Let's Play Math!

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! Here is a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college. Some articles were submitted by their authors, other were drawn from the immense backlog in my blog reader. If you like to learn new things, you are sure to find something of interest.

Living Books for Math

A child’s intercourse must always be with good books, the best that we can find… We must put into their hands the sources which we must needs use for ourselves, the best books of the best writers.
…
For the mind is capable of dealing with only one kind of food; it lives, grows and is nourished upon ideas only; mere information is to it as a meal of sawdust to the body.

— Charlotte Mason
Toward A Philosophy of Education

Princess Kitten and I took a longer than usual holiday break from homeschooling, but now I’m in plan-for-the-new-semester mode. I hope to include more living math in our schedule, so I decided to illustrate this edition of the MTaP carnival with a few of my favorite living math books. I’d love to hear more living book suggestions in the comments!

If you click on a book cover, the links take you to Amazon.com, where you can read reviews and other details (and where I earn a few cents through Skimlinks if you actually buy the book), but all of these books should be available through your public library or via inter-library loan.

Let the mathematical fun begin…

TRY THIS PUZZLE

By tradition, we start the carnival with a puzzle in honor of our 46th edition. 46 is a centered triangular number.

• Study the diagram to see how centered triangular numbers are constructed. Every centered triangular number is equal to 1(mod 3). Can you see why?

• We start with n=0 for the single dot in the middle, n=1 includes the center + the smallest triangle, etc. Counting in this way, what value of n will have 46 dots?

• Can you find all the centered triangular numbers less than 100?

• Every centered triangular number 10 or greater contains three consecutive regular triangular numbers. Draw a few big centered triangles (n>3). Can you outline the three triangular numbers in each sketch?

ELEMENTARY CONCEPTS

12 Ways to Get to 11 is more than just a fun counting book. Introduce young children to number bonds and partitions — new ways to look at the world of numbers!

• Beanienus faces the challenge of teaching numbers to an active daughter in Rocket, soccer, musical chairs and Math.

• Kristen and her girls have fun with math in For the Love of the Rods. (And they reviewed 12 Ways to Get to 11, too.)

• Heather shows how to Make Your Own Math Games: Egg-O.

• MathWire offers a bit of seasonal fun in Snowman Probability and the Last Snowman Standing Game. Meanwhile, Haley creates beautiful, wintry symmetry in Paper Snowflakes 101.

• Jennifer and her son explore transformations in Cookie Cutter Geometry.

• While Mama makes dinner, Malke’s daughter creates Marshmallow Math: Solids & Sculpture. (And the story continues here, here, here, and here.)

ARITHMETIC

The Man Who Counted features classic mathematical puzzles in an exotic setting, following the fictional adventures of Persian sheep-herder turned mathematician Beremiz as he uses his wits to gain fame, fortune, and a beautiful wife.

• IMACS presents a clock-based game in An Introduction to Modular Addition and adds a couple new rules in More Modular Arithmetic.

• Gaurav asks, “Do you multiply this way?” My challenge: Don’t memorize this method as a trick, but study until you see why it works. How is it similar to the standard method?

• Phyllis demonstrates a variety of hands-on ways to teach Beginning Division.

• Ashley shares 5 Great Sites for Learning Math, and Jen shares her smart phone discoveries in Math Apps — Carnival of fun.

• Jen’s students add a “Types of Graphs” foldable to their math journals. Be sure to check out her other math journal ideas, too.

• Maria teaches all the basic fraction concepts in Free fraction videos online, part 1 and Part 2.

• Rebecca offers as series of counting challenges in her lesson plan, Combinatorics for Breakfast. What, no Spam?!

• David demonstrates a useful system for Combining Integers Instead of Adding and Subtracting Them.

BASIC ALGEBRA & GEOMETRY

Flatland: A Romance of Many Dimensions, a classic of mathematical fiction, follows the adventures of A. Square as he transcends his assumptions about reality and explores several geometric worlds.

• Mimi’s class has been Learning from Our (Algebra) Mistakes.

• Mrs. H. put together a Linear Function Review Booklet for her algebra 1 students.

