Homeschool Memories: Putting Bill Gates in Proportion

Posted on 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

        Playful Math Carnival 183 via Math Hombre

        Posted on by Denise Gaskins
        Have fun with math at the Playful Math Blog Carnival

        If you’re into math education — or just curious about how learning math could possibly be fun — you’ll definitely want to check out the latest edition of the Playful Math Carnival.

        It’s a collection of awesome blog posts curated by John Golden and published on the Math Hombre website:

        The whole point of the carnival is to show that math doesn’t have to be tedious or repetitive. Through a bunch of fun and engaging posts, we celebrate math that’s playful, creative, and totally relevant to everyday life.

        Because what could be more relevant than having fun while we learn?

        In this edition, you’ll find everything from math puzzles and games to humor and much more — so many people creating great math content.

        If you want to mix up your math teaching and make it more enjoyable for your students (and for yourself), definitely check out the Playful Math Carnival.

        Happy reading!

        Go Visit the Carnival

        What Is Thinking Thursday?

        Posted on by Denise Gaskins
        Thinking Thursday math journal prompt

        There’s a new math journaling prompt this week.

        Have your kids tried it yet?

        This week’s prompt features one of my explain-your-reasoning to get kids thinking (and writing) about math while avoiding the formality that turns so many students away from geometry proofs. Or you might prefer last week’s prompt, featuring a classic math brainteaser and encouraging students to create their own related puzzles.

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

        Check it out:

        Visit Thinking Thursday

        Continue reading What Is Thinking Thursday?

        What Is Math Game Monday?

        Posted on 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?

        Musings: Math is Communication

        Posted on by Denise Gaskins
        Young boy writing math expressions

        The question came up on a homeschool math forum:

        “My first grader and I were playing with equivalent expressions. We were trying to see how many ways we could write the value ‘3.’

          “He wrote down 10 – 2 × 3 + 1.

            “When I tried to explain the problem with his calculation, he got frustrated and didn’t want to do math.

              “How can I help him understand order of operations?”

              [If you think this sounds like too complex of a math expression for a first grader, you may want to read my blog post about math manipulatives and big ideas.]

              Order of operations doesn’t matter in this instance. What matters is communication.

              The mother didn’t know how to read what her son wrote.

              He could help her understand by putting parentheses around the part he wanted her to read first.

              He doesn’t need to know abstract rules for arbitrary calculations, or all the different ways we might possibly misunderstand each other. He just needs to know how to say what is in his mind.

              Continue reading Musings: Math is Communication

              FAQ: The Value of Math Rebellion

              Posted on by Denise Gaskins
              Math Rebels fight for truth, justice, and creative reasoning

              I’ve been getting questions about my Math Journaling Adventures books:

              “I’m so excited to try math journaling! We bought your Logbook Alpha, and my 11-year-old math-averse son is trying to be a math rebel at every turn.

                “But I feel uncomfortable with the idea of rebellion. Doesn’t he need to learn how to solve math problems the right way?”

                One of my favorite things about math is that there really is no “right” way to solve math problems.

                As I pointed out in my ongoing Mental Math series, even a problem as basic as 6+8 can be approached from many directions. So perhaps I should say, the “right” way is however the student wants to make sense of the problem.

                In math, sense-making and reasoning are always the most important things.

                Continue reading FAQ: The Value of Math Rebellion

                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

                    Mental Math: Advanced Subtraction

                    Posted on by Denise Gaskins
                    mother and daughter talking about math homework

                    As our children grow and develop their math skills, the mental math strategies grow with them.

                    The basics of mental math don’t change:

                    • Use friendly numbers.
                    • Estimate and adjust the answer.

                    But we have new ways to help children do math in their heads as the numbers get bigger and the problems more challenging.

                    For example, how might kids figure out a multi-digit subtraction like 67 − 38?

                    First, we need to adjust our mindset…

                    Continue reading Mental Math: Advanced Subtraction

                    Geometric Math Art, Recovered

                    Posted on by Denise Gaskins
                    Geometric pattern by Denise Gaskins

                    I’ve been updating my old book files to a new publishing program, and in the process discovering anew how often websites change and disappear. So frustrating!

                    Thankfully, the Internet Archive keeps some things that we can look back at. It doesn’t always work, but today it came to the rescue and let me recover the wonderful workbook from the Metropolitan Museum of Art, Islamic Art And Geometric Design, plus some of the pattern pages at the old School of Islamic Geometric Design.

                    I reference these pages in my Geometric Coloring Designs series (available at my Playful Math Store), so I was glad to find they weren’t lost forever.

                    Math Art = a great way to spark energy when your students hit the mathematical doldrums.

                    If you’d like to play around with math art patterns, each image below links to Eric Broug’s step-by-step instructions for creating the design. Also, Broug made printable pages to get students started, which you can download here. No compass construction required!

                    Pattern 1

                    Geometric design pattern by Eric Broug

                    Pattern 2

                    Geometric design pattern by Eric Broug

                    Pattern 3

                    Geometric design pattern by Eric Broug

                    There are two more patterns on the old SIGD site, but I can’t get those instructions to load. That might be my antique rural internet connection, however, so feel free to do some exploring on your own.

                    And have fun drawing math with your kids!

                     
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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.

                    “Geometric Math Art, Recovered” copyright © 2025 by Denise Gaskins. Image at the top of the post copyright © Denise Gaskins.