Math Game Monday: The Partitions Game

Posted on by Denise Gaskins
Learn a new game with Math Game Monday

This game features the Cuisenaire rods, but you may play with any math manipulative based on length: Montessori bead chains, Mortensen or Math-U-See blocks, etc. Or draw pictures on graph paper.

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.

The Partitions Game

Math Concepts: partitions, part/whole, addition, multiplication, algebra.

Players: two or more.

Equipment: Cuisenaire rods (or other math manipulatives) or graph paper, pencil and paper (optional).

Continue reading Math Game Monday: The Partitions Game

Ostomachion: Divide the Square

Posted on by Denise Gaskins
archimedes, studying

“Puzzles are made of the things that the mathematician, no less than the child, plays with, and dreams and wonders about, for they are made of things and circumstances of the world he [or she] lives in.”

—Edward Kasner

Long ages ago, one of the greatest mathematicians of all time played with a children’s puzzle.

The puzzle was called “The Ivory Challenge”—or something like that, translations vary. Ostomachion in Greek. Fourteen ivory polygons (flat shapes with straight sides) were supposed to fit into a square box.

Archimedes solved that puzzle. But like any good mathematician, he didn’t stop there. The solution to any puzzle is only the beginning, a doorway to further adventures.

So Archimedes asked himself one of the big questions of mathematics: “How many ways?”

The Ostomachion is a rather complex puzzle, and our students may struggle to figure out where to start. One of the classic tools in any mathematician’s toolbox is to make it simpler. So let’s begin our own investigation with a simpler challenge:

  • How many ways can you bisect a square?

Continue reading Ostomachion: Divide the Square

Make Your Own Nim Games

Posted on by Denise Gaskins
tower of rocks on a beach

Nim is a pure strategy game for two players. On each turn, players remove an option until finally no choice remains.

Game options might include:

  • How many stones to take from a pile.
  • Which position to claim on a gameboard.
  • How far to count in a given sequence.

The rules can vary at the players’ whim (as long as both players agree). How many possibilities do you start with, what are the rules for removing options, and how do you win or lose the game? Everything is open to change. And with every tweak, players must reanalyze their strategy.

Continue reading Make Your Own Nim Games

2026 Mathematics Game

Posted on by Denise Gaskins
2026 annual math game

Now that we’re a few months into the year, many of our New Near’s resolutions have probably fallen by the wayside. It’s inevitable, according to Mark Twain, that we shall “cast our reformation to the winds and go to cutting our ancient shortcomings considerably shorter than ever.”

But there is one resolution that I enjoy keeping—the resolve to play more math.

My favorite way to celebrate at any time of the year is by playing the Year Game. It’s a prime opportunity for players of all ages to fulfill the two most popular resolutions: spending more time with family and friends, and getting more exercise.

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

Continue reading 2026 Mathematics Game

Playful Math 184: Carnival of Living Math

Posted on by Denise Gaskins
Playful Math Carnival 184

Welcome to the 184th 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.

With all the links, a blog carnival can feel overwhelming. Bookmark this article, so you can take your time reading the posts.

“Living math” means bringing our children face-to-face with the big ideas of mathematics to help them develop their reasoning skills. When the ideas of math come to life for our children, their minds delight in seeing how numbers and shapes connect to each other and exploring these relationships.

Scattered between the playful math links below, you’ll find quotations from my new book Charlotte Mason’s Living Math, along with several paintings of children playing and learning which I considered for the book but ran out of room.

“The lesson” by Rafael Frederico, 1895.

By tradition, we start the carnival with a puzzle/activity in honor of our 184th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Continue reading Playful Math 184: Carnival of Living Math

Mental Math: Do’s and Don’ts

Posted on by Denise Gaskins
Father and son working on math homework

Over the course of this series, we’ve seen how mental math relies on a child’s own creative ways of thinking. In mental math, children develop understanding of how numbers interact with each other in many ways.

In this way, they learn the true 3R’s of math: to Recognize and Reason about the Relationships between numbers.

And the principles that underlie mental calculation are also fundamental to algebra, so that flexibility and confidence in mental math is one of the best predictors of success in high school math and beyond.

But as we went through the various example problems, did you find the written-out calculations hard to follow?

Don’t force your children to write down their mental math. It looks dreary when I write the calculations out step by step, but that’s not how it works in a child’s mind. With regular practice, this sort of thinking becomes second nature.

Continue reading Mental Math: Do’s and Don’ts

FAQ: Playful Math Journaling

Posted on by Denise Gaskins
Girl student thinking about her math journal prompt

Ever since the school year started, I’ve been getting questions about how to use my new Math Journaling Adventures logbooks.

[SIDE NOTE: These logbooks are included in this month’s Thanksgiving Sale! You’ll get an automatic 10% discount off all print books, applied at checkout, no special code required.]

“I love the way your math books get my children thinking.

    “Finally, they are having fun with math!

      “But sometimes I have no idea what the journaling prompt is all about or how to teach it. Where can I buy a solutions manual?”

      Um, that’s not how math journals work.

      The cool thing about journaling prompts is that they have no “right” answer. They are explorations into different parts of the world of math, nature walks in the land of numbers, shapes, and patterns. Springboards into whatever our children want to investigate, whatever sparks their interest.

      A few of the problem-solving prompts may have specific answers, but it really doesn’t matter if our kids find the exact solution a math professional might give. If they write what makes sense to them, they’ve accomplished the goal.

      If later, they think of something they hadn’t noticed, or they want to change their answer — well, that is mathematical thinking, too.

      Continue reading FAQ: Playful Math Journaling

      Fun New Math Story

      Posted on by Denise Gaskins
      Characters from Modultown math story

      Hey, look! A new book from the folks at Natural Math, now on Kickstarter:

      Modultown! A Math-Inspired Children’s Book

      Experience a whimsical puzzle hunt in a new fantastic world full of friendship and surprises, from the authors of Funville Adventures.

      When human siblings Emmy and Leo find themselves magically transported to Modultown, they make new friends and combine their different perspectives to solve challenges that flesh out the mechanics of modular arithmetic.

      Playing in Modultown unlocks pathways into number theory, computer science, genetics, and other essential modern fields.

      Continue reading Fun New Math Story

      Two Hands-On Craft Projects

      Posted on by Denise Gaskins
      photo: Cutting a paper square

      Here are a couple of fun foldable projects to try with your kids.

      Both of the projects below start with squares of paper. Do you know how to convert any piece of paper into a square? Here are two methods.

      • Can you tell why they work, how each method creates a true square?
      • What if you didn’t have a rectangular page to start with — could you still create a square?

      Continue reading Two Hands-On Craft Projects