Making Sense of Arithmetic

Making-SenseHomeschoolers have an advantage in teaching math: As our students grow, our own understanding of math grows with them because we see how the ideas build on each other.

This is especially true for those of us with large families. We pass through the progression of concepts with each student, and every pass lays down another layer in our own minds.

If you’d like to short-cut that process, check out Graham Fletcher’s Making Sense of Elementary Math video series. He’ll walk you through the topics, showing how manipulatives help build early concepts and gradually give way to abstract calculations.

“Understanding the vertical progression of mathematics is really important in the conceptual development of everyone’s understanding. This whole Making Sense Series has truly forced me to be a better teacher.”

— Graham Fletcher

The Progression of Addition and Subtraction

The Progression of Addition and Subtraction by Graham Fletcher.

The Progression of Multiplication

The Progression of Multiplication by Graham Fletcher.

The Progression of Division

The Progression of Division by Graham Fletcher.

If you enjoyed these videos, be sure to follow Graham’s blog Questioning My Metacognition. He’s working on the progression of fractions next….


[“Stairs!” photo by Richard Leeming (CC BY 2.0) via Flickr.]

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Do You Blog About Math?

[Image by Mike Licht, NotionsCapital.com (CC BY 2.0) via Flickr.]

It’s carnival time again. Activities, games, lessons, hands-on fun — if you’ve written a blog post about math, we’d love to have you join our Math Teachers at Play (MTaP) math education blog carnival.

Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up through first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

Don’t procrastinate: The deadline for entries is Friday, August 19. The carnival will be posted next week at The Usual Mayhem.

Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers.

Would You Like to Host the Carnival?

Hosting the blog carnival is fun because you get to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival often brings a nice little spike in traffic to your blog. If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

Explore the Other Math Carnivals

While you’re waiting for next week’s Math Teachers at Play carnival, you may enjoy:


Free-Learning-Guide-Booklets2Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.


Join the Fun: Math & Magic Virtual Book Club

Math-Magic-WonderlandEleven weeks of mathematical playtime kicks off this week over at Learners in Bloom blog.

Each week, we’ll be playing with the math, language, and logic topics found in a single chapter. I’ll be posting ideas for extension activities, videos demonstrating the concepts for the week, and additional resources. I’m really excited for the opportunity to share all the extra ideas that have been floating around my brain which I didn’t have room to include in the book (as in Marco Polo’s famous words: “I did not tell half of what I saw.”)

— Lilac Mohr

Here’s a Quick Taste of Week One

This Week’s Activities

Lilac’s blog post includes a full schedule for the eleven-week book club, featuring plenty of classic math puzzlers to play with. Here are the topics for this week.

  • Read Chapter 1: Mrs. Magpie’s Manual
  • Alliteration
  • Memorizing digits of Pi
  • Palindromes
  • Calculating your age on other planets

It looks like a lot of fun. I highly recommend the book (read my review), and I’m sure you and your children will enjoy discovering math and magic with Lulu and Elizabeth.

Check it out: Math & Magic in Wonderland Virtual Book Club, Week One.


Free-Learning-Guide-Booklets2Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.


FAQ: Trouble Finding the Right Math Program

“I can’t find a home school math program my son likes. We’ve tried Singapore Math, Right Start, Saxon, and Math Mammoth. We subscribed to a month of IXL Math to keep him in practice, but he hates that, too. I know I shouldn’t have changed so many times, but this was our first year of homeschooling, and I was trying to please him. But I’m running out of things to try. Do you think Life of Fred might work?”

Rock-Surfing

You’ve tried all those math programs in one year? Many people recommend that new homeschoolers take a few months off to “detox” from the classroom setting, to relax and enjoy the freedom of making their own choices. But your son might want a few months to detox from his homeschool experience.

I suggest you set aside all those books and focus on games and informal math. Try to avoid schoolish lessons until your son starts to enjoy learning for its own sake. The Internet offers an abundance of creative math ideas.

