The ball is traveling around a shape that can’t exist in our real world: the Penrose triangle. This illusion is the basis for some cool art, like Escher’s Waterfall. And I’m using it in my Math You Can Play books as a design on the back of my playing cards:

Want to Play Around with the Penrose Triangle?

Here’s a few links so you can try it for yourself:

I’ve sent the first two Math You Can Play books to a copy editor (she edits the text part), so my focus this month is on finishing the illustrations and downloadable game boards. And designing the book covers — I think I’ll call this latest iteration done.

If everything stays on schedule, both Counting & Number Bonds and Addition & Subtraction should be available by mid- to late-spring. Fingers crossed…

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

Did you know that playing games is one of the Top 10 Ways To Improve Your Brain Fitness? So slip into your workout clothes and pump up those mental muscles with the Annual Mathematics Year Game Extravaganza!

For many years mathematicians, scientists, engineers and others interested in math have played “year games” via e-mail. We don’t always know whether it’s possible to write all the numbers from 1 to 100 using only the digits in the current year, but it’s fun to see how many you can find.

Use the digits in the year 2015 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.

You must use all four digits. You may not use any other numbers.

Solutions that keep the year digits in 2-0-1-5 order are preferred, but not required.

You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.

You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.

My Special Variations on the Rules

You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.

You MAY NOT use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. Math Forum allows these, but I’ve decided I prefer my arithmetic straight.

[Feature photo above by Jimmie, and “79” image (right) by Steve Bowbrick via flickr (CC BY 2.0).]

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

Welcome to the 79th edition of the Math Teachers At Play (MTaP) 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, game, or trivia tidbits. If you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Since I’ve been spending all my free time working on my upcoming Math You Can Play book series, I’m in the mood for games. So I found a few games featuring prime and nonprime numbers [which category is #79 — do you know?], and I’ll sprinkle some of my best-loved math game books throughout the carnival.

TRY THESE NUMBER GAMES

Students can explore prime and non-prime numbers with two free classroom favorites: The Factor Game (pdf lesson download) or Tax Collector. For $15-20 you can buy a downloadable file of the beautiful, colorful, mathematical board game Prime Climb. Or try the following game by retired Canadian math professor Jerry Ameis:

Math Concepts: multiples, factors, composites, and primes. Players: only two. Equipment: pair of 6-sided dice, 10 squares each of two different colors construction paper, and the game board (click the image to print it, or copy by hand).

On your turn, roll the dice and make a 2-digit number. Use one of your colored squares to mark a position on the game board. You can only mark one square per turn.

If your 2-digit number is prime, cover a PRIME square.

If any of the numbers showing are factors of your 2-digit number, cover one of them.

BUT if there’s no square available that matches your number, you lose your turn.

The first player to get three squares in a row (horizontal/vertical/diagonal) wins. Or for a harder challenge, try for four in a row.

And now, on to the main attraction: the blog posts. Many 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.

Have you ever heard of Math Storytelling Day? On September 25, people around the world celebrate mathematics by telling stories together. The stories can be real — like my story below — or fictional like the tale of Wizard Mathys from Fantasia and his crystal ball communication system.

My story begins with an unexpected adventure in pain. Appendicitis sidewhacked my life last week, but that’s not the story. It’s just the setting. During my recovery, I spent a lot of time in the smaller room of my hospital suite. I noticed this semi-random pattern in the floor tile, which made me wonder:

Did they choose the pattern to keep their customers from getting bored while they were … occupied?

Is the randomness real? Or can I find a line of symmetry or a set of tiles that repeat?

If I take pictures from enough different angles, could I transfer the whole floor to graph paper for further study?

And if the nurse finds me doing this, will she send me to a different ward of the hospital? Do hospitals have psychiatric wards, or is that only in the movies?

What is the biggest chunk of squares I could “break out” from this pattern that would create the illusion of a regular, repeating tessellation?

I gave up on the graph paper idea (for now) and printed the pictures to play with. By my definition, “broken” pattern chunks need to be contiguous along the sides of the tiles, like pentominoes. Also, the edge of the chunk must be a clean break along the mortar lines. The piece can zigzag all over the place, but it isn’t allowed to come back and touch itself anywhere, even at a corner. No holes allowed.

