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!

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FAQ: Remembering What We Learn

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

“When we do our daily lessons, my son does great. Everything seems to click. But when he sees the same topic later, in a review or on a test, it’s like he’s never heard of it before. How can I help him pull math up from the dregs of lost memory?”

This is a common problem, and there’s no easy answer.

You see, it’s easy for humans to convince ourselves we understand something when someone else explains it. It seems to make sense, but it doesn’t stick in our minds.

If you think of times when you’ve tried to learn something new, you can probably remember the feeling—you thought you had it, but then when you tried to do it yourself, your mind went blank.

So how can we help our kids when they can’t remember what to do?

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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.

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Math Prompt: True-False-True

Posted on by Denise Gaskins
girl writing in a notebook, sitting on couch with her corgi

Book, Charlotte Mason's Living MathOne of the stretch goals for my Charlotte Mason’s Living Math Kickstarter campaign is to add a math journaling prompt to the end of each chapter. So, I’ve been playing around with ideas to get readers writing.

Since the book’s all about how to build mathematical reasoning, I’m looking for ways to prompt creative thinking and flexibility in math calculations.

Check Out the Kickstarter

I found some fun ideas in Guy Gattegno and Martin Hoffman’s Handbook of Activities for the Teaching of Mathematics (which you can download here), including the following riff off a puzzle created by Lewis Carroll.

Continue reading Math Prompt: True-False-True

Coming Soon: Charlotte Mason’s Living Math

Posted on by Denise Gaskins
Charlotte Mason's Living Math Kickstarter

Coming Soon! In March, I’ll be launching my newest book, Charlotte Mason’s Living Math: How to Apply the Principles of Education to Help Children Develop Mathematical Reasoning.

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:

Visit the Prelaunch Page ❯

(If you back the campaign on launch day, that encourages the Kickstarter folks to share it with more people.)

Continue reading Coming Soon: Charlotte Mason’s Living Math

Mental Math: Advanced Division

Posted on by Denise Gaskins
Father and daughter working mental math

The farther we go in math, the more division disappears. It ceases to exist as a separate concept.

Instead, we learn to see division as:

  • an inverse multiplication
  • a fraction (ratio)
  • a proportional relationship

Each of these perspectives offers us a new way to think about and make sense of our calculations.

Continue reading Mental Math: Advanced Division

Mental Math: Advanced Multiplication, Part 2

Posted on by Denise Gaskins
Father and son celebrate a mental math answer

The methods in last week’s Advanced Multiplication post only work for certain numbers, but we have another, more powerful multiplication tool: We can always use a ratio table to make sense of any multiplication.

Ratios are the beginning of proportional thinking. We can systematically alter the numbers in a ratio to reach any quantity required by our problem.

Students begin working with ratios in story problems that help them visualize and make sense of a proportional relationship.

Continue reading Mental Math: Advanced Multiplication, Part 2

Mental Math: Advanced Multiplication, Part 1

Posted on by Denise Gaskins
Mother and daughter working mental math together

Mental math is the key to algebra because the same principles underlie them both.

As our children learn to do calculations in their heads, they make sense of how numbers work together and build a strong foundation of understanding.

Remember that while mental math is always done WITH the mind, reasoning our way to the answer, it doesn’t have to be only IN the mind. Make sure your students have scratch paper or a whiteboard handy to jot down intermediate steps as needed.

Besides, math is always more fun when kids get to use colorful markers on a whiteboard.

Continue reading Mental Math: Advanced Multiplication, Part 1

Homeschool Memories: Bill Gates Proportions II

Posted on by Denise Gaskins
Woman on a shopping spree to buy books

Once upon a time, when my kids and I were young…

Later the same year, not too long after our discussion of the Bill Gates proportions, I stumbled on some more data. I discovered that the median American family’s net worth was $93,100 in 2004, most of that being home equity.

This gave me another chance to play around with proportions. And since I was preparing a workshop for our regional homeschooling conference, I wrote a sample problem:

The median American family has a net worth of about $100 thousand. Bill Gates has a net worth of $56 billion. If Average Jane Homeschooler spends $100 in the vendor hall, what would be the equivalent expense for Gates?

In the last post, I explained that a proportion sets two ratios equal to each other, like equivalent fractions. Each ratio must compare similar thing to similar thing in the same order.

In this case, we are interested in the ratio “Expense compared to Net Worth.”

Continue reading Homeschool Memories: Bill Gates Proportions II