Morning Coffee: What Is Mathematics?

Posted on by Denise Gaskins
Morning Coffee Lifelong Learning for Parents

One of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.

Here are a few stories to read as you sip your morning brew. . .

Download your printable Morning Coffee journal

This week’s rabbit hole started with a thought-provoking blog post by Sara Van Der Werf…

“We are all mathematicians. We all have the power to notice, describe, and generalize patterns. You have all had this ability since birth.

    “If we believe this then every day we must plan lessons that allow students to act as mathematicians. We must put something in front of our students to notice. We must put something in front of our students to describe, to generalize.”

    —Sara Van Der Werf

    Read more about how to develop mathematical thinking in this fourth installment of professional development for homeschooling parents.

     
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    Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store. Or join my email newsletter.

    This blog is reader-supported. If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.

    “Morning Coffee: What Is Mathematics?” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.

    Monday is Square Root Day

    Posted on by Denise Gaskins
    square tree with roots

    On May 5, we celebrate one of the rarest math holidays: Square Root Day, 5/5/25.

    Here are a few ideas for playing math with squares and roots.

    What is a Square Root?

    Five is the square root of twenty-five, which means it is the number we can “square” (multiply times itself) to get 25.

    The root is the base number from which the square grows. In physical terms, it is the side of the square.

    Imagine a straight segment of length 5, perhaps a stick or a piece of chalk. Now lay that segment down and slide it sideways for a distance equal to its length. Drag the stick across sand, or pull the chalk across paper or a slate.

    Notice how this sideways motion transforms the one-dimensional length into a two-dimensional shape, a square.

    The area of this shape is the square of its root: 5 × 5 = 25.

    What do you think would happen if you could drag the square through a third dimension, or drag that resulting shape through a fourth dimension?
    How many shapes do you suppose might grow from that original root of 5?

    Continue reading Monday is Square Root Day

    ALL Mathy Merchandise on Sale Now

    Posted on by Denise Gaskins
    Cool Cats Play Math T-shirt

    April has been a crazy month here at my little one-person business, which means promotion fell through the cracks.

    I try to run a sale on something every month, to give you a reason to drop by my Playful Math Store. And I’m supposed to post blogs and social media about the discount, so nobody misses saving money on something they’ve been waiting for.

    This month’s sale was a hefty 20% off every bit of mathy merchandise in the store. Cool T-shirts, fun mugs, handy totebags, and more!

    My plan was to offer a big discount before all the tariffs kick in and mess up my pricing, since even items that are produced in the US often use components from overseas, which makes me expect prices to rise over the coming months.

    Continue reading ALL Mathy Merchandise on Sale Now

    Skit: The Handshake Problem

    Posted on by Denise Gaskins
    The handshake problem

    If seven people meet at a party, and each person shakes the hand of everyone else exactly once, how many handshakes are there in all?

    Our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned.

    I threatened to hand out a ten question pop quiz on integer arithmetic, but instead my pre-algebra students presented this skit.

    Download a Printable Script

    Cast

    1-3 narrators (or more, if you have a large group)
    7 friends (non-speaking parts, adjust to fit your group)

    Props

    Each friend will need a sheet of paper with a number written on it big and bold enough to be read by the audience. The numbers needed are 0, 1, 2, 3, … up to one less than the number of friends. Each friend keeps his paper in a pocket until needed.

    Continue reading Skit: The Handshake Problem

    Charlotte Mason Math: Living Books

    Posted on by Denise Gaskins
    “The Reading Lesson” painting by Jonathan Pratt, public domain

    [An addendum to my earlier Charlotte Mason Math series.]

    “Our business is to give [children] mind-stuff, and both quality and quantity are essential. Naturally, each of us possesses this mind-stuff only in limited measure, but we know where to procure it; for the best thought the world possesses is stored in books; we must open books to children, the best books; our own concern is abundant provision and orderly serving.”

    — Charlotte Mason, Toward A Philosophy of Education

    Most homeschool teachers, whatever our curriculum or schooling approach, understand the importance of teaching with living books. We read aloud biographies, historical fiction, or the classics of literature. We scour library shelves for the most creative presentations of scientific topics that interest our children, and encourage our high school students to go back to the original documents whenever possible.

    And we teach math with a textbook.

    Not that textbooks are inherently bad, because math is an abstract science. We need to meet the ideas  — the “mind-stuff” — of math on their own terms, and textbooks can help with that.