I’m counting the plain squares as the unit and each of the smaller rectangles as a half square. So far, the biggest chunk of repeating tiles I’ve managed to break out is 283 squares.

What Math Stories Will You Tell?

Have you and your children created any mathematical stories this year? I’d love to hear them! Please share your links in the comments section below.

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

Welcome to the 76th 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.

By tradition, we start the carnival with a puzzle in honor of our 76th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

PUZZLE: CRYSTAL BALL CONNECTION PATTERNS

In the land of Fantasia, where people communicate by crystal ball, Wizard Mathys has been placed in charge of keeping the crystal connections clean and clear. He decides to figure out how many different ways people might talk to each other, assuming there’s no such thing as a crystal conference call.

Mathys sketches a diagram of four Fantasian friends and their crystal balls. At the top, you can see all the possible connections, but no one is talking to anyone else because it’s naptime. Fantasians take their siesta very seriously. That’s one possible state of the 4-crystal system.

On the second line of the diagram, Joe (in the middle) wakes up from siesta and calls each of his friends in turn. Then the friends take turns calling each other, bringing the total number of possible connection-states up to seven.

Finally, Wizard Mathys imagines what would happen if one friend calls Joe at the same time as the other two are talking to each other. That’s the last line of the diagram: three more possible states. Therefore, the total number of conceivable communication configurations for a 4-crystal system is 10.

For some reason Mathys can’t figure out, mathematicians call the numbers that describe the connection pattern states in his crystal ball communication system Telephone numbers.

Can you help Wizard Mathys figure out the Telephone numbers for different numbers of people?
T(0) = ?
T(1) = ?
T(2) = ?
T(3) = ?
T(4) = 10 connection patterns (as above)
T(5) = ?
T(6) = ?
and so on.

Hint: Don’t forget to count the state of the system when no one is on the phone crystal ball.

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; I’ve drawn others from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, here’s a quick Table of Contents:

Update: The crowdfunding campaign is now closed and the book is in the final stages. It should be headed to the printer soon. Check the Playing With Math homepage for publication and ordering information.

There’s a problem: Most people don’t like math. Why is that? Perhaps it has something to do with the way math is taught in school. As a teacher to my own kids and mentor to homeschooling parents, I’ve been fighting math anxiety for decades.

This book is one part of the solution.

Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers features more than thirty authors who tell delightful stories of learning to appreciate math and of sharing their enthusiasm with their communities, families, or students. After every chapter is a puzzle, game, or activity to get you and your kids playing with math, too.

You can read a couple of excerpts at PlayingWithMath.org:

Whether you love math and want to share it with your kids, or whether you fear and loathe math and need help getting over that hurdle so you won’t pass your fear on, Playing With Math will encourage you to see math more deeply and play with it more freely.

I’ve been waiting for this book for years, and I’m thrilled to see it finally come together. As I read the advance copy (review coming soon!), I am amazed at how many different ways there are to think about math. Each writer has a new perspective and unique insight, and my quotes journal is filling up with inspiration.

A Word from the Editor

The idea of crowd-funding may be new to you. Here’s how it works:

Today is the first day of our crowd-funding campaign. For a contribution of $25, we’ll send you a book as soon as it’s printed.

You can contribute anything from $1 to $5000 (with rewards at each contribution level) to help us pay for our illustrators, editors, page layout person, and printing. This is our way of asking for community support for this book as part of the production process. We hope to build lots of energy around the ideas in the book through this campaign.

Besides contributing, here’s another way you can help: Think of five friends who would enjoy this book.

Do you have friends who get frustrated helping their kids with math homework?

Or who teach young kids but don’t feel comfortable with math themselves?

Do you have friends who enjoy math?

Or who want ideas to share with the kids in their lives?

Do you know someone who might want to start a math circle?

Would you send them a quick message, to let them know we’re here?

I’m hoping for the power of exponential growth with this. Our outrageous goal is to change the way people all over this country, and maybe even the world, think about math. If you each send this to five friends who might enjoy the book, and each of them sends it to five friends, and each of them … Well, pretty soon we cover the world, right?

In fact, if we kept it going through eleven steps, that would make 5 to the 11th power, or over 40 million people. Does Sue dream big? Yep.

