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Hello <<First Name>>,

Winter is here in earnest. We had a slushy snow storm blow in this weekend, and then everything froze overnight. It looks pretty, as long as the power stays on. I hope your family is enjoying whatever the weatherman sends you. After all, any season can be snuggle-on-a-couch-and-read weather.

Here is your February edition of the "Let's Play Math!" blog newsletter.

Have fun!

Denise

Math Snack: Fractal Valentines

Playful, no-preparation math activities for all ages

What better way to say "I love you forever!" than with a pop-up fractal Valentine? My math club kids made these a couple years back, and they turned out great.

To make your card, choose two colors of construction paper or card stock. One color will make the pop-up hearts on the inside of your card. The other color will be the front and back of the card, and will also peek through the cut areas between the hearts. Fold the papers in half and cut them to card size.

Set the outer card aside and focus on the inside. The fractal cutting pattern is simple: press the fold, cut a curve, tuck inside, repeat. Detailed instructions (with photos): A Pop-Up Sierpinski Valentine Card. Or try this alternate technique (folding on the slant, instead of straight down): Fractal Pop Up Valentine.

Finally, glue the cards together. Fold the pop-up parts of the inner card toward the center, then use a glue stick (or be very careful with liquid glue) to go around the outer, uncut areas. Wrap the outer card around it, and set a book on top to hold it all together while the glue dries. Trim away any of the inner card that sticks out around the edges.

Open the card and make sure the hearts are popping up properly. Decorate the front and back of your fractal valentine card as desired.

For further investigation, Cynthia Lanius offers a wonderful Fractals Unit for Elementary and Middle School Students (That Adults are Free to Enjoy). You may also like this joke Fractal Flowchart.

[Thanks to the bloggers at Nazareth College Math Department for the original fractal valentine post.]

More Tasty Tidbits

A few of my favorite posts about math and teaching

What do you get when you cross a toddler's geometry book with a logic puzzle? Christopher Danielson's Building a Better Shapes Book. Free download, great for all ages!

The Moebius Noodles team has put together a three-week learning adventure for anyone who works with children: Multiplication Explorers will begin on February 9, so you only have a few days left to register. My preschool-2nd grade group loved these activities last year.

Brian Stockus wants students (and teachers) to develop Fraction Number Sense, a robust and flexible understanding of how fractions behave. And Kassia Wedekind shows one way to teach it in Over or Under?: A Fraction Number Sense Routine.

Do you know what random really looks like? "What most people think of as random is usually anything but," Patrick Vennebush says in Making Heads or Tails of Randomness.

Ben Orlin has been writing a fun and thought-provoking series on How to Avoid Thinking in Math Class.

Dan Kennedy, chairman of the math department at the Baylor School, Chattanooga, formulates a calculus problem to end all calculus problems. Made me laugh!

Explore the math carnival

The January math education blog carnival is open for your browsing pleasure, featuring 23 playful ways to explore mathematics from preschool to high school:

Math Teachers at Play (MTaP) Blog Carnival #82

Blog and Book Updates

A quick peek at what I'm working on

My first two Math You Can Play number games books are off to the copy editor, which means I'm on track for a mid- to late-spring publication date. Now I need to focus on the graphics, and I hope to post one or two of the games on my blog this month.

But instead of talking about my books, I'd like to introduce you to Tina Cardone's book, Nix the Tricks.

A little over two years ago, Cardone stopped complaining about her high school students' lack of understanding and started doing something about it. With the help of teachers from around the online world, she put together a collection of "math tricks" that confuse students or keep them from understanding the math they study.

Math tricks are rhymes, rules, or catchy mnemonics that help students get right answers in the short term. Such tricks don't build strong understanding of the concepts, so they can't support future learning.

For instance, Marilyn Burns blogged recently about a question in the Math Reasoning Inventory:
12.6 × 10 = ?
Of nearly eight thousand students interviewed nationwide, more than half answered incorrectly, and the two most common wrong answers were 120.6 and 12.60. Why? Because those students had mastered the trick of multiplying by ten: just add a zero!

"Students are capable of developing rich conceptual understanding," Cardone says. But unfortunately, "Many students will wait for the shortcut and promptly forget the reasoning behind it ... If students do not understand, they are not doing math."

Ranging from elementary school addition to polynomial synthetic division, Nix the Tricks suggests alternative ways to approach tricksy topics and help students make sense of the math.

The book has done well for a self-published title, with more than 10,000 downloads and over 200 copies sold.

Last month, Tina released an expanded 2nd edition of Nix the Tricks. You can download the pdf or ebook file free, or buy a paperback at Amazon. Highly recommended for anyone who teaches math!

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