## Math Game Monday: Michigan (Boodle)

“Michigan (Boodle)” is free on this website for one week only. It’s an excerpt from Math You Can Play Combo: Number Games for Young Learners, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. Read more about my playful math books here.

Many parents remember struggling to learn math. We hope to provide a better experience for our children.

And one of the best ways for children to enjoy learning is through hands-on play.

This game reinforces numerical order and helps children get acquainted with a standard deck of playing cards. But mostly, it’s just plain family fun!

## Michigan (Boodle)

Math Concepts: numerical order, sorting by attribute (card suits), standard rank of playing cards (aces high), thinking ahead.

Players: three or more, up to as many as fit around your table.

Equipment: one complete deck of cards (including face cards), plus four boodle cards from a second deck; small prizes to go on the boodle cards. Provide a card holder for young children.

## Math Game Monday: Wythoff’s Nim

“Wythoff’s Nim” is free on this website for one week only. It’s an excerpt from 312 Things To Do with a Math Journal, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. Read more about my playful math books here.

Many parents remember struggling to learn math. We hope to provide a better experience for our children.

And one of the best ways for children to enjoy learning is through hands-on play.

Use this strategy game to prompt math writing: What did your children notice about the game? How did they decide their moves? How is this a Nim game?

## Wythoff’s Nim

Math Concepts: chess moves, strategic thinking.

Players: only two.

Equipment: chess set or graph paper.

## Celebrating Math with Pi Day

Are your students doing anything special for Pi Day?

Back when we were homeschooling, my kids and I always felt stir-crazy after two months with no significant break. We needed a day off — and what better way could we spend it than to play math all afternoon?

I love any excuse to celebrate math!

Pi Day is March 14. If you write dates in the month/date format, then 3/14 at 1:59 is about as close as the calendar can get to 3.14159etc.

(Otherwise, you can celebrate Pi Approximation Day on July 22, or 22/7.)

Unfortunately, most of the activities on teacher blogs and Pinterest focus on the pi/pie wordplay or on memorizing the digits. With a bit of digging, however, I found a few puzzles that let us sink our metaphorical teeth into real mathematical meat.

### What’s the Big Deal? Why Pi?

In math, symmetry is beautiful, and the most completely symmetric object in the (Euclidean) mathematical plane is the circle. No matter how you turn it, expand it, or shrink it, the circle remains essentially the same.

Every circle you can imagine is the exact image of every other circle there is.

This is not true of other shapes. A rectangle may be short or tall. An ellipse may be fat or slim. A triangle may be squat, or stand upright, or lean off at a drunken angle. But circles are all the same, except for magnification. A circle three inches across is a perfect, point-for-point copy of a circle three miles across, or three millimeters.

What makes a circle so special and beautiful? Any child will tell you, what makes a circle is its roundness. Perfectly smooth and plump, but not too fat.

The definition of a circle is “all the points at a certain distance from the center.” Can you see why this definition forces absolute symmetry, with no pointy sides or bumped-out curves?

One way to express that perfect roundness in numbers is to compare it to the distance across. How many times would you have to walk back and forth across the middle of the circle to make the same distance as one trip around?

The ratio is the same for every circle, no matter which direction you walk.

That’s pi!

### Puzzles with Pi

For all ages:

Sarah Carter created this fun variation on the classic Four 4s puzzle for Pi Day:

Using only the digits 3, 1, 4 once in each calculation, how many numbers can you make?

You can use any math you know: add, subtract, multiply, square roots, factorials, etc. You can concatenate the digits, putting them together to make a two-digit or three-digit number.

For older students:

1. Imagine the Earth as a perfect sphere with a long rope tightly wrapped around the equator. Then increase the length of the rope by 10 feet, and magically lift it off the Earth to float above the equator. Will an ant be able to squeeze under the rope without touching it? What about a cat? A person?

