Playful Math on Kickstarter

Posted on by Denise Gaskins

Have you noticed that we live in a wonderful era of mathematical innovation? Not only at the “it’s all over my head” level — which is growing faster than anyone can keep up with — but also at the Cool Math For Kids level.

For instance, our children can enjoy Patterns of the Universe, and Prime Climb, and This is Not a Maths Book, and Which One Doesn’t Belong?, and Tiny Polka Dot, and Math & Magic in Wonderland, and Spiraling Pentagons, and …

So many things! I’m sure I forgot one (or several) of your favorite modern-classic math books or toys. I’d love to hear about them in the comments.

And here are a few bits of new playful math. Click, support, and share!

Math Renaissance

In alternating chapters, Rodi Steinig tells stories about her math circle and exactly what happens there, while her daughter Rachel discusses why so many kids hate math, documents the ways math is taught in the classroom — and ways that can be improved.

I first discovered Rodi’s work through her chapter in Sue VanHattum’s wonderful collection Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers. I’ve been a fan of Rodi’s math circle blog for years, and I can’t wait to get my hands on her new book.

Funville Adventures

When 9-year-old Emmy and her 5-year-old brother Leo go down an abandoned dilapidated slide, they are magically transported into Funville — a land inhabited by ordinary-looking beings, each with a unique power to transform objects.

I had the fun of previewing this book. It’s a cute little fairy tale that should help launch family conversations about math.

Trouble with Monkeys

A boy wants to surprise his dad, but meddlesome monkeys keep getting in the way. The boy is interviewed by the local news, and the story escalates to involve pirates, ballerinas, ninjas — and the magic of our place value number system.

Lucy Ravitch, math blogger and author of The Pancake Menu, teams up with artist Travis Hanson (one of my favorite comic bloggers) to create a story that will build number sense.

This story reminds me of the Cookie Factory Model for long division. Place Value is a key to understanding many things in math.

GregTangMath Home Kit

I haven’t seen these games in person, but they sure look like fun.

And Others?

If you know a project we should all check out, please share in the Comments section below.

Rabbit Trails and Fibonacci Poetry

Posted on by Denise Gaskins

Homeschool Memories…

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.

I knew what I was going to share at our Tuesday Teatime and Poetry Reading that afternoon.

Continue reading Rabbit Trails and Fibonacci Poetry

There Ain’t No Free Candy

Posted on by Denise Gaskins

Ah, the infinite chocolate bar. If only it could work in real life! But can your children find the mistake? Where does the extra chocolate come from?

Here’s a hint: It’s related to this classic brainteaser. And here’s a video from Christopher Danielson (talkingmathwithkids.com), showing how the chocolate bar dissection really works.

Happy munchings!

CREDITS: Feature photo (top) by Yoori Koo via Unsplash. “Hershey Bar Math” video by Christopher Danielson via YouTube. The infinite chocolate gif went viral long ago, and I have no idea who was the original artist.

Playful Math Education Carnival 106 with Math Art

Posted on by Denise Gaskins

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?

Click here for all the mathy goodness!

Dot Grid Doodling

Posted on by Denise Gaskins

What can you DO with a page full of dots?

Yesterday, I mentioned my new series of paperback dot grid notebooks, and I promised to share a few ideas for mathematical doodling.

But first, let me share my new dot-grid journals for kids. Aren’t they pretty?

Click Here for More Information

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.

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!
  • See if you can draw a rotational-symmetry design, like Don’s “Order 4” graphs.
  • Or experiment with the more flexible rules in John’s “Knot Fun” lesson.
  • And my latest obsession: the “ultimate” tutorial series on Celtic Knotwork, which explores the link between knots and their underlying graphs.
My favorite knot doodle so far.
Inspirations: A Recreational Mathematics Journal
Reflections: A Math Teacher’s Journal
Explorations: A Math Student’s Journal
Contemplations: A Homeschooler’s Journal

Before you start doodling: How to Break In Your New Math Journal.

Feature photo (top): Sommermorgen (Alte Holzbrücke in Pretzfeld) by Curt Herrmann, via Wikimedia Commons. [Public domain]

Confession: I Am Not Good at Math

Posted on by Denise Gaskins

I want to tell you a story. Everyone likes a story, right? But at the heart of my story lies a confession that I am afraid will shock many readers.

confessionPeople assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math.

Apply logic to that statement.

The conclusion simply isn’t valid.

Continue reading Confession: I Am Not Good at Math

My Favorite Math Games

Posted on by Denise Gaskins

Take a break from textbook math and enjoy yourself!

I like to use games as a warm-up with my co-op math classes. Some homeschoolers make every Friday a game day, and some turn gaming into a family lifestyle.

favorite-math-games

“Playing games with your kids offers a host of educational benefits, plus you build relationships and make memories. I am constantly amazed by the amount of learning that happens when I sit down to play games with my children.”

