Math Teachers at Play #39

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest.

Several of these articles were submitted by the bloggers; others were drawn from my overflowing blog reader. Don’t try to skim everything all at once, but take the time to enjoy browsing. Savor a few posts today, and then come back for another helping tomorrow or next week.

Most of the photos below are from the 2010 MAA Found Math Gallery; click each image for more details. Quotations are from Mike Cook’s Canonical List of Math Jokes.

Let the mathematical fun begin…

TRY THIS PUZZLE

By tradition, we start the carnival with a puzzle in honor of our 39th edition. Using the rules of the Year Game …

• Easy: Can you make 39 with four 3s?

• Tricky: Can you make 39 with four 4s?

• Really tough: Can you make 39 with this year’s digits, keeping the numbers in order (2, 0, 1, 1)?

EARLY CONCEPTS

Ralph: Dad, will you do my math for me tonight?
Dad: No, son, it wouldn’t be right.
Ralph: Well, you could try.

• Christopher Danielson has an interesting circular conversation with a 4-year old.

• Bon Crowder encourages teachers to think deeply about preschool math in Counting Isn’t an Inherent Concept and What is Subitizing?

• Randa Clay offers five Free Preschool & Kindergarten Printable Math Worksheets for your little ones.

• Karyn Tripp shares her Dice Math Rainbow game. As she says, “Playing math is so much more fun than plain old worksheets, right?”

• Heidi uses Visual Instruction Plans to teach her students two favorite math games.

• Mathwire links to a variety of geometric explorations in Problem Solving: Pattern Blocks.

ARITHMETIC

Q: What is 15 – 3 × 5 + 20 – 4 × 5 + 36 – 9 × 4 + 72 – 9 × 8 + 56 – 7 × 8…?
A: A lot of work for nothing.

• Maria Muscarella introduces the Pyramath Card Game for practicing arithmetic operations from addition to powers. And if you leave a comment this weekend, you may win a free deck.

• Maria Miller reviews Tux Math, a free program for practicing arithmetic facts, while Kendra shares a variety of Multiplication Resources for students working on the times tables.

• Rachel Lynette presents a Math Scavenger Hunt to try with your students.

• Gisele Glosser offers a series of lessons on The Wonder of Fractions with interactive questions so students can check their understanding.

• Climbing Gecko explains in two different ways Why Anything ÷ Zero Is Impossible.

• Yan Kow Cheong has fun adding spice to NCTM’s search for “real-life problems” in Censored Math Questions from Singapore.

• John Scammell shows students how to create a Pythagorean spiral on card stock to explore irrational numbers in Radical Number Line.

BASIC ALGEBRA & GEOMETRY

The combined age of a ship and its boiler is 48 years. The ship is twice as old as the boiler was when the ship was half as old as the boiler will be when the boiler is three times as old as the ship was when the ship was three times as old as the boiler. How old is the ship?

• William Emeny mixes math with Random Art to give students practice in plotting coordinates in the first quadrant.

• Josh Rappaport breaks the Distributive Property into tiny steps, using Visual Symbols.

• Maria Droujkova shares a friend’s creative approach to binomial products in Multiplying polynomials: Quilts from Judy Chaffee.

• Breedeen Murray asks her students to write a proof, and they discover the importance of clear definitions: Rosie’s Round Table.

• Jeremiah Dyke takes students to the local park to explore Parabolas and Water Fountains.

• What would it be like to have A Mathematician for President? For my contribution to the carnival, I present President Garfield’s proof of the Pythagorean Theorem.

ADVANCED MATH

Q: How many mathematicians does it take to screw in a lightbulb?
A: One, who gives it to six Californians, thereby reducing it to an earlier riddle.

Q: What do you get when you cross an elephant with a banana?
A: Elephant banana sine theta in a direction mutually perpendicular to the two as determined by the right hand rule.

• Murray Bourne explains step by step How to find the equation of a quadratic function from its graph.

• Amy Gruen offers a brilliant strategy of Color Coding: For Sketching Piecewise Functions.

• Gary Ernest Davis points out that “questions stimulate one to find creative answers” in The answer is π^2/6: What’s the question?