2. If you ride a bicycle over a puddle of water, the wheels will leave wet marks on the road. Obviously, each wheel leaves a periodic pattern. How the two patterns are related? Do they overlap? Does their relative position depend on the length of the puddle? The bicycle? The size of the wheels?

3. Draw a semicircle. Along its diameter draw smaller semicircles (not necessarily the same size) that touch each other. Because there are no spaces in between, the sum of the diameters of the small semicircles must equal the diameter of the large one. What about their perimeter, the sum of their arc lengths?

4. Choose any smallish number N. How can you cut a circular shape into N parts of equal area with lines of equal lengths, using only a straight-edge and compass? Hint: The lines don’t have to be straight.

[Solutions at Alexander Bogomolny’s Pi Page. Scroll down to “Extras.”]

It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.

— Edward Titchmarsh

Here are a few pi-related links you may find interesting:

Or for pure silliness:

Have fun playing math with your kids!

## Playful Math Education 162: The Math Games Carnival

Welcome to the 162nd edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

Bookmark this post, so you can take your time browsing.

There’s so much playful math to enjoy!

By tradition, we start the carnival with a puzzle/activity in honor of our 162nd edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

## Try This Puzzle/Activity

The number 162 is a palindromic product:

162 = 3 x 3 x 2 x 3 x 3
and 162 = 9 x 2 x 9

• How would you define palindromic products?
• What other numbers can you find that are palindromic products?
• What do you notice about palindromic products?
• What questions can you ask?

Make a conjecture about palindromic products. (A conjecture is a statement you think might be true.)

Make another conjecture. How many can you make? Can you think of a way to investigate whether your conjectures are true or false?

## New Project: The Tabletop Math Games Collection

Coming Soon! On January 30th, I’ll be launching a brand new book series, the Tabletop Math Games Collection.

And the Kickstarter prelaunch page is now live. That means you can sign up to get an email from Kickstarter as soon as the campaign launches:

(free Kickstarter account required)

### Test Out 4 Free Sample Games

Math games build mental flexibility and strategic reasoning in players of all ages. And even people who hated math in school can enjoy the friendly challenge of a game.

I’ve put together a free printable sampler file, with four ready-to-play card games you can enjoy today.

I think you’ll love it!

• Or a teacher looking for ways to encourage creative thinking?
• Or a gamer ready to try something new with your friends?

Then the Tabletop Math Games Collection is perfect for you.

These are NOT the typical memory-and-speed-based math games you’ve probably seen online, but true battles of wit and skill (plus a bit of luck). Even the preschool games can be fun for adults, too.

Most of the games take only seconds to learn and less than 15 minutes to play, making them perfect ice-breakers for family gatherings, classroom warmups, or for launching a group game night.

Don’t miss the fun!

## The Colors-of-Fall Carnival: Playful Math #160

Welcome to the 160th edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

Bookmark this post, so you can take your time browsing.

There’s so much playful math to enjoy!

By tradition, we start the carnival with a puzzle/activity in honor of our 160th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

## Try This Puzzle/Activity

Appropriately for an October carnival, 160 is an evil number.

A number is evil if it has an even number of ones in binary form. Can you find the binary version of 160? (Hint: Exploding Dots.)

160 is also a polyiamond number. If you connect 9 equilateral triangles side-to-side, a complete set of 9-iamond shapes would have 160 pieces.

But sets that large can be overwhelming. Try playing with smaller sets of polyiamonds. Download some triangle-dot graph paper and see how many different polyiamond shapes you can make.

What do you notice? Does it make you wonder?

What designs can you create with your polyiamonds?

Photo by Daiga Ellaby on Unsplash

## Get a Weekly Dose of Playful Math

Our leaves haven’t started to turn yet, but summer’s on the wane, farmers are busy with harvest, and the back-to-school rush has calmed down into a daily routine.

But if you’re like me, you keep tweaking that routine, constantly looking for the perfect balance for your family or classroom. I especially love to discover easy ways to add more playful math to our schedule.

So here’s a collection of sites that offer fresh math resources on a weekly or monthly basis throughout the school year.

Which one will you try?

### KenKen Classroom

Every week, they’ll email you a set of free KenKen arithmetic puzzles for all ages. As the challenge level subtly shifts week to week, students develop their math and logical thinking skills without even knowing it.

### #MathStratChat

Pose an interesting math problem. How can you figure it out? What else could you do? How many different ways can you find? Which strategy do you like best for this problem?

Follow Pam Harris on your favorite social media site to get a new problem every Wednesday.

### The Parallel Universe

Dr Simon Singh, author of the No. 1 bestseller Fermat’s Last Theorem and The Simpsons and Their Mathematical Secrets has created a set of weekly maths challenges – just 15-30 minutes of interesting, fun and challenging tidbits of mystery and history, activities and oddities, puzzles and problems.

Help students expand their mathematical horizons beyond the school curriculum and build strong mathematical thinking skills. Stretch your brain every week!

## Playful Math: Getting Students To Write Their Own

To wrap up our week of exploring the resources from Word Problems from Literature, let’s talk about getting students to write their own math.

First up, I’m sharing an excerpt from the Word Problems Student Workbook. The “Story Problem Challenge” is one of my favorite math club activities.

Following that, you’ll find an amazing online mathemagical adventure for middle school: The Arithmetiquities. It’s great fun, and a great inspiration for students to create their own math stories.

Have fun writing math with your kids!

### The Story Problem Challenge

What do you get when you cross a library book or favorite movie with a math worksheet? A great alternative to math homework!

The rules are simple:

(1) Choose a worksheet calculation to be the basis for your word problem.

(2) Solve the calculation.

(3) Consider where these numbers could make sense in your book or movie universe. How might the characters use math? What sort of things would they count or measure? Do they use money? Do they build things, or cook meals, or make crafts? Do they need to keep track of how far they have traveled? Or how long it takes to get there?

To make the game easier, you may change the numbers to make a more realistic problem. But you must keep the same type of calculation. For example, if your worksheet problem was 18÷3, you could change it to 18÷6 or 24÷3 or even 119÷17 to fit your story, but you can’t make it something like 18−3.

Remember that some quantities are discrete and countable, such as hobbits and fireworks. Other quantities are continuous, such as a barrel of wine or a length of fabric. Be sure to consider both types when you are deciding what to use in your problem.

Then share your problem with friends, and you try their problems. Can you stump each other?

Old books are in the public domain, so you can always use characters like Robin Hood, Sherlock Holmes, or Winnie-the-Pooh (but not the newer Disney version with the red jacket). But most books and movies are the protected intellectual property of their authors or estates, or of the company who bought those rights.

When you write problems for your own private use, feel free to use your favorite characters from any story. That’s like fan fiction, secret, just for your own pleasure.

But if you decide to share your creation beyond your own home or classroom, then be sure to “genericize” it first. Change or remove the proper names, using general descriptions instead.

For example, if you love the Harry Potter series, you might want to use Harry or Hermione in your story problems. Instead, write about “the boy wizard destined to fight an evil sorcerer.” Or “the bright young witch who can master any spell.”

Or if you like the Star Wars movies, you might write about “an interstellar justice warrior with an energy sword.” Or “an alien master of martial arts training a cocky but inexperienced apprentice.”

We’d love to add your story to the Student Math Makers Gallery.

### The Arithmetiquities

When the world of Sfera is threatened by the machinations of a malevolent sorcerer, it will be up to a band of unlikely heroes to become the brightest light in the darkness.

The adventurers fan out across the land to find and retrieve the Arithmetiquities, a set of ancient mathemagical artifacts.

The Arithmetiquities is a fantasy adventure story told through a sequence of 36 mathematical puzzles.

“Though it is still before sunrise, Lumparland Harbor is already bustling. Sailing ships moor at the misty docks, bringing travelers and goods to the seaside town. Three dwarves disembark from different ships, each adventurer returning home from some faraway locale. The three women gather at the end of the pier.

“The strangers discover that they all live along the main road that leads from the harbor, so they decide to split the cost of a wagon. Egga lives 10 miles away, Floora lives 20 miles away, and Greeta lives 30 miles away. The wagon ride costs \$1.50 per mile regardless of the number of passengers.

“How much should each of the adventurers pay so that each one has a fair fare?”

—Jason Ermer, “Lumparland Harbor,” The Arithmetiquities Chapter I

CREDITS: Feature photo (top) by Hannah Olinger via Unsplash.com.

## How To Make Time for Exploration

Perhaps the most common objection I hear to using math games and enrichment activities is, “I don’t have the time. I can’t even get through our regular math book!”

Well, here’s one possible solution: Use a “Minimalist Math” outline to guide your instruction, turning your regular textbook into a backup resource, teaching only the topics your children don’t already know, leaving more time free for exploration and playful discovery.

### Minimalist Math: Getting Down to Basics

Michelle at ResearchParent.com condensed the elementary math curriculum down to 360 problems per year, just 10 per week.

Take just a few puzzles each day, and talk math with your kids:

• What do they notice in the problem?
• Does it remind them of anything?
• How might they try to figure it out?
• Does it make them wonder about numbers, shapes, or patterns?

Use colorful markers on a whiteboard for low-stress exploration. If your children can solve a problem and explain their reasoning, you don’t need to study that topic. When they get stuck, ask leading questions to help them think it through.

If you’re both stymied, that’s when you pull out your regular textbook (or look the topic up online).

### Practice with Games

Of course, children still need plenty of practice to master the math facts and solidify their knowledge.

Since you’re not spending as much time on lessons and homework, you can plan on playing lots of math games. Games are a fun, low-stress way to firm up math skills.

Check out My Best (Free) Math Games for All Ages, and follow the Math Game Monday posts on my blog.

To enrich your child’s mind with the great ideas of mathematics and whet their appetite for learning, nothing beats a “living” math book.

A living book is one that brings our minds into direct contact with the great ideas of life.

Check out my Math with Living Books lists to get started, and ask your librarian for more suggestions.

### For Older Students

Michelle’s Minimalist Math Curriculum goes through 6th grade (so far). But you could use the Corbettmaths 5-a-Day problems in the same way for older students.

And for enrichment activities to fill up your free math time, I can’t think of a better resource for all ages than the NrichMaths website.

“When I first started homeschooling, math became the most overwhelming, unpleasant part of our day. As someone who loves math, I didn’t want to continue on a path that was leading to such bad attitudes.

“My Minimalist Math Curriculum covers the same breadth of topics as a traditional curriculum without all the repetition. You are welcome to use what I created in whatever way serves your family.”

Michelle, Research Parent
Mathematics Activities for Kids

CREDITS: Photos by Aron Visuals, Andrew Ebrahim, and Melissa Askew via Unsplash.com.

## New to Playful Math? Start Here

Do you want your children to enjoy learning math? Teach them how to play!

After the troubles of recent years, it’s even more important for families to play together. So I’ve made the ebook version of Let’s Play Math Sampler: 10 Family-Favorite Games for Learning Math Through Play permanently free.

What a great way to introduce your child to the joy of learning!

With excerpts taken from my most popular books, the Let’s Play Math Sampler features ten kid-tested games covering math concepts from counting to prealgebra.

Pick up a copy today, and make math a playful family adventure.

… or request a copy from your library or local bookshop.

“Math is so many things — beauty, structure, problem solving, communication, language, creativity — but here’s what I’ve learned as I’ve tried to help my children develop positive relationships with math: It All Begins With Play. Anything by Denise Gaskins is a fantastic place to start. These books are filled with the perfect combination of perspective and practicality.”

—Michele Johnson, Instagram post