New Membership Tiers: One-on-One Mentorship

Two women chatting over tea

Over the years, in my public writing and in personal correspondence, I’ve tried to help younger parents by sharing the things I wish someone would have told me forty years ago. Oftentimes, I will answer a question but never hear back what the person ended up doing or how their family got along.

It leaves me feeling as though I could have done more to encourage them along the way.

In the past few years, I’ve watched a professional writer I admire organize several more formal mentorships for younger indie authors to grow their writing and publishing careers. I think a similar program could be helpful for homeschooling families.

So now I’m offering two new Patreon membership tiers that give you a direct one-on-one connection with me through email or email-plus-video.

My goal is to help you think about math as a creative, playful investigation where you and your children explore concepts together using the math program or curriculum of your choice. This is not a tutoring arrangement. I will help you understand and teach math, but I will not do the teaching for you.

Continue reading New Membership Tiers: One-on-One Mentorship

Hints for the Patty Paper Trisection

drafting tools

No peeking! This post is for those of you who have given the trisection proof a good workout on your own.

If you have a question about the proof or a solution you would like to share, please post a comment here.

But if you haven’t yet worked at the puzzle, go back and give it a try.

When someone just tells you the answer, you miss out on the fun. Figure it out for yourself — and then check the answer just to prove that you got it right.

Continue reading Hints for the Patty Paper Trisection

Puzzle: Patty Paper Trisection

student using drafting tools

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.

Continue reading Puzzle: Patty Paper Trisection

Mental Math: Early Addition

child counting on fingers

From the very beginning of a child’s experience with math, we want to focus on reasoning, making sense of numbers, thinking about how they relate to each other and how we can use these relationships to solve problems.

The basic idea of addition is putting like things together: combining parts to make a whole thing, putting together sets to make a collection, or starting with an original amount and adding the increase as it grows. Connecting two numbers in relationship with a third number we call the sum.

When you work with young children learning addition, remember the two key mental-math strategies I mentioned in the previous post.

  • Use friendly numbers.

For early single-digit addition, the most important friendly numbers are 5 and 10, the pairs of numbers that make 10, and the doubles.

  • Estimate, then adjust.

When children apply their creative minds to reasoning about math, they can use friendly numbers to get close to an answer, and then tweak the result as needed.

Continue reading Mental Math: Early Addition

Tell Children Interesting Things

quote by John Conway

“You don’t educate people by telling them useful things; you educate people by telling them interesting things.”

— John Conway

If you want help educating your children with interesting things about math, check out Denise Gaskins’ Playful Math store.

We’re currently running a huge back-to-school sale on ALL of my playful math ebooks, problem-solving activities, math journaling task cards, and math art projects.

So many great ways to play with math!

The 20% discount will automatically apply when you check out. No discount code required.

Check it out:

Back to School Sale 2025