## Updated Geometric Coloring Designs (Free)

I created these coloring pages for my homeschool co-op math kids, and then collected them into a downloadable 42-page PDF coloring book for your family to enjoy.

The booklet includes several ready-to-color designs, a wide assortment of graph paper, advanced create-your-own tessellation pages, and links to all sorts of online math art resources.

But when I posted the link to Twitter, a friend noticed that several of the resource links were broken. (Thanks, Mark!)

While I was fixing those, I added some new links (to the wonderful School of Islamic Geometric Design pattern templates and classroom resources).

So even if you’ve downloaded the file before, you may want to pick up this new-and-improved edition.

## 8 Weeks of Playful Math for Families

Yes, your kids CAN learn to love math. Keep your children’s math skills fresh with my 8-week email series of math games and activities.

No purchase necessary! Just sign up for my email newsletter, and every week for the next two months you’ll automatically receive one of my favorite math club activities or an excerpt from my series of math game books.

Plus you’ll get a free download of my 24-page booklet How To Solve Math Problems: A Common-Sense Approach. And I’ll send you occasional news updates with playful math tips, resource links, and book sales or other promotions.

Don’t like email? Then check out my new Let’s Play Math Sampler: 10 Family-Favorite Games for Learning Math Through Play. For the price of a cup of coffee, it’s a great way to get started with playful math.

PHOTO CREDITS: “The smiling sisters” photo by Caroline Hernandez and “Puddle Jumping” by Rupert Britton via Unsplash.com.

## Math Activity: Polite Numbers

Did you know that numbers can be polite? In math, a polite number is any number we can write as the sum of two or more consecutive positive whole numbers.

(Consecutive means numbers that come one right after another in the counting sequence.)

For example, five is a polite number, because we can write it as the sum of two consecutive numbers:
5 = 2 + 3

Nine is a doubly polite number, because we can write it two ways:
9 = 4 + 5
9 = 2 + 3 + 4

And fifteen is an amazingly polite number. We can write fifteen as the sum of consecutive numbers in three ways:
15 = 7 + 8
15 = 4 + 5 + 6
15 = 1 + 2 + 3 + 4 + 5

How many other polite numbers can you find?

### What Do You Notice?

Are all numbers polite?

Or can you find an impolite number?

Can you make a collection of polite and impolite numbers? Find as many as you can.

How many different ways can you write each polite number as a sum of consecutive numbers?

What do you notice about your collection of polite and impolite numbers?

Can you think of a way to organize your collection so you can look for patterns?

### What Do You Wonder?

Make a conjecture about polite or impolite numbers. A conjecture is a statement that you think might be true.

For example, you might make a conjecture that “All odd numbers are…” — How would you finish that sentence?

Make another conjecture.

And another.

Can you make at least five conjectures about polite and impolite numbers?

Can you think of any way to test your conjectures, to know whether they will always be true or not?

### Real Life Math Is Social

This is how mathematics works. Mathematicians play with numbers, shapes, or ideas and explore how those relate to other ideas.

After collecting a set of interesting things, they think about ways to organize them, so they can look for patterns and connections. They make conjectures and try to imagine ways to test them.

And mathematicians compare their ideas with each other. In real life, math is a very social game.

So play with polite and impolite numbers. Compare your conjectures with a friend.

And check out the list of student conjectures at the Ramblings of a Math Mom blog.

CREDITS: Numbers photo (top) by James Cridland via Flickr (CC BY 2.0). I first saw this activity at Dave Marain’s Math Notations blog, and it’s also available as a cute printable Nrich poster. For a detailed analysis, check out Wai Yan Pong’s “Sums of Consecutive Integers” article.

## Holiday Math Puzzles and Activities for Christmas, Winter Break

Do you know of any great math-related seasonal games, crafts, or activities I missed? Please add them to the comments section below.

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. 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.

Every year, 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.

### LET IT SNOW! LET IT SNOW! LET IT SNOW!

• Clarissa (@c0mplexnumber) demonstrates how to make beautiful, challenging origami snowflakes. She recommends beginners try the first few folds — which create a pretty cool design on their own. Let it Snow…

### PUZZLES UNDER THE TREE

• Unfortunately, the holidays come smack in the middle of flu season. Did you come down with The Grinch Bug?
• Speaking of Christmas carols, the Christmas Price Index shows the current cost for one set of each of the gifts given in the song “The Twelve Days of Christmas.” I wonder what’s the cumulative cost of all the gifts, when you count each repetition in the song?

### CHRISTMAS ADVENTURES WITH ALEXANDRIA JONES

Alexandria Jones and her family are fictional characters from my old Mathematical Adventures newsletter. Their stories appear sporadically as I find time to transcribe them from the back-issues. You can find them all on this blog page.

Here are all the Alexandria Jones stories Christmas stories, with activity and craft ideas…

Do you need to keep your kids busy and work in a bit of math practice? Try these Christmas word problems:

Or visit the sites below for worksheets to cover all ages:

CREDITS: “Circle Packing” feature graphic (top) by fdecomite via Flickr (CC BY 2.0). Picture pattern puzzles from Visual Patterns website.

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!

CREDITS: “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?