The Playful Math Carnival is like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school. This month’s edition features articles from bloggers all across the internet.^{†}

You’re sure to find something that will delight both you and your child.

By tradition, we start the carnival with a puzzle in honor of our 123rd edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

^{†}Or more, depending on how you count. And on whether I keep finding things to squeeze in under the looming deadline. But if there are more, then there are certainly 36. Right?

The 1-2-3 Puzzle

Write down any whole number. It can be a single-digit number, or as big as you like.

For example:
64,861,287,124,425,928

Now, count up the number of even digits (including zeros), the number of odd digits, and the total number of digits it contains. Write those numbers down in order, like this:
even 12, odd 5, total 17

Then, string those numbers together to make a new long number, like so:
12,517

Perform the same operation on this new number. Count the even digits, odd digits, and total length:
even 1, odd 4, total 5

And do it again:
145
even 1, odd 2, total 3

If you keep going, will your number always turn into 123?

Check out my new printables for playing math with your kids:

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 new 70+ Things to Do with a Hundred Chart book.

This fall, my homeschool co-op math class will play with math journaling.

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

Noticing and Wondering

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.

Puzzles Are Math Experiments

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:

Explore Shapes

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?

Explore Angles

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?

Explore Squares

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?

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.

Welcome to the 115th edition of the Playful 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.

In honor of Women’s History Month, this carnival features quotes from fifteen women mathematicians.

They came from many countries and followed a variety of interests.

They conquered new topics in mathematics and expanded the world’s understanding of old ones.

They wrestled with theorems, raised children, published articles, won awards, faced discrimination, led professional organizations, and kept going through both success and failure.

Some gained international renown, but most enjoyed quiet lives.

They studied, learned, and lived (and some still live) as most of us do — loving their families and friends, joking with colleagues, hoping to influence students.

I think you’ll find their words inspiring.

“What I really am is a mathematician. Rather than being remembered as the first woman this or that, I would prefer to be remembered, as a mathematician should, simply for the theorems I have proved and the problems I have solved.”
—Julia Robinson (1919–1985)

“All in all, I have found great delight and pleasure in the pursuit of mathematics. Along the way I have made great friends and worked with a number of creative and interesting people. I have been saved from boredom, dourness, and self-absorption. One cannot ask for more.”
—Karen Uhlenbeck (b. 1942)

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

Welcome to the 114th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of articles by bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.

By the way, I found a cool, semi-self-referential trivia tidbit about our carnival number: 2^{7} − 14 = 114. And if you put 114 dots into a 1←7 Exploding Dots machine, you’ll get the code 222. Pretty neat!

As you scroll through the links below, you find several puzzle graphics from the wonderful Visual Patterns website. Use them as conversation-starters with your kids: What do you notice? How does each pattern grow? For older students: Can you write a formula to describe how each pattern? What will it look at stage 43?

A BIT OF FUN

Setting the mood: Enjoy this bit of seasonal fidgeting from Vi Hart (@vihartvihart).

If you don’t understand some of the references, that’s normal! Pick a phrase, Google it, and enjoy the fun of learning something new.

TABLE OF CONTENTS

And now, on to the main attraction: the blog posts. Some articles were submitted by their authors; others were drawn from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, click one of these links.

I’ve been following Sonya’s Arithmophobia No More blog for a couple of years, and I love the work she is doing. But this month, she’s teamed up with Lacy at Play, Discover, Learn (another great blog to follow!) to offer a humongous bundle of playful math.

You get math journaling pages, games, creative task cards, thought-provoking worksheets, and video training resources to help you build your child’s understanding of math from arithmetic to early algebra. Wow!

These activities are perfect for homeschooling families or anyone looking to supplement their child’s current math curriculum with effective discovery-based activities. If you’ve ever wondered what to do with those Cuisenaire rods you picked up on sale way back when, this bundle is for you.

I’m so looking forward to using some of these ideas with my elementary homeschool co-op kids next year!

If you’ve been reading my blog for very long, you’ve probably seen how much I love the blog, books, and classes available from the Natural Math folks.

Their newest book is just off the presses — Funville Adventures, a math adventure chapter book.

And until December 20, they’re having a holiday sale. Make your own bundle of any Natural Math books. Playful algebra, calculus for 5-year-olds, inquiry problems and more: Great deal!

(US customers only: We’re sorry we can’t offer bulk discounts for our international readers, but the complexities of international duties and tax laws are too much for this very small family business.)

Do You Know of Any Math Deals?

If you’ve seen a great deal or holiday price on a math resource you love, please share!

Add your deal to the comment section below, so we can all take advantage of the math joy this season.

Today we have a guest post from Lucy Ravitch, author of the new Kickstarter picture book Trouble with Monkeys: A math concept story of place value. She’s sharing a few ideas from her Math Activity Thursday (M.a.Th.) video series. Enjoy!

Hello, math fans and enthusiasts! Each week I try to give you and your family a fun math activity to try. Two months ago I posted this video with ten ways to turn play dough into an engaging activity for lower and upper elementary math.

