Prealgebra & Geometry Games Now Available

Publication Day!

Prealgebra & Geometry: Math Games for Middle School hits the online bookstores today.

Check Your Favorite Store

You can prepare your children for high school math by playing with positive and negative integers, number properties, mixed operations, algebraic functions, coordinate geometry, and more. Prealgebra & Geometry features 41 kid-tested games, offering a variety of challenges for students in 4–9th grades and beyond.

A true understanding of mathematics requires more than the ability to memorize procedures. This book helps your children learn to think mathematically, giving them a strong foundation for future learning.

And don’t worry if you’ve forgotten all the math you learned in school. I’ve included plenty of definitions and explanations throughout the book. It’s like having a painless math refresher course as you play.

Continue reading Prealgebra & Geometry Games Now Available

Playful Math Carnival 144: Anniversary Edition

Welcome to the 144th 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 would start the carnival with a puzzle/activity in honor of our 144th edition. But this time, I want to take a peek back at the history of our carnival.

But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Continue reading Playful Math Carnival 144: Anniversary Edition

FAQ: Playful Math for Older Students

My students are so busy that time-consuming math projects are a luxury. How is it possible for older kids to play with mathematics?

Too often, the modern American school math curriculum is a relentless treadmill driving students toward calculus. (Does this happen in other countries, too?)

But that’s definitely not the only way to learn. For most students, it’s not the best way, either.

Here are a few ideas to get your older children playing with math…

Continue reading FAQ: Playful Math for Older Students

The Gerrymander Math Project

With a big election on the horizon, now is a great time to talk about the math of politics.

Does “One person, one vote” make a fair democracy?

Or does it give the majority license to trample a minority?

How can planners arrange voting districts to give everyone the best representation? And is that really what politicians would do, if they had the choice?

Try the Gerrymander Project with your students to investigate these questions and spark real-world mathematical discussion.

First, Create a Map

[Or buy a copy of my printable activity guide, The Gerrymander Project: Math in the World of Politics, which includes a prepared city map with more detailed instructions, answers, and journaling prompts. My publisher has extended the 10% discount code TBLTOP10 through to Election Day, 3 November 2020.]

  • Print a blank hundred chart or outline a 10×10 square on grid paper. This represents your city. Give it a name.
  • Pull out your colored pencils. Choose one color for your city’s Majority Party and another for the Minority Party.
  • Color 10 squares in a neutral color for non-voting areas. These might be malls or parks or the downtown business district — your choice.
  • Color the remaining 90 blocks in a random distribution so that 60% are the Majority color and 40% the Minority. How will you choose which squares to make which colors? Can you think of a way to use dice or playing cards to make your choices random, yet still get the right proportion?

Slip your finished map into a clear page protector, so you can mark on it with dry-erase markers. Or make several copies, so you can write on them without destroying the original.

Then Gerrymander Your City

“Gerrymandering” is the American political tradition of adjusting the voting district boundaries to favor one’s own party at the expense of one’s opponents.

The city has hired you to mark out 10 new voting districts of 9 squares each (not counting the neutral squares, which can go in any district). The squares in each district must touch side-to-side, not just meet at a corner.

So now you get to play “political hack.”

First, see how fair you can make the map:

  • What happens if you ignore the party colors and make your districts as compact as possible, so the people living nearest to each other vote together? Will the Majority Party always win?
  • Can you give all your voters a proportional representation? Both parties should win the number of districts that most closely matches their percentage of the voting population.

Next, try your hand at gerrymandering, but make sure all the squares in each district stay connected. Can you create ten voting districts that will guarantee:

  • A come-from-behind triumph for the Minority Party? They need to carry at least six districts to wrest control of the City Council from their opponents.
  • The greatest possible margin of victory for the Majority Party? Can you keep the Minority from winning any districts at all?

Share Your Thoughts

I’d love to hear your students’ reaction to this project. Please share in the comments section below.

For myself, the more I play with this project, the more I admire the work done by the framers of the U.S. Constitution. Our Electoral College divides the country into “districts” based on state boundaries, giving each a vote roughly proportional to its population — but in a way that slightly strengthens the Minority Party. The system may not be perfect, but it’s done an amazing job through the centuries of maintaining a balance of power, making sure that neither major political party can destroy the other.

Which is NOT to say that our country always protects the rights of true minorities. Clearly, that’s an ongoing struggle.

But overall, the political parties stay relatively balanced, making for a stable government. After more than two centuries, we still have, as Ben Franklin said, “a republic, if you can keep it.”

FAQ: I’ve Ruined My Daughter

My daughter is only eleven, but I’m afraid I’ve ruined her chance of getting into college because she is so far behind in math. We’ve tried tutors, but she still has trouble, and standardized testing puts her three years below grade level. She was a late reader, too, so maybe school just isn’t her thing. What else can I do?

Standardized tests are not placement tests. They cannot tell you at what level your daughter should be studying. They aren’t designed that way. The “placement” they give is vague and general, not indicative of her grade level but rather a way of comparing her performance on that particular test with the performance of other students.

There can be many different reasons for a low score. I’ve listed a few of them in my post In Honor of the Standardized Testing Season.

Continue reading FAQ: I’ve Ruined My Daughter

Math Game: What Two Numbers?

Here’s a simple, conversational game you can play anywhere — no equipment necessary. It’s great for helping your children develop number fluency and algebraic thinking.

Excerpted from my upcoming book, Prealgebra & Geometry: Math Games for Middle School, scheduled for publication in early 2021. Sign up for my newsletter to get updates.

What Two Numbers?

Math Concepts: addition, multiplication, inverse operations, positive and negative numbers.

Players: two or more.

Equipment: no equipment needed.

Continue reading Math Game: What Two Numbers?

Math Game: War with Special Decks

The all-time most-visited page on this site is my post about Math War: The Game That Is Worth 1,000 Worksheets. It’s easy to adapt to almost any math topic, simple to learn, and quick to play. My homeschool co-op students love it.

But Math War isn’t just for elementary kids. Several teachers have shared special card decks to help middle and high school students practice math by playing games.

Take a look at the links below for games from prealgebra to high school trig. And try the Math War Trumps variation at the end of the post to boost your children’s strategic-thinking potential.

Have fun playing math with your kids!

Continue reading Math Game: War with Special Decks

Math for Star Wars Day

May the Fourth be with you!

Here is a math problem in honor of one of our family’s favorite movies…

Han Solo was doing much-needed maintenance on the Millennium Falcon. He spent 3/5 of his money upgrading the hyperspace motivator. He spent 3/4 of the remainder to install a new blaster cannon. If he spent 450 credits altogether, how much money did he have left?

Stop and think about how you would solve it before reading further.

Continue reading Math for Star Wars Day

Homeschooling Tip #1: Start with Play

For children, learning always begins with play. This is how they wrap their minds around new ideas and make them their own.

“There should be no element of slavery in learning. Enforced exercise does no harm to the body, but enforced learning will not stay in the mind. So avoid compulsion, and let your children’s lessons take the form of play.”

—Plato, The Republic

If we want our children to enjoy learning math, our first job is to establish an attitude of playfulness.

This is especially important for anyone working with a discouraged child or a child who is afraid of math. The best way to help a discouraged child is to put away the workbook. Try something different, fun, and challenging.

Continue reading Homeschooling Tip #1: Start with Play

How to Homeschool Math

Far too many people find themselves suddenly, unexpectedly homeschooling their children. This prompts me to consider what advice I might offer after more than three decades of teaching kids at home.

Through my decades of homeschooling five kids, we lived by two rules:

Do math. Do reading.

As long as we hit those two topics each day, I knew the kids would be fine. Do some sort of mathematical game or activity. Read something from that big stack of books we collected at the library.

Conquer the basics of math and reading, then everything else will fall into place.

Continue reading How to Homeschool Math