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

This April, the creative people at Moebius Noodles are inviting parents, teachers, playgroup hosts, and math circle leaders to join an open online course about multiplication. My preschool-2nd grade homeschool math group is eager to start!

Each week there will be five activities to help kids learn multiplication by exploring patterns and structure, with adaptations for ages 2-12.

The course starts April 6 and runs for four weeks.

Preliminary Syllabus

Week 1: Introduction.
What is multiplication? Hidden dangers and precursors of math difficulties. From open play to patterns: make your own math. 60 ways to stay creative in math. Our mathematical worries and dreams.

Week 2: Inspired by calculus.
Tree fractals. Substitution fractals. Multiplication towers. Doubling and halving games. Zoom and powers of the Universe.

Week 3: Inspired by algebra.
Factorization diagrams. Mirror books and snowflakes. Combination and chimeras. Spirolaterals and Waldorf stars: drafting by the numbers. MathLexicon.

Week 4: Times tables.
Coloring the monster table. Scavenger hunt: multiplication models and intrinsic facts. Cuisenaire, Montessori, and other arrays. The hidden and exotic patterns. Healthy memorizing.

Sounds like lots of fun!

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

Do you like Pinterest? I’ve enjoyed exploring the site lately, so I set up a few boards where I can pin the goodies I find. It may take awhile before I get all the old games and posts from this blog loaded up, so save the links and come back often…

Playful Math Games & Activities

As our children (and their parents!) play around with mathematical ideas and the relationships between them, we develop deep understanding that is strong enough to support future learning. Playful math links include math games, activities, and interesting lesson plans.

Making abstract math visual: Math doodles let us see and experiment with a wide range of mathematical structures — and even to feel them, if we include hands-on 3D doodles in clay or other media. Links include art projects, geometry constructions, and physical models to explore.

A variety of math teaching ideas for homeschool families or classroom teachers. Learning mathematics is more than just answer-getting: help your students make conceptual connections. These links are more “schooly” than on the other boards, and they include conceptual lessons that build your own understanding of mathematics as well as that of your students. And math notebooking resources, too.

Since early 2009, the Math Teachers at Play (MTaP) blog carnival has offered tips, tidbits, games, and activities for students and teachers of preschool through pre-college mathematics. Now published once a month, the carnival welcomes entries from parents, students, teachers, homeschoolers, and just plain folks. If you like to learn new things and play around with ideas, you are sure to find something of interest.

And that’s the end of my Pinterest boards (so far).

What are some of your favorite Pinterest sites? Please share a link in the comments!

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

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

Welcome to the 70th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of 42+ 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 70th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

“This Advent Calendar has a new activity for each day in the run-up to Christmas. All the activities are based on the theme of Planet Earth.”

Secondary Advent Calendar

“Behind each door of the Advent Calendar is one of our favourite activities with videos. Watch and enjoy!”

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

Half of our students were missing from this month’s homeschool teen math circle, but I challenged the three who did show up to wrap their brains around some large numbers. Human intuition serves us well for the numbers we normally deal with from day to day, but it has a hard time with numbers outside our experience. We did a simple yet fascinating activity.

First, draw a line across a page of your notebook. Label one end of the line $20 (the amount of money I had in my purse), and mark the other end as $1 trillion (rough estimate of the US government’s yearly overspending, the annual deficit):

Where on that line do you think $1 million would be?

Go ahead, try it! The activity has a much greater impact when you really do it, rather than just reading. Don’t try to over-think this, just mark wherever it feels right to you.

The kids were NOT eager to commit themselves, but I waited in silence until everyone made a mark.

Okay, now, where do you think $1 billion would be?

This was a bit easier. Once they had committed to a place for a million, they went about that much farther down the line to mark a billion.

Happy 11/12/13, otherwise known as “tenty-one, tenty-two, tenty-three.”

Do your young children have trouble counting in the teens? Try making up Funny Numbers to help them! It’s a great habit to develop, because Funny Numbers will come in handy as mental math tools throughout their school math career.

If you’d like to make your own Happy Math Day post, check out the instructions here: Every Day Is Mathematics Day. And please share a link in the comments section below — I’d love to see what math holiday you invent!

In addition to the 115 puzzle patterns (as of this writing), the site features a Gallery page of patterns submitted by students. And under the “Teachers” tab, Fawn shares a form to guide students in thinking their way through to the algebraic formula for a pattern.