    But it’s not enough.

    Continue reading Charlotte Mason Math: Living Books

    Musings: Math Is a Social Game

    Posted on by Denise Gaskins
    photo of three young girls talking about numbers

    Childhood Memories

    When I was in school, math was something each person did on their own for homework, quizzes or tests.

    Even when the teacher sent us to work on the chalkboard, each person did their own problem. We would never think to collaborate on math.

    To look at someone else’s answer was considered cheating.

    Continue reading Musings: Math Is a Social Game

    Morning Coffee: Anyone Can Learn Math

    Posted on by Denise Gaskins
    Morning Coffee Lifelong Learning for Parents

    One of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.

    Here are a few stories to read as you sip your morning brew:

    Once again, my rabbit hole started with a thought-provoking blog post from Dan Finkel…

    “Not everyone can become a great artist — but a great artist can come from anywhere.”
    —Ego, from Ratatouille

      “Ego’s parsing of the phrase anyone can cook is not obvious, and it’s not really the primary meaning of the phrase. The truth is, there are really three meanings all wrapped up there: anyone can learn to have the joy and pleasure of cooking in their life, even if they don’t become a master chef. Some people will get serious about it. And the visionaries who change the way we think about the art can come from anywhere — lock them out of the field and we all suffer.”
      —Dan Finkel

      Read more about how anyone can learn math in this third installment of professional development for homeschooling parents.

       
      * * *

      Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store. Or join my email newsletter.

      This blog is reader-supported. If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.

      “Morning Coffee: Anyone Can Learn Math” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.

      Math Journal: The 1-2-3 Puzzle

      Posted on by Denise Gaskins
      colorful numbers 1, 2, 3

      Math Journaling Adventures series by Denise GaskinsThere’s still time to check out my Math Journaling Adventures project and discover how playful writing activities will help your students learn mathematics. Preorder your books today!

      Meanwhile, here’s a math puzzle to share with your kids…

      Write down any whole number. It can be a single-digit number, or as big as you like. For example:

      64,861,287,124,425,928

      Now, count up the number of even digits (including zeros), the number of odd digits, and the total number of digits your number contains. Write those counted numbers down in order, like this:

      64,861,287,124,425,928
      even 12, odd 5, total 17

      Continue reading Math Journal: The 1-2-3 Puzzle

      Only Two Days Left for Math Journaling Adventures

      Posted on by Denise Gaskins
      Math Journaling Adventures series by Denise Gaskins
      • If you’re a parent trying to help your child learn math…
      • Or a teacher looking for creative ideas for your classroom…
      • Or a homeschooling parent hoping to enrich your student’s understanding…

      Then you’ll love the Math Journaling Adventures series because these logbooks guide your children to explore mathematics at a deeper level, building a strong foundation to support future learning.

      It’s a fun way to enrich any math curriculum, and great for unschoolers, too.

      But you have to ACT FAST: The Kickstarter campaign ends in 2 days!

      Order Your Copy Today ❯

      Continue reading Only Two Days Left for Math Journaling Adventures

      Podcast: Using Math Journals and Games

      Posted on by Denise Gaskins
      mother and daughter math journaling

      I have a new podcast interview, and I think you’ll enjoy it!

      Check out Cindy Rollins’s The New Mason Jar on your favorite podcast app, or listen on the website:

      Go to the podcast ❱

      Here’s an excerpt…

      Writing to Learn

      Just as a nature journal records our children’s explorations and discoveries in nature, so a math journal tracks our children’s explorations in the world of mathematics.

        In a math journal, children record their experiences with numbers, shapes, and patterns through drawing or writing. Journaling teaches them to see with mathematical eyes — not just to remember what we adults tell them, but to create their own math.

          The process of writing forces children to pin down their thoughts, to transform nebulous concepts into firm ideas, to struggle with vagueness and build understanding.

            As William Zinsser says in his book Writing to Learn: “Writing is how we think our way into a subject and make it our own. Writing enables us to find out what we know, and what we don’t know.”

              Through journaling, children develop a richer mathematical mindset. They begin to see connections and grow confident in their ability to think through new problems.

              We had a great discussion! Listen to the whole thing:

              Go to the podcast ❱

               
              * * *

              Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store. Or join my free email newsletter.

              This blog is reader-supported. If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.

              “Podcast: Using Math Journals and Games” copyright © 2025 by Denise Gaskins. Image at the top of the post copyright © AntonLozovoy / Depositphotos.