What Is Multiplication, Anyway?

At some point during the process of teaching multiplication to our children, we really need to come to terms with this question:

What IS multiplication?

Did your device hide the video? Find it on YouTube here.

“What’s my answer? It’s not one that society’s going to like. Because society expects — demands, even — that mathematics be concrete, real-world, absolute, having definitive answers.

    I can’t give a definitive answer.

      Multiplication manifests itself in different ways. So maybe the word ‘is’ there is just too absolute. And it’s actually at odds with what mathematicians do.

        Mathematicians do attend to real-world, practical scenarios — by stepping away from them, looking at a bigger picture.”

        —James Tanton, What is Multiplication?

        For Further Study

        You may also enjoy these posts from my blog archive:

        Memorizing the Times Table: A Life Skills Approach

        Continuing on my theme of times table facts, here’s the inimitable James Tanton:

        Did your device hide the video? Find it on YouTube here.

        “If our task is to memorize this table, please make it about mathematics — about thinking your way through a challenge, and what can I do to make my life easier.”

        —James Tanton, Making Memorising Multiplication Facts (if one really must) a meaningful Life Skill Lesson

        For Further Study

        You may also enjoy my blog post series about working through the times tables, paying attention to mathematical relationships (and a bit of prealgebra) along the way.

        Times Tables Series

        Click the button to see the whole series. Scroll down to the first post to go through it in order.

        Only Three Facts to Memorize

        A comment from a friend got me playing around with multiplication. I found a few videos from some of my favorite math people, so I’ll be sharing over the next few days.

        Here’s one from Sonya Post of Learning Well at Home. Also, Sonya just hosted Playful Math Education Carnival #143, which is well worth your time to explore!

        Did your device hide the video? Find it on YouTube here.

        “When students have to drill multiplication facts, it’s frustrating, unproductive and it makes them hate math. A better way to master the multiplication table is work on the skills that allow students to multiply quickly and efficiently.”

        —Sonya Post, Why We Don’t Drill Multiplication Facts – What We Do Instead

        Doubling and Halving

        Making doubles and halves are a great foundation for all sorts of math.

        Do you ever play the doubling game with your children? One player picks a starting number, and then you take turns doubling it until your mental math skills run out. How far can you go?

        Or try the halving game: One player chooses a starting number, and you take turns cutting it in half. How tiny can you go?

        As Sonya demonstrated, these skills help your child master their multiplication facts. And they are fantastic preparation for exponents and logarithms, too!

        What Are Mixed Numbers?

        I just discovered a fascinating fact: In some places in the world, mixed numbers apparently don’t exist.

        So that made me curious about my blog readers:

        • Did you learn about mixed numbers in school?
        • Do you ever use mixed numbers in daily life?
        • Are your children learning to work with them?

        And if you DO know mixed numbers, can you simplify this mess:

        [If you enjoy dry math humor, the answer is worth the work.]

        Continue reading What Are Mixed Numbers?

        New Printable Puzzle Books: Diffy Inception

        The best way to practice math is to play with it—to use the patterns and connections between math concepts in your pursuit of something fun or beautiful.

        Diffy Inception puzzles have their own symmetric beauty, but mostly they are just plain fun. Students can practice subtraction and look for patterns in the difference layers.

        I just published four new activity books to our online store:

        Notes to the teacher include puzzle instructions, game variations, journaling prompts, and more. Plus answers for all puzzles.

        Available with 8 1/2 by 11 (letter size) or A4 pages.

        Click for a Preview

        My publishing company runs this online store, so you can find all my playful math books there — including an exclusive pre-publication ebook edition of my newest title, Prealgebra & Geometry: Math Games for Middle School. Click here to browse the Tabletop Academy Press store.

        Exciting New Homeschool Math Program

        Homeschooling friends, check out this new homeschool math program that’s fun, rigorous, and engaging — a delightful, hands-on course that helps parents (and their children) understand math.

        Introduction to Cuisenaire Rod Structures Course

        I had the privilege of previewing this class as Sonya and Lacy put it together. I highly recommend it to anyone who struggles with math, or who wants to take a non-traditional approach.

        By focusing on making sense of number relationships, and by teaching algebra before arithmetic, this course provides a stress-free path to rich mathematical mastery.

        And for all they provide, including weekly live workshops and a slew of printable math journal pages that prompt deep thinking, the price is a steal!

        Continue reading Exciting New Homeschool Math Program

        More Dover Samples

        “Without mathematics you can’t do anything! Everything around you is mathematics. Everything around you is numbers.”

        —Anna Claybourne, I Can Be a Math Magician


        Dover Publications sent out a new email today with fun coloring and craft samples. And several puzzles from I Can Be a Math Magician: Fun STEM Activities for Kids by Anna Claybourne.

        Enjoy!

        If you’d like to receive future Dover Sampler emails, you can sign up here.

        THE FINE PRINT: I am an Amazon affiliate. If you follow the book link above and buy something, I’ll earn a small commission (at no cost to you).

        Free Number Sense Resources from Steve Wyborney

        If you teach children in the primary grades, you’ll enjoy this new series from the wonderful Steve Wyborney. Every day for the rest of the school year, Steve will post a new estimation or number sense resource for grades K–8 (or any age!) at his blog:

        “This is my way of providing support and encouragement – as well as bringing math joy to your classroom… I’m going to stick with you all year long.”

        —Steve Wyborney

        Click to visit Steve’s blog

        FAQ: I’ve Ruined My Daughter

        My daughter is only eleven, but I’m afraid I’ve ruined her chance of getting into college because she is so far behind in math. We’ve tried tutors, but she still has trouble, and standardized testing puts her three years below grade level. She was a late reader, too, so maybe school just isn’t her thing. What else can I do?

        Standardized tests are not placement tests. They cannot tell you at what level your daughter should be studying. They aren’t designed that way. The “placement” they give is vague and general, not indicative of her grade level but rather a way of comparing her performance on that particular test with the performance of other students.

        There can be many different reasons for a low score. I’ve listed a few of them in my post In Honor of the Standardized Testing Season.

        Continue reading FAQ: I’ve Ruined My Daughter