Math Game Monday: Power Up

Posted on by Denise Gaskins
Learn a new game with Math Game Monday

This game gives students a fun reason to think about calculating with exponents.

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!

Power Up

Math Concepts: powers (exponents).
Players: only two.
Equipment: one printed character sheet for each player, two six-sided dice, pencils or markers. Calculator optional.

Continue reading Math Game Monday: Power Up

Introduction to the Science of Counting

Posted on by Denise Gaskins
fantasy elf archer

One of my favorite rabbit-trails to explore in middle school math is the science of counting and probability.

It’s a great topic because the calculations are relatively easy, mostly multiplication and division. But there’s a lot of thinking that goes into figuring out just what calculations we need to do.

Counting is not only for little kids! It’s part of discrete mathematics, which means the study of things that are not continuous—things that come in discrete chunks—and it’s important in game design, computer programing, and cryptography.

Prealgebra and Geometry games book

This post is a section of my Prealgebra & Geometry Games book where my daughter and I explore the fundamental counting principle, the key to solving many counting and probability puzzles.

Continue reading Introduction to the Science of Counting

Probability Puzzles with Obsolete Coins

Posted on by Denise Gaskins
jar of coins

I love math puzzles, and Henry Ernest Dudeney is the foremost puzzlemeister of all time.

Whenever I need a diversion from the pressing day-to-day busyness of life, I like to crack open one of his books. And get humbled. He stumps me as often as not, but I enjoy the challenge.

Today, I’ve got two of his somewhat-easier puzzles from Amusements in Mathematics, dealing with the probability of obsolete coins tossed or pulled from a bag.

Okay, so the penny isn’t obsolete quite yet, even though the US government quit making them. But the “penny” in these puzzles is the old British pence, which went out of date seemingly ages ago, along with all the other non-decimal coins that made old math puzzles so confusing.

Probability puzzles are great for middle school students because the arithmetic itself is simple. The challenge is in figuring out exactly what calculation to do.

Have fun playing math with your kids!

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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

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

        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

              Happy Pythagorean Triple Day!

              Posted on by Denise Gaskins
              Pythagorean Theorem demonstrated with tangrams

              Thursday is Pythagorean Triple Day, one of the rarest math holidays.

              The numbers of Thursday’s date: 7/24/25 or 24/7/25, fit the pattern of the Pythagorean Theorem: 7 squared + 24 squared = 25 squared.

              Any three numbers that fit the a2 + b2 = c2 pattern form a Pythagorean Triple.

              Continue reading Happy Pythagorean Triple Day!

              Math Journal: Playing with My Own Ignorance

              Posted on by Denise Gaskins
              photo of a girl wondering about math

              Mary Everest Boole, wife of English mathematician George Boole, once described algebra as “thinking logically about the fact of our own ignorance.”

              This definition made me chuckle. Like any human being, I am ignorant on many things, but I usually avoid thinking about that.

              So I wondered what would happen if I took Mrs. Boole’s advice and tried thinking logically about my ignorance.

              How far could I go?

              Perhaps you’d like to try this experiment with your children. All you need is a pen and paper or a whiteboard and markers and a bit of curiosity.

              Math Journaling Adventures series by Denise GaskinsAnd if you enjoy this exploration, check out my Math Journaling Adventures project to discover how playful writing activities can help your students learn mathematics. Preorder your books today!

              Continue reading Math Journal: Playing with My Own Ignorance

              The Best Math Game Ever

              Posted on by Denise Gaskins

              The Substitution Game features low-floor, high-ceiling cooperative play that works with any age (or with a mixed-age group) — and you can use it while distance learning, too. It’s great for building algebraic thinking.

              Excerpted from my new book, Prealgebra & Geometry: Math Games for Middle School. Look for it at your favorite online bookstore.

              The Substitution Game

              Math Concepts: addition, subtraction, multiplication, division, order of operations, integers, fractions, equivalence and substitution.

              Players: any number (a cooperative game).

              Equipment: whiteboard and markers (preferred) or pencil and paper to share. Calculator optional.

              Continue reading The Best Math Game Ever

              Math Game: Hit Me

              Posted on by Denise Gaskins

              I believe this was the first math game I ever invented. Of course, ideas are common currency, so I’m sure other math teachers thought of it before I did. But to me, it was original.

              I’ve blogged about the game before, but here’s the updated version as it appears in my new book Prealgebra & Geometry: Math Games for Middle School — scheduled for publication in early 2021. Sign up for my newsletter to get updates.

              Hit Me

              Math Concepts: integer addition, absolute value.

              Players: two or more.

              Equipment: playing cards (two decks may be needed for a large group).

              Continue reading Math Game: Hit Me