  • For example, download the Wuzzit Trouble or DragonBox apps to play with, but don’t make it a homework assignment.
  • Or let him choose one of the activities at Gordon Hamilton’s Math Pickle website and explore it for a day or a week or as long as it remains interesting.
  • Browse through the Primary Level 1 or Level 2 puzzles and games at the Nrich Mathematics website for more ideas.

Look for more playful math on my blog’s resource pages:

Explore Big Concepts: Infinity

Math that captures a child’s imagination can make the more tedious work seem bearable. For instance, in the 1920s, mathematician David Hilbert created a story about an imaginary grand hotel with an infinite number of rooms.

Explore Big Concepts: Fractals

Sierpinski-tortillasTake a mental trip to infinity by playing with fractals. Cynthia Lanius’s online Fractals Unit for Elementary and Middle School Students offers a child-friendly starting point.

Fractals are self-similar, which means that subsections of the object look like smaller versions of the whole thing.

Most children enjoy exploring the concept of infinity with hands-on fractal patterns, such as this Sierpinski triangle made of tortilla chips. Talk about what you notice and wonder: How does the triangle grow? How many chips will we need for the next stage?

The Daily Four

If you worry that your son needs to keep practicing traditional arithmetic during his break, try making him a series of Daily Four pages:

  • Fold a sheet of plain paper in half both ways, making four quarter sections.
  • Write one math problem in each part. Choose them from any of your math books.
  • Make sure each problem is different — one addition, one fractions, one multiplication, or whatever — and that none of them are hard enough to cause frustration.
  • Don’t worry about an answer sheet. Show him how to use a calculator to check his work.

You can make up a whole week’s worth of these problem sheets at once, with a balanced mix of problems for each day. Your son won’t feel overwhelmed, but you’ll know he’s reviewing his number skills.

Or download some of the Corbettmaths 5-a-Day practice sheets for him. Some problems may seem too easy while others require concepts he hasn’t studied yet. Easy review won’t hurt anything, but do let him skip the problems that feel too hard.

Explore-Big-Concepts


Credits: “Rock Surfer Boy” by Ken Bosma and “Boy” by Isengardt via Flickr. (CC BY 2.0) Hotel Infinity video by Tova Brown.

Click for details about Let's Play Math bookThis post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.


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Playful Math Carnival #100 via Three J’s Learning

Check out the new carnival of playful math for all ages at Three J’s Learning blog. You’re sure to enjoy this great collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun.

Wow, the 100th Math Teachers at Play! Such an honor to put together this milestone edition.

I asked the 3J’s for observations and facts about 100:

  • It is written with a 1 and two 0s
  • Square number (10 x 10)
  • It is a sum of two squares 64 + 36


Click here to go read the carnival blog!

It’s so cool to see carnival number 100. Thank you to ALL the hosts and to everyone who has participated over the years!

Past carnivals are still full of mathy treasure. Check them out:


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Education Bloggers: Share Your Post!

photo by Omar Omar via flickr[Image by Omar Omar (CC BY 2.0) via Flickr.]

If you are a homeschooler or classroom teacher, student or independent learner, or anyone else who writes about math, now is the time to send in your favorite blog post for next week’s Math Teachers at Play (MTaP) math education blog carnival.

Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers.

Don’t procrastinate: The deadline for entries is this Friday, July 22. The carnival will be posted next week at Three J’s Learning.

Need an Idea-Starter?