• Sue VanHattum links to A Free Calculus Text that “uses a radically different organization than the standard course, so I don’t know if I could use it at my school. But I definitely want to read the whole thing now.” For her pre-calc class, she’s found another free resource: RISPs: Rich Starting Points.

• And taking a break from class, Ms. Cookie discovers a video that’s Too Cool Not To Share, while Shecky Riemann spends his day off Kickin’ Back With Cantor.

MATHEMATICAL PUZZLES

Yeah, I used to think it was just recreational… then I started doin’ it during the week… you know, simple stuff: differentiation, kinematics. Then I got into integration by parts… I started doin’ it every night: path integrals, holomorphic functions. Now I’m on diophantine equations and sinking deeper into transfinite analysis. Don’t let them tell you it’s just recreational.

Just say {}.

• David Wetzel says, “Problem solving in math promotes critical thinking and math reasoning skills, as students develop solutions to complex mathematical situations.” He challenges his students to find a knight’s tour in Math Problem Solving Game.

• Dan MacKinnon offers more insight into knight moves and explains Euler’s method of closing a knight’s tour.

• Kaavya Jayram shares logic puzzles from one of my favorite books, The Lady or the Tiger, while Ivan poses a couple of Lemonade pouring problems.

• Colleen Young recommends a math puzzle flexible enough to cover topics from addition to complex numbers: Arithmagons.

• Dave Richeson points out the problem-solving value of Extreme examples and counterexamples.

• Brent Yorgey challenges his readers in Post without words #1 and introduces us to The wonderful world of Mike Reilly.

• Tanya Khovanova shares several Recent Geeky Jokes, plus instructions from John Conway on the best way to walk up the stairs. Okay, so those aren’t really puzzles — but these two posts are.

ABOUT TEACHING MATH

One of my undergrad professors was asked what kind of problems would be on the final. His answer: “Just study the old tests. The problems will be the same, just the numbers will be different. But not all the numbers will be different. Pi will be the same. Planck’s constant will be the same… ”

Another professor, when asked how many problems there would be on the final, turned to the student and replied, “I think you will have lots of problems on the final.”

• Jimmie presents Notebooking With Creative Interviews, saying, “A lesson about the googol turns into a fun creative writing exercise.” Be sure to check out her other math notebooking pages and her very thorough math notebooking lens, too.

• Caroline Mukisa warns us, “Math skills drop more than any other subject according to research from Duke University. Here are 15 fun ways to maintain your child’s math skills over the long summer vacation.”

• Rebecca Hanson shows how a simple warm-up exercise can develop deep understanding in her series How do the Chinese do it? [parts 2, 3, 4, 5, 6, 7].

• David Cox encourages students, “Embrace the conflict that arises when what you thought was true turns out to be, well, not so much.” Check out his post ( )conceptions.

• Avery offers a series about Teaching Problem Solving [parts 2, 3], while Sue wonders whether playing chess has anything to do with learning math.

• Darren Kuropatwa compiles a slideshow of 24 TED Talks for math teachers in Math @ TED. Mr. H. sorts through the National Academies Press Free PDFs and finds several of interest to math educators. And Pat Ballew provides a great resource for teachers now and (as the dates roll around again) in years to come, with his marvelous On This Day in Math series.

MIGHT BE SPAM

One final entry: 8 Ancient Labyrinths to Quiet Your Mind is a travel advertisement, but at least it’s related to math, and I learned something from it. Do you know the difference between a maze and a labyrinth? It makes sense that if we have two words, there should be some distinction, but I never knew what it was. I wish all ads were this interesting!

VISIT OUR SISTER CARNIVALS

• Carnival of Mathematics
• Mathematics and Multimedia
• Carnevale della Matematica
• Carnaval de Matemáticas

FINAL COMMENTS

And that rounds up this edition of the Math Teachers at Play blog carnival. I hope you enjoyed the ride. The next installment of our carnival will open on July 15 at Math Mama Writes. If you would like to contribute, please use this handy submission form or email Sue directly. (We had trouble with the submission form this month. We hope they’ll get it fixed.) Posts must be relevant to students or teachers of preK-12 mathematics. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

Past posts and future hosts can be found on our blog carnival index page.