How can you use these patterns to develop algebraic thinking with younger students? Mike Lawler and sons demonstrate Pattern #1 in the YouTube video below.

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

(29)Blank 100 Grid Number Investigations: Challenge your students to deduce the secret behind each pattern of shaded squares. Then have them make up pattern puzzles of their own.
[Created by Stuart Kay. Free registration required to download pdf printable.]

Share Your Ideas

Can you think of anything else we might do with a hundred chart? Add your ideas in the Comments section below, and I’ll add the best ones to our master list.

This was a fun activity from Moebius Noodles for our PK-1st grade Homeschool Math in the Park group. The children take turns making a maze and setting a dinosaur inside. Then the other dinosaurs (parents or siblings) try to guess whether their friend is on the land or in the water.

Player #1

(1) First, draw a big circle on the white board. This is your lake.

(2) With a finger or a bit of cloth, erase a small section of the circle to create the opening for your maze.

(3) Starting at one edge of the opening, draw a random squiggle inside the circle. Make your squiggle end at the other edge of the opening.

(4) Set your dinosaur anywhere inside the maze.

Player #2

(1) Now it’s your turn to guess. Is the dinosaur standing on the land? Is it swimming in the water?

(2) How will you figure out if you guessed right?

(3) Check by jumping across the lines of the maze. Each jump takes you across a boundary: Splash! (Into the water.) Thump! (Back on the land.) Splash! Thump! … Until you reach the dinosaur inside.

(4) Or go to the maze entrance and walk your dinosaur along the path. Can you find your way?

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

Feature photo (above) by L. Marie. Math comic by davidd. Both via flickr (CC BY 2.0).

Hooray for September 25th — it’s Math Storytelling Day!

Celebrate Math Storytelling Day by making up and sharing math stories. Everyone loves a story, so this is a great way to motivate your children to play around with math. What might a math story involve? Patterns, logic, history, puzzles, relationships, fictional characters, … and yes, even numbers.

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest.

By tradition, we start the carnival with a couple of puzzles in honor of our 66th edition.

Let the mathematical fun begin!

Puzzle 1

Our first puzzle is based on one of my favorite playsheets from the Miquon Math workbook series. Fill each shape with an expression that equals the target number. Can you make some cool, creative math?

Click the image to download the pdf playsheet set: one page has the target number 66, and a second page is blank so you can set your own target number.

Gordon Hamilton of Math Pickle recently posted these videos on how to make algebra 1 puzzles on rectangles. As I was watching, Kitten came in and looked over my shoulder. She said, “Those look like fun!”

They look like fun to me, too, and I bet your beginning algebra students will enjoy them:

It reminds me of string art designs, but the app makes it easy to vary the pattern and see what happens.

What do your students notice about the patterns?

What questions can they ask?

I liked the way the app uses “minutes” as the unit that describes the star you want the program to draw. That makes it easier (for me, at least) to notice and understand the patterns, since minutes are a more familiar and intuitive unit than degrees, let alone radians.

Do you enjoy math? I hope so! If not, browsing this post just may change your mind. Welcome to the Math Teachers At Play blog carnival — a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college.

Let the mathematical fun begin!

POLYHEDRON PUZZLE

By tradition, we start the carnival with a puzzle in honor of our 62nd edition:

An Archimedean solid is a polyhedron made of two or more types of regular polygons meeting in identical vertices. A rhombicosidodecahedron (see image above) has 62 sides: triangles, squares, and pentagons.

How many of each shape does it take to make a rhombicosidodecahedron?

Click for template.

My math club students had fun with a Polyhedra Construction Kit. Here’s how to make your own:

Collect a bunch of empty cereal boxes. Cut the boxes open to make big sheets of cardboard.

Print out the template page (→) and laminate. Cut out each polygon shape, being sure to include the tabs on the sides.

Turn your cardboard brown-side-up and trace around the templates, making several copies of each polygon. I recommend 20 each of the pentagon and hexagon, 40 each of the triangle and square.

Draw the dark outline of each polygon with a ballpoint pen, pressing hard to score the cardboard so the tabs will bend easily.

Cut out the shapes, being careful around the tabs.

Use small rubber bands to connect the tabs. Each rubber band will hold two tabs together, forming one edge of a polyhedron.

So, for instance, it takes six squares and twelve rubber bands to make a cube. How many different polyhedra (plural of polyhedron) will you make?

Can you build a rhombicosidodecahedron?

And now, on to the main attraction: the 62 blog posts. Many of the following articles were submitted by their authors; others were drawn from the immense backlog in my blog reader. If you’d like to skip directly to your area of interest, here’s a quick Table of Contents:

Homeschoolers, after-schoolers, unschoolers, or anyone else: if you’re a parent with kids at home, you need this book. If you work with children in any way (grandparent, aunt/uncle, teacher, child care, baby sitter, etc.) you need this book. Or if you hated math in school and never understood how anyone could enjoy it, you need this book!

Moebius Noodles is a travel guide to the Math Universe for adventurous families (and it has lots of beautiful pictures, too!) featuring games and activities that draw out the rich, mathematical properties of everyday objects in ways accessible to parents and children:

A snowflake is an example of a fractal and an invitation to explore symmetry.

Cookies offer combinatorics and calculus games.

Paint chips come in beautiful gradients, and floor tiles form tessellations.

Welcome to the Math Teachers At Play blog carnival — a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college. If you like to learn new things and play around with ideas, you are sure to find something of interest.

Let the mathematical fun begin…

PUZZLE 1

By tradition, we start the carnival with a pair of puzzles in honor of our 58th edition. Click to download the pdf:

PUZZLE 2

A Smith number is an integer the sum of whose digits is equal to the sum of the digits in its prime factorization.

Got that? Well, 58 will help us to get a better grasp on that definition. Observe:

58 = 2 × 29

and

5 + 8 = 13
2 + 2 + 9 = 13

And that’s all there is to it! I suppose we might say that 58’s last name is Smith. [Nah! Better not.]

What is the only Smith number that’s less than 10?

There are four more two-digit Smith numbers. Can you find them?

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; others were drawn from the immense backlog in my Google Reader. Enjoy!

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

It’s always a challenge to keep up with homeschooling during the holiday season, but here’s a wonderful way to weave mathematics into your daily schedule: The Nrich Advent Calendars offer a fun math game or activity for every day in December until Christmas Eve. Click the image to visit the calendar that fits your student’s level.

Advent Calendar 2012 – Primary

Advent Calendar 2012 – Secondary

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

Tell Me a (Math) Story
What better way could there be to do math than snuggled up on a couch with your little one, or side by side at the sink while your middle-school student helps you wash the dishes, or passing the time on a car ride into town?

Homeschooling with Math Anxiety Series
Our childhood struggles with schoolwork gave most of us a warped view of mathematics. Yet even parents who suffer from math anxiety can learn to enjoy math with their children.

20 Best Math Games and Puzzles
Arithmetic games for elementary and middle school students, and geometric puzzles for middle and high school.

How to Conquer the Times Table
Challenge your student to a joint experiment in mental math. Over the next two months, without flashcards or memory drill, how many math facts can the two of you learn together? We will use the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible.

Sunday, October 21, is the worldwide hexaflexagon party in honor of Martin Gardner’s birthday. Gardner’s article about hexaflexagons launched his career as a recreational math guru who inspired people all around the world to love math.

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! We have games, lessons, and learning activities from preschool math to calculus. If you like to learn new things and play around with mathematical ideas, you are sure to find something of interest.

Scattered between all the math blog links, I’ve included highlights from the Common Core Standards for Mathematical Practice, which describe the types of expertise that teachers at all levels — whether in traditional, experimental, or home schools — should seek to develop in their math students.

Let the mathematical fun begin…

TRY THESE PUZZLES

By tradition, we start the carnival with a couple of puzzles in honor of our 52nd edition. Since there are 52 playing cards in a standard deck, I chose two card puzzles from the Maths Is Fun Card Puzzles page:

A blind-folded man is handed a deck of 52 cards and told that exactly 10 of these cards are facing up. How can he divide the cards into two piles (which may be of different sizes) with each pile having the same number of cards facing up?

What is the smallest number of cards you must take from a 52-card deck to be guaranteed at least one four-of-a-kind?

The answers are at Maths Is Fun, but don’t look there. Having someone give you the answer is no fun at all!