If you haven’t written anything about math lately, here are some ideas to get your creative juices flowing…

  • Elementary Concepts: As Liping Ma showed, there is more to understanding and teaching elementary mathematics than we often realize. Do you have a game, activity, or anecdote about teaching math to young students? Please share!
  • Arithmetic/Pre-Algebra: This section is for arithmetic lessons and number theory puzzles at the middle-school-and-beyond level. We would love to hear your favorite math club games, numerical investigations, or contest-preparation tips.
  • Beginning Algebra and Geometry: Can you explain why we never divide by zero, how to bisect an angle, or what is wrong with distributing the square in the expression \left(a + b \right)^2 ? Struggling students need your help! Share your wisdom about basic algebra and geometry topics here.
  • Advanced Math: Like most adults, I have forgotten enough math to fill several textbooks. I’m eager to learn again, but math books can be so-o-o tedious. Can you make upper-level math topics come alive, so they will stick in my (or a student’s) mind?
  • Mathematical Recreations: What kind of math do you do, just for the fun of it?
  • About Teaching Math: Other teachers’ blogs are an important factor in my continuing education. The more I read about the theory and practice of teaching math, the more I realize how much I have yet to learn. So please, fellow teachers, don’t be shy — share your insights!

Would You Like to Host the Carnival? Please?!

Hosting the blog carnival is fun because you get to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival often brings a nice little spike in traffic to your blog. If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

Explore the Other Math Carnivals

While you’re waiting for next week’s Math Teachers at Play carnival, you may enjoy:


Free-Learning-Guide-Booklets2Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.


Review: Math & Magic in Wonderland

Are you looking for a fun book to read over the summer? I just finished Lilac Mohr’s delightful Math & Magic in Wonderland, and I loved it.

Highly recommended, for kids or adults!

About the Book

Math-Magic-WonderlandA Jubjub bird disguised as a lark,
Borogroves concealing a snark,
When you’re in Tulgey Wood, you must
Be careful whom it is you trust…

With the discovery of Mrs. Magpie’s Manual of Magic for Mathematical Minds, Lulu and Elizabeth embark on an exciting journey to a realm inspired by Lewis Carroll’s poetry. The twins must use ingenuity and sagacity to solve classic logic puzzles that promise to uncover the book’s secrets and earn them The Vorpal Blade. In this interactive novel, the reader is invited to play along with the two heroines on their grand mathematical adventure.

Do you have the smarts to help Lulu and Elizabeth outwit the frumious Bandersnatch?

It’s time to enter Wonderland and find out!

–from the back cover of Math & Magic in Wonderland by Lilac Mohr

What I Liked

Puns, poetry, and plenty of puzzles. Tangrams, tessellations, truth-tellers and liars. History tidbits and many classics of recreational mathematics.

The sisters Lulu and Elizabeth seem real — though perhaps more widely read than most of us. They are different from each other. They make mistakes and have disagreements. But they never deteriorate into the cliché of sibling rivalry that passes for characterization in too many children’s books.

In each chapter, the girls must solve a language, math, or logic puzzle to proceed along their journey. Then a “Play Along” section offers related puzzles for the reader to try.

No matter how challenging the topic, the book never talks down to the reader.

What I Didn’t Like

… Um … Honestly, I can’t think of anything.

Since it’s traditional to criticize the editing of self-published books, I will say this: There was at least one place where the wording seemed a bit awkward. I would have phrased the sentence differently. But don’t ask me to identify the page — I was too caught up in the story to bother jotting down such a quibble. And I tried flipping through the book as I wrote this post, but I can’t find it again.

Buy, or Don’t Buy?

Buy. Definitely buy.

Unless you hate logic puzzles and despise Lewis Carroll’s poetry.

But for everyone else, this book is truly a gem. If you like The Cat in Numberland or The Man Who Counted, then I’m sure you’ll enjoy Math & Magic in Wonderland.

Useful Links

Disclaimer: Like almost all book links on my blog, the links in this post take you to Amazon.com, where you can read descriptions and reviews. I make a few cent’s worth of affiliate commission if you make a purchase — but nowhere near enough to influence my opinion about the book.

And Now for the Giveaway

Math-Magic-WonderlandLilac offered a paperback copy of Math & Magic in Wonderland for one lucky reader of Let’s Play Math blog.

The giveaway is done. Congratulations, Keshua!

But the comments section below remains open, and I’d still love to hear your answers:

  • Tell us about your favorite language, math, or logic puzzle book! Or share a book you’ve been wanting to read.