Once again, some of my favorite websites offer a seasonal selection of activities to encourage your children’s (and your own!) mathematical creativity, one for each day in the run-up to Christmas.

Including an especially tough Advent meta-puzzle for truly determined problem-solvers…

Click the images below to visit the corresponding December Math Calendar pages.

For Primary Students

Easier activities for elementary and middle school.

A problem or game that uses dice for each day in the run up to Christmas.

When you get to the Nrich website, click a number to go to that day’s math.

For Secondary Students

Activities for middle and high school.

Most of the tasks require dotty paper or circles which you can find on the Nrich Printable Resources page.

When you get to the Nrich website, click a number to go to that day’s math.

“Because sometimes, in the midst of all the family fun, it’s good to put your headphones in and retreat into a word of your own, this year’s advent calendar brings you some of our favourite Plus podcasts. From the secrets of the Universe to the maths of football stadiums, there should be something there for everyone. Happy listening and happy Christmas from the Plus team!”

When you get to the +Plus Magazine website, you can tell which links are live because they jump to a larger size when you tap or mouse over the picture.

One link becomes live each day — so come back tomorrow and discover something new!

Christmas Meta-Puzzle

Or try your hand at the biggest mathematical mystery of them all — and save Christmas!

“It’s nearly Christmas and something terrible has happened: one of Santa’s five helpers — Jo Ranger, Fred Metcalfe, Kip Urples, Meg Reeny, and Bob Luey — has stolen all the presents during the North Pole’s annual Sevenstival. You need to find the culprit before Christmas is ruined for everyone.”

If you solve all the clues and enter the answer on Christmas day, you may win a present for yourself, too.

Still More Mathy Fun

Colleen Young has collected several more holiday math calendars — enough to keep your kids playing and learning well into the New Year. Take a look!

“Peanuts Christmas Panorama” photo [top] by Kevin Dooley via Flicker. (CCBY2.0)

Playful Math Education Carnival 123: Hundred Chart Edition

Do you enjoy math? I hope so!

If not, browsing this post just may change your mind.

Welcome to the 123rd edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun.

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 $\left ( 1 + 2 + 3 \right )^{2} = 36 \:$ 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?

70+ Things To Do with a Hundred Chart

Do the holidays mess with your schedule? They sure do mine!

Every year, we get busy. Distracted. Just can’t focus on lessons.

I love easy activities that require minimal preparation so I can pull something out and play when we’re having one of those no-energy days.

If that sounds good to you, too, then you’ll want to check out my new ebook 70+ Things To Do with a Hundred Chart: Number, Shape, and Logic Activities from Preschool to Middle School.

Long years ago, when I did workshops at homeschooling conferences, I used to share a list of seven ways to play with a hundred chart. The all-time most visited post on my blog offers 34 playful activities. Now I’ve more than doubled that total for this book.

So many ways to play! One of them is sure to be perfect for you and your children.

Take your child on a mathematical adventure with these playful, practical activities.

Who knew math could be so much fun?

“It is exactly the kind of math exploration that I want to undertake with my kids.

“After reading through the book, I noticed myself making more room to trust my kids’ ability to make connections and not try to dominate by telling them how math ‘should’ work.

“An excellent way for me to move outside my math and teaching comfort zones and explore math more deeply with my kids.”

— Olisia Barron, author of ThimbleberryHome.wordpress.com

P.S.: If you have a blog and would like to host a giveaway for 70+ Things To Do with a Hundred Chart (or any of my other books), I’d be glad to provide the prize. Leave a comment below or use the contact form on my “About” page, and we’ll set up all the details.

Math Is Like a Nature Walk

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.

from a comment on the Living Math Forum

CREDITS: Background photo courtesy of Annie Spratt on Unsplash.

Play. Discuss. Notice. Wonder.

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.

Playing Complex Fractions with Your Kids

CREDITS: Background photo courtesy of Steve Shreve on Unsplash.

Math Journals for Elementary and Middle School

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 hope you enjoy them, too!

Math Journaling Prompts

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

Here are a few ideas:

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.

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?

Or Try Some Math Doodles

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

How Would YOU Use a Math Journal?

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