BY 2.0) via Flickr.

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

]]>Learning math is more like taking a meandering nature walk than like climbing a ladder of one-topic-after-another. Kids need to wander around the concepts, notice things, wonder about them, and enjoy the journey.

— Denise Gaskins

from a comment on the Living Math Forum

CREDITS: Background photo courtesy of Annie Spratt on Unsplash.

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

]]>Each monthly Playful Math Education Blog Carnival brings you a great new collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun.

It’s like a free online magazine of mathematical adventures. Enjoy!

Sonya put together this carnival of evergreen links — helpful and inspiring no matter when you read them — featuring math comics, a couple conversations on Euler, Truchet and infinity tiles, Islamic art, counting and counting ropes, negative numbers, and more.

Click Here to Read the Carnival Blog

Do you have a favorite blog post about math activities, games, lessons, or hands-on fun? The Playful Math Blog Carnival would love to feature your article!

We welcome math topics from preschool through the first year of calculus. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

To submit a blog article for consideration, fill out this form:

Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers.

Give each player four to six miscellaneous cards (such as the face cards and jokers you removed from the card deck) to serve as the cars of their number trains.

Lay these cards face down in a horizontal row, as shown. Shuffle the math card deck and spread it on the table as a fishing pond.

On your turn, draw one card and play it face up on one of your train cars. The numbers on your train must increase from left to right, but they do not need to be in consecutive order. If you do not have an appropriate blank place for your card, you have two choices:

• Mix the new card back into the fishing pond.

• Use the new number to replace one of your other cards, and then discard the old one.

The first player to complete a train of numbers that increases from left to right wins the game.

**House Rule:** Decide how strict you will be about the “increases from left to right” rule and repeated numbers. Does “1, 3, 3, 7, 8” count as a valid number train? Or will the player have to keep trying for a card to replace one of the threes?

**For older players:** You can adapt Number Train to play with more advanced students:

- Play Joe Schwartz’s version with two-digit numbers.
- Check out John Golden’s fantastic Decimal Point Pickle.
- Or experiment with exponential number trains.

This post is an excerpt from my book *Counting & Number Bonds: Math Games for Early Learners*, available now at your favorite online book dealer.

One of *my* favorite stores, Rainbow Resource Center, is offering several of my books at a great discount.

Check them out!

]]>You don’t need a set of worksheets or lesson plans to learn math. All you need is an inquiring mind and something interesting to think about.

Play. Discuss. Notice. Wonder.

Enjoy.

— Denise Gaskins

Playing Complex Fractions with Your Kids

CREDITS: Background photo courtesy of Steve Shreve on Unsplash.

It looks a bit cluttered. Possible tweak: Remove the brackets and instead use a thicker dividing line to show the thirds.

While I’m thinking about that, would you like a sneak peek at an activity from the book?

You don’t need a set of worksheets or lesson plans to learn math. All you need is an inquiring mind and something interesting to think about.

Play. Discuss. Notice. Wonder.

Enjoy.

Here’s how you can play complex fractions with your kids…

Print a few blank 120 charts and turn them sideways, so each chart has ten rows with twelve squares in each row.

Cut out the rows to make fraction strips with twelve squares on each strip.

Color a different set of squares on each strip. On some strips, arrange the colored squares all together at one end. On other strips, mix them around.

If we count each strip as one whole thing, what fraction of its squares are colored?

Match the strips that represent the same fraction.

On some of the strips, there will be more than one way to name the fraction. For example, if six squares are colored, we can call that 6/12 or 2/4 or 1/2 of the strip. These alternate names are easiest to see when the colored squares are all at one end of the strip, because you can fold the strip to show the halves or fourths.

How many different fraction names can you find for each set of colored squares?

We could also call the strip with six colored squares “1 1/2 thirds” of the whole strip. Can you show by folding why that name makes sense?

Or we could call the strip with five colored squares “2 1/2 sixths.”

When we have a fraction within a fraction like this, we call it a complex fraction, because it is more complicated than a common (or simple) fraction.

Another way to say it: Complex fractions have other fractions inside them.

A complex fraction is like a puzzle, challenging us to find its secret identity — the common fraction that names the same amount of stuff.

For example, how much is 3 1/3 fourths? One fourth would be three of the twelve squares on a fraction strip. So three fourths would be three sets of those three squares, or nine squares. Then we need to add one-third of the final fourth, which is one of the remaining three squares. So 3 1/3 fourths must be ten squares in all.

3 1/3 fourths = 10/12 = 5/6

How many complex fractions can you find in your set of fraction strips?

Can you figure out how much a one-and-a-halfth would be?

