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.

Click here to submit your blog post

**Don’t procrastinate: The deadline for entries is this Friday, September 21.** The carnival will be posted next week at nebusresearch blog.

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: “Chica usando ordenador” sketch (top) by Olga Berrios (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.

]]>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).

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.

]]>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.

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.

]]>Click here to submit your blog post

**Don’t procrastinate: The deadline for entries is this Friday, August 24.** The carnival will be posted next week at Find the Factors blog.

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.

Help! I can’t keep the carnival going on my own.

Hosting the blog carnival can be a lot of work, but it’s fun to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival usually brings a nice little spike in traffic to your blog.

If you think you’d like to join in the fun, read the instructions on our Playful Math Blog Carnival homepage. Then leave a comment or email me to let me know which month you’d like to take.

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: “L.A. County Fair” photo (top) by Omar Bárcena (CC BY 2.0) via Flickr.]/span>

“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:

“As we go through each lesson, it seems like my daughter has a good handle on the concepts, but when we get to the test she forgets everything. When I ask her about it, she shrugs and says, ‘I don’t know.’ What do you do when your child completely loses what she has learned?”

Forgetting is the human brain’s natural defense mechanism. It keeps us from being overwhelmed by the abundance of sensory data that bombards us each moment of every day.

Our children’s minds will never work like a computer that can store a program and recall it flawlessly months later.

Sometimes, for my children, a gentle reminder is enough to drag the forgotten concept back out of the dust-bunnies of memory.

Other times, I find that they answer “I don’t know” out of habit, because it’s easier than thinking about the question. And because they’d prefer to be doing something else.

And still other times, I find out they didn’t understand the topic as well as I thought they did when we went through it before.

No matter how we adults try to explain the concepts, some kids want to be answer-getters. They don’t want to do the hard work of thinking a concept through until it makes a connection in their minds. They want to memorize a few steps and crank through the lesson to get it over with.

In all these cases, what helps me the most is conversation.

My children and I always talk about our math. I ask questions like “What do you think? What do you remember? Can you explain the question to me? What are they asking for?”

And, whether the child’s answer is right or wrong, I practice my poker face. Trying not to give anything away, I ask, “How did you figure it out? Can you think of a way to confirm your answer?”

Not sure how to talk about math with your children?

If you have preschool and elementary-age kids, read Christopher Danielson’s inspiring book and blog:

For middle school and older students, check out Fawn Nguyen’s wonderful collection of Math Talks. Be sure to read the “Teachers” page for tips and talking points:

“You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds.”

— Christopher Danielson

Talking Math with Your Kids

Games are a great way to practice math. Check out these (free!) math games for all ages:

And if you have elementary-age children, here are a few grade-level tips to help them learn (and remember) math concepts:

- Roadmap to Mathematics: Kindergarten
- Roadmap to Mathematics: 1st Grade
- Roadmap to Mathematics: 2nd Grade
- Roadmap to Mathematics: 3rd Grade

Credits: Girl in field photo by SOURCE Hydration Systems and Sandals technology via Flickr. (CC BY 2.0) Nigerian classroom photo by Doug Linstedt and young girl studying by pan xiaozhen 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

Check out the new playful math blog carnival at *Math Hombre* blog. John put together a great collection of 30+ math games, activities, and teaching tips:

The carnival features hands-on papercrafts, open-ended projects, challenging puzzles, inspiring tips, and thoughtful essays. And comics, too.

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. Check them out:

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!

Simon Gregg put this carnival together a few weeks ago, and I should have posted a link before now, but it’s been a hard few months here, and too many things got shoved aside. Still the posts are evergreen — helpful and inspiring no matter when you read them.

This carnival offers summer camp activities, dancing geometric patterns, new books to enjoy, pattern blocks, the math of peg solitaire, Q-bitz fraction talks, and a taste of some great math conversations on Twitter. And plenty 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!

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

**Don’t procrastinate: The deadline for entries is this Friday, May 25.** The carnival will be posted next week at Math Hombre blog.

I’ve been working on my next *Playful Math Singles* book, based on the popular Things to Do with a Hundred Chart post.

My hundred chart list began many years ago as seven ideas for playing with numbers. Over the years, it grew to its current 30+ activities.

Now, in preparing the new book, my list has become a monster. I’ve collected almost 70 ways to play with numbers, shapes, and logic from preschool to middle school. Just yesterday I added activities for fraction and decimal multiplication, and also tips for naming complex fractions. Wow!

Gonna have to edit that cover file…

In the “Advanced Patterns” chapter, I have a section on math debates. The point of a math debate isn’t that one answer is “right” while the other is “wrong.” You can choose either side of the question — the important thing is how well you support your argument.

Here’s activity #69 in the current book draft.

When you add fractions, you face a problem that most people never consider. Namely, you have to decide exactly what you are talking about.

For instance, what is one-tenth plus one-tenth?

Well, you might say that:

of one hundred chart

+ of the same chart

= of that hundred chart

But, you might also say that:

of one chart

+ of another chart

= of the *pair* of charts

That is, you started off counting on two independent charts. But when you put them together, you ended up with a double chart. Two hundred squares in all. Which made each row in the final set worth of the whole pair of charts.

So what happens if you see this question on a math test:

+ = ?

If you write the answer “”, you know the teacher will mark it wrong.

Is that fair? Why, or why not?

CREDITS: Feature photo (above) by Thor/geishaboy500 via Flickr (CC BY 2.0). “One is one … or is it?” video by Christopher Danielson via TED-Ed. This math debate was suggested by Marilyn Burns’s blog post Can 1/3 + 1/3 = 2/6? It seemed so!

“In 2018, I want to change the world.

…

I want to make it possible for more children to claim math as their favorite subject.

…

Math is how we describe our world when words are not enough. Everyone deserves to speak math and to play math, to enjoy its beauty and its power.”

— Geoff White

The Grade 10 Math Crunch, or Hitting the Wall at Grade 10

CREDITS: Background photo by Bobby Johnson on Unsplash.

“At heart, mathematical thinking is little more than formalized common sense. It always has been. Which means it is something we can all do.”

— Keith Devlin

How Today’s Pros Solve Math Problems

If you have some time to spend pondering big ideas, dig into Devlin’s entire series of posts about what real-world mathematics looks like and the implications for math education:

- Déjà Vu, All Over Again
- How Today’s Pros Solve Math Problems: Part 1
- How Today’s Pros Solve Math Problems: Part 2
- How Today’s Pros Solve Math Problems: Part 3 (The Nueva School course)
- Calculation was the price we used to have to pay to do mathematics

And a related series on K–12 school math:

- All The Mathematical Methods I Learned in My University Math Degree Became Obsolete in My Lifetime
- Number Sense: The Most Important Mathematical Concept in 21st Century K-12 Education

“Make no mistake about it, acquiring that modern-day mathematical skillset definitely requires spending time carrying out the various procedures. Your child or children will still spend time ‘doing math’ in the way you remember.

“But whereas the focus used to be on mastering the skills with the goal of carrying out the procedures accurately — something that, thanks to the learning capacity of the human brain, could be achieved without deep, conceptual understanding — the focus today is on that conceptual understanding.

“That is a very different goal, and quite frankly a much more difficult one to reach.”

— Keith Devlin

All The Mathematical Methods I Learned in My University Math Degree Became Obsolete in My Lifetime