—Caitlin Fitzpatrick Curley
Gameschool Challenge

Family Games for All Ages

“Games put children in exactly the right frame of mind for learning difficult things. Children relax when they play — and they concentrate. They don’t mind repeating certain facts or procedures over and over, if repetition is part of the game.”

—Peggy Kaye
Games for Math

Accessible to Young Children

“Coming back from winter break can be hard. Everyone is sleepy, unfocused, and daydreaming of the holiday gifts that await them at home after school. And that’s just the teachers!”

—Andrew Gael
Beat the Back to School Blues…Play a Math Game

For Elementary Students

“If you play these games and your child learns only that hard mental effort can be fun, you will have taught something invaluable.”

—Peggy Kaye
Games for Math

Middle School to Adult

“Mathematics is mental play, the essence of creative problem solving. This is the truth we need to impart to our children, more important than fractions or decimals or even the times tables. Math is a game, playing with ideas.”

—Denise Gaskins
Let’s Play Math: How Families Can Learn Math Together—and Enjoy It

Your Turn: What Are Your Favorite Games?

They don’t have to be math! Please share in the comment section below!

 
* * *

This blog is reader-supported.

If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.

If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.

Which I am going to say right now. Thank you!

“My Favorite Math Games” copyright © 2017 by Denise Gaskins. Image at the top of the post copyright © Denise Gaskins.

2017 Mathematics Game

Posted on by Denise Gaskins

Two of the most popular New Year’s Resolutions are to spend more time with family and friends, and to get more exercise. The 2017 Mathematics Game is a prime opportunity to do both at once.

So grab a partner, slip into your workout clothes, and pump up those mental muscles!

For many years mathematicians, scientists, engineers and others interested in mathematics have played “year games” via e-mail and in newsgroups. We don’t always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find. This year may prove to be a challenge.

— Math Forum Year Game Site

Rules of the Game

Use the digits in the year 2017 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 2-0-1-7 order are preferred, but not required.
  • You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.
  • 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 use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. I’m including these because Math Forum allows them, but I personally try to avoid the beasts. I feel much more creative when I can wrangle a solution without invoking them.

Click here to continue reading.

New Hundred Chart Game: Jigsaw Gomoku

Posted on by Denise Gaskins

100chart

Counting all the fractional variations, my massive blog post 30+ Things to Do with a Hundred Chart now offers nearly forty ideas for playing around with numbers from preschool to prealgebra.

Here is the newest entry:

(34) The Number Puzzle Game: Rachel created this fun cross between the hundred-chart jigsaw puzzle (#7) and Gomoku (#23). You can download the free 120-board version here or buy the complete set at Teachers Pay Teachers.

 
* * *

This blog is reader-supported.

If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.

If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.

Which I am going to say right now. Thank you!

“New Hundred Chart Game: Jigsaw Gomoku” copyright © 2016 by Denise Gaskins. Image at the top of the post copyright © geishaboy500 (CC BY 2.0).

A New Graph-It Puzzle

Posted on by Denise Gaskins

Since I’ve been posting new Alexandria Jones stories this week (beginning here), I’ve gone back and re-read the old Christmas posts. I noticed that the original Graph-It Game included a religious design, but nothing for those who don’t celebrate Christmas.

So I updated the post with a new, non-religious puzzle. Here it is, if you want to play…

Graph-It Game Design

For this design, you will need graph paper with coordinates from −8 to +8 on both the x- and y-axis. Connect the points in each line. Stop at the periods, and then start a new line at the next point.

(-8,8) – (-8,0) – (0,8) – (-8,8) – (-4,4) – (0,4) – (0,8) – (8,8) – (4,4) – (0,8).

(8,8) – (8,0) – (4,0) – (4,-4) – (8,0) – (8,-8) – (0,-8) – (4,-4) – (0,-4) – (0,-8) – (-8,0) – (-8, -8) – (0,-8).

(-8,-8) – (4,4) – (0,4) – (4,0) – (4,4) – (8,0).

(8,-8) – (-4,4) – (-4,-4) – (0,-4) – (-4,0) – (-8,0).

(0,-2) – (0,-4) – (4,0) – (2,0) – (2,-2) – (-2,-2) – (-2,2) – (2,2) – (2,0) – (1,1) – (1,0) – (2,0) – (0,-2) – (-2,0) – (0,2) – (1,1) – (-1,1) – (-1,-1) – (1,-1) – (1,0) – (-4,0) – (0,4) – (0,-1) – (-1,0) – (0,1) – (1,0) – (0,-1) – (0,-2).

Color in your design and hang it up for the whole family to enjoy!

Now Make Your Own

Of course, the fun of the Graph-It Game is to make up your own graphing puzzle. Can you create a coordinate design for your friends to draw?

Want More?

You can see all the Alexandria Jones Christmas posts at a glance here:

CREDITS: “Love Christmas Lights” photo by Kristen Brasil via Flickr (CC BY 2.0).