• Kerry applies algebra to a variety of problems in her Mathspig Zombie Maths Series.

• Mr. Koh challenges us with an algebra puzzle about the Properties of Numbers.

• Ryan’s class uses basic geometry to solve the mystery of The Chopped Cubes.

• Guillermo shows how coordinate geometry can help simplify proofs in Diagonals of a Parallelogram. Check also his short Proof that log 2 is an irrational number.

ADVANCED MATH

The Language of Mathematics: Making the Invisible Visible (or the earlier version, Mathematics: The Science of Patterns) helps answer the question, “Why do we have to learn this?” If you’ve ever wondered what mathematicians mean when they say math is “beautiful” — read this book!

• Murray plays around with Biorhythm Graphs: “A bit of fun — a non-scientific application of composite sine curves!”

• Mr. Chase argues with his algebra 2 book in Inverse functions and the horizontal line test and then has a bit of fun in Function World.

• John shares a couple of problems from his preservice high school teachers’ final. How would you fare?

• Riley gives his students the run-around in What did you do to the x-axis?!? Using the most relevant context possible.

• Alexander explains the Star of David Theorems in Pascal Triangle.

• Robert opines that everyone should learn programming, and he offers several suggestions for where to start.

• Sue reviews Math Girls: A Novel Way to Learn Some Deep Math: “I would highly recommend this book for anyone at the level of pre-calculus and above who enjoys math.”

MATHEMATICAL PUZZLES

What Is the Name of This Book?: The Riddle of Dracula and Other Logical Puzzles is finally back in print. (And Alice in Puzzle-Land, too. Thank you, Dover Publications!) Try your hand at a few traditional brain teasers, and explore the Island of Knights and Knaves. Can you tell the difference between a sane human and an insane vampire?

• Gary shares a few puzzles that elementary-age children can understand but adults can enjoy exploring as well: Numberplay: Tanton Wordless. [Errata: Moving your mouse over the second picture will display solutions for four of the six puzzles shown, implying that two are impossible --- but really, only one is impossible. Can you find the missing solution?]

• MathCounts is a great source of problems for middle school and older students. Mrs. Lin offers Mathcounts competition preparation strategies I, along with a blogful of questions and solutions.

• My entry for the carnival is the 2012 Mathematics Game, a terrific puzzle for middle school and beyond.

• Fawn offers a series of challenges in Puzzles and Brainteasers, Set 3, Set 4, and Set 5.

• Can you solve Pat’s Interesting Rectangle Partitioning?

• John presents A Renaissance math puzzle. Intrigued, Thony digs into history in The story of a problem.

ABOUT TEACHING MATH

Martin Gardner inspired many of us to become mathematicians and math teachers. Now our children can enjoy 50 of his best “Mathematical Games” columns in one volume, The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. What a treasure!

• Bon hosts an interesting series of interviews with Mathematician Parents.

• Gisele offers several ideas for making Math Connections with other subjects.

• Erlina asks What are the uses of examples in teaching mathematics?, and answers the question with an example of well-chosen examples.

• Christopher argues that being a good teacher is not about problem-solving skills, It’s about understanding.

• Math Rules wonders, “How much of a class should be conceptual and how much should be procedural?“, and Kate shares her favorite Math Lesson Formula.

MORE MATH CARNIVALS

I love reading math biographies. Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem is the “biography” of a math problem. It’s the next book on my library-loan list, and I can’t wait for it to arrive…

• Mathematics and Multimedia Blog Carnival 19

• Carnival of Mathematics 84

• Mathblogging.org Weekly Picks

• Carnevale della Matematica
  which is also available as a pdf ebook.

• Carnaval de Matemáticas

FINAL COMMENTS

That rounds out this edition of the Math Teachers at Play carnival. I hope you enjoyed the ride. The next installment of our carnival will open on February 17 at Math Hombre. If you would like to contribute, please use this handy submission form or email John directly. Posts must be relevant to students or teachers of preschool through precollege 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.

We need more volunteers. Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn hosting the Math Teachers at Play blog carnival, please speak up!

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Have more fun on Let’s Play Math! blog:

• Math Teachers at Play #39
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• Math Teachers at Play #5