If you want to make your own dough from scratch here are a few simple recipes. I encourage you to let your children play freely at first, before trying these activities.

Below I have identified some of the math concepts that your kids will experience as they play.

1. Toss It

Practice counting. With older children, record your results and make a graph of the data.

How many times can you catch it in a row? What’s your average number of tosses?

Talk about attributes. Does the size or color of the play dough balls make a difference?

How high are you tossing it? Talk about measuring systems. Do you use feet and inches, or meters and centimeters?

If you know how to juggle, time how long you can keep the balls going.

2. Smash It

Make several small balls or pieces. Then play as you smash them.

Play a NIM game: Make 10-15 small play dough balls. Take turns. On your turn, you can smash one ball or two. Whoever smashes the last ball wins the game.

Or smash your math facts: Choose several equations for your children to practice. Write each answer on a 3×5 card. Lay out each card next to a play dough piece. As you call out the equations, kids smash the play dough next to the correct card.

3. Shape It

Have fun molding your play dough. Roll it out to cut shapes.

Try making 3D shapes while practicing your math vocabulary. MathisFun.com has a great section about solid geometry. Can you find three math terms that are new for you?

Roll out the dough and cut 2D shapes. Discuss their attributes. Can you cut your shape in half to be symmetrical?

4. Hide Things in It

Find small objects around the house and enclose them inside play dough.

Take turns hiding small objects in play dough. Optional: Give a one-minute time limit to guess before opening it. This gives you and your kids a chance to talk about size, shape, or other attributes.

Have challenges to use the least amount of dough to hide identical objects. Two players have two minutes to hide an object in as little play dough as possible. The object must be completely concealed within the dough. What methods will you use?

5. Make Imprints on It

Show off your design skills and observe textures.

You can practice counting as you poke and press your fingers or objects into the dough. Older children can discuss the distance between impressions and/or the pressure applied.

As you and your kids make designs, talk about what you notice: Is your design symmetrical? What tools did you use (toothpicks, pencils, marbles, fingers, toy cars)? Which objects make interesting textures?

6. Cut It

Use a butter knife or the edge of a ruler to cut your play dough. Discuss findings as you play and explore.

In the video, I posed the question: how many sections do you get if you make only three cuts? Try it and see.

Does the number of pieces change if you use a shape other than a flat circle?

Discuss making straight cuts that will intersect or be parallel. Bring in more geometry terms.

Experiment with a different number of cuts.

7. Weigh It

Pull out a kitchen scale or balancing scales to use with dough.

Older children can make conversions between ounces to grams. They can make calculations about doubling or multiplying the measured weight. With younger kids, try using balancing scales. Compare the weights between pieces.

Try making two pieces that weigh exactly the same. This is harder than it sounds! For small children, this gives them the opportunity to see that the mass (weight) of an object can come in different shapes.

8. Measure It

Use a ruler or measuring tape while you play. There are several ways you can measure your dough — height, width, and length.

How long can you extend one ounce of dough? Pick your own size/weight of play dough and see who can get the longest. What fraction of a yard or meter is it?

Discuss height and what it takes to make dough stand vertically. How tall can you get three ounces to stand? Can anything help make it taller?

9. Roll It

Make sure you have plenty of room for this activity. Playing outside or on smooth floors works best.

With one push how far does your play dough roll? Is there an ideal size for a piece? Is there an ideal weight for rolling?

Is the ground sloped? What effects does the rolling surface have?

Why do some shapes roll easily while others don’t? Can you create a not-round shape that will roll?

10. Compare It

Compare similarities and differences between dough colors and types. Consider comparing the previously listed activities

If you made your own dough, compare consistency between batches. Is homemade dough denser or lighter than store-bought dough?

What are differences between the dough you played with and the dough that has not been touched?

Which of these activities do you think will take the shortest amount of time? The longest? Or put the activities in order based on how much dough you will need — least to greatest.

May you and your students have fun as you play with dough!

About the Author

Lucy blogs at kidsmathteacher.com and is the author/creator of Kids Menu Books. The first book in that series is The Pancake Menu, an interactive book that lets kids practice math as they play restaurant.

And be sure to visit Lucy’s Kickstarter project! She’s teamed up with artist Trav Hanson to create the delightful picture book Trouble with Monkeys: A math concept story of place value.

Well, I hadn’t planned on spending my day that way. But one of the great things about homeschooling is the freedom to follow rabbit trails.

While browsing the Carnival of Homeschooling, I found a link to Farm School blog’s article Fib Foolery, which sent me to Gotta Book for his articles The Fib and More Fibbery (read the comments on both threads, but be warned that some are crude) and several other posts, all of which set me off on a morning of poetic fun.

A “Fib” is a Fibonacci poem. It’s based on syllable count, like a haiku, but the lines follow the Fibonacci counting series: 1, 1, 2, 3, 5, 8… Each number is the sum of the previous two numbers.

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?

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.

Math Doodle Links

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!