That is one piece, of such a size that it takes one and one-half pieces to make a complete fraction strip.

A one-and-a-halfth is a very useful fraction and was a favorite of the ancient Egyptian scribes, who used it to solve all sorts of practical math problems.

How about a one-and-a-thirdth? How many of those pieces make a whole strip? What common fraction names the same amount of stuff?

Or how much would a two-thirdth be? In that case, it only takes two-thirds of a piece to make a complete strip. So the whole piece must be greater than one. A two-thirdth’s secret identity is a mixed number. Can you unmask it?

Make up some challenge fraction mysteries of your own.

I’m still working on the graphics for my hundred chart book. Here’s the latest version of the complex fraction strips.

I like this one much better.

What do you think?

CREDITS: The slogan “Make Math Your Own” comes from Maria Droujkova, founder and director of the Natural Math website. Maria likes to say: “Make math your own, to make your own math!”

*70+ Things to Do with a Hundred Chart* is part of my Playful Math Singles series. Coming soon to your favorite online bookstore…

Check out the new playful math blog carnival at *nebusresearch* blog. Joseph put together a great collection of math games, activities, and teaching tips:

The carnival features classic puzzles, geometric art, Friedman numbers, scrambled times tables, mathematical comics, the friendship paradox, and a free online topology game. And much more — too many topics to list!

A few of the entries may push the limits of “school level” math, but there’s plenty of mathy fun to go around.

Click here to go read the carnival blog

And if you’re a blogger, be sure to submit your blog post for next month’s carnival!

Past carnivals are still full of mathy treasure. See them all on Pinterest:

- Browse all the past editions of the
*Math Teachers at Play*blog carnival - Or scroll back through the archives on my blog.

CREDITS: Carnival photos (above) by Casey Horner and reyhan afif on Unsplash.

Each monthly Playful Math Education Blog Carnival brings you a great new collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun. It’s like a free online magazine of mathematical adventures. What fun!

Iva Sallay put together this carnival of evergreen links — helpful and inspiring no matter when you read them.

This carnival offers math art and poetry, kid-made books, journaling, logic, and talking math with kids. Same and Different, How Many, and other puzzles. And more!

Click Here to Read the Carnival Blog

Do you have a favorite blog post about math activities, games, lessons, or hands-on fun? The Playful Math Blog Carnival would love to feature your article!

We welcome math topics from preschool through the first year of calculus. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

To submit a blog article for consideration, fill out this form:

Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers.

CREDITS: “One Galaxy” drawing by Sara Divenuto, age 10, via Hubble Space Telescope / ESA on Flickr (CC BY 2.0).

But my earlier dot-grid notebooks were designed for adults. Too thick, too many pages. And the half-cm dot grid made lines too narrow for young writers.

So I created a new series of paperback dot-grid journals for my elementary and middle school students.

I hope you enjoy them, too!

Click here for more information

So, what can your kids do with a math journal?

Here are a few ideas:

- Make up their own word problems. See this blog post for examples.

- Enjoy a living math book, and then diagram the story.

- Play with some of Don Steward’s investigations of grid geometry.

- Sample the essay prompts from my Writing to Learn Math and Writing to Learn Math II posts.

- Try a set of math puzzles from the Julia Robinson Festival.

- Or explore Don Cohen’s Map to Calculus for Young People.

I’m sure we’ll use several of these activities in my homeschool co-op math class this fall.

Learning math requires more than mastering number facts and memorizing rules. At its heart, math is a way of thinking.

So more than anything else, we need to teach our kids to think mathematically — to make sense of math problems and persevere in figuring them out.

Help your children learn to see with mathematical eyes, noticing and wondering about math problems.

Whenever your children need to learn a new idea in math, or whenever they get stuck on a tough homework problem, that’s a good time to step back and make sense of the math.

Kids can write their noticings and wonderings in the math journal. Or you can act as the scribe, writing down (without comment) everything child says.

For more tips on teaching students to brainstorm about math, check out these online resources from The Math Forum:

Problem-solving is a habit of mind that you and your children can learn and grow in. Help your kids practice slowing down and taking the time to fully understand a problem situation.

Almost anything your child notices or wonders can lead to a math experiment.

For example, one day my daughter played an online math game…

A math journal can be like a science lab book. Not the pre-digested, fill-in-the-blank lab books that some curricula provide. But the real lab books that scientists write to keep track of their data, and what they’ve tried so far, and what went wrong, and what finally worked.

Here are a few open-ended math experiments you might try:

- Pick out a 3×3 set of dots. How many different shapes can you make by connecting those dots? Which shapes have symmetry? Which ones do you like the best?

- What if you make shapes on isometric grid paper? How many different ways can you connect those dots?

- Limit your investigation to a specific type of shape. How many different triangles can you make on a 3×3 set of dots? How many different quadrilaterals? What if you used a bigger set of dots?

- On your grid paper, let one dot “hold hands” with two others. How many different angles can you make? Can you figure out their degree without measuring?

- Are there any angles you can’t make on your dot grid? If your paper extended forever, would there be any angles you couldn’t make?

- Does it make a difference whether you try the angle experiments on square or isometric grid paper?

- How many different squares can you draw on your grid paper? (Don’t forget the squares that sit on a slant!) How can you be sure that they are perfectly square?

- Number the rows and columns of dots. Can you find a pattern in the corner positions for your squares? If someone drew a secret square, what’s the minimum information you would need to duplicate it?

- Does it make a difference whether you try the square experiments on square or isometric grid paper?

Create math art. Check out my math doodling collection on Pinterest and my Dot Grid Doodling blog post. Can you draw an impossible shape?

I’d love to hear your favorite math explorations or journaling tips!

Please share in the comments section below.

**P.S.:** Do you have a blog? If you’d like to feature a math journal review and giveaway, I’ll provide the prize. Send a message through my contact form or leave a comment below, and we’ll work out the details.

“When I began my college education, I still had many doubts about whether I was good enough for mathematics. Then a colleague said the decisive words to me: it is not that I am worthy to occupy myself with mathematics, but rather that mathematics is worthy for one to occupy oneself with.”

— Rózsa Péter

Mathematics is beautiful

essay in *The Mathematical Intelligencer*

I would like to win over those who consider mathematics useful, but colourless and dry — a necessary evil…

No other field can offer, to such an extent as mathematics, the joy of discovery, which is perhaps the greatest human joy.

The schoolchildren that I have taught in the past were always attuned to this, and so I have also learned much from them.

It never would have occurred to me, for instance, to talk about the Euclidean Algorithm in a class with twelve-year-old girls, but my students led me to do it.

I would like to recount this lesson.

What we were busy with was that I would name two numbers, and the students would figure out their greatest common divisor. For small numbers this went quickly. Gradually, I named larger and larger numbers so that the students would experience difficulty and would want to have a procedure.

I thought that the procedure would be factorization into primes.

They had still easily figured out the greatest common divisor of 60 and 48: “Twelve!”

But a girl remarked: “Well, that’s just the same as the difference of 60 and 48.”

“That’s a coincidence,” I said and wanted to go on.

But they would not let me go on: “Please name us numbers where it isn’t like that.”

“Fine. 60 and 36 also have 12 as their greatest common divisor, and their difference is 24.”

Another interruption: “Here the difference is twice as big as the greatest common divisor.”

“All right, if this will satisfy all of you, it is in fact no coincidence: the difference of two numbers is always divisible by all their common divisors. And so is their sum.”

Certainly that needed to be stated in full, but having done so, I really did want to move on.

However, I still could not do that.

A girl asked: “Couldn’t they discover a procedure to find the greatest common divisor just from that?”

They certainly could! But that is precisely the basic idea behind the Euclidean Algorithm!

So I abandoned my plan and went the way that my students led me.

— Rózsa Péter

quoted at the MacTutor History of Mathematics Archive

- Euclidean Algorithm Explained Visually
- Euclid’s Game on a Hundred Chart
- Kid-Friendly Prime Factorization

Note: When the video narrator says “Greatest Common Denominator,” he really means “Greatest Common *Divisor*.”

This is my third contribution to the blogging challenge #MTBoSBlaugust.

I’m aiming for at least one post each week. A simple, modest goal. But if I manage it, that will be four times the pace I’ve set in recent months.

So far, so good…

CREDITS: “Pink toned thoughts on a hike” photo courtesy of Simon Matzinger on Unsplash.

My son can’t stand long division or fractions. We had a lesson on geometry, and he enjoyed that — especially the 3-D shapes. If we can just get past the basics, then we’ll have time for the things he finds interesting. But one workbook page takes so long, and I’m sick of the drama. Should we keep pushing through?

Those upper-elementary arithmetic topics are important. Foundational concepts. Your son needs to master them.

Eventually.

But the daily slog through page after page of workbook arithmetic can wear *anyone* down.

Many children find it easier to focus on math when it’s built into a game.

Take a look at Colleen King’s Math Playground website. Or try one of the ideas on John Golden’s Math Hombre Games blog page.

Or sometimes a story helps, like my Cookie Factory Guide to Long Division.

Games are great for practicing math your child has already learned. But for introducing new concepts, you’ll probably want to follow your textbook.

Still, even with textbook math, there are ways to make the journey less tedious:

- Most children do not need to do every problem on a workbook page, or every page in a section. There is a lot of extra review built into any math program.

- You don’t have to finish a section before you work whatever comes after it. Use sticky bookmarks to keep track of your position in two or three chapters at a time. Do a little bit of the mundane arithmetic practice, and then balance that with some of the more interesting topics your son enjoys.

- As much as possible, do math out loud with a whiteboard for scratch work. Somehow, working with colorful markers makes arithmetic more bearable.

- Set a timer for math, and make the time short enough that he feels the end is in sight. I suggest no more than thirty minutes a day for now. And whenever the timer rings, stop immediately — even if you are in the middle of a problem.

Doing math in short sessions helped us avoid the emotional melt-downs my daughter used to have.

Thinking is hard work, and if I asked for too much, she would crash.

Because I sat with her and worked together every problem, I knew what she understood and when we could skip a problem. Or sometimes even jump several pages. Which meant that, even with short lessons, we still got through our book on time.

But as I said before, textbooks include a whole lot of repetition.

Too much repetition deadens the brain.

So we also took *long* breaks from our textbook program. Entire school-year-long breaks, just playing with math. Letting “enrichment” activities be our whole curriculum.

As healthy as vegetables are, you would never limit your son to eating just lima beans and corn.

Similarly, be sure to feed him a varied math diet.

For example, you can follow his interest in geometry beyond the standard school topics.

Explore tessellations, Escher art, and impossible shapes such as the Penrose triangle.

Building Lego scenes is a practical application of 3-D geometry. He might even want to try stop motion animation.

Talk about how math works in real life. Ponder the choices on John Stevens’s “Would You Rather?” blog or try some of the challenges at Andrew Stadel’s Estimation 180 website. Many of these require three-dimensional reasoning.

This is my second contribution to the blogging challenge #MTBoSBlaugust.

I’m aiming for at least one post each week. A simple, modest goal. But if I manage it, that will be four times the pace I’ve set in recent months.

Two posts down…

CREDITS: Frustrated Child photo by by Pixabay on Pexels.com. Penrose Lego by Erik Johansson via Flickr (CC BY 2.0). Homework Hands photo by Tamarcus Brown on Unsplash.

This post is an excerpt from my book * Let’s Play Math: How Families Can Learn Math Together—and Enjoy It,* as are many of the articles in my

Sounds like a good excuse to play some math!

- Joel David Hamkins’s Graph Coloring for Kids and Graph Theory for Kids.
- Marshall Hampton’s Mathematical Coloring Book.
- Martin Holtham’s Mathematical Colouring Pages.
- Follow the links at Clarissa Grandi’s Artful Maths blog.
- My own Geometric Coloring Designs book includes printable coloring pages plus links to a variety of creative math art project ideas.
- And some classic Free Math from Dover Publications.

If you know of any other free math coloring resources, please share a link in the comments below.

This month, I’ve joined a blog posting challenge called #MTBoSBlaugust.

At first, I thought of trying to post every day, but there’s no way I will keep up with that. So I’ll set my goal for at least one post each week.

A simple, modest goal. But if I manage it, that will be four times the pace I’ve set in recent months.

One post down…

CREDITS: “School Crayons” photo by Sharon McCutcheon on Unsplash.

Check out the new playful math blog carnival at *Three J’s Learning* blog. Joshua put together a great collection of math games, activities, and teaching tips:

The carnival features a “square dancing” puzzle, strategy game discussions, divisibility rules, fake theorems, and mathematical oceans in disguise. And much more!

Click here to go read the carnival blog

And if you’re a blogger, be sure to submit your blog post for next month’s carnival!

Past carnivals are still full of mathy treasure. See them all on Pinterest:

- Browse all the past editions of the
*Math Teachers at Play*blog carnival - Or scroll back through the archives on my blog.

CREDITS: Carnival photos (above) by Scott Trento and Craig Smith on Unsplash.

Each monthly carnival brings you a great new collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun. It’s like a free online magazine of mathematical adventures. What fun!

Sue VanHattum put together this carnival of evergreen links — helpful and inspiring no matter when you read them.

This carnival offers summer math resources, a four-4s puzzle, set theory for kids, magic math books, fresh insight into the Math War game, counting challenges, and the Fundamental Theorem of calculus. And more!

Click Here to Read the Carnival Blog

Do you have a favorite blog post about math activities, games, lessons, or hands-on fun? The Playful Math Blog Carnival would love to feature your article!

We welcome math topics from preschool through the first year of calculus. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

To submit a blog article for consideration, fill out this form: