Middle school – Denise Gaskins' Let's Play Math

Rescuing Cool Math for Older Kids

Posted on May 27, 2026May 27, 2026 by Denise Gaskins

mother and teen daughter do homework together

Do you have math dreams for your children?

Here are some dreams shared the authors of Avoid Hard Work!

For our children, we dream that mathematics…

… makes sense.
… is more than just arithmetic.
… is joyous.
… makes them strong.
… is meaningful.
… is creative.
… is full of fascinating questions.
… opens up many paths to solutions.
… is friendly.
… solves big problems and makes the world better.
… is a powerful tool they can master.
… is beautiful.
… lets them learn in their own ways.
… is connected to their lives.
… asks “why” and not just “how.”
… opens the world.

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Math Game Monday: The Number That Must Not Be Named

Posted on May 4, 2026March 21, 2026 by Denise Gaskins

$Learn a new math game every week, for free$

This challenging game stretches everyone’s working memory and offers children the delightful possibility of stumping an adult.

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.

So what are you waiting for? Let’s play some math!

The Number That Must Not Be Named

Math Concepts: addition, subtraction, multiplication, division, integers, fractions, factoring, powers and roots, prime numbers, and other number properties.

Players: two or more (a cooperative game).

Equipment: none.

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Math Prompt: True-False-True

Posted on March 4, 2026March 4, 2026 by Denise Gaskins

girl writing in a notebook, sitting on couch with her corgi

One 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

Mental Math: Advanced Multiplication, Part 2

Posted on February 4, 2026January 3, 2026 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

Homeschool Memories: Bill Gates Proportions II

Posted on January 21, 2026January 3, 2026 by Denise Gaskins

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

Homeschool Memories: Putting Bill Gates in Proportion

Posted on January 14, 2026January 3, 2026 by Denise Gaskins

Money Bag, dollar banknotes and stacked coins on wooden table

Once upon a time…

We were getting ready for the annual homeschool co-op speech contest, and a friend emailed me for help.

“Can you help us figure out how to figure out this problem?

“This is related to C’s speech. I think we have all the information we need, but I’m not sure:

“The average household income in the United States is $60,000/year. And a man’s annual income is $56 billion.

“Is there a way to figure out what this man’s value of a million dollars would be, compared to the person who earns $60,000/year? In other words, I would like to say—$1,000,000 to us is like 10 cents to Bill Gates.”

We found out later that her son’s numbers weren’t exactly right. He hadn’t understood the difference between income and net worth, so he made Gates sound richer than reality.

But the basic math principles never change, and it’s fun to play with big numbers.

Continue reading Homeschool Memories: Putting Bill Gates in Proportion

What Is Math Game Monday?

Posted on December 15, 2025February 23, 2026 by Denise Gaskins

$Learn a new math game every week, for free$

There’s a new Math Game Monday this week.

Have your kids tried it yet?

This week’s game is one of my favorites for upper-elementary and middle school students, offering plenty of practice doing estimation and mental math with fractions. Or you might prefer last week’s game, featuring a classic two-player logic puzzle that develops strategic reasoning.

Or, if you’re reading this post later and missed those, there’s another great new game this week for you to play.

Check it out:

Visit Math Game Monday

Continue reading What Is Math Game Monday?

How to Think like a School Math Genius

Posted on October 22, 2025September 4, 2025 by Denise Gaskins

$Teen student thinking$

“The true joy in mathematics, the true hook that compels mathematicians to devote their careers to the subject, comes from a sense of boundless wonder induced by the subject.

“There is transcendental beauty, there are deep and intriguing connections, there are surprises and rewards, and there is play and creativity.

“Mathematics has very little to do with crunching numbers. Mathematics is a landscape of ideas and wonders.”

—James Tanton

James Tanton has a new website. It looks cool, and it’s a great place to discover the things he’s working on these days.

But his wonderful, old-fashioned site full of great insights and interesting problems is gone.

😞 I hate it when some part of the internet that I love disappears. So here’s my attempt to recover one tiny bit of the old site, five tips for creative problem solving through intellectual play.

Continue reading How to Think like a School Math Genius

Puzzle: Patty Paper Trisection

Posted on August 20, 2025August 20, 2025 by Denise Gaskins

One of the great unsolved problems of antiquity was to trisect any angle, to cut it into thirds with only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass.

Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator.

One “cheat” that works is to fold your paper.

I will show you how it works, and your job is to show why.

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