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?

The Principality of Mathematics

Here’s the full quote:

“The Principality of Mathematics is a mountainous land, but the air is very fine and health-giving, though some people find it too rare for their breathing. People who seek their work or play in this principality find themselves braced by effort and satisfied with truth.”

— Charlotte Mason, Ourselves

Charlotte Mason and Math

Math was not one of Charlotte Mason’s primary interests. She didn’t think or write as deeply about it as she did other subjects.

She even wrote, “It is unnecessary to exhibit mathematical work done in the P.U.S. as it is on the same lines and reaches the same standard as in other schools.”

This leaves us modern parents and teachers having to read our own interpretations into her words. It should be no surprise when we come to different conclusions. Someday, perhaps, I’ll publish my own vision for a Charlotte Mason approach to homeschooling math.

In the meantime, the following articles describe a method that allows even the youngest children to explore the Principality of Mathematics:

In the years since writing those posts, Sonya and Lacy combined all their ideas into an easy-to-implement program that I think Mason herself would have enjoyed. Here’s my review:

CREDITS: Quote background photo (top) by Kalen Emsley via Unsplash.com.

Mathematical Days of Christmas

Enjoy this bit of seasonal fidgeting from Vi Hart.

If you don’t understand some of the references, that’s normal! Pick a phrase, Google it, and relish the fun of learning something new.

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

For More Holiday Math

CREDITS: Lamppost photo (top) by Aaron Burden via Unsplash.com.

Math Advent Calendars for 2020

Would you like to add some no-preparation-required fun to your math lessons this month?

Check out these creative mathematical Advent calendars, each featuring one puzzle or activity per day for December 1–24.

Some of the calendars may show a previous year’s date. (This is 2020 after all!) But the puzzles are evergreen — you can enjoy them anytime.

For more Advent-math links, visit Colleen Young’s Mathematical Advent Calendars post. And don’t miss my massive blog post Holiday Math Puzzles and Activities for Christmas, Winter Break.

Can You Do the Math Salute?

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

How Is This Math?

The idea that math is only about numbers, calculations, and textbook exercises is one of the greatest lies we learn in school. Of course, nobody ever comes straight out and actually says that. But the whole system teaches us every day what counts for math and what doesn’t.

James Tanton’s math salute is a physical puzzle.

How in the world did he do that?

Physical puzzles don’t fit into our cultural understanding of math. But the process of figuring out the puzzle is the same problem-solving process we use to figure out other puzzles — including the puzzles we call math.

In fact, real mathematics is all about figuring out puzzles without a teacher showing you what to do. Problem-solving is a universally useful skill.

As master teacher W. W. Sawyer said:

“Everyone knows that it is easy to do a puzzle if someone has told you the answer. That is simply a test of memory. You can claim to be a mathematician only if you can solve puzzles that you have never studied before. That is the test of reasoning.”

—W. W. Sawyer, Mathematician’s Delight

So tackle the puzzle of the math salute. Show it to your kids. (And don’t be surprised if they figure it out before you do!)

[THE FINE PRINT: I am an Amazon affiliate. If you follow the link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]

Printable Activity Guides

Since my publishing house opened its online store last month, I’ve been busy stocking the shelves with printable math activities for all ages.

It’s a fun collection of low- or no-prep ideas for playing math with your kids.

And it’s still growing. I’m pouring through old notes of my favorite projects from years of playing math with the kids in our math clubs and homeschool co-op enrichment classes, looking for ideas.

Which One Will You Try?

We’ve made the first two Geometric Coloring Designs books permanently free.

[The Let’s Play Math Sampler is also permafree, though it’s an ebook, so it’s on a different virtual shelf. You can find it under the “Free Books” section.]

For the rest, we’ve kept our prices as low as possible to fit struggling family budgets — less than a cup of coffee at my favorite cafe, back when we could still go out for a sweet, creamy cuppa.

Just go to our online store and click the “Printable Activity Guides” button to check out all the mathy fun.

Click Any Title for Details

Here are all the books we’ve posted so far.

Free Books:

Math Art:

Games and Puzzles:

Math Facts and Number Play:

Problem-Solving Skills:

Someday, I hope to combine these books into a creative math “uncurriculum” for homeschoolers. Stay tuned to this blog for more news about that. Eventually…

Not Attained by Chance

I’ve been collecting quotes about life and learning. They make great discussion-starters or essay/journaling prompts.

This is one of my favorites.

“Learning is not attained by chance, it must be sought for with ardor and attended to with diligence.”

—Abigail Adams

[Aw, face it. They’re all my favorites. That’s why I collect them!]

If you like quotes, too, you might enjoy browsing my collection:

Math & Education Quotations

Make Sense of Math

So, I decided to rewrite the Standards for Mathematical Practice into student-friendly language.

Here’s the final installment…

Math Tip #8: Make Sense of Math.

  • Use the patterns you discover to help you solve problems.
  • Don’t get lost in the details of a problem. Look for general truths.
  • Apply common sense to math situations.
  • Think about how different things are similar.
  • Think about how similar things are different.
  • Remember that your mind is your most important math tool.
  • Pay attention to your thinking process. What patterns do you find there?

Continue reading Make Sense of Math

The Professor of Legend

The traditional mathematics professor of the popular legend is absentminded.

    He usually appears in public with a lost umbrella in each hand.

      He prefers to face the blackboard and to turn his back to the class.

        He writes a, he says b, he means c; but it should be d.

          Some of his sayings are handed down from generation to generation.

            • “In order to solve this differential equation you look at it till a solution occurs to you.”
            • “This principle is so perfectly general that no particular application of it is possible.”
            • “Geometry is the science of correct reasoning on incorrect figures.”
            • “My method to overcome a difficulty is to go round it.”
            • “What is the difference between method and device? A method is a device which you used twice.”

            George Pólya
            How To Solve It

            If you’re not familiar with Polya’s work, here’s a 4-page summary of his problem-solving method.

            Or check out David Butler’s wonderful Solving Problems Poster, which encapsulates Pólya’s system in a visual, easy-to-follow way that works with younger students, too.

            4 steps to solving problems

            CREDITS: “Professor” cartoon (top) by André Santana via Pixabay.